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Surface r-modes and burst oscillations of neutron stars

机译：中子星的表面r模和爆发振荡

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We study the r-modes propagating in steadily mass accreting, nuclear burning, and geometrically thin envelopes on the surface of rotating neutron stars. For the modal analysis, we construct envelope models that are fully radiative or have a convective region. We simply call the former radiative models and the latter convective models in this paper. As the angular rotation frequency Omega is increased, the oscillation frequency omega of the r-modes in the thin envelopes deviates appreciably from the asymptotic frequency omega = 2mOmega/l'(l' + 1) defined in the limit of Omega --> 0, where omega is the frequency observed in the corotating frame of the star, and m and l 0 are the indices of the spherical harmonic function Y-l'(m) representing the angular dependence of the modes. We find that the amplitudes of the fundamental r-modes with no radial nodes of the eigenfunctions are strongly confined to the equatorial region, and omega becomes only weakly dependent on Omega, gathering in a frequency range of omega/2pi less than or similar to 10 Hz, at rapid rotation rates. We also find that the fundamental r-modes in the convective models are destabilized by strong nuclear burning in the convective region. Because of excessive heating by nuclear burning, the corotating-frame oscillation frequency omega of the r-modes in the convective models becomes larger, and hence the inertial-frame oscillation frequency sigma becomes smaller than those of the corresponding r-modes in the radiative models, where sigma = omega -mOmega is negative for the r-modes of positive m. We find that the relative frequency change f = -(sigma(conv) - sigma(rad))/sigma(rad) is always positive and becomes less than similar to0.01 for the fundamental r-modes of l' > m + 1 at sigma(rad)/2pi similar to 300 Hz for m = 1 or at sigma(rad)/2pi similar to 600 Hz for m = 2, and that we need to consider the r-modes of l' much larger than m for values of f as small as similar to0.001, where sigma(conv) and sigma(rad) denote the oscillation frequencies for the convective and the radiative envelope models, respectively. [References: 37]
机译：我们研究了旋转中子星表面上稳定增长的质量吸积，核燃烧和几何上薄的包膜传播的r模式。对于模态分析，我们构建完全辐射或具有对流区域的包络模型。在本文中，我们仅将前者称为辐射模型，而将后者称为对流模型。随着角旋转频率Omega的增加，薄包络中r模式的振荡频率omega明显偏离Omega-> 0的极限中定义的渐近频率omega = 2mOmega / l'（l'+ 1）。 ，其中ω是在恒星旋转框架中观察到的频率，m和l 0是球谐函数Y-1'（m）的指数，表示模式的角度依赖性。我们发现没有本征函数的径向节点的基本r模的振幅强烈地限制在赤道区域，而ω则仅对ω的依赖性很小，聚集在ω/ 2pi小于或近似于10的频率范围内Hz，快速旋转。我们还发现，对流模型中的基本r型由于对流区域的强核燃烧而不稳定。由于核燃烧产生的过多热量，对流模型中r模式的同构框架振荡频率ω变大，因此惯性框架振荡频率sigma小于辐射模型中相应的r模式的振荡框架。 ，其中sigma = omega -mOmega对于正m的r模式为负。我们发现相对频率变化f =-（sigma（conv）-sigma（rad））/ sigma（rad）始终为正，并且对于l'> m + 1的基本r模式，变得小于0.01。对于s = 1的sigma（rad）/ 2pi类似于300 Hz，对于m = 2的sigma（rad）/ 2pi类似于600 Hz，我们需要考虑l'的r模远大于m f的值小至类似于0.001，其中sigma（conv）和sigma（rad）分别表示对流模型和辐射包络模型的振荡频率。 [参考：37]

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