Per-Observation Detections Table

From the 'Modified Source Region' section of the Source Extent and Errors column descriptions page:

The modified source region and modified background region for each source are defined as the areas of intersection of the source region and background region for that source with the field-of-view, excluding any overlapping source regions.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The modified elliptical aperture and modified elliptical background aperture for each source and science energy band are defined as the areas of intersection of the elliptical aperture and elliptical background aperture for that source with the field of view, excluding any overlapping source regions.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The modified elliptical aperture and modified elliptical background aperture for each source and science energy band are defined as the areas of intersection of the elliptical aperture and elliptical background aperture for that source with the field of view, excluding any overlapping source regions.

From the 'Modified Source Region' section of the Source Extent and Errors column descriptions page:

The modified source region and modified background region for each source are defined as the areas of intersection of the source region and background region for that source with the field-of-view, excluding any overlapping source regions.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed blackbody model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, a blackbody temperature, and a blackbody model amplitude.

The best-fit blackbody model amplitude and the associated two-sided 68% confidence limits, proportional to the ratio of the blackbody emitting source radius, \(R\), and the distance to the source, \(d\). The amplitude is defined as:

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed blackbody model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, a blackbody temperature, and a blackbody model amplitude.

The best-fit blackbody model amplitude and the associated two-sided 68% confidence limits, proportional to the ratio of the blackbody emitting source radius, \(R\), and the distance to the source, \(d\). The amplitude is defined as:

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed blackbody model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, a blackbody temperature, and a blackbody model amplitude.

The best-fit blackbody model amplitude and the associated two-sided 68% confidence limits, proportional to the ratio of the blackbody emitting source radius, \(R\), and the distance to the source, \(d\). The amplitude is defined as:

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed blackbody model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, a blackbody temperature, and a blackbody model amplitude.

The best-fit blackbody model temperature (kT) in units of keV and the associated two-sided 68% confidence limits.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed blackbody model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, a blackbody temperature, and a blackbody model amplitude.

The best-fit blackbody model temperature (kT) in units of keV and the associated two-sided 68% confidence limits.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed blackbody model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, a blackbody temperature, and a blackbody model amplitude.

The best-fit blackbody model temperature (kT) in units of keV and the associated two-sided 68% confidence limits.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed blackbody model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, a blackbody temperature, and a blackbody model amplitude.

The best-fit total equivalent neutral hydrogen column density, \(N_{H}\), and the associated two-sided 68% confidence limits from an absorbed blackbody model fit, in units of 10²⁰ cm^-2.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed blackbody model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, a blackbody temperature, and a blackbody model amplitude.

The best-fit total equivalent neutral hydrogen column density, \(N_{H}\), and the associated two-sided 68% confidence limits from an absorbed blackbody model fit, in units of 10²⁰ cm^-2.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed blackbody model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, a blackbody temperature, and a blackbody model amplitude.

The best-fit total equivalent neutral hydrogen column density, \(N_{H}\), and the associated two-sided 68% confidence limits from an absorbed blackbody model fit, in units of 10²⁰ cm^-2.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed blackbody model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, a blackbody temperature, and a blackbody model amplitude.

The fit statistic defined as the value of the \(\chi^{2}\) (data variance) statistic per degree of freedom for the best-fitting blackbody model.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed bremsstrahlung model is fit over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, bremsstrahlung temperature, and bremsstrahlung model amplitude.

The best-fit bremsstrahlung model temperature (kT) in units of keV and the associated two-sided 68% confidence limits.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed bremsstrahlung model is fit over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, bremsstrahlung temperature, and bremsstrahlung model amplitude.

The best-fit bremsstrahlung model temperature (kT) in units of keV and the associated two-sided 68% confidence limits.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed bremsstrahlung model is fit over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, bremsstrahlung temperature, and bremsstrahlung model amplitude.

The best-fit bremsstrahlung model temperature (kT) in units of keV and the associated two-sided 68% confidence limits.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed bremsstrahlung model is fit over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, bremsstrahlung temperature, and bremsstrahlung model amplitude.

The best-fit total equivalent neutral hydrogen column density, \(N_{H}\), and the associated two-sided 68% confidence limits from an absorbed bremsstrahlung model fit, in units of 10²⁰ cm^-2.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed bremsstrahlung model is fit over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, bremsstrahlung temperature, and bremsstrahlung model amplitude.

The best-fit total equivalent neutral hydrogen column density, \(N_{H}\), and the associated two-sided 68% confidence limits from an absorbed bremsstrahlung model fit, in units of 10²⁰ cm^-2.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed bremsstrahlung model is fit over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, bremsstrahlung temperature, and bremsstrahlung model amplitude.

The best-fit total equivalent neutral hydrogen column density, \(N_{H}\), and the associated two-sided 68% confidence limits from an absorbed bremsstrahlung model fit, in units of 10²⁰ cm^-2.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed bremsstrahlung model is fit over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, bremsstrahlung temperature, and bremsstrahlung model amplitude.

The best-fit bremsstrahlung model normalization and the associated two-sided 68% confidence limits. The model normalization is defined by:

where \(n_{e}\) and \(n_{i}\) are the electron and ion number densities, respectively, in cm^-3 and \(D\) is the distance to the source in cm.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed bremsstrahlung model is fit over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, bremsstrahlung temperature, and bremsstrahlung model amplitude.

The best-fit bremsstrahlung model normalization and the associated two-sided 68% confidence limits. The model normalization is defined by:

where \(n_{e}\) and \(n_{i}\) are the electron and ion number densities, respectively, in cm^-3 and \(D\) is the distance to the source in cm.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed bremsstrahlung model is fit over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, bremsstrahlung temperature, and bremsstrahlung model amplitude.

The best-fit bremsstrahlung model normalization and the associated two-sided 68% confidence limits. The model normalization is defined by:

where \(n_{e}\) and \(n_{i}\) are the electron and ion number densities, respectively, in cm^-3 and \(D\) is the distance to the source in cm.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed bremsstrahlung model is fit over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, bremsstrahlung temperature, and bremsstrahlung model amplitude.

The fit statistic defined as the value of the \(\chi^{2}\) (data variance) statistic per degree of freedom for the best-fitting bremsstrahlung model.

From the Position and Position Errors column descriptions page:

The location of the source region (that includes a detection) in chip coordinates for an observation is defined by the effective CHIPX and CHIPY pixel positions corresponding to the off-axis angles (θ, φ).

From the Position and Position Errors column descriptions page:

The location of the source region (that includes a detection) in chip coordinates for an observation is defined by the effective CHIPX and CHIPY pixel positions corresponding to the off-axis angles (θ, φ).

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture total counts represent the total number of source plus background counts measured in the modified source and background regions (cnts_aper, cnts_aperbkg), and in the modified elliptical aperture and modified elliptical background aperture (cnts_aper90, cnts_aper90bkg), uncorrected by the PSF aperture fraction.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture total counts represent the total number of source plus background counts measured in the modified source and background regions (cnts_aper, cnts_aperbkg), and in the modified elliptical aperture and modified elliptical background aperture (cnts_aper90, cnts_aper90bkg), uncorrected by the PSF aperture fraction.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture total counts represent the total number of source plus background counts measured in the modified source and background regions (cnts_aper, cnts_aperbkg), and in the modified elliptical aperture and modified elliptical background aperture (cnts_aper90, cnts_aper90bkg), uncorrected by the PSF aperture fraction.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture total counts represent the total number of source plus background counts measured in the modified source and background regions (cnts_aper, cnts_aperbkg), and in the modified elliptical aperture and modified elliptical background aperture (cnts_aper90, cnts_aper90bkg), uncorrected by the PSF aperture fraction.

From the Source Flags column descriptions page:

The confusion code in the per-observation detections table is defined identically to the confusion code in the stacked observations detections table.

From the Source Flags column descriptions page:

The dither warning flag for a compact detection is a Boolean that has a value of TRUE if the highest statistically significant peak in the power spectrum of the detection's source region ellipse count rate at the dither frequency of at a beat frequency of the dither frequency of the observation in any science energy band. Otherwise, the value is False.

The dither warning flag for an extended (convex hull) source is always NULL.

From the Source Variability column descriptions page:

The dither warning flag consists of a Boolean whose value is TRUE if the highest statistically significant peak in the power spectrum of the source region count rate, for the science energy band with the highest variability index, occurs either at the dither frequency of the observation or at a beat frequency of the dither frequency. Otherwise, the dither warning flag is FALSE. This value is calculated for each science energy band.

From the Source Flags column descriptions page:

The edge code in the per-observation detections table is defined identically to the edge code in the stacked observations detections table.

From the Source Flags column descriptions page:

The extent code in the per-observation detections table is defined identically to the extent code in the stacked observations detections table.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source energy fluxes (flux_aper) and associated two-sided confidence limits represent the background-subtracted fluxes in the modified source region (photflux_aper) and in the modified elliptical aperture (photflux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure. The conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source energy fluxes (flux_aper) and associated two-sided confidence limits represent the background-subtracted fluxes in the modified source region (photflux_aper) and in the modified elliptical aperture (photflux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure. The conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source energy fluxes (flux_aper) and associated two-sided confidence limits represent the background-subtracted fluxes in the modified source region (photflux_aper) and in the modified elliptical aperture (photflux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure. The conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source energy fluxes (flux_aper) and associated two-sided confidence limits represent the background-subtracted fluxes in the modified source region (photflux_aper) and in the modified elliptical aperture (photflux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure. The conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source energy fluxes (flux_aper) and associated two-sided confidence limits represent the background-subtracted fluxes in the modified source region (photflux_aper) and in the modified elliptical aperture (photflux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure. The conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source energy fluxes (flux_aper) and associated two-sided confidence limits represent the background-subtracted fluxes in the modified source region (photflux_aper) and in the modified elliptical aperture (photflux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure. The conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed blackbody model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, a blackbody temperature, and a blackbody model amplitude.

The blackbody flux and the associated two-sided 68% confidence limits represent the integrated 0.5-7 keV flux derived from the best-fit absorbed blackbody model, in units of erg/s/cm².

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed blackbody model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, a blackbody temperature, and a blackbody model amplitude.

The blackbody flux and the associated two-sided 68% confidence limits represent the integrated 0.5-7 keV flux derived from the best-fit absorbed blackbody model, in units of erg/s/cm².

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed blackbody model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, a blackbody temperature, and a blackbody model amplitude.

The blackbody flux and the associated two-sided 68% confidence limits represent the integrated 0.5-7 keV flux derived from the best-fit absorbed blackbody model, in units of erg/s/cm².

