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

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 $\chi \lesssim 5°$ is observed. Furthermore, a measured angle $\chi \gtrsim 12°$ would indicate $\xi \gtrsim {10}^6$, which is at least 10 times larger than that suggested previously.

Figure 1

Dipole field decay timescale ${\tau }_{\mathrm{D}}$ versus tilt angle $\chi$. This figure shows a comparison between ${\tau }_{\mathrm{D}}(\chi )$ derived using timing data (colored lines) and that obtained based on the magnetic field decay theory (black lines). The NS is assumed to have PD internal fields. See the text for details.

Figure 2

The same as Fig. 1, however, the NS is assumed to have TD internal fields. See the text for details.