Starquakes in millisecond pulsars and gravitational waves emission

TL;DR

This paper models starquakes in accreting millisecond pulsars to estimate their gravitational wave emission potential, providing theoretical upper limits on ellipticity and equilibrium frequencies consistent with observations.

Contribution

It introduces a Newtonian model to quantify the ellipticity and frequency limits of starquake-induced gravitational waves in accreting neutron stars, considering different equations of state.

Findings

Ellipticity due to starquakes ranges from 10^{-9} to 10^{-5}.

Equilibrium frequencies align with observed pulsar frequencies and stay below 716.36 Hz.

The model constrains gravitational wave emission from accreting neutron stars.

Abstract

So far, only transient Gravitational waves (GWs) produced by catastrophic events of extra-galactic origin have been detected. However, it is generally believed that there should be also continuous sources of GWs within our galaxy, such as accreting neutron stars (NSs). In fact, in accreting NSs, centrifugal forces can be so strong to break the neutron star crust (causing a starquake), thus producing a quadrupole moment responsible for the continuous emission of GWs. At equilibrium, the angular momentum gained by accretion and lost via GWs emission should balance each other, stopping the stellar spin-up. We hereinafter investigate the above physical picture within the framework of a Newtonian model describing compressible, non-magnetized, and self-gravitating NSs. In particular, we calculate the rotational frequency need to break the stellar crust of an accreting pulsar and we estimate the upper limit for the ellipticity due to this event. Depending on the equation of state (EoS) and on the mass of the star, we calculated that the starquake-induced ellipticity ranges from $10^{-9}$ to $10^{-5}$. The corresponding equilibrium frequency that we find is in good agreement with observations and, for all the scenarios, it is below the observational limit frequency of $716.36$ Hz. Finally, we also discuss possible observational constraints on the ellipticity upper limit of accreting pulsars.