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.

中文翻译：

---

关于这颗中子星的内部物理，PSR J1640-4631 能告诉我们什么？

脉冲星的引力波发射 (GWE) 不仅可以使它们成为连续引力波搜索的有希望的目标，而且还可以在其计时数据中留下印记。我们使用包含 GWE 和偶极磁场衰减的模型来解释 PSR J1640-4631 的测量制动指数。结合 PSR J1640-4631 的时序数据和磁场衰减理论，我们提出了一种限制进动周期数 $\xi$ 的新方法，该方法目前高度不确定，但可以与内部物理密切相关。中子星及其 GWE。我们建议未来对 PSR J1640-4631 倾角 $\chi$ 的观测不仅有助于约束 $\xi$，还可能提供有关该脉冲星内部磁场配置的信息。我们发现 $\xi$ 会比之前的估计值大，除非观察到一个小角度 $\chi\lesssim5^\circ$。此外，测量的角度 $\chi\gtrsim12^\circ$ 将表示 $\xi\gtrsim 10^6$，这至少是之前建议的十倍。