Astronomical Calibration of the Chandra Clock
Harvard-Smithsonian Center for Astrophysics / CXC
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
The final result is that there are 35 µs unaccounted for, with an
uncertainty of approximately 12 µs.
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
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
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.
In this section we will consider all known and applied
corrections, and potential sources of errors.
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.
Uncertainties in the orbit ephemeris are included in the clock
correlation analysis, and are anyway less than 1 µs.
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.
The absolute time error in RXTE observational data, after
application of the fine clock correction, is less than 2 µs.
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.
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.
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.
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.
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.
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
We recommend coordinated observations with
RXTE of PSR B1821-24.
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.
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.
Chandra Data Archive: http://cxc.harvard.edu/cda
E-mail: arots (at) head-cfa.harvard.edu
Tags2003 : absolute timing : Chandra : Crab : CXC : Rots : RXTE
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