We examine the eigenfrequencies of gravitational waves from the protoneutron stars (PNSs) provided via the core-collapse supernovae, focusing on how the frequencies depend on the dimension of numerical simulations especially for the early phase after core bounce. As expected, we find that the time evolution of gravitational wave frequencies depends strongly on the dimension of numerical simulation as well as the equation of state for high density matter. Even so, we find that the fundamental frequency as a function of PNS average density and the ratio of the specific eigenfrequencies to the fundamental frequency as a function of PNS properties are independent of the dimension of the numerical simulations, where the dependence of the equation of state is also very weak in this early postbounce phase. Thus, one can safely discuss the gravitational wave frequencies of the PNSs as a function of the PNS average density or compactness even with the frequencies obtained from the one dimensional simulations. We also provide phenomenological relation between the compactness and average density as well as the relation among the $f$-, $p$-, and $g$- mode frequencies.

中文翻译：

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数值模拟对原质子星引力波的尺寸依赖性

我们研