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed bremsstrahlung model is fit over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, bremsstrahlung temperature, and bremsstrahlung model amplitude.

The bremsstrahlung flux and the associated two-sided 68% confidence limits represent the integrated 0.5-7 keV flux derived from the best-fit absorbed bremsstrahlung model, in units of erg/s/cm².

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed bremsstrahlung model is fit over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, bremsstrahlung temperature, and bremsstrahlung model amplitude.

The bremsstrahlung flux and the associated two-sided 68% confidence limits represent the integrated 0.5-7 keV flux derived from the best-fit absorbed bremsstrahlung model, in units of erg/s/cm².

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed bremsstrahlung model is fit over the energy range 0.5-7.0 keV; the free parameters to be fitted are: a total equivalent neutral hydrogen absorbing column density, bremsstrahlung temperature, and bremsstrahlung model amplitude.

The bremsstrahlung flux and the associated two-sided 68% confidence limits represent the integrated 0.5-7 keV flux derived from the best-fit absorbed bremsstrahlung model, in units of erg/s/cm².

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed power law model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are the total equivalent neutral hydrogen absorbing column density, power law photon index, and power law amplitude.

The power law model flux and the associated two-sided 68% confidence limits represent the integrated 0.5-7 keV flux derived from the best-fitting absorbed power law model, in units of erg/s/cm².

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Aperture Model Energy Fluxes' section of the Source Fluxes column descriptions page:

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed power law model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are the total equivalent neutral hydrogen absorbing column density, power law photon index, and power law amplitude.

The power law model flux and the associated two-sided 68% confidence limits represent the integrated 0.5-7 keV flux derived from the best-fitting absorbed power law model, in units of erg/s/cm².

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed power law model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are the total equivalent neutral hydrogen absorbing column density, power law photon index, and power law amplitude.

The power law model flux and the associated two-sided 68% confidence limits represent the integrated 0.5-7 keV flux derived from the best-fitting absorbed power law model, in units of erg/s/cm².

From the Source Significance column descriptions page:

Likelihood and flux significance are reported per band for all detected sources that fall in the valid field of view. Likelihoods are computed for each source detection in a stack, from MLE fits to data from all valid observations for the source. Likelihoods from each individual observation are also computed.

Flux significance is a simple estimate of the ratio of the flux measurement to its average error. The mode of the marginalized probability distribution for photflux_aper is used as the flux measurement and the average error, \(\sigma_{e}\), is defined to be:

which are both used to estimate flux significance.

From the Spectral Properties column descriptions page:

Hardness ratios appear in both the Master Sources Table and the Per-Observation Detections Table with the field names hard_xy, hard_xy_hilim, and hard_xy_lolim. The hardness ratios that appear in the Master Sources Table are determined from the Bayesian probability distribution functions (PDFs) of the aperture source photon fluxes derived from the source regions of the contributing individual source observations contained in the Per-Observation Detections Table. Only energy bands hard (h, 2.0-7.0 keV), medium (m, 1.2-2.0 keV) and soft (s, 0.5-1.2 keV) are used.

For two given energy bands, they are defined at the single observation level as the flux value in the softer band, subtracted from the flux value in the harder band, relative to their sum. However, since the PDFs are used, this definition is based on probabilistic considerations. Just like the fluxes are random variables with associated probabilities, so are the hardness ratios. Specifically, the values listed are the ones that maximize the following PDF:

By convention for the catalog, band x is always the higher energy band. As an example, hard_ms is the medium-to-soft band hardness ratio, defined as:

Note that this definition of hardness ratio is different than that used in Chandra Source Catalog Release 1, where the denominator in the ratio was obtained from combining all three energy bands: soft, medium, and hard.

As the reported values for each of these quantities represent the maximum a posteriori values of their given PDFs, the column hardness ratio values might differ slightly from that calculated directly from the aperture fluxes reported in the catalog.

Hardness ratios using the broad, ultra-soft, and HRC bands are not included in the catalog. The two-sided confidence limits associated with the ACIS hardness ratios are computed from the marginalized probability distributions and always lie within the range -1 to 1. If an aperture flux marginalized probability distribution cannot be computed for a given energy band, then no colors associated with that band are reported. At the stack and master level, the hardness ratios are also evaluated using the expressions above, but using respectively all the observations in the stack or best Bayesian block.

In Chandra Source Catalog Release 2, the individual source detection hardness ratios are also assessed for variability among the individual observations. See the description of Source Variability. A detailed description of hardness ratios can be found in the hardness ratios and variability memo.

From the Spectral Properties column descriptions page:

Hardness ratios appear in both the Master Sources Table and the Per-Observation Detections Table with the field names hard_xy, hard_xy_hilim, and hard_xy_lolim. The hardness ratios that appear in the Master Sources Table are determined from the Bayesian probability distribution functions (PDFs) of the aperture source photon fluxes derived from the source regions of the contributing individual source observations contained in the Per-Observation Detections Table. Only energy bands hard (h, 2.0-7.0 keV), medium (m, 1.2-2.0 keV) and soft (s, 0.5-1.2 keV) are used.

For two given energy bands, they are defined at the single observation level as the flux value in the softer band, subtracted from the flux value in the harder band, relative to their sum. However, since the PDFs are used, this definition is based on probabilistic considerations. Just like the fluxes are random variables with associated probabilities, so are the hardness ratios. Specifically, the values listed are the ones that maximize the following PDF:

By convention for the catalog, band x is always the higher energy band. As an example, hard_ms is the medium-to-soft band hardness ratio, defined as:

Note that this definition of hardness ratio is different than that used in Chandra Source Catalog Release 1, where the denominator in the ratio was obtained from combining all three energy bands: soft, medium, and hard.

As the reported values for each of these quantities represent the maximum a posteriori values of their given PDFs, the column hardness ratio values might differ slightly from that calculated directly from the aperture fluxes reported in the catalog.

Hardness ratios using the broad, ultra-soft, and HRC bands are not included in the catalog. The two-sided confidence limits associated with the ACIS hardness ratios are computed from the marginalized probability distributions and always lie within the range -1 to 1. If an aperture flux marginalized probability distribution cannot be computed for a given energy band, then no colors associated with that band are reported. At the stack and master level, the hardness ratios are also evaluated using the expressions above, but using respectively all the observations in the stack or best Bayesian block.

In Chandra Source Catalog Release 2, the individual source detection hardness ratios are also assessed for variability among the individual observations. See the description of Source Variability. A detailed description of hardness ratios can be found in the hardness ratios and variability memo.

From the Spectral Properties column descriptions page:

Hardness ratios appear in both the Master Sources Table and the Per-Observation Detections Table with the field names hard_xy, hard_xy_hilim, and hard_xy_lolim. The hardness ratios that appear in the Master Sources Table are determined from the Bayesian probability distribution functions (PDFs) of the aperture source photon fluxes derived from the source regions of the contributing individual source observations contained in the Per-Observation Detections Table. Only energy bands hard (h, 2.0-7.0 keV), medium (m, 1.2-2.0 keV) and soft (s, 0.5-1.2 keV) are used.

For two given energy bands, they are defined at the single observation level as the flux value in the softer band, subtracted from the flux value in the harder band, relative to their sum. However, since the PDFs are used, this definition is based on probabilistic considerations. Just like the fluxes are random variables with associated probabilities, so are the hardness ratios. Specifically, the values listed are the ones that maximize the following PDF:

By convention for the catalog, band x is always the higher energy band. As an example, hard_ms is the medium-to-soft band hardness ratio, defined as:

Note that this definition of hardness ratio is different than that used in Chandra Source Catalog Release 1, where the denominator in the ratio was obtained from combining all three energy bands: soft, medium, and hard.

As the reported values for each of these quantities represent the maximum a posteriori values of their given PDFs, the column hardness ratio values might differ slightly from that calculated directly from the aperture fluxes reported in the catalog.

Hardness ratios using the broad, ultra-soft, and HRC bands are not included in the catalog. The two-sided confidence limits associated with the ACIS hardness ratios are computed from the marginalized probability distributions and always lie within the range -1 to 1. If an aperture flux marginalized probability distribution cannot be computed for a given energy band, then no colors associated with that band are reported. At the stack and master level, the hardness ratios are also evaluated using the expressions above, but using respectively all the observations in the stack or best Bayesian block.

In Chandra Source Catalog Release 2, the individual source detection hardness ratios are also assessed for variability among the individual observations. See the description of Source Variability. A detailed description of hardness ratios can be found in the hardness ratios and variability memo.

From the Spectral Properties column descriptions page:

Hardness ratios appear in both the Master Sources Table and the Per-Observation Detections Table with the field names hard_xy, hard_xy_hilim, and hard_xy_lolim. The hardness ratios that appear in the Master Sources Table are determined from the Bayesian probability distribution functions (PDFs) of the aperture source photon fluxes derived from the source regions of the contributing individual source observations contained in the Per-Observation Detections Table. Only energy bands hard (h, 2.0-7.0 keV), medium (m, 1.2-2.0 keV) and soft (s, 0.5-1.2 keV) are used.

For two given energy bands, they are defined at the single observation level as the flux value in the softer band, subtracted from the flux value in the harder band, relative to their sum. However, since the PDFs are used, this definition is based on probabilistic considerations. Just like the fluxes are random variables with associated probabilities, so are the hardness ratios. Specifically, the values listed are the ones that maximize the following PDF:

By convention for the catalog, band x is always the higher energy band. As an example, hard_ms is the medium-to-soft band hardness ratio, defined as:

Note that this definition of hardness ratio is different than that used in Chandra Source Catalog Release 1, where the denominator in the ratio was obtained from combining all three energy bands: soft, medium, and hard.

As the reported values for each of these quantities represent the maximum a posteriori values of their given PDFs, the column hardness ratio values might differ slightly from that calculated directly from the aperture fluxes reported in the catalog.

Hardness ratios using the broad, ultra-soft, and HRC bands are not included in the catalog. The two-sided confidence limits associated with the ACIS hardness ratios are computed from the marginalized probability distributions and always lie within the range -1 to 1. If an aperture flux marginalized probability distribution cannot be computed for a given energy band, then no colors associated with that band are reported. At the stack and master level, the hardness ratios are also evaluated using the expressions above, but using respectively all the observations in the stack or best Bayesian block.

In Chandra Source Catalog Release 2, the individual source detection hardness ratios are also assessed for variability among the individual observations. See the description of Source Variability. A detailed description of hardness ratios can be found in the hardness ratios and variability memo.

