Formation scenarios and mass-radius relation for neutron stars

TL;DR

This paper investigates how the accreted crust affects neutron star radii, deriving formulas to quantify the radius increase based on different formation scenarios and nuclear compositions, assuming a specific core EOS.

Contribution

It introduces a precise formula relating crust EOS differences to radius changes and extends it to include effects of stellar rotation.

Findings

Accreted crusts increase neutron star radius by over 100 meters at 1.4 solar masses.

Derived a universal formula linking crust EOS differences to radius increase.

Provided an analytic dependence of radius difference on star mass and radius.

Abstract

Neutron star crust, formed via accretion of matter from a companion in a low-mass X-ray binary (LMXB), has an equation of state (EOS) stiffer than that of catalyzed matter. At a given neutron star mass, M, the radius of a star with an accreted crust is therefore larger, by DR(M), than for usually considered star built of catalyzed matter. Using a compressible liquid drop model of nuclei, we calculate, within the one-component plasma approximation, the EOSs corresponding to different nuclear compositions of ashes of X-ray bursts in LMXB. These EOSs are then applied for studying the effect of different formation scenarios on the neutron-star mass-radius relation. Assuming the SLy EOS for neutron star's liquid core, derived by Douchin & Haensel (2001), we find that at M=1.4 M_sun the star with accreted crust has a radius more than 100 m larger that for the crust of catalyzed matter. Using smallness of the crust mass compared to M, we derive a formula that relates DR(M) to the difference in the crust EOS. This very precise formula gives also analytic dependence of DR on M and R of the reference star built of catalyzed matter. The formula is valid for any EOS of the liquid core. Rotation of neutron star makes DR(M) larger. We derive an approximate but very precise formula that gives difference in equatorial radii, DR_eq(M), as a function of stellar rotation frequency.