# What can PSR J1640-4631 tell us about the internal physics of this neutron star?

## TL;DR

This paper models the braking index of PSR J1640-4631 considering gravitational wave emissions and magnetic field decay, proposing a new method to constrain neutron star interior physics through observational tilt angles.

## Contribution

It introduces a novel approach linking the neutron star's precession cycles to its internal physics and gravitational wave emissions, based on timing data and magnetic decay theory.

## Key findings

- The precession cycle count $\xi$ is likely larger than previous estimates.
- Future tilt angle measurements can significantly constrain the interior magnetic field configuration.
- A tilt angle $\chi
ightarrow12^\circ$ suggests $\xi
ightarrow10^6$, much higher than earlier predictions.

## Abstract

Gravitational wave emissions (GWEs) of pulsars could not only make them promising targets for continuous gravitational wave searches but also leave imprints in their timing data. We interpret the measured braking index of PSR J1640-4631 with a model involving both the GWE and dipole magnetic field decay. Combining the timing data of PSR J1640-4631 and the theory of magnetic field decay, we propose a new approach of constraining the number of precession cycles, $\xi$, which is highly uncertain currently but can be tightly related to the interior physics of a neutron star and its GWE. We suggest that future observation of the tilt angle $\chi$ of PSR J1640-4631 would not merely help to constrain $\xi$ but also possibly provide information about the internal magnetic field configuration of this pulsar. We find that $\xi$ would be larger than previous estimates unless a tiny angle $\chi\lesssim5^\circ$ is observed. Furthermore, a measured angle $\chi\gtrsim12^\circ$ would indicate $\xi\gtrsim 10^6$, which is at least ten times larger than that suggested previously.