From the Spectral Properties column descriptions page:

Hardness ratios appear in both the Master Sources Table and the Per-Observation Detections Table with the field names hard_xy, hard_xy_hilim, and hard_xy_lolim. The hardness ratios that appear in the Master Sources Table are determined from the Bayesian probability distribution functions (PDFs) of the aperture source photon fluxes derived from the source regions of the contributing individual source observations contained in the Per-Observation Detections Table. Only energy bands hard (h, 2.0-7.0 keV), medium (m, 1.2-2.0 keV) and soft (s, 0.5-1.2 keV) are used.

For two given energy bands, they are defined at the single observation level as the flux value in the softer band, subtracted from the flux value in the harder band, relative to their sum. However, since the PDFs are used, this definition is based on probabilistic considerations. Just like the fluxes are random variables with associated probabilities, so are the hardness ratios. Specifically, the values listed are the ones that maximize the following PDF:

By convention for the catalog, band x is always the higher energy band. As an example, hard_ms is the medium-to-soft band hardness ratio, defined as:

Note that this definition of hardness ratio is different than that used in Chandra Source Catalog Release 1, where the denominator in the ratio was obtained from combining all three energy bands: soft, medium, and hard.

As the reported values for each of these quantities represent the maximum a posteriori values of their given PDFs, the column hardness ratio values might differ slightly from that calculated directly from the aperture fluxes reported in the catalog.

Hardness ratios using the broad, ultra-soft, and HRC bands are not included in the catalog. The two-sided confidence limits associated with the ACIS hardness ratios are computed from the marginalized probability distributions and always lie within the range -1 to 1. If an aperture flux marginalized probability distribution cannot be computed for a given energy band, then no colors associated with that band are reported. At the stack and master level, the hardness ratios are also evaluated using the expressions above, but using respectively all the observations in the stack or best Bayesian block.

In Chandra Source Catalog Release 2, the individual source detection hardness ratios are also assessed for variability among the individual observations. See the description of Source Variability. A detailed description of hardness ratios can be found in the hardness ratios and variability memo.

From the Spectral Properties column descriptions page:

Hardness ratios appear in both the Master Sources Table and the Per-Observation Detections Table with the field names hard_xy, hard_xy_hilim, and hard_xy_lolim. The hardness ratios that appear in the Master Sources Table are determined from the Bayesian probability distribution functions (PDFs) of the aperture source photon fluxes derived from the source regions of the contributing individual source observations contained in the Per-Observation Detections Table. Only energy bands hard (h, 2.0-7.0 keV), medium (m, 1.2-2.0 keV) and soft (s, 0.5-1.2 keV) are used.

For two given energy bands, they are defined at the single observation level as the flux value in the softer band, subtracted from the flux value in the harder band, relative to their sum. However, since the PDFs are used, this definition is based on probabilistic considerations. Just like the fluxes are random variables with associated probabilities, so are the hardness ratios. Specifically, the values listed are the ones that maximize the following PDF:

By convention for the catalog, band x is always the higher energy band. As an example, hard_ms is the medium-to-soft band hardness ratio, defined as:

Note that this definition of hardness ratio is different than that used in Chandra Source Catalog Release 1, where the denominator in the ratio was obtained from combining all three energy bands: soft, medium, and hard.

As the reported values for each of these quantities represent the maximum a posteriori values of their given PDFs, the column hardness ratio values might differ slightly from that calculated directly from the aperture fluxes reported in the catalog.

Hardness ratios using the broad, ultra-soft, and HRC bands are not included in the catalog. The two-sided confidence limits associated with the ACIS hardness ratios are computed from the marginalized probability distributions and always lie within the range -1 to 1. If an aperture flux marginalized probability distribution cannot be computed for a given energy band, then no colors associated with that band are reported. At the stack and master level, the hardness ratios are also evaluated using the expressions above, but using respectively all the observations in the stack or best Bayesian block.

In Chandra Source Catalog Release 2, the individual source detection hardness ratios are also assessed for variability among the individual observations. See the description of Source Variability. A detailed description of hardness ratios can be found in the hardness ratios and variability memo.

From the Spectral Properties column descriptions page:

Hardness ratios appear in both the Master Sources Table and the Per-Observation Detections Table with the field names hard_xy, hard_xy_hilim, and hard_xy_lolim. The hardness ratios that appear in the Master Sources Table are determined from the Bayesian probability distribution functions (PDFs) of the aperture source photon fluxes derived from the source regions of the contributing individual source observations contained in the Per-Observation Detections Table. Only energy bands hard (h, 2.0-7.0 keV), medium (m, 1.2-2.0 keV) and soft (s, 0.5-1.2 keV) are used.

For two given energy bands, they are defined at the single observation level as the flux value in the softer band, subtracted from the flux value in the harder band, relative to their sum. However, since the PDFs are used, this definition is based on probabilistic considerations. Just like the fluxes are random variables with associated probabilities, so are the hardness ratios. Specifically, the values listed are the ones that maximize the following PDF:

By convention for the catalog, band x is always the higher energy band. As an example, hard_ms is the medium-to-soft band hardness ratio, defined as:

Note that this definition of hardness ratio is different than that used in Chandra Source Catalog Release 1, where the denominator in the ratio was obtained from combining all three energy bands: soft, medium, and hard.

As the reported values for each of these quantities represent the maximum a posteriori values of their given PDFs, the column hardness ratio values might differ slightly from that calculated directly from the aperture fluxes reported in the catalog.

Hardness ratios using the broad, ultra-soft, and HRC bands are not included in the catalog. The two-sided confidence limits associated with the ACIS hardness ratios are computed from the marginalized probability distributions and always lie within the range -1 to 1. If an aperture flux marginalized probability distribution cannot be computed for a given energy band, then no colors associated with that band are reported. At the stack and master level, the hardness ratios are also evaluated using the expressions above, but using respectively all the observations in the stack or best Bayesian block.

In Chandra Source Catalog Release 2, the individual source detection hardness ratios are also assessed for variability among the individual observations. See the description of Source Variability. A detailed description of hardness ratios can be found in the hardness ratios and variability memo.

From the Spectral Properties column descriptions page:

Hardness ratios appear in both the Master Sources Table and the Per-Observation Detections Table with the field names hard_xy, hard_xy_hilim, and hard_xy_lolim. The hardness ratios that appear in the Master Sources Table are determined from the Bayesian probability distribution functions (PDFs) of the aperture source photon fluxes derived from the source regions of the contributing individual source observations contained in the Per-Observation Detections Table. Only energy bands hard (h, 2.0-7.0 keV), medium (m, 1.2-2.0 keV) and soft (s, 0.5-1.2 keV) are used.

For two given energy bands, they are defined at the single observation level as the flux value in the softer band, subtracted from the flux value in the harder band, relative to their sum. However, since the PDFs are used, this definition is based on probabilistic considerations. Just like the fluxes are random variables with associated probabilities, so are the hardness ratios. Specifically, the values listed are the ones that maximize the following PDF:

By convention for the catalog, band x is always the higher energy band. As an example, hard_ms is the medium-to-soft band hardness ratio, defined as:

Note that this definition of hardness ratio is different than that used in Chandra Source Catalog Release 1, where the denominator in the ratio was obtained from combining all three energy bands: soft, medium, and hard.

As the reported values for each of these quantities represent the maximum a posteriori values of their given PDFs, the column hardness ratio values might differ slightly from that calculated directly from the aperture fluxes reported in the catalog.

Hardness ratios using the broad, ultra-soft, and HRC bands are not included in the catalog. The two-sided confidence limits associated with the ACIS hardness ratios are computed from the marginalized probability distributions and always lie within the range -1 to 1. If an aperture flux marginalized probability distribution cannot be computed for a given energy band, then no colors associated with that band are reported. At the stack and master level, the hardness ratios are also evaluated using the expressions above, but using respectively all the observations in the stack or best Bayesian block.

In Chandra Source Catalog Release 2, the individual source detection hardness ratios are also assessed for variability among the individual observations. See the description of Source Variability. A detailed description of hardness ratios can be found in the hardness ratios and variability memo.

From the Spectral Properties column descriptions page:

Hardness ratios appear in both the Master Sources Table and the Per-Observation Detections Table with the field names hard_xy, hard_xy_hilim, and hard_xy_lolim. The hardness ratios that appear in the Master Sources Table are determined from the Bayesian probability distribution functions (PDFs) of the aperture source photon fluxes derived from the source regions of the contributing individual source observations contained in the Per-Observation Detections Table. Only energy bands hard (h, 2.0-7.0 keV), medium (m, 1.2-2.0 keV) and soft (s, 0.5-1.2 keV) are used.

For two given energy bands, they are defined at the single observation level as the flux value in the softer band, subtracted from the flux value in the harder band, relative to their sum. However, since the PDFs are used, this definition is based on probabilistic considerations. Just like the fluxes are random variables with associated probabilities, so are the hardness ratios. Specifically, the values listed are the ones that maximize the following PDF:

By convention for the catalog, band x is always the higher energy band. As an example, hard_ms is the medium-to-soft band hardness ratio, defined as:

Note that this definition of hardness ratio is different than that used in Chandra Source Catalog Release 1, where the denominator in the ratio was obtained from combining all three energy bands: soft, medium, and hard.

As the reported values for each of these quantities represent the maximum a posteriori values of their given PDFs, the column hardness ratio values might differ slightly from that calculated directly from the aperture fluxes reported in the catalog.

Hardness ratios using the broad, ultra-soft, and HRC bands are not included in the catalog. The two-sided confidence limits associated with the ACIS hardness ratios are computed from the marginalized probability distributions and always lie within the range -1 to 1. If an aperture flux marginalized probability distribution cannot be computed for a given energy band, then no colors associated with that band are reported. At the stack and master level, the hardness ratios are also evaluated using the expressions above, but using respectively all the observations in the stack or best Bayesian block.

In Chandra Source Catalog Release 2, the individual source detection hardness ratios are also assessed for variability among the individual observations. See the description of Source Variability. A detailed description of hardness ratios can be found in the hardness ratios and variability memo.

From the Source Variability column descriptions page:

The probability that the arrival times of the events within the source region are inconsistent with a constant source count rate throughout the observation. High values of this quantity imply that the source is not consistent with a constant rate, and that the source is likely variable. The probability is computed by means of a hypothesis rejection test from a one-sample Kuiper's test applied to the unbinned event data, with corrections applied for good time intervals and for the source region dithering across regions of variable exposure (e.g., chip edges) during the observation. Probability values are calculated for each science energy band. Note that this variability diagnostic does not treat the source and background separately.

