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arXiv 1104.0385astro-ph.HEastro-ph.SRgr-qc
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中子星的形成方案和质量-半径关系

Formation scenarios and mass-radius relation for neutron stars

J. L. Zdunik, P. Haensel

摘要:

中子星壳是由低质量X射线双星(LMXB)中的伴星吸积物质形成的,其状态方程比催化物质的状态方程更严格。因此,在给定的中子星质量M下,具有吸积壳的恒星的半径比通常认为的由催化物质构成的恒星的半径大DR(M)。本文采用可压缩的核液滴模型,在单组分等离子体近似下,计算了LMXB中X射线爆发灰烬不同核成分对应的EOS。这些EOS然后应用于研究不同的形成方案上的中子星的质量半径关系的效果。假设中子星的液核采用Douchin & Haensel(2001)导出的SLy状态方程,我们发现在M=1.4 M_sun时,具有吸积壳的恒星比具有催化物质壳的恒星半径大100 m以上。利用地壳质量相对于M的微小性,我们推导出一个公式,该公式将DR(M)与地壳EOS的差异联系起来。这个非常精确的公式也给出了DR对由催化物质构成的参考星的M和R的解析依赖关系。该公式适用于液核的任何物态方程。中子星的自转使DR(M)变大。我们导出了一个近似但非常精确的公式,给出了赤道半径差DR_eq(M)作为恒星自转频率的函数。

英文摘要:

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.

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