The permanent ellipticity of the neutron star in PSR J1023+0038

TL;DR

This paper presents a formalism indicating that the millisecond pulsar PSR J1023+0038 likely has a permanent ellipticity, which could lead to continuous gravitational wave emission, explained through its spin-down rates and observational data.

Contribution

The study introduces a comprehensive torque-based formalism that links pulsar magnetospheric activity, accretion phenomena, and gravitational wave emission without assuming additional stellar ellipticity.

Findings

PSR J1023+0038 has a misaligned mass quadrupole moment of (0.92-1.88)×10^{36} g cm^2.

Ellipticity of the pulsar is estimated between (0.48-0.93)×10^{-9}.

The formalism explains observed X-ray pulsations and gamma-ray emissions coherently.

Abstract

A millisecond pulsar having an ellipticity, that is an asymmetric mass distribution around its spin-axis, could emit continuous gravitational waves, which have not been detected so far. An indirect way to infer such waves is to estimate the contribution of the waves to the spin-down rate of the pulsar. The transitional pulsar PSR J1023+0038 is ideal and unique for this purpose, because this is the only millisecond pulsar for which the spin-down rate has been measured in both accreting and non-accreting states. Here we infer, from our formalism based on the complete torque budget equations and the pulsar magnetospheric origin of observed $\gamma$-rays in the two states, that PSR J1023+0038 should emit gravitational waves due to a permanent ellipticity of the pulsar. The formalism also explains some other main observational aspects of this source in a self-consistent way. As an example, our formalism naturally infers the accretion disc penetration into the pulsar magnetosphere, and explains the observed X-ray pulsations in the accreting state using the standard and well-accepted scenario. This, in turn, infers the larger pulsar spin-down power in the accreting state, which, in our formalism, explains the observed larger $\gamma$-ray emission in this state. Exploring wide ranges of parameter values of PSR J1023+0038, and not assuming an additional source of stellar ellipticity in the accreting state, we find the misaligned mass quadrupole moment of the pulsar in the range of $(0.92-1.88)\times10^{36}$ g cm$^2$, implying an ellipticity range of $(0.48-0.93)\times10^{-9}$.