A simple, flexible method for timing cross-calibration of space missions

TL;DR

The paper tackles the challenge of cross-calibrating timing across space missions when different JPL ephemerides and source positions are used. It introduces a flexible method that simulates geocentric TOAs based on a reference Crab pulsar timing solution (the JBE in DE200/FK5) and then refits timing models using arbitrary JPL ephemerides (e.g., DE430/DE440) and source coordinates with PINT, enabling consistent TOA comparisons without reprocessing all data. Validation across simulations and end-to-end NICER data shows inter-ephemeris TOA consistency at about $\lesssim 5\,\mu$s, and the approach is applied to thousands of Crab observations from 15 missions (1996–2025). The authors release the TOAExtractor tool and a TOA database to support future calibration work, demonstrating a practical path toward robust, multi-mission timing cross-calibration and highlighting energy- and time-dependent X-ray/radio delays that warrant coordinated follow-up. This work thus improves the reliability of high-energy timing analyses and underpins precision tests in multiwavelength pulsar studies.

Abstract

The timing (cross-)calibration of astronomical instruments is often done by comparing pulsar times-of-arrival (TOAs) to a reference timing model. In high-energy astronomy, the choice of solar system ephemerides and source positions used to barycenter the photon arrival times has a significant impact on the procedure, requiring a full reprocessing of the data each time a new convention is used. Our method, developed as part of the activities of the International Astronomical Consortium for High Energy Calibration (IACHEC), adapts an existing pulsar solution to arbitrary JPL ephemerides and source positions by simulating geocentric TOAs and refitting timing models (implemented with PINT). We validate the procedure and apply it to thousands of observations of the Crab pulsar from 15 missions spanning 1996--2025, demonstrating inter-ephemeris TOA consistency at the $\lesssim5 μ$s level, using the DE200/FK5-based Jodrell Bank Monthly Ephemeris as a common reference. We release the TOAExtractor open-source tool and a TOA database to support future calibration and scientific studies. Instrument timing performance is broadly consistent with mission specifications; the X-ray-to-radio phase offset varies with energy and time at a level that is marginally consistent with the uncertainties of the radio ephemeris, motivating coordinated multiwavelength follow-up.

Figures (7)

• Figure 1: Example of deadtime correction of a NuSTAR pulse profile (ObsID 10002001009), using the method described in Section \ref{['sec:deadtime']}. The blue line shows the exposure correction, the red line the raw profile and the black line the deadtime-corrected profile.
• Figure 2: Folded profile from NICER (obsid 101301013) modeled with the combination of symmetric and asymmetric Lorentzians described in Section \ref{['sec:toa']}.
• Figure 3: Results of the validation procedure for the model refitting described in Section \ref{['sec:validation']}. We fit a DE430 model to DE200-simulated TOAs, then simulated TOAs with the new model and calculated the residuals to the original DE200 model. For each instance of the simulation, we plot the mean residual in the upper panel and the rms of the residuals in the lower panel. The procedure works remarkably well, with residuals and rms comparable or lower to the injected error bars in the simulated data (0.1 $\rm \mu s$).
• Figure 4: End-to-end validation of the procedure in Section \ref{['sec:jpleph']} using NICER datasets. (Left) Difference between the TOA residuals (labeled $\rm t_{eph}$) calculated from datasets barycentered using the DE200 ($\rm t_{200}$), DE430 ($\rm t_{430}$), and DE440 ($\rm t_{440}$) JPL ephemerides. (Left) a histogram of the corresponding cases. We did not consider observations where the TOA uncertainty was $>15\,\rm \mu s\xspace$. The uncertainty of these TOAs was typically $\sim5\,\rm \mu s\xspace$, and residual differences are always well inside error bars.
• Figure 5: Interactive summary plot produced by TOAExtractor. This plot allows for a simple exploration of the residuals, by showing diagnostic information as the user hovers over each point. The horizontal grey band indicates the X-ray residual measured by rotsAbsoluteTimingCrab2004. Vertical red lines indicate glitch epochs (In this static image it might be difficult to distinguish them from some large error bars from the data points, but the difference becomes clear in the interactive interface). Problematic observations and time intervals are easily identified: some observations with large residuals might be due to low count rates, temporary instrumental issues, or local issues with the radio ephemerides (e.g. the large deviation around April 2020, MJDs 58925--58975, due to the closure of the observatory for the COVID pandemic; recent glitches can also make the solution less reliable).