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arXiv 0901.1268astro-ph.SR
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均匀旋转中子星和夸克星的开普勒频率

Keplerian frequency of uniformly rotating neutron stars and quark stars

P. Haensel, J. L. Zdunik, M. Bejger, J. M. Lattimer

摘要:

我们计算了刚性旋转中子星和夸克星壳的开普勒(质量脱落)位形。我们检验了Lattimer和Prakash提出的开普勒频率经验公式f_K的正确性,f_K(M)=C(M/M_sun)^1/2(R/10 km)^-3/2,其中M是开普勒位形的引力质量,R是相同引力质量的非旋转位形的圆周半径,C = 1.04 kHz。数值计算使用精确的2-D代码的基础上的多域谱方法。我们使用了一组有代表性的状态方程(EOSs)的中子星和夸克星。我们发现,对于具有真实物态方程的中子星,当M_sun < M < 0.9 M_max,stat时,f_K(M)的经验公式在百分之几以内成立,其中M_max,stat是物态方程中不旋转中子星的最大允许质量,C=C_NS=1.08 kHz.对于0.5 M_sun < M < 0.9 M_max,stat的夸克星,得到了类似的精度。对于最大地壳质量,我们得到C_QS = 1.15 kHz,并且C_QS的值对地壳质量不是很敏感。我们所有的C值都明显大于相对论Roche模型的分析值,C_Roche = 1.00 kHz。对于0.5 M_sun < M < 0.9 M_max,stat,质量为M的开普勒组态的赤道半径R_K(M),在很好的近似下,与相同质量的非自转恒星的半径成正比,R_K(M)= aR(M),a_NS \approx a_QS \approx 1.44。a_QS的值与夸克星外壳的质量有很弱的依赖关系。这两个a都小于相对论Roche模型的分析值a_Roche = 1.5。

英文摘要:

We calculate Keplerian (mass shedding) configurations of rigidly rotating neutron stars and quark stars with crusts. We check the validity of empirical formula for Keplerian frequency, f_K, proposed by Lattimer & Prakash, f_K(M)=C (M/M_sun)^1/2 (R/10km)^-3/2, where M is the (gravitational) mass of Keplerian configuration, R is the (circumferential) radius of the non-rotating configuration of the same gravitational mass, and C = 1.04 kHz. Numerical calculations are performed using precise 2-D codes based on the multi-domain spectral methods. We use a representative set of equations of state (EOSs) of neutron stars and quark stars. We show that the empirical formula for f_K(M) holds within a few percent for neutron stars with realistic EOSs, provided 0.5 M_sun < M < 0.9 M_max,stat, where M_max,stat is the maximum allowable mass of non-rotating neutron stars for an EOS, and C=C_NS=1.08 kHz. Similar precision is obtained for quark stars with 0.5 M_sun < M < 0.9 M_max,stat. For maximal crust masses we obtain C_QS = 1.15 kHz, and the value of C_QS is not very sensitive to the crust mass. All our C's are significantly larger than the analytic value from the relativistic Roche model, C_Roche = 1.00 kHz. For 0.5 M_sun < M < 0.9 M_max,stat, the equatorial radius of Keplerian configuration of mass M, R_K(M), is, to a very good approximation, proportional to the radius of the non-rotating star of the same mass, R_K(M) = aR(M), with a_NS \approx a_QS \approx 1.44. The value of a_QS is very weakly dependent on the mass of the crust of the quark star. Both a's are smaller than the analytic value a_Roche = 1.5 from the relativistic Roche model.

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