New and updated timing models for seven young energetic X-ray pulsars, including the Big Glitcher PSR J0537-6910

TL;DR

This work delivers long-baseline timing models for seven young, energetic X-ray pulsars using NICER data (2017–2025) supplemented by Chandra and NuSTAR observations. Six targets yield rotation-phase-connected timing across the NICER era, with PSR J1813−1749 remaining incoherent due to data sparsity; PSR J0537−6910 exhibits an extensive glitch history (23 glitches with NICER) and a notable correlative pattern between glitch size and the time to the next glitch. The study also reports the first NuSTAR-based pulsed spectrum for PSR J0537−6910 and documents braking-index evolution for PSR B0540−69 from ~0 to ~1.6, as well as refined timing positions for Calvera and PSR J1849−0001. These updated models support multi-energy astrophysics, pulsar timing in gravitational-wave searches, and future instrumentation planning. Overall, the work underscores the critical role of long-term, high-cadence X-ray timing for understanding neutron-star physics and for enabling precision GW searches with ground- and space-based detectors.

Abstract

We present new timing models and update our previous ones for the rotational evolution of seven young energetic pulsars, including four of the top five in spin-down luminosity Edot among all known pulsars. For each of the six pulsars that were monitored on a regular basis by NICER, their rotation phase-connected timing model covers the entire period of NICER observations, in many cases from 2017-2025. For PSR J0058-7218, which was only identified in 2021, we extend the baseline of its timing model by 3 years and report detections of its first three glitches. The timing model for PSR J0537-6910 over the entire 8 years of NICER monitoring is presented, including a total of 23 glitches; we also report its spin frequency and pulsed spectrum from a 2016 NuSTAR observation. For PSR B0540-69, its complete timing model from 2015-2025 is provided, including a braking index evolution from near 0 to 1.6 during this period. The 8-year timing model for PSR J1412+7922 (also known as Calvera) is reported, which includes a position that is consistent with that measured from imaging. For PSR J1811-1925, we present its 3.5-year timing model. For PSR J1813-1749, its incoherent timing model is extended through early 2025 using new Chandra observations. For PSR J1849-0001, its 7-year timing model is provided, including a position that is consistent with and more accurate than its imaging position and its first glitch that is one of the largest ever measured. Our timing models of these seven X-ray pulsars enable their study at other energies and in gravitational wave data.

Figures (17)

• Figure 1: Pulsar spin period $P$ and spin period time derivative $\dot{P}$. Circles denote pulsars whose values are taken from the ATNF Pulsar Catalogue (manchesteretal05, version 2.3.0), and stars indicate pulsars considered in this work (see Table \ref{['tab:psr']}). Dashed lines indicate characteristic age $\tau_{\rm c}\equiv P/2\dot{P}$, and dotted lines indicate magnetic field strength $B=3.2\times10^{19}\hbox{G}(P\dot{P})^{1/2}$.
• Figure 2: Timing residuals of PSR J0058$-$7218 from a best-fit of NICER pulse times-of-arrival with the timing model given in Table \ref{['tab:0058']} and the RMS residual illustrated by the shaded region between $\pm 0.339\hbox{ms}$. Errors are 1$\sigma$ uncertainty. The vertical dotted lines indicate the approximate times of 3 spin-up glitches (MJD 59807, 60011, 60293).
• Figure 3: Timing residuals of PSR J0537$-$6910 from a best-fit of NICER pulse times-of-arrival with the timing model given in Table \ref{['tab:0537']} and RMS residuals illustrated by the shaded regions. Errors are 1$\sigma$ uncertainty. Segments are labeled by numbers and separated by the occurrence of a glitch, each of which is denoted by a vertical dotted line.
• Figure 4: Evolution of spin frequency time derivative $\dot{\nu}$ of PSR J0537$-$6910, where $\dot{\nu}$ is from the timing model of each segment (see Table \ref{['tab:0537']} for NICER and Table 1 of antonopoulouetal18 for RXTE). Errors are 1$\sigma$ uncertainty. Dashed line shows a linear fit of NICER and RXTE data with best-fit $\ddot{\nu}=-7.85\times 10^{-22}\hbox{Hz s$^{-2}$}$.
• Figure 5: Glitch $\Delta\nu$ (top) and $\Delta\dot{\nu}$ (bottom) as functions of time. Errors in $\Delta\dot{\nu}$ are 1$\sigma$ uncertainty.