From the Source Variability column descriptions page:

The probability that the arrival times of the events within the source region are inconsistent with a constant source count rate throughout the observation. High values of this quantity imply that the source is not consistent with a constant rate, and that the source is likely variable. The probability is computed by means of a hypothesis rejection test from a one-sample K-S test applied to the unbinned event data, with corrections applied for good time intervals and for the source region dithering across regions of variable exposure (e.g., chip edges) during the observation. Probability values are calculated for each science energy band. Note that this variability diagnostic does not treat the source and background separately.

From the Source Significance column descriptions page:

Likelihood and flux significance are reported per band for all detected sources that fall in the valid field of view. Likelihoods are computed for each source detection in a stack, from MLE fits to data from all valid observations for the source. Likelihoods from each individual observation are also computed.

The fundamental metric used to decide whether a source is included in CSC 2.0 is the likelihood,

where \(P\) is the probability that an MLE fit to a point or extended source model, in a region with no source, would yield a change in fit statistic as large or larger than that observed, when compared to a fit to background only.

The likelihood is closely related to the probability, \(P_{\mathrm{Pois}}\), that a Poisson distribution with a mean background in the source aperture would produce at least the number of counts observed in the aperture. This quantity, called detect_significance, is also reported in CSC 2.0. Smoothed background maps are used to estimate mean background, and detect_significance is expressed in terms of the number of \(\sigma\), \(z\), in a zero-mean, unit standard deviation Gaussian distribution that would yield an upper integral probability \(P_{\mathrm{Gaus}}\), from \(z\) to \(\infty\), equivalent to \(P_{\mathrm{Pois}}\). That is,

where

From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page:

Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended.

In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a non-linear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified.

A much simpler and more robust approach makes use of the identity:

which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a root-sum-square intrinsic source size:

that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the well-known result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D.

Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are non-negative, evaluating the right-hand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the right-hand side evaluated at the mean parameter values, therefore, yields the uncertainty:

where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where

A source is extended if its root-sum-square intrinsic size is larger than the root-sum-square error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\).

From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page:

Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended.

In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a non-linear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified.

A much simpler and more robust approach makes use of the identity:

which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a root-sum-square intrinsic source size:

that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the well-known result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D.

Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are non-negative, evaluating the right-hand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the right-hand side evaluated at the mean parameter values, therefore, yields the uncertainty:

where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where

A source is extended if its root-sum-square intrinsic size is larger than the root-sum-square error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\).

From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page:

Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended.

In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a non-linear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified.

A much simpler and more robust approach makes use of the identity:

which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a root-sum-square intrinsic source size:

that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the well-known result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D.

Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are non-negative, evaluating the right-hand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the right-hand side evaluated at the mean parameter values, therefore, yields the uncertainty:

where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where

A source is extended if its root-sum-square intrinsic size is larger than the root-sum-square error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\).

From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page:

Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended.

In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a non-linear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified.

A much simpler and more robust approach makes use of the identity:

which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a root-sum-square intrinsic source size:

that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the well-known result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D.

Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are non-negative, evaluating the right-hand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the right-hand side evaluated at the mean parameter values, therefore, yields the uncertainty:

where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where

A source is extended if its root-sum-square intrinsic size is larger than the root-sum-square error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\).

From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page:

Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended.

In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a non-linear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified.

A much simpler and more robust approach makes use of the identity:

which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a root-sum-square intrinsic source size:

that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the well-known result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D.

Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are non-negative, evaluating the right-hand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the right-hand side evaluated at the mean parameter values, therefore, yields the uncertainty:

where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where

A source is extended if its root-sum-square intrinsic size is larger than the root-sum-square error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\).

From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page:

Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended.

In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a non-linear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified.

A much simpler and more robust approach makes use of the identity:

which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a root-sum-square intrinsic source size:

that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the well-known result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D.

Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are non-negative, evaluating the right-hand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the right-hand side evaluated at the mean parameter values, therefore, yields the uncertainty:

where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where

A source is extended if its root-sum-square intrinsic size is larger than the root-sum-square error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\).

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The elliptical apertures for each source are defined as the ellipses that include the 90% encircled counts fraction of the PSF in each science energy band at the source location, which are used to extract the aperture counts, count rates, and photon and energy fluxes. The elliptical apertures are co-located with the source region. The elliptical background apertures for each science energy band are scaled, annular ellipses co-located with the background region for that source. The parameter values that define the elliptical aperture and the elliptical background aperture for each source are the semi-major axis, semi-minor axis, and position angle of the major axis of each, in addition to the inner and outer annuli of the elliptical background aperture.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The elliptical apertures for each source are defined as the ellipses that include the 90% encircled counts fraction of the PSF in each science energy band at the source location, which are used to extract the aperture counts, count rates, and photon and energy fluxes. The elliptical apertures are co-located with the source region. The elliptical background apertures for each science energy band are scaled, annular ellipses co-located with the background region for that source. The parameter values that define the elliptical aperture and the elliptical background aperture for each source are the semi-major axis, semi-minor axis, and position angle of the major axis of each, in addition to the inner and outer annuli of the elliptical background aperture.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The elliptical apertures for each source are defined as the ellipses that include the 90% encircled counts fraction of the PSF in each science energy band at the source location, which are used to extract the aperture counts, count rates, and photon and energy fluxes. The elliptical apertures are co-located with the source region. The elliptical background apertures for each science energy band are scaled, annular ellipses co-located with the background region for that source. The parameter values that define the elliptical aperture and the elliptical background aperture for each source are the semi-major axis, semi-minor axis, and position angle of the major axis of each, in addition to the inner and outer annuli of the elliptical background aperture.

From the 'Convolved Source Extent' section of the Source Extent and Errors column descriptions page:

In order to estimate the intrinsic extent of a source in the sky, one first needs to realize that the measured extent of the source on the detector is the result of a convolution between the source itself and the PSF corresponding to that particular observation. It is therefore necessary to estimate the convolved extent of the source and of the PSF, and then perform a deconvolution.

The extent of the convolved source is estimated in a given science energy band with a rotated elliptical Gaussian parametrization of the raw extent of a source, i.e., the extent of a source before deconvolution has been performed. The corresponding ellipse has the following form:

Where

Here, \(\phi\) (pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(c_{1}\) and \(c_{2}\) are the \(1\sigma\) radii along the major and minor axes of the source ellipse (mjr_axis_raw, mnr_axis_raw); \(s_{0}\) is the amplitude of the source elliptical Gaussian distribution.

For source extent purposes, the parameters of the ellipse are estimated by performing a spatial transform with a Mexican-Hat wavelet (also known as Ricker wavelet) directly on the counts in the raw source region, provided that more than 15 counts have been detected (for less than 15 counts, the error in the determination of the source size is comparable to the size itself). Note that this region describes the raw size of the source, and it is therefore different from the source region derived by wavdetect. Below we describe how that region is fitted to the observed distribution of counts.

The idea is simple: the two-dimensional correlation integral (i.e., the transform) between the wavelet function \(W\) and the ellipse function \(S\) is defined as:

where \(\mathbf{\alpha} = (c_{1},c_{2},\phi)\) are the semi-major axis, semi-minor axis, and rotational angle of the Mexican-Hat wavelet. This correlation should be maximized when the scale and position of the wavelet coincide with that of the source. Spcifically, the quantity \(\psi(x,y;\mathbf{\alpha}) = C(x,y;\mathbf{\alpha})/\sqrt{c_{1} c_{2}}\) is maximized if the dimensions of the ellipse and the Mexican-Hat wavelength are related as: \(c_{i} = \sqrt{3} \sigma_{i} \) and \(\phi = \phi_{0}\). We can therefore estimate the parameters of the source extent ellipse by maximizing \(\phi(x,y;\mathbf{\alpha})\). Note that this assumes that sources can always be described as elliptical Gaussians. In practice, the maximization is evaluated as a discrete version of the equations above on the pixels of the image. In CSC2, the optimization of the correlation integral is performed using the Sherpa fitting tool.

From the 'Convolved Source Extent' section of the Source Extent and Errors column descriptions page:

In order to estimate the intrinsic extent of a source in the sky, one first needs to realize that the measured extent of the source on the detector is the result of a convolution between the source itself and the PSF corresponding to that particular observation. It is therefore necessary to estimate the convolved extent of the source and of the PSF, and then perform a deconvolution.

The extent of the convolved source is estimated in a given science energy band with a rotated elliptical Gaussian parametrization of the raw extent of a source, i.e., the extent of a source before deconvolution has been performed. The corresponding ellipse has the following form:

Where

Here, \(\phi\) (pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(c_{1}\) and \(c_{2}\) are the \(1\sigma\) radii along the major and minor axes of the source ellipse (mjr_axis_raw, mnr_axis_raw); \(s_{0}\) is the amplitude of the source elliptical Gaussian distribution.

For source extent purposes, the parameters of the ellipse are estimated by performing a spatial transform with a Mexican-Hat wavelet (also known as Ricker wavelet) directly on the counts in the raw source region, provided that more than 15 counts have been detected (for less than 15 counts, the error in the determination of the source size is comparable to the size itself). Note that this region describes the raw size of the source, and it is therefore different from the source region derived by wavdetect. Below we describe how that region is fitted to the observed distribution of counts.

The idea is simple: the two-dimensional correlation integral (i.e., the transform) between the wavelet function \(W\) and the ellipse function \(S\) is defined as:

where \(\mathbf{\alpha} = (c_{1},c_{2},\phi)\) are the semi-major axis, semi-minor axis, and rotational angle of the Mexican-Hat wavelet. This correlation should be maximized when the scale and position of the wavelet coincide with that of the source. Spcifically, the quantity \(\psi(x,y;\mathbf{\alpha}) = C(x,y;\mathbf{\alpha})/\sqrt{c_{1} c_{2}}\) is maximized if the dimensions of the ellipse and the Mexican-Hat wavelength are related as: \(c_{i} = \sqrt{3} \sigma_{i} \) and \(\phi = \phi_{0}\). We can therefore estimate the parameters of the source extent ellipse by maximizing \(\phi(x,y;\mathbf{\alpha})\). Note that this assumes that sources can always be described as elliptical Gaussians. In practice, the maximization is evaluated as a discrete version of the equations above on the pixels of the image. In CSC2, the optimization of the correlation integral is performed using the Sherpa fitting tool.

From the 'Convolved Source Extent' section of the Source Extent and Errors column descriptions page:

In order to estimate the intrinsic extent of a source in the sky, one first needs to realize that the measured extent of the source on the detector is the result of a convolution between the source itself and the PSF corresponding to that particular observation. It is therefore necessary to estimate the convolved extent of the source and of the PSF, and then perform a deconvolution.

