How is the timing system of the Follow-up X-Ray Telescope calibrated in flight?

What pulsar timing calibration actually measures

A timing system is only as good as its ability to record when a photon arrived. The paper tests this by pointing the Follow-up X-ray Telescope (FXT) at pulsars whose rotation is already known from other observatories, then measuring the times of arrival (TOAs) of their pulses. If the instrument's clock and readout are correct, the pulses should land at the phases predicted by a reference ephemeris — a model of the pulsar's rotation and position.

FXT has two independently operating modules, FXTA and FXTB, each with Wolter-I optics and a pnCCD camera. Because the modules are separate, the calibration can check two things at once: whether each module matches the external reference, and whether the two modules match each other. The second check matters because a shared error in both modules would not show up in an external comparison alone.

Three readout modes set very different timing limits

The pnCCD can be read out in three modes, and the choice of mode determines how finely time can be sampled. In full frame mode (FF), a frame takes 50 ms. In partial windowed mode (PW), a frame takes 2.2 ms. In timing mode (TM), each row takes 23.68 μs and a full frame takes 9.4352 ms.

The pulsars were matched to modes accordingly: 1RXS J170849.0–400910, with an 11 s spin period, was observed in FF; PSR B1509–58, at 150 ms, in PW; and the Crab pulsar (33 ms), PSR B1821–24 (3.05 ms) and PSR B1937+21 (1.56 ms) in TM. This pairing is the design logic of the calibration: slower pulsars can be resolved in coarser modes, while millisecond pulsars require the fine row-level sampling of TM.

In the slower modes, the two modules agree within large errors

For RXJ1708 in FF mode, the averaged TOA phase was 0.221 ± 0.006 (stat) ± 0.002 (sys) with FXTA and 0.220 ± 0.008 (stat) ± 0.001 (sys) with FXTB, against a reference main peak position of 0.222 ± 0.005. The residuals relative to the reference ephemeris were −11 ± 91 ms in FXTA and −26 ± 103 ms in FXTB. The statistical uncertainty dominates these residuals, so the FF comparison is consistent but not a tight constraint.

For PSR B1509–58 in PW mode, the mean phases were 0.392 ± 0.007 (stat) ± 0.002 (sys) in FXTA and 0.391 ± 0.007 (stat) ± 0.002 (sys) in FXTB, against a reference of 0.389 ± 0.011 (stat) ± 0.004 (sys). The residuals were 0.54 ± 2.10 ms and 0.28 ± 2.08 ms respectively. In both modes the paper concludes that the FXTA and FXTB timing systems are mutually consistent and aligned with NICER, but the millisecond-scale error bars show that these modes alone cannot establish microsecond-level accuracy.

The Crab pulsar arrives early relative to the radio ephemeris

The Crab pulsar provides the sharpest external check because it can be compared with the Jodrell Bank Monthly Ephemeris (JBE), a radio-based reference. The measured advance of the Crab's main peak relative to JBE is 357 ± 14 (stat) ± 54 (sys) μs in FXTA and 394 ± 14 (stat) ± 67 (sys) μs in FXTB.

This is a comparison against a specific reference, not a claim that the pulsar itself changed. The systematic uncertainty of these residuals sets an upper limit on the in-flight timing accuracy of 54 μs for FXTA and 67 μs for FXTB. The paper also compares the Crab TOAs with the mean phase of NICER TOA data, where the residuals are 30 ± 67 μs in FXTA and −7 ± 78 μs in FXTB — a much closer agreement, which shows how much the choice of reference matters when reading these numbers.

Millisecond pulsars tighten the accuracy estimate

The Crab residuals are limited by systematics, so the paper turns to two millisecond pulsars in TM mode to sharpen the estimate. For PSR B1821–24, the residuals are 3 ± 18 μs in FXTA and −42 ± 16 μs in FXTB. For PSR B1937+21, they are 15 ± 7 μs in FXTA and 19 ± 7 μs in FXTB.

Based on these two pulsars, the preliminary absolute timing accuracy is estimated at 6 μs for FXTA and 31 μs for FXTB in TM mode. The word preliminary is doing real work here: the estimate rests on the current set of observations, and the paper states that regular TM-mode pulsar observations are scheduled several times per year to monitor performance and establish a reliable absolute timing accuracy by accumulating additional data.

FXTA leads FXTB by about 20 microseconds

Averaging the residual delays of FXTA relative to FXTB over observations where both modules had TOAs gives a systematic delay of 20 ± 19 (stat) ± 21 (sys) μs. The paper reports this as the systematic delay of FXTA timing results relative to FXTB, and it is consistent with zero within the combined uncertainty.

The local clock data add context for why the modules might differ. The relative deviation from the nominal 0.1 μs local cycle is on the order of 10⁻⁶ for both modules, but the crystal oscillators behave differently: FXTB's local clock cycle is longer than FXTA's, FXTA shows a secular drift of about 2.9 × 10⁻¹⁰ per day versus about 1.3 × 10⁻⁹ per day for FXTB, and the RMS after removing the drift is 0.07 × 10⁻⁶ in FXTA and 0.15 × 10⁻⁶ in FXTB. The paper concludes that FXTA's local clock is more stable than FXTB's after launch.

Which accuracy number applies to which mode

The calibration does not produce a single accuracy figure for FXT. FF and PW are verified as mutually consistent and aligned with NICER, but their residuals are at the millisecond level, so they support consistency checks rather than microsecond timing claims. TM mode carries the quantitative accuracy estimate: 6 μs for FXTA and 31 μs for FXTB, derived from PSR B1821–24 and PSR B1937+21, with the Crab comparison against JBE providing a looser upper limit of 54 μs and 67 μs respectively.

The practical priority that follows is module- and mode-specific. FXTA is both the more stable clock and the module with the smaller preliminary accuracy estimate, while FXTB's larger estimate and larger drift rate make its TM timing the more uncertain of the two. The 20 μs inter-module delay is consistent with zero at current precision, so it should be treated as a measured offset to monitor, not as a correction already established. The scheduled repeat pulsar observations are what will decide whether these preliminary numbers hold.

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