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arXiv 0812.3708astro-phgr-qc
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超流中子星振荡模的普适性?

Universality in oscillation modes of superfluid neutron stars?

K. S. Wong, L. M. Lin, P. T. Leung

摘要:

相对论性普通流态中子星的$f$模具有普遍的标度行为。在这里,我们研究是否“普通”$f_{\rm o}$ -和“超流”$f_{\rm s}$ -模式的超流中子星也表现出类似的普遍行为。我们首先考虑一个简单的情况下,中子超流体和正常流体是解耦的,并与每一个流体的多方状态方程建模。我们发现,$f_{\rm o}$模式服从相同的标度律建立的$f$模式orindary流体星。然而,$f_{\rm s}$模式的振荡频率服从不同的标度律,这可以从牛顿引力下的均匀双流体恒星模型解析推导出来。其次,通过参数化的卷吸模型研究了两种流体之间的耦合效应。我们发现,耦合在一般情况下,打破了普遍的行为中看到的解耦流体。基于相对论变分原理,导出了卷吸引起的$f_{\rm s}$模平方频率一阶位移的近似表达式。

英文摘要:

It has been well established that the $f$-mode of relativistic ordinary-fluid neutron stars displays a universal scaling behavior. Here we study whether the "ordinary" $f_{\rm o}$- and "superfluid" $f_{\rm s}$-modes of superfluid neutron stars also show similar universal behavior. We first consider a simple case where the neutron superfluid and normal fluid are decoupled, and with each fluid modeled by a polytropic equation of state. We find that the $f_{\rm o}$-mode obeys the same scaling laws as established for the $f$-mode of orindary-fluid stars. However, the oscillation frequency of the $f_{\rm s}$-mode obeys a different scaling law, which can be derived analytically from a homogenous two-fluid stellar model in Newtonian gravity. Next the coupling effect between the two fluids is studied via a parameterized model of entrainment. We find that the coupling in general breaks the universal behavior seen in the case of decoupled fluids. Based on a relativistic variational principle, an approximated expression is derived for the first-order shift of the $f_{\rm s}$-mode squared frequency due to the entrainment.

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