The extent of the convolved source is estimated in a given science energy band with a rotated elliptical Gaussian parametrization of the raw extent of a source, i.e., the extent of a source before deconvolution has been performed. The corresponding ellipse has the following form:

Where

Here, \(\phi\) (pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(c_{1}\) and \(c_{2}\) are the \(1\sigma\) radii along the major and minor axes of the source ellipse (mjr_axis_raw, mnr_axis_raw); \(s_{0}\) is the amplitude of the source elliptical Gaussian distribution.

For source extent purposes, the parameters of the ellipse are estimated by performing a spatial transform with a Mexican-Hat wavelet (also known as Ricker wavelet) directly on the counts in the raw source region, provided that more than 15 counts have been detected (for less than 15 counts, the error in the determination of the source size is comparable to the size itself). Note that this region describes the raw size of the source, and it is therefore different from the source region derived by wavdetect. Below we describe how that region is fitted to the observed distribution of counts.

The idea is simple: the two-dimensional correlation integral (i.e., the transform) between the wavelet function \(W\) and the ellipse function \(S\) is defined as:

where \(\mathbf{\alpha} = (c_{1},c_{2},\phi)\) are the semi-major axis, semi-minor axis, and rotational angle of the Mexican-Hat wavelet. This correlation should be maximized when the scale and position of the wavelet coincide with that of the source. Spcifically, the quantity \(\psi(x,y;\mathbf{\alpha}) = C(x,y;\mathbf{\alpha})/\sqrt{c_{1} c_{2}}\) is maximized if the dimensions of the ellipse and the Mexican-Hat wavelength are related as: \(c_{i} = \sqrt{3} \sigma_{i} \) and \(\phi = \phi_{0}\). We can therefore estimate the parameters of the source extent ellipse by maximizing \(\phi(x,y;\mathbf{\alpha})\). Note that this assumes that sources can always be described as elliptical Gaussians. In practice, the maximization is evaluated as a discrete version of the equations above on the pixels of the image. In CSC2, the optimization of the correlation integral is performed using the Sherpa fitting tool.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The elliptical apertures for each source are defined as the ellipses that include the 90% encircled counts fraction of the PSF in each science energy band at the source location, which are used to extract the aperture counts, count rates, and photon and energy fluxes. The elliptical apertures are co-located with the source region. The elliptical background apertures for each science energy band are scaled, annular ellipses co-located with the background region for that source. The parameter values that define the elliptical aperture and the elliptical background aperture for each source are the semi-major axis, semi-minor axis, and position angle of the major axis of each, in addition to the inner and outer annuli of the elliptical background aperture.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The elliptical apertures for each source are defined as the ellipses that include the 90% encircled counts fraction of the PSF in each science energy band at the source location, which are used to extract the aperture counts, count rates, and photon and energy fluxes. The elliptical apertures are co-located with the source region. The elliptical background apertures for each science energy band are scaled, annular ellipses co-located with the background region for that source. The parameter values that define the elliptical aperture and the elliptical background aperture for each source are the semi-major axis, semi-minor axis, and position angle of the major axis of each, in addition to the inner and outer annuli of the elliptical background aperture.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The elliptical apertures for each source are defined as the ellipses that include the 90% encircled counts fraction of the PSF in each science energy band at the source location, which are used to extract the aperture counts, count rates, and photon and energy fluxes. The elliptical apertures are co-located with the source region. The elliptical background apertures for each science energy band are scaled, annular ellipses co-located with the background region for that source. The parameter values that define the elliptical aperture and the elliptical background aperture for each source are the semi-major axis, semi-minor axis, and position angle of the major axis of each, in addition to the inner and outer annuli of the elliptical background aperture.

From the 'Convolved Source Extent' section of the Source Extent and Errors column descriptions page:

In order to estimate the intrinsic extent of a source in the sky, one first needs to realize that the measured extent of the source on the detector is the result of a convolution between the source itself and the PSF corresponding to that particular observation. It is therefore necessary to estimate the convolved extent of the source and of the PSF, and then perform a deconvolution.

The extent of the convolved source is estimated in a given science energy band with a rotated elliptical Gaussian parametrization of the raw extent of a source, i.e., the extent of a source before deconvolution has been performed. The corresponding ellipse has the following form:

Where

Here, \(\phi\) (pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(c_{1}\) and \(c_{2}\) are the \(1\sigma\) radii along the major and minor axes of the source ellipse (mjr_axis_raw, mnr_axis_raw); \(s_{0}\) is the amplitude of the source elliptical Gaussian distribution.

For source extent purposes, the parameters of the ellipse are estimated by performing a spatial transform with a Mexican-Hat wavelet (also known as Ricker wavelet) directly on the counts in the raw source region, provided that more than 15 counts have been detected (for less than 15 counts, the error in the determination of the source size is comparable to the size itself). Note that this region describes the raw size of the source, and it is therefore different from the source region derived by wavdetect. Below we describe how that region is fitted to the observed distribution of counts.

The idea is simple: the two-dimensional correlation integral (i.e., the transform) between the wavelet function \(W\) and the ellipse function \(S\) is defined as:

where \(\mathbf{\alpha} = (c_{1},c_{2},\phi)\) are the semi-major axis, semi-minor axis, and rotational angle of the Mexican-Hat wavelet. This correlation should be maximized when the scale and position of the wavelet coincide with that of the source. Spcifically, the quantity \(\psi(x,y;\mathbf{\alpha}) = C(x,y;\mathbf{\alpha})/\sqrt{c_{1} c_{2}}\) is maximized if the dimensions of the ellipse and the Mexican-Hat wavelength are related as: \(c_{i} = \sqrt{3} \sigma_{i} \) and \(\phi = \phi_{0}\). We can therefore estimate the parameters of the source extent ellipse by maximizing \(\phi(x,y;\mathbf{\alpha})\). Note that this assumes that sources can always be described as elliptical Gaussians. In practice, the maximization is evaluated as a discrete version of the equations above on the pixels of the image. In CSC2, the optimization of the correlation integral is performed using the Sherpa fitting tool.

From the 'Convolved Source Extent' section of the Source Extent and Errors column descriptions page:

In order to estimate the intrinsic extent of a source in the sky, one first needs to realize that the measured extent of the source on the detector is the result of a convolution between the source itself and the PSF corresponding to that particular observation. It is therefore necessary to estimate the convolved extent of the source and of the PSF, and then perform a deconvolution.

The extent of the convolved source is estimated in a given science energy band with a rotated elliptical Gaussian parametrization of the raw extent of a source, i.e., the extent of a source before deconvolution has been performed. The corresponding ellipse has the following form:

Where

Here, \(\phi\) (pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(c_{1}\) and \(c_{2}\) are the \(1\sigma\) radii along the major and minor axes of the source ellipse (mjr_axis_raw, mnr_axis_raw); \(s_{0}\) is the amplitude of the source elliptical Gaussian distribution.

For source extent purposes, the parameters of the ellipse are estimated by performing a spatial transform with a Mexican-Hat wavelet (also known as Ricker wavelet) directly on the counts in the raw source region, provided that more than 15 counts have been detected (for less than 15 counts, the error in the determination of the source size is comparable to the size itself). Note that this region describes the raw size of the source, and it is therefore different from the source region derived by wavdetect. Below we describe how that region is fitted to the observed distribution of counts.

The idea is simple: the two-dimensional correlation integral (i.e., the transform) between the wavelet function \(W\) and the ellipse function \(S\) is defined as:

where \(\mathbf{\alpha} = (c_{1},c_{2},\phi)\) are the semi-major axis, semi-minor axis, and rotational angle of the Mexican-Hat wavelet. This correlation should be maximized when the scale and position of the wavelet coincide with that of the source. Spcifically, the quantity \(\psi(x,y;\mathbf{\alpha}) = C(x,y;\mathbf{\alpha})/\sqrt{c_{1} c_{2}}\) is maximized if the dimensions of the ellipse and the Mexican-Hat wavelength are related as: \(c_{i} = \sqrt{3} \sigma_{i} \) and \(\phi = \phi_{0}\). We can therefore estimate the parameters of the source extent ellipse by maximizing \(\phi(x,y;\mathbf{\alpha})\). Note that this assumes that sources can always be described as elliptical Gaussians. In practice, the maximization is evaluated as a discrete version of the equations above on the pixels of the image. In CSC2, the optimization of the correlation integral is performed using the Sherpa fitting tool.

From the 'Convolved Source Extent' section of the Source Extent and Errors column descriptions page:

In order to estimate the intrinsic extent of a source in the sky, one first needs to realize that the measured extent of the source on the detector is the result of a convolution between the source itself and the PSF corresponding to that particular observation. It is therefore necessary to estimate the convolved extent of the source and of the PSF, and then perform a deconvolution.

The extent of the convolved source is estimated in a given science energy band with a rotated elliptical Gaussian parametrization of the raw extent of a source, i.e., the extent of a source before deconvolution has been performed. The corresponding ellipse has the following form:

Where

Here, \(\phi\) (pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(c_{1}\) and \(c_{2}\) are the \(1\sigma\) radii along the major and minor axes of the source ellipse (mjr_axis_raw, mnr_axis_raw); \(s_{0}\) is the amplitude of the source elliptical Gaussian distribution.

For source extent purposes, the parameters of the ellipse are estimated by performing a spatial transform with a Mexican-Hat wavelet (also known as Ricker wavelet) directly on the counts in the raw source region, provided that more than 15 counts have been detected (for less than 15 counts, the error in the determination of the source size is comparable to the size itself). Note that this region describes the raw size of the source, and it is therefore different from the source region derived by wavdetect. Below we describe how that region is fitted to the observed distribution of counts.

The idea is simple: the two-dimensional correlation integral (i.e., the transform) between the wavelet function \(W\) and the ellipse function \(S\) is defined as:

where \(\mathbf{\alpha} = (c_{1},c_{2},\phi)\) are the semi-major axis, semi-minor axis, and rotational angle of the Mexican-Hat wavelet. This correlation should be maximized when the scale and position of the wavelet coincide with that of the source. Spcifically, the quantity \(\psi(x,y;\mathbf{\alpha}) = C(x,y;\mathbf{\alpha})/\sqrt{c_{1} c_{2}}\) is maximized if the dimensions of the ellipse and the Mexican-Hat wavelength are related as: \(c_{i} = \sqrt{3} \sigma_{i} \) and \(\phi = \phi_{0}\). We can therefore estimate the parameters of the source extent ellipse by maximizing \(\phi(x,y;\mathbf{\alpha})\). Note that this assumes that sources can always be described as elliptical Gaussians. In practice, the maximization is evaluated as a discrete version of the equations above on the pixels of the image. In CSC2, the optimization of the correlation integral is performed using the Sherpa fitting tool.

