Braking index of the frequently glitching PSR J0537$-$6910

TL;DR

PSR J0537-6910 exhibits abundant large glitches, leading to a negative long-term braking index $n'$, which cannot be explained by external torques alone. The authors combine a multi-component neutron-star model with vortex creep and a putative permanent spin-down shift per glitch to show that an underlying magnetospheric braking index near $n\approx3$ can reproduce the observed $n'$ when modest permanent shifts of order $10^{-14}\ \mathrm{Hz\,s^{-1}}$ accumulate over many glitches. Crustquakes emerge as a natural mechanism for producing these permanent shifts, with consequences including potential transient X-ray changes, radio activation, and gravitational-wave emission. The work provides a framework to disentangle internal and external torques in glitching pulsars and makes testable predictions for glitch timing and multiwavelength signals, motivating targeted future observations.

Abstract

The pulsar J0537$-$6910 undergoes spin-up glitches more frequently than any other known pulsar, at a rate of roughly thrice per year. Its glitches are typically large and accompanied by spin-down rate changes $Δ\dotν$ that partially recover with a nearly constant positive frequency second derivative $\ddotν$ for the post-glitch intervals. The long-term value of $\ddotν$, however, is negative because $\dotν$ has decreased over the years of observations. We wish to determine if permanent shifts (non-relaxing parts of the glitch change $Δ\dotν$ in the spin-down rate, like those observed in the Crab pulsar) can explain the long-term enhancement of the spin-down rate which results in an effective negative braking index. We demonstrate, as a proof of concept, that the actual braking index associated with the pulsar's braking torque can be n~3 if the internal superfluid torque and permanent shifts are considered. We use published RXTE and NICER data to calculate the average permanent shift per glitch needed to bring an underlying braking index $n$ to the effective long-term value n' =-1.2 inferred from the data. We use this average value as the actual permanent shift in each glitch and extract the contributions of the internal and external torques to $\ddotν$, under the assumption that the next glitch occurs when all glitch-induced offsets to internal torques are fully restored. We find that if the braking index of the magnetospheric torque is close to n~3, moderate permanent changes of the spin-down rate are required, similar to those inferred for the Crab pulsar. The natural mechanism to produce such permanent changes is crustquakes. Crustal failure associated with PSR J0537$-$6910 glitches can have interesting and potentially observable consequences, such as transient changes of the X-ray emission, activation of radio emission, or emission of gravitational waves.

Figures (1)

• Figure 1: Upper panel: The model for inter-glitch evolution of $\dot{\nu}$ from glitch j to glitch $j+1$. The black solid line depicts the observed inter-glitch evolution. Assuming that the recovery of the glitch offset in the internal torque is completed exactly at the time of arrival of the next glitch, the observed glitch step $\Delta\dot{\nu}_{\rm j}$ in spin-down rate is the sum of the permanent part $\Delta \dot{\nu}_{\rm per\ j}$ and the recovering part $\Delta \dot{\nu}_{\rm ig,j}$ under $\ddot\nu_{\rm ig,j}$ due to the internal torque, as shown in blue. Subtracting the contribution of the internal torque from the total observed $\ddot\nu_{\rm obs,j}$ gives $\ddot\nu_{\rm 0,j}$, the slope of the purple line, due to the external torque. The permanent shift $\Delta\dot\nu_{\rm per, j}$ is only partially counteracted by an amount $\ddot\nu_{\rm 0,j} t_{\rm g,j}$ as shown by the purple line. The combined effect results in a remaining decrease of $\dot{\nu}$, with an inferred slope $\ddot\nu_{\rm long-term,j}$ (orange line). Lower panel: The long-term evolution over many glitches, shown in orange, implies an effective negative $\ddot\nu_{\rm long-term}$ and negative effective braking index.