Spin evolution of neutron stars in two modes: implication for millisecond pulsars

TL;DR

This paper explores how neutron star spin frequencies evolve in low-mass X-ray binaries, revealing two distinct modes influenced by accretion rates, which impacts our understanding of millisecond pulsar formation and gravitational wave emission.

Contribution

It introduces a new numerical model showing two different spin evolution modes based on accretion rates, challenging previous assumptions about neutron star spin-up processes.

Findings

Neutron stars can approach different spin equilibrium values depending on accretion mode.

Transient accretion can significantly increase spin frequency even at low average accretion rates.

Traditional models may misestimate spin evolution, especially during accretion rate changes.

Abstract

An understanding of spin frequency ($\nu$) evolution of neutron stars in the low-mass X-ray binary (LMXB) phase is essential to explain the observed $\nu$-distribution of millisecond pulsars (MSPs), and to probe the stellar and binary physics, including the possibility of continuous gravitational wave emission. Here, using numerical computations we conclude that $\nu$ can evolve in two distinctly different modes, as $\nu$ may approach a lower spin equilibrium value ($\nu_{\rm eq,per}$) for persistent accretion for a long-term average accretion rate ($\dot{M}_{\rm av}$) greater than a critical limit ($\dot{M}_{\rm av,crit}$), and may approach a higher effective spin equilibrium value ($\nu_{\rm eq,eff}$) for transient accretion for $\dot{M}_{\rm av} < \dot{M}_{\rm av,crit}$. For example, when $\dot{M}_{\rm av}$ falls below $\dot{M}_{\rm av,crit}$ for an initially persistent source, $\nu$ increases considerably due to transient accretion, which is counterintuitive. We also find that, contrary to what was suggested, a fast or sudden decrease of $\dot{M}_{\rm av}$ to zero in the last part of the LMXB phase is not essential for the genesis of spin-powered MSPs, and neutron stars could spin up in this $\dot{M}_{\rm av}$-decreasing phase. Our findings imply that the traditional way of $\nu$-evolution computation is inadequate in most cases, even for initially persistent sources, and may not even correctly estimate whether $\nu$ increases or decreases.