Formation scenarios and mass-radius relation for neutron stars

Abstract

Aims. A neutron star crust, which is formed by accretion of matter from a companion in a low-mass X-ray binary (LMXB), has a stiffer equation of state (EOS) 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 ΔR(M) than for the usually considered star built of catalyzed matter. Methods. Using a compressible liquid drop model of nuclei, we calculated, within the one-component plasma approximation, the EOSs corresponding to different nuclear compositions of the ashes of X-ray bursts in LMXB. These EOSs are then applied to study the effect of different formation scenarios on the neutron-star mass-radius relation. Results. Assuming the SLy EOS for neutron star's liquid core, we find that at M = 1.4 M⊙ the star with accreted crust has a radius more than 100 m larger than for the crust of catalyzed matter. Using smallness of the crust mass compared to M, we derive a formula that relates ΔR(M) to the difference in the crust EOS. This very precise formula also gives analytic dependence of ΔR 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 the ΔR(M) larger. We derive an approximate but very precise formula that gives the difference in equatorial radii, ΔReq(M), as a function of stellar rotation frequency. © 2011 ESO.