From the Source Flags column descriptions page:

The multi-chip code in the per-observation detections table is defined identically to the edge code in the stacked observations detections table.

From the Position and Position Errors column descriptions page:

The angular location of the source region aperture that includes a detection, relative to the optical axis of the individual observation, is defined by the off-axis angle θ and azimuthal angle φ.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source energy fluxes (flux_aper) and associated two-sided confidence limits represent the background-subtracted fluxes in the modified source region (photflux_aper) and in the modified elliptical aperture (photflux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure. The conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source energy fluxes (flux_aper) and associated two-sided confidence limits represent the background-subtracted fluxes in the modified source region (photflux_aper) and in the modified elliptical aperture (photflux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure. The conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source energy fluxes (flux_aper) and associated two-sided confidence limits represent the background-subtracted fluxes in the modified source region (photflux_aper) and in the modified elliptical aperture (photflux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure. The conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source energy fluxes (flux_aper) and associated two-sided confidence limits represent the background-subtracted fluxes in the modified source region (photflux_aper) and in the modified elliptical aperture (photflux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure. The conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source energy fluxes (flux_aper) and associated two-sided confidence limits represent the background-subtracted fluxes in the modified source region (photflux_aper) and in the modified elliptical aperture (photflux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure. The conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source energy fluxes (flux_aper) and associated two-sided confidence limits represent the background-subtracted fluxes in the modified source region (photflux_aper) and in the modified elliptical aperture (photflux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure. The conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon.

From the Source Flags column descriptions page:

pileup_warning is a double precision value that reports the observed per-frame count rate of the brightest 3×3 pixel island in an ACIS detection's source region, averaged over the observation. This value may be correlated with pileup models to crudely estimate the pileup fraction for the detection. For the standard 3.2 sec ACIS frame time, the estimated pileup fraction is roughly equal to pileup_warning/2 for pileup_warning values ≲0.2.

The value is unreliable if the saturated source flag is TRUE.

pileup_warning for an extended (convex hull) detection is always NULL.

From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page:

Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended.

In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a non-linear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified.

A much simpler and more robust approach makes use of the identity:

which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a root-sum-square intrinsic source size:

that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the well-known result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D.

Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are non-negative, evaluating the right-hand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the right-hand side evaluated at the mean parameter values, therefore, yields the uncertainty:

where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where

A source is extended if its root-sum-square intrinsic size is larger than the root-sum-square error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\).

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The elliptical apertures for each source are defined as the ellipses that include the 90% encircled counts fraction of the PSF in each science energy band at the source location, which are used to extract the aperture counts, count rates, and photon and energy fluxes. The elliptical apertures are co-located with the source region. The elliptical background apertures for each science energy band are scaled, annular ellipses co-located with the background region for that source. The parameter values that define the elliptical aperture and the elliptical background aperture for each source are the semi-major axis, semi-minor axis, and position angle of the major axis of each, in addition to the inner and outer annuli of the elliptical background aperture.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The elliptical apertures for each source are defined as the ellipses that include the 90% encircled counts fraction of the PSF in each science energy band at the source location, which are used to extract the aperture counts, count rates, and photon and energy fluxes. The elliptical apertures are co-located with the source region. The elliptical background apertures for each science energy band are scaled, annular ellipses co-located with the background region for that source. The parameter values that define the elliptical aperture and the elliptical background aperture for each source are the semi-major axis, semi-minor axis, and position angle of the major axis of each, in addition to the inner and outer annuli of the elliptical background aperture.

From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page:

Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended.

In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a non-linear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified.

A much simpler and more robust approach makes use of the identity:

which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a root-sum-square intrinsic source size:

that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the well-known result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D.

Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are non-negative, evaluating the right-hand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the right-hand side evaluated at the mean parameter values, therefore, yields the uncertainty:

where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where

A source is extended if its root-sum-square intrinsic size is larger than the root-sum-square error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\).

From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page:

Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended.

In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a non-linear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified.

A much simpler and more robust approach makes use of the identity:

which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a root-sum-square intrinsic source size:

that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the well-known result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D.

Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are non-negative, evaluating the right-hand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the right-hand side evaluated at the mean parameter values, therefore, yields the uncertainty:

where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where

A source is extended if its root-sum-square intrinsic size is larger than the root-sum-square error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\).

From the 'Convolved Source Extent' section of the Source Extent and Errors column descriptions page:

In order to estimate the intrinsic extent of a source in the sky, one first needs to realize that the measured extent of the source on the detector is the result of a convolution between the source itself and the PSF corresponding to that particular observation. It is therefore necessary to estimate the convolved extent of the source and of the PSF, and then perform a deconvolution.

The extent of the convolved source is estimated in a given science energy band with a rotated elliptical Gaussian parametrization of the raw extent of a source, i.e., the extent of a source before deconvolution has been performed. The corresponding ellipse has the following form:

Where

Here, \(\phi\) (pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(c_{1}\) and \(c_{2}\) are the \(1\sigma\) radii along the major and minor axes of the source ellipse (mjr_axis_raw, mnr_axis_raw); \(s_{0}\) is the amplitude of the source elliptical Gaussian distribution.

For source extent purposes, the parameters of the ellipse are estimated by performing a spatial transform with a Mexican-Hat wavelet (also known as Ricker wavelet) directly on the counts in the raw source region, provided that more than 15 counts have been detected (for less than 15 counts, the error in the determination of the source size is comparable to the size itself). Note that this region describes the raw size of the source, and it is therefore different from the source region derived by wavdetect. Below we describe how that region is fitted to the observed distribution of counts.

The idea is simple: the two-dimensional correlation integral (i.e., the transform) between the wavelet function \(W\) and the ellipse function \(S\) is defined as:

where \(\mathbf{\alpha} = (c_{1},c_{2},\phi)\) are the semi-major axis, semi-minor axis, and rotational angle of the Mexican-Hat wavelet. This correlation should be maximized when the scale and position of the wavelet coincide with that of the source. Spcifically, the quantity \(\psi(x,y;\mathbf{\alpha}) = C(x,y;\mathbf{\alpha})/\sqrt{c_{1} c_{2}}\) is maximized if the dimensions of the ellipse and the Mexican-Hat wavelength are related as: \(c_{i} = \sqrt{3} \sigma_{i} \) and \(\phi = \phi_{0}\). We can therefore estimate the parameters of the source extent ellipse by maximizing \(\phi(x,y;\mathbf{\alpha})\). Note that this assumes that sources can always be described as elliptical Gaussians. In practice, the maximization is evaluated as a discrete version of the equations above on the pixels of the image. In CSC2, the optimization of the correlation integral is performed using the Sherpa fitting tool.

From the 'Convolved Source Extent' section of the Source Extent and Errors column descriptions page:

In order to estimate the intrinsic extent of a source in the sky, one first needs to realize that the measured extent of the source on the detector is the result of a convolution between the source itself and the PSF corresponding to that particular observation. It is therefore necessary to estimate the convolved extent of the source and of the PSF, and then perform a deconvolution.

The extent of the convolved source is estimated in a given science energy band with a rotated elliptical Gaussian parametrization of the raw extent of a source, i.e., the extent of a source before deconvolution has been performed. The corresponding ellipse has the following form:

Where

Here, \(\phi\) (pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(c_{1}\) and \(c_{2}\) are the \(1\sigma\) radii along the major and minor axes of the source ellipse (mjr_axis_raw, mnr_axis_raw); \(s_{0}\) is the amplitude of the source elliptical Gaussian distribution.

For source extent purposes, the parameters of the ellipse are estimated by performing a spatial transform with a Mexican-Hat wavelet (also known as Ricker wavelet) directly on the counts in the raw source region, provided that more than 15 counts have been detected (for less than 15 counts, the error in the determination of the source size is comparable to the size itself). Note that this region describes the raw size of the source, and it is therefore different from the source region derived by wavdetect. Below we describe how that region is fitted to the observed distribution of counts.

The idea is simple: the two-dimensional correlation integral (i.e., the transform) between the wavelet function \(W\) and the ellipse function \(S\) is defined as:

where \(\mathbf{\alpha} = (c_{1},c_{2},\phi)\) are the semi-major axis, semi-minor axis, and rotational angle of the Mexican-Hat wavelet. This correlation should be maximized when the scale and position of the wavelet coincide with that of the source. Spcifically, the quantity \(\psi(x,y;\mathbf{\alpha}) = C(x,y;\mathbf{\alpha})/\sqrt{c_{1} c_{2}}\) is maximized if the dimensions of the ellipse and the Mexican-Hat wavelength are related as: \(c_{i} = \sqrt{3} \sigma_{i} \) and \(\phi = \phi_{0}\). We can therefore estimate the parameters of the source extent ellipse by maximizing \(\phi(x,y;\mathbf{\alpha})\). Note that this assumes that sources can always be described as elliptical Gaussians. In practice, the maximization is evaluated as a discrete version of the equations above on the pixels of the image. In CSC2, the optimization of the correlation integral is performed using the Sherpa fitting tool.

From the 'Convolved Source Extent' section of the Source Extent and Errors column descriptions page:

In order to estimate the intrinsic extent of a source in the sky, one first needs to realize that the measured extent of the source on the detector is the result of a convolution between the source itself and the PSF corresponding to that particular observation. It is therefore necessary to estimate the convolved extent of the source and of the PSF, and then perform a deconvolution.

The extent of the convolved source is estimated in a given science energy band with a rotated elliptical Gaussian parametrization of the raw extent of a source, i.e., the extent of a source before deconvolution has been performed. The corresponding ellipse has the following form:

Where

Here, \(\phi\) (pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(c_{1}\) and \(c_{2}\) are the \(1\sigma\) radii along the major and minor axes of the source ellipse (mjr_axis_raw, mnr_axis_raw); \(s_{0}\) is the amplitude of the source elliptical Gaussian distribution.

For source extent purposes, the parameters of the ellipse are estimated by performing a spatial transform with a Mexican-Hat wavelet (also known as Ricker wavelet) directly on the counts in the raw source region, provided that more than 15 counts have been detected (for less than 15 counts, the error in the determination of the source size is comparable to the size itself). Note that this region describes the raw size of the source, and it is therefore different from the source region derived by wavdetect. Below we describe how that region is fitted to the observed distribution of counts.

