The Evolution of Pulsar PSR J1640-4631 with High Braking Index (n>3) in the Magnetic Dipole and Gravitational Wave Radiation Models

The study of pulsar spin period evolution provides insights into the braking mechanisms of neutron stars. The braking index of pulsars, which is closely related to their radiation, reflects the process of kinetic energy loss in pulsars. Traditionally, based on the magnetic dipole radiation model, the expected braking index is n=3. However, actual observations have found that the braking indices of most pulsars are less than 3. There are also pulsars whose braking indices exceed the predictions of the magnetic dipole model, such as PSR J1640-4631, which has a braking index of n =3.15\pm0.03. It is currently known to be a pulsar with a relatively high confidence level and a braking index greater than 3, indicating that in addition to magnetic dipole radiation, there may be other mechanisms for rotational energy loss in neutron stars. The combined influence of two kinetic energy loss mechanisms is considered on pulsar braking: magnetic dipole radiation and gravitational wave radiation. On this basis, we have successfully reproduced the high braking index of PSR J1640-4631. Furthermore, we have delved into the evolution of this pulsar's braking index, which falls within a specific range of 3 < n < 5 . Assuming an initial spin period of 20 ms for the pulsar, we have computed its long-term evolution of the spin period, illustrating that it is a pulsar of a unique type.