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

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 (${\nu }_{\mathrm{eq},\mathrm{per}}$) for persistent accretion for a long-term average accretion rate (${\dot{M}}_{\mathrm{av}}$) greater than a critical limit (${\dot{M}}_{\mathrm{av},\mathrm{crit}}$), and may approach a higher effective spin equilibrium value (${\nu }_{\mathrm{eq},\mathrm{eff}}$) for transient accretion for ${\dot{M}}_{\mathrm{av}}<{\dot{M}}_{\mathrm{av},\mathrm{crit}}$. For example, when ${\dot{M}}_{\mathrm{av}}$ falls below ${\dot{M}}_{\mathrm{av},\mathrm{crit}}$ 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 ${\dot{M}}_{\mathrm{av}}$ 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 ${\dot{M}}_{\mathrm{av}}$-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.

arXiv comment5 pages, 3 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society Letters

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• Modeling the Galactic Neutron Star Population for Use in Continuous Gravitational Wave Searches