论文标题
球形恒星的表环频率不均匀
Epicyclic frequencies of spheroidal stars with non-uniform density
论文作者
论文摘要
我们考虑具有不均匀密度的旋转恒星的重力电位，以推导绕恒星绕的颗粒的轨道和上环状频率。我们假设恒星由恒定密度的同心球体组成，并具有恒星内部密度的整体幂律分布。在最低顺序近似情况下，我们恢复了Maclaurin球体的已知结果，即径向环环频率中的最大值发生在$ r = \ sqrt {2} ae $，对于偏心率$ \ geq 1/\ sqrt {2} $。我们发现，这些特征频率的性质基于旋转星的几何形状有所不同。对于块状球体，轨道类似于逆行 - kerr轨道，而径向环环的位置随着恒星内部的密度变化变得更陡峭，径向环环轨道的位置接近恒星表面。相反，围绕斜面的球体周围的轨道类似于前旋风，但是对于岩石形的恒星而言，不存在略有稳定的轨道。轨道频率比扁平（prate）星的开普勒值大（较小），其相等性为$ e \ rightarrow 0 $或$ r \ rightarrow \ rightarrow \ infty $。角速度和角动量的径向曲线允许围绕任何扁平/扁平球体的任何性质的稳定积聚盘。
We consider the gravitational potential of a rotating star with non-uniform density to derive the orbital and epicyclic frequencies of the particles orbiting the star. We assume that the star is composed of concentric spheroids of constant density, with a global power-law distribution of density inside the star. At the lowest order approximation, we recover the known result for the Maclaurin spheroid that the maximum in the radial epicyclic frequency occurs at $r=\sqrt{2}ae$, for eccentricities $\geq 1/\sqrt{2}$. We find that the nature of these characteristic frequencies differs based on the geometry of the rotating star. For an oblate spheroid, the orbits resemble retrograde-Kerr orbits and the location of the radial epicyclic maximum approaches the stellar surface as the density variation inside the star becomes steeper. On the contrary, orbits around a prolate spheroid resemble prograde-Kerr orbits, but the marginally stable orbit does not exist for prolate-shaped stars. The orbital frequency is larger (smaller) than the Keplerian value for an oblate (prolate) star with the equality attained as $e \rightarrow 0$ or $r \rightarrow \infty$. The radial profiles of the angular velocity and the angular momentum allow for a stable accreting disc around any nature of oblate/prolate spheroid.