The idea is simple: the two-dimensional correlation integral (i.e., the transform) between the wavelet function \(W\) and the ellipse function \(S\) is defined as:

where \(\mathbf{\alpha} = (c_{1},c_{2},\phi)\) are the semi-major axis, semi-minor axis, and rotational angle of the Mexican-Hat wavelet. This correlation should be maximized when the scale and position of the wavelet coincide with that of the source. Spcifically, the quantity \(\psi(x,y;\mathbf{\alpha}) = C(x,y;\mathbf{\alpha})/\sqrt{c_{1} c_{2}}\) is maximized if the dimensions of the ellipse and the Mexican-Hat wavelength are related as: \(c_{i} = \sqrt{3} \sigma_{i} \) and \(\phi = \phi_{0}\). We can therefore estimate the parameters of the source extent ellipse by maximizing \(\phi(x,y;\mathbf{\alpha})\). Note that this assumes that sources can always be described as elliptical Gaussians. In practice, the maximization is evaluated as a discrete version of the equations above on the pixels of the image. In CSC2, the optimization of the correlation integral is performed using the Sherpa fitting tool.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed power law model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are the total equivalent neutral hydrogen absorbing column density, power law photon index, and power law amplitude.

The best-fit amplitude of the power law model and associated two-sided 68% confidence limits in units of photons/s/cm²/keV defined at 1 keV.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed power law model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are the total equivalent neutral hydrogen absorbing column density, power law photon index, and power law amplitude.

The best-fit amplitude of the power law model and associated two-sided 68% confidence limits in units of photons/s/cm²/keV defined at 1 keV.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed power law model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are the total equivalent neutral hydrogen absorbing column density, power law photon index, and power law amplitude.

The best-fit amplitude of the power law model and associated two-sided 68% confidence limits in units of photons/s/cm²/keV defined at 1 keV.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed power law model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are the total equivalent neutral hydrogen absorbing column density, power law photon index, and power law amplitude.

The best-fit power law photon index and the associated two-sided 68% confidence limits, \(\gamma\), defined as:

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed power law model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are the total equivalent neutral hydrogen absorbing column density, power law photon index, and power law amplitude.

The best-fit power law photon index and the associated two-sided 68% confidence limits, \(\gamma\), defined as:

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed power law model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are the total equivalent neutral hydrogen absorbing column density, power law photon index, and power law amplitude.

The best-fit power law photon index and the associated two-sided 68% confidence limits, \(\gamma\), defined as:

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed power law model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are the total equivalent neutral hydrogen absorbing column density, power law photon index, and power law amplitude.

The best-fit equivalent neutral hydrogen absorbing column, \(N_{H}\), and the associated two-sided 68% confidence limits from an absorbed power law model spectral fit in units of 10²⁰ cm^-2.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed power law model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are the total equivalent neutral hydrogen absorbing column density, power law photon index, and power law amplitude.

The best-fit equivalent neutral hydrogen absorbing column, \(N_{H}\), and the associated two-sided 68% confidence limits from an absorbed power law model spectral fit in units of 10²⁰ cm^-2.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed power law model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are the total equivalent neutral hydrogen absorbing column density, power law photon index, and power law amplitude.

The best-fit equivalent neutral hydrogen absorbing column, \(N_{H}\), and the associated two-sided 68% confidence limits from an absorbed power law model spectral fit in units of 10²⁰ cm^-2.

From the 'Spectral Model Fits' section of the Spectral Properties column descriptions page:

If there are at least 150 net (background-subtracted) counts in the energy range 0.5-7.0 keV present in the source region of an ACIS observation, then power law, blackbody, and bremsstrahlung models are fitted to PI spectra extracted from the source region, with the final flux value and limits calculated using modelflux.

The absorbed power law model spectral fit is performed over the energy range 0.5-7.0 keV; the free parameters to be fitted are the total equivalent neutral hydrogen absorbing column density, power law photon index, and power law amplitude.

The power law model spectral fit statistic is defined as the value of the \(\chi^{2}\) (data variance) statistic per degree of freedom for the best-fitting absorbed power law model.

From the 'PSF Aperture Fractions' section of the Source Fluxes column descriptions page:

The PSF aperture fraction represents the fraction of the PSF that is included in the modified source and background regions (psf_frac_aper, psf_frac_bkgaper), and the modified elliptical aperture and modified elliptical background aperture (psf_frac_aper90, psf_frac_aper90bkg).

From the 'PSF Aperture Fractions' section of the Source Fluxes column descriptions page:

The PSF aperture fraction represents the fraction of the PSF that is included in the modified source and background regions (psf_frac_aper, psf_frac_bkgaper), and the modified elliptical aperture and modified elliptical background aperture (psf_frac_aper90, psf_frac_aper90bkg).

From the 'PSF Aperture Fractions' section of the Source Fluxes column descriptions page:

The PSF aperture fraction represents the fraction of the PSF that is included in the modified source and background regions (psf_frac_aper, psf_frac_bkgaper), and the modified elliptical aperture and modified elliptical background aperture (psf_frac_aper90, psf_frac_aper90bkg).

From the 'PSF Aperture Fractions' section of the Source Fluxes column descriptions page:

The PSF aperture fraction represents the fraction of the PSF that is included in the modified source and background regions (psf_frac_aper, psf_frac_bkgaper), and the modified elliptical aperture and modified elliptical background aperture (psf_frac_aper90, psf_frac_aper90bkg).

From the 'Point Spread Function Extent' section of the Source Extent and Errors column descriptions page:

The same approach as for the convolved source extent is used to estimate the elliptical parameters that best represent the instrumental point spread function (PSF) in each science band at the location of the source. The inputs are the PSF counts in the source region. The parameterization of the PSF can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source (see below).

The point spread function extent is a rotated elliptical Gaussian parameterization of the raw extent of the point spread function (PSF) at the location of the source. The parameterization of the PSF is computed from a wavelet transform analysis of the PSF counts in the source region in a given science energy band, and can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source. The point spread function extent is defined by the values and associated errors of the \(1\sigma\) radii along the major and minor axes, and position angle of the major axis of the point spread function ellipse that the detection process would assign to a monochromatic PSF at the location of the source, and whose energy is the effective energy of the given energy band. The point spread function has the following form:

Here, \(\psi\) (psf_pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(b_{1}\) and \(b_{2}\) are the \(1\sigma\) radii along the major and minor axes of the PSF ellipse (psf_mjr_axis_raw, psf_mnr_axis_raw); \(p_{0}\) is the amplitude of the PSF elliptical Gaussian distribution, and

From the 'Point Spread Function Extent' section of the Source Extent and Errors column descriptions page:

The same approach as for the convolved source extent is used to estimate the elliptical parameters that best represent the instrumental point spread function (PSF) in each science band at the location of the source. The inputs are the PSF counts in the source region. The parameterization of the PSF can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source (see below).

The point spread function extent is a rotated elliptical Gaussian parameterization of the raw extent of the point spread function (PSF) at the location of the source. The parameterization of the PSF is computed from a wavelet transform analysis of the PSF counts in the source region in a given science energy band, and can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source. The point spread function extent is defined by the values and associated errors of the \(1\sigma\) radii along the major and minor axes, and position angle of the major axis of the point spread function ellipse that the detection process would assign to a monochromatic PSF at the location of the source, and whose energy is the effective energy of the given energy band. The point spread function has the following form:

Here, \(\psi\) (psf_pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(b_{1}\) and \(b_{2}\) are the \(1\sigma\) radii along the major and minor axes of the PSF ellipse (psf_mjr_axis_raw, psf_mnr_axis_raw); \(p_{0}\) is the amplitude of the PSF elliptical Gaussian distribution, and

From the 'Point Spread Function Extent' section of the Source Extent and Errors column descriptions page:

The same approach as for the convolved source extent is used to estimate the elliptical parameters that best represent the instrumental point spread function (PSF) in each science band at the location of the source. The inputs are the PSF counts in the source region. The parameterization of the PSF can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source (see below).

The point spread function extent is a rotated elliptical Gaussian parameterization of the raw extent of the point spread function (PSF) at the location of the source. The parameterization of the PSF is computed from a wavelet transform analysis of the PSF counts in the source region in a given science energy band, and can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source. The point spread function extent is defined by the values and associated errors of the \(1\sigma\) radii along the major and minor axes, and position angle of the major axis of the point spread function ellipse that the detection process would assign to a monochromatic PSF at the location of the source, and whose energy is the effective energy of the given energy band. The point spread function has the following form:

Here, \(\psi\) (psf_pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(b_{1}\) and \(b_{2}\) are the \(1\sigma\) radii along the major and minor axes of the PSF ellipse (psf_mjr_axis_raw, psf_mnr_axis_raw); \(p_{0}\) is the amplitude of the PSF elliptical Gaussian distribution, and

From the 'Point Spread Function Extent' section of the Source Extent and Errors column descriptions page:

The same approach as for the convolved source extent is used to estimate the elliptical parameters that best represent the instrumental point spread function (PSF) in each science band at the location of the source. The inputs are the PSF counts in the source region. The parameterization of the PSF can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source (see below).

The point spread function extent is a rotated elliptical Gaussian parameterization of the raw extent of the point spread function (PSF) at the location of the source. The parameterization of the PSF is computed from a wavelet transform analysis of the PSF counts in the source region in a given science energy band, and can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source. The point spread function extent is defined by the values and associated errors of the \(1\sigma\) radii along the major and minor axes, and position angle of the major axis of the point spread function ellipse that the detection process would assign to a monochromatic PSF at the location of the source, and whose energy is the effective energy of the given energy band. The point spread function has the following form:

Here, \(\psi\) (psf_pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(b_{1}\) and \(b_{2}\) are the \(1\sigma\) radii along the major and minor axes of the PSF ellipse (psf_mjr_axis_raw, psf_mnr_axis_raw); \(p_{0}\) is the amplitude of the PSF elliptical Gaussian distribution, and

From the 'Point Spread Function Extent' section of the Source Extent and Errors column descriptions page:

The same approach as for the convolved source extent is used to estimate the elliptical parameters that best represent the instrumental point spread function (PSF) in each science band at the location of the source. The inputs are the PSF counts in the source region. The parameterization of the PSF can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source (see below).

The point spread function extent is a rotated elliptical Gaussian parameterization of the raw extent of the point spread function (PSF) at the location of the source. The parameterization of the PSF is computed from a wavelet transform analysis of the PSF counts in the source region in a given science energy band, and can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source. The point spread function extent is defined by the values and associated errors of the \(1\sigma\) radii along the major and minor axes, and position angle of the major axis of the point spread function ellipse that the detection process would assign to a monochromatic PSF at the location of the source, and whose energy is the effective energy of the given energy band. The point spread function has the following form:

Here, \(\psi\) (psf_pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(b_{1}\) and \(b_{2}\) are the \(1\sigma\) radii along the major and minor axes of the PSF ellipse (psf_mjr_axis_raw, psf_mnr_axis_raw); \(p_{0}\) is the amplitude of the PSF elliptical Gaussian distribution, and

From the 'Point Spread Function Extent' section of the Source Extent and Errors column descriptions page:

The same approach as for the convolved source extent is used to estimate the elliptical parameters that best represent the instrumental point spread function (PSF) in each science band at the location of the source. The inputs are the PSF counts in the source region. The parameterization of the PSF can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source (see below).

