论文标题
对紧凑型恒星的径向振荡的可靠描述
A reliable description of the radial oscillations of compact stars
论文作者
论文摘要
我们开发了一种用于解决非旋转紧凑型恒星的固定径向振荡的Sturm-Liouville微分方程溶液的数值算法。我们的方法基于Numerov的方法，该方法在特征值问题中将Sturm-liouville微分方程转换。在我们的发展中，我们提供了一种策略，可以正确处理具有不同机械性能的层之间的恒星边界和界面。假设波动遵守背景状态相同的方程式，我们分析了各种不同的恒星模型，并且精确地确定了数百个本征频和本本征。如果状态方程不存在界面不连续性，则基本的径向本征完全在与最大的重力质量相对应的临界中央能量密度上变得不稳定。但是，在存在界面不连续性的情况下，存在稳定的配置，中央密度超过临界的配置，并且重力质量较小。
We develop a numerical algorithm for the solution of the Sturm-Liouville differential equation governing the stationary radial oscillations of nonrotating compact stars. Our method is based on the Numerov's method that turns the Sturm-Liouville differential equation in an eigenvalue problem. In our development we provide a strategy to correctly deal with the star boundaries and the interfaces between layers with different mechanical properties. Assuming that the fluctuations obey the same equation of state of the background, we analyze various different stellar models and we precisely determine hundreds of eigenfrequencies and of eigenmodes. If the equation of state does not present an interface discontinuity, the fundamental radial eigenmode becomes unstable exactly at the critical central energy density corresponding to the largest gravitational mass. However, in the presence of an interface discontinuity, there exist stable configurations with a central density exceeding the critical one and with a smaller gravitational mass.
