Internal superfluid response and torque evolution in the giant glitch of PSR J1718-3718

TL;DR

This work addresses the peculiar post-glitch evolution of PSR J1718-3718 following its giant 2007 glitch by adopting an extended vortex creep model that includes both inward and outward vortex motion and a time-varying external torque. Using MCMC with priors on crustal moment-of-inertia participation, the study quantifies uncertainties and reveals that inward creep and a long-term torque change dominate the observed increase in spin-down rate, consistent with a crustquake triggering both vortex dynamics and a change in moment of inertia. The fit yields physically plausible numbers, including approximately $2.4 imes 10^{12}$ inward-moving vortices distributed across about 142 crustal plates of typical size ~0.03 km, and demonstrates that post-glitch behavior can simultaneously constrain internal superfluid dynamics and external torque evolution. Overall, the framework provides a quantitative link between glitch physics, crustal dynamics, and magnetospheric coupling, offering a path to probe neutron-star interiors with sparse timing data.

Abstract

We investigate the post-glitch rotational evolution of pulsars by analyzing the 2007 giant glitch of PSR J1718$-$3718 using a vortex creep model that incorporates both inward and outward nonlinear vortex motion, along with a time-varying external torque. A comprehensive fitting framework is developed, constrained by prior knowledge of moment of inertia participation from previous glitch studies. We apply a Markov Chain Monte Carlo approach to quantify uncertainties and parameter correlations. The model reproduces the observed timing data and yields physically consistent values for moment of inertia fractions and creep timescales. Our results indicate that inward creep and a long-term change in external torque dominate the observed increase in spin-down rate, pointing to structural changes within the star-likely triggered by a crustquake that initiated both vortex motion and a change in the moment of inertia. We estimate that the glitch involved approximately $2.4 \times 10^{12}$ inward-moving vortices and $\sim 142$ crustal plates with a typical size of $\sim 0.03$ km. This study demonstrates that detailed post-glitch modeling of sparse timing data can simultaneously constrain internal superfluid dynamics and external torque evolution, providing a quantitative framework to probe the structural properties of neutron star interiors.

Figures (3)

• Figure 1: Timing residuals for PSR J1718$-$3718 during MJD 51901--58115, obtained from a timing model incorporating a single glitch. The circles, inverted triangles, triangles, and squares represent the observation data obtained by receivers with center frequencies of 1369 MHz, 1374 MHz, 1465 MHz, and 3100 MHz, respectively. The glitch epoch is marked with a vertical dashed line, with the number in parentheses at the top indicating its sequence number. The gray shaded areas indicate periods of data gaps longer than one year.
• Figure 2: Glitch in PSR J1718$-$3718: Panel (a) shows the relative change of spin frequency ($\Delta\nu$), that is, the change in pulsar rotation frequency relative to the frequency model before the glitch. Panel (b) is an enlarged view of the post-glitch $\Delta\nu$ evolution, centered on its mean value to highlight the recovery details. Panel (c) shows the evolution of the spin-down rate ($\dot{\nu}$) over time before and after the glitch. The vertical grey-dashed line and the numbers in between parentheses at the top represent the glitch epoch and the reference number of glitch occurrences, respectively. In Panel (c), the red curves represent the fit using the superfluid glitch model (see Section \ref{['sec:fits']}), with the corresponding fit parameters provided in Table \ref{['tab:posterior']}.
• Figure 3: Posterior distributions of the fitting parameters of the vortex creep model for PSR J1718--3718 glitch. The diagonal panels show the marginalized posterior distributions for each parameter, while the off-diagonal panels show the 2D correlations between parameters. The crustal fractional MoIs associated with vortex outward and inward creep are $I_{\mathrm{nl}}/I$ and $I_{\mathrm{i}}/I$, with the corresponding creep relaxation timescales being $\tau_{\mathrm{nl}}$ and $\tau_{\mathrm{i}}$, respectively. While $t_0$ represents the waiting time for outward vortex creep, the parameter $t_{\mathrm{i}}$ characterizes the initial magnitude of the lag perturbation that drives the inward vortex motion, related to the crustquake's intensity. Both the fractional Mol and the time parameters are presented on a logarithmic scale in the figure. $\dot{\nu}_0$ and $\ddot{\nu}$ are the first- and second-order derivatives of spin frequency driven by an external mechanism (e.g., the pulsar wind model), with units of $10^{-13}$ Hz/s and $10^{-24} \rm{Hz/s}^2$, respectively.