The point spread function extent is a rotated elliptical Gaussian parameterization of the raw extent of the point spread function (PSF) at the location of the source. The parameterization of the PSF is computed from a wavelet transform analysis of the PSF counts in the source region in a given science energy band, and can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source. The point spread function extent is defined by the values and associated errors of the \(1\sigma\) radii along the major and minor axes, and position angle of the major axis of the point spread function ellipse that the detection process would assign to a monochromatic PSF at the location of the source, and whose energy is the effective energy of the given energy band. The point spread function has the following form:

Here, \(\psi\) (psf_pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(b_{1}\) and \(b_{2}\) are the \(1\sigma\) radii along the major and minor axes of the PSF ellipse (psf_mjr_axis_raw, psf_mnr_axis_raw); \(p_{0}\) is the amplitude of the PSF elliptical Gaussian distribution, and

From the 'Point Spread Function Extent' section of the Source Extent and Errors column descriptions page:

The same approach as for the convolved source extent is used to estimate the elliptical parameters that best represent the instrumental point spread function (PSF) in each science band at the location of the source. The inputs are the PSF counts in the source region. The parameterization of the PSF can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source (see below).

The point spread function extent is a rotated elliptical Gaussian parameterization of the raw extent of the point spread function (PSF) at the location of the source. The parameterization of the PSF is computed from a wavelet transform analysis of the PSF counts in the source region in a given science energy band, and can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source. The point spread function extent is defined by the values and associated errors of the \(1\sigma\) radii along the major and minor axes, and position angle of the major axis of the point spread function ellipse that the detection process would assign to a monochromatic PSF at the location of the source, and whose energy is the effective energy of the given energy band. The point spread function has the following form:

Here, \(\psi\) (psf_pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(b_{1}\) and \(b_{2}\) are the \(1\sigma\) radii along the major and minor axes of the PSF ellipse (psf_mjr_axis_raw, psf_mnr_axis_raw); \(p_{0}\) is the amplitude of the PSF elliptical Gaussian distribution, and

From the 'Point Spread Function Extent' section of the Source Extent and Errors column descriptions page:

The same approach as for the convolved source extent is used to estimate the elliptical parameters that best represent the instrumental point spread function (PSF) in each science band at the location of the source. The inputs are the PSF counts in the source region. The parameterization of the PSF can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source (see below).

The point spread function extent is a rotated elliptical Gaussian parameterization of the raw extent of the point spread function (PSF) at the location of the source. The parameterization of the PSF is computed from a wavelet transform analysis of the PSF counts in the source region in a given science energy band, and can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source. The point spread function extent is defined by the values and associated errors of the \(1\sigma\) radii along the major and minor axes, and position angle of the major axis of the point spread function ellipse that the detection process would assign to a monochromatic PSF at the location of the source, and whose energy is the effective energy of the given energy band. The point spread function has the following form:

Here, \(\psi\) (psf_pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(b_{1}\) and \(b_{2}\) are the \(1\sigma\) radii along the major and minor axes of the PSF ellipse (psf_mjr_axis_raw, psf_mnr_axis_raw); \(p_{0}\) is the amplitude of the PSF elliptical Gaussian distribution, and

From the 'Point Spread Function Extent' section of the Source Extent and Errors column descriptions page:

The same approach as for the convolved source extent is used to estimate the elliptical parameters that best represent the instrumental point spread function (PSF) in each science band at the location of the source. The inputs are the PSF counts in the source region. The parameterization of the PSF can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source (see below).

The point spread function extent is a rotated elliptical Gaussian parameterization of the raw extent of the point spread function (PSF) at the location of the source. The parameterization of the PSF is computed from a wavelet transform analysis of the PSF counts in the source region in a given science energy band, and can be compared with the parameterization of the detected source to determine whether the latter is consistent with a point source. The point spread function extent is defined by the values and associated errors of the \(1\sigma\) radii along the major and minor axes, and position angle of the major axis of the point spread function ellipse that the detection process would assign to a monochromatic PSF at the location of the source, and whose energy is the effective energy of the given energy band. The point spread function has the following form:

Here, \(\psi\) (psf_pos_angle_raw) is the clockwise angle between the positive x-axis and the ellipse major axis; \(b_{1}\) and \(b_{2}\) are the \(1\sigma\) radii along the major and minor axes of the PSF ellipse (psf_mjr_axis_raw, psf_mnr_axis_raw); \(p_{0}\) is the amplitude of the PSF elliptical Gaussian distribution, and

From the Source Flags column descriptions page:

The saturated detection flag for a compact detection is a Boolean that has a value of TRUE if the observation was obtained using ACIS and the detection is severely piled-up, to the extent that the source image may be flat-topped or have a central hole. Detection properties (including the value of pileup warning) are unreliable for all ACIS energy bands. Otherwise, the value is FALSE.

sat_src_flag for an extended (convex hull) source is always NULL.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source counts represent the net number of background-subtracted source counts in the modified source region (src_cnts_aper) and in the modified elliptical aperture (src_cnts_aper90), corrected by the appropriate PSF aperture fractions.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source counts represent the net number of background-subtracted source counts in the modified source region (src_cnts_aper) and in the modified elliptical aperture (src_cnts_aper90), corrected by the appropriate PSF aperture fractions.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source counts represent the net number of background-subtracted source counts in the modified source region (src_cnts_aper) and in the modified elliptical aperture (src_cnts_aper90), corrected by the appropriate PSF aperture fractions.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source counts represent the net number of background-subtracted source counts in the modified source region (src_cnts_aper) and in the modified elliptical aperture (src_cnts_aper90), corrected by the appropriate PSF aperture fractions.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source counts represent the net number of background-subtracted source counts in the modified source region (src_cnts_aper) and in the modified elliptical aperture (src_cnts_aper90), corrected by the appropriate PSF aperture fractions.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source counts represent the net number of background-subtracted source counts in the modified source region (src_cnts_aper) and in the modified elliptical aperture (src_cnts_aper90), corrected by the appropriate PSF aperture fractions.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source count rates and associated two-sided confidence limits are defined as the background-subtracted source count rates in the modified source region (src_rate_aper) and in the modified elliptical aperture (src_rate_aper90), corrected by the appropriate PSF aperture fractions and livetime.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source count rates and associated two-sided confidence limits are defined as the background-subtracted source count rates in the modified source region (src_rate_aper) and in the modified elliptical aperture (src_rate_aper90), corrected by the appropriate PSF aperture fractions and livetime.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source count rates and associated two-sided confidence limits are defined as the background-subtracted source count rates in the modified source region (src_rate_aper) and in the modified elliptical aperture (src_rate_aper90), corrected by the appropriate PSF aperture fractions and livetime.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source count rates and associated two-sided confidence limits are defined as the background-subtracted source count rates in the modified source region (src_rate_aper) and in the modified elliptical aperture (src_rate_aper90), corrected by the appropriate PSF aperture fractions and livetime.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source count rates and associated two-sided confidence limits are defined as the background-subtracted source count rates in the modified source region (src_rate_aper) and in the modified elliptical aperture (src_rate_aper90), corrected by the appropriate PSF aperture fractions and livetime.

From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page:

Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^-1 cm^-2 to ergs s^-1 cm^-2 is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine background-marginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits.

Fluxes are determined for each per-observation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits.

The aperture source count rates and associated two-sided confidence limits are defined as the background-subtracted source count rates in the modified source region (src_rate_aper) and in the modified elliptical aperture (src_rate_aper90), corrected by the appropriate PSF aperture fractions and livetime.

From the Source Flags column descriptions page:

The streak detection flag for a compact detection is a Boolean that has a value of TRUE if the observation was obtained using ACIS and if the mean chip coordinates of the source region fall within a defined region enclosing an identified readout streak. Otherwise, the value is FALSE.

The streak detection flag for an extended (convex hull) detection is TRUE if any part of the extended (convex hull) detection region overlaps a defined region enclosing an identified readout streak. Otherwise, the value is FALSE.

From the Position and Position Errors column descriptions page:

The angular location of the source region aperture that includes a detection, relative to the optical axis of the individual observation, is defined by the off-axis angle θ and azimuthal angle φ.

From the Source Flags column descriptions page:

The variability code for a compact detection is a 16-bit coded bytes that has all bits set to zero if variability is not detected within the observation in any science energy band. Otherwise, the bits are set as follows:

The appropriate bit in the variability code corresponding to a specific science energy band is set to 0 if the variability index for that science energy band is less than or equal to 2, otherwise the bit shall be set to 1.

The variability code for an extended (convex hull) detection is always NULL.

From the Source Variability column descriptions page:

An index in the range [0,10] that combines (a) the Gregory-Loredo variability probability with (b) the fractions of the multi-resolution light curve output by the Gregory-Loredo analysis that are within 3σ and 5σ of the average count rate, to evaluate whether the source region flux is uniform throughout the observation. See the Gregory-Loredo Probability How and Why topic for a definition of this index value, which is calculated for each science energy band.

From the Source Variability column descriptions page:

The maximum count rate (var_max) is the maximum value of the source region count rate derived from the multi-resolution light curve output by the Gregory-Loredo analysis. This value is calculated for each science energy band.

From the Source Variability column descriptions page:

The mean count rate (var_mean) is the time-averaged source region count rate derived from the multi-resolution light curve output by the Gregory-Loredo analysis. This value is calculated for each science energy band.

From the Source Variability column descriptions page:

The minimum count rate (var_min) is the minimum value of the source region count rate derived from the multi-resolution light curve output by the Gregory-Loredo analysis. This value is calculated for each science energy band.

From the Source Variability column descriptions page:

The probability that the source region count rate lightcurve is the result of multiple, uniformly sampled time bins, each with different rates, as opposed to the result of a single, uniform rate time bin. This probability is based upon the odd ratios (for describing the lightcurve with two or more bins of potentially different rates) calculated from a Gregory-Loredo analysis of the arrival times of the events within the source region. Corrections to the event rate are applied accounting for good time intervals and for the source region dithering across regions of variable exposure (e.g., chip edges) during the observation. Probability values are calculated for each science energy band.

From the Source Variability column descriptions page:

The count rate standard deviation (var_sigma) is the time-averaged 1σ statistical variability of the source region count rate derived from the multi-resolution light curve output by the Gregory-Loredo analysis. This value is calculated for each science energy band.