Astronomical Calibration of the Chandra Clock

Arnold Rots
Harvard-Smithsonian Center for Astrophysics / CXC

Abstract

We have determined the absolute timing of the Chandra clock for an observation of the Crab pulsar, taking into account all known effects. This determination is based on an intercomparison of the phase of the main pulse in the pulse profile between this Chandra observation and an RXTE observation made less than four days later, both referenced to the same Jodrell Bank timing ephemeris.

The final result is that there are 35 µs unaccounted for, with an uncertainty of approximately 12 µs.

Objective

We set out to compare the time stamps of Chandra event data, after all known corrections are applied, with absolute time and measure the discrepancy, if any.

Our method is to determine the absolute phase of the primary pulse of the Crab pulsar, derived from a Chandra observation, with respect to the standard Jodrell Bank timing ephemeris. We then do the same with an RXTE observation. Since the RXTE clock is known to keep accurate absolute time within 2 µs, the difference between the two phases yields the Chandra absolute time error.

Observations

We used a proprietary HRC timing observation of the Crab pulsar. The telemetry was saturated by about 50%. The time resolution of this observation is 15.6 µs.

Within four days, a regular RXTE Crab Pulsar monitoring observation of 1 ks was performed with a time resolution of 250 µs.

The standard monthly Crab timing ephemeris from Jodrell Bank was used as posted on their web page. It has a nominal accuracy of 0.6 milliperiod, though this is not material as long as the frequency and its derivatives do not introduce time gradients in the X-ray data. This is unlikely to be the case since the two RXTE observations covered by this ephemeris show a variation of only 1 milliperiod over 30 days.

Analysis and Results

The data were analyzed using the program faseBin which forms the core of the Ftool fasebin. Auxiliary information came from the CXO and RXTE definitive orbit ephemeris files and JPL solar system ephemeris DE200 (since that is what the Jodrell Bank timing ephemeris is based on).

The resultant pulse profiles had a bin size of 5 milliperiods. Subsequently, a baseline of unpulsed signal was subtracted and a parabolic fit made to the three highest points to determine the phase of the primary pulse. For the HRC data we used the entire spectrum; for the RXTE observation we used PCA data between 2 and 16 keV; we confirmed that there is no dependence on energy in this respect: 0.5 to 2 keV gives the same answer but poorer signal-to-noise. faseBin takes the 285 µs clock correction derived by William Davis into account, as well as the truncation of the time stamps.

The entire RXTE pulse profile is shown in Fig. 1. Fig. 2 shows a detail view of the RXTE main pulse peak. The resultant phases show that the Chandra peak is leading the RXTE peak by 1.5 milliperiods, with an uncertainty of about 0.3 milliperiods. This amounts to 50 µs. However, the Chandra data were processed with an extrapolated clock correlation. William Davis provided us with a correction based on the comparison of the applied clock parameters with those derived from a properly interpolated clock correlation. That correction is 15 µs, reducing the difference to 35 µs, with an uncertainty of approximately 10 µs.

Discussion

In this section we will consider all known and applied corrections, and potential sources of errors.

Clock Correlations

For the clock correlation correction we rely on the work by William Davis et al. and refer to their presentation. Their result shows that 285±5 µs should be added to Chandra's time. In addition, Davis quotes a random error of 4 µs.

Orbit Ephemeris

Uncertainties in the orbit ephemeris are included in the clock correlation analysis, and are anyway less than 1 µs.

Timing Ephemeris

The timing ephemeris from Jodrell Bank does sometimes contain errors other than caused by glitches, presumably due to variations in dispersion measure. However, since the comparison is made against the RXTE data, only the relative stability of this ephemeris over a period of 3 days is important. From past experience, we feel confident that such is the case, there have been no recent glitches, and the phase change from the month before is only 1 milliperiod.

RXTE Clock

The absolute time error in RXTE observational data, after application of the fine clock correction, is less than 2 µs.

Instrumental Delay

An instrumental delay of 20 µs has been measured for HRC. This delay was subtracted from the event time stamps in the Level-1 CXC processing; we have verified this.

Time Binning

The time stamps attached to the events by the HRC represent the last integer multiple of 15.625 µs and are therefore systematically early. To correct for this, faseBin adds half of the bin size to the time stamps.

HRC Time Stamping

It is known that the HRC attaches time stamps to the wrong event. This is corrected for by the CXC Level-1 processing.

Telemetry Saturation

Due to telemetry saturation, only about 70% of the detected events were telemetered down. Consequently, not all time stamps can be properly corrected for the HRC time stamp switching. It is not clear to us whether these events are filtered out by the CXC Level-2 processing, but even if they are not, these events would end up with a random phase and hence be removed in the unpulsed baseline subtraction.

Energy Dependence

We have tested the RXTE data for an energy dependence in the pulse phase. In the range 0.5-16 keV the upper limit on such a dependency is 0.1 milliperiod. We conclude that this does not play a role.

faseBin

The program faseBin has been thoroughly tested. No bugs have manifested themselves that could insert time offsets in the Chandra observations. Besides, since the same code was used to analyze the RXTE as well as the Chandra observations, it is likely that any hypothetical error would have affected both datasets in the same way, and hence would have canceled.

Conclusion

We conclude that, at least at one point in time, when all system engineering corrections are applied, the Chandra clock ran 35 µs ahead of absolute time, with a compounded uncertainty of about 12 µs.

An alternative way of phrasing this conclusion is that when we determine the Chandra clock offset through an astronomical observation, we find that the time stamps that are currently in use are lagging absolute time by 250±10 µs. Hence there is a discrepancy of 35±12 µs with the determination of Davis et al. who find 285±6 µs (compound error).

As to the origin of this discrepancy (which is significant) we are completely in the dark at this time.

We recommend coordinated observations with RXTE of PSR B1821-24.

Acknowledgments

The assistance of William S. Davis and Craig Markwardt has been invaluable in removing all known sources of error.
In addition, we gratefully acknowledge the help of Michael Juda, Gail Rohrbach, Ian Evans, and Ken Glotfelty in this endeavor.

Figure Captions

Fig. 1 Crab pulse profile as measured by RXTE. The phase is tied to the Jodrell Bank radio timing ephemeris. The bin size is 5 milliperiods.

Fig. 2 Detail of the primary pulse from Fig. 1.

Contact

Chandra Data Archive: http://cxc.harvard.edu/cda

E-mail: arots (at) head-cfa.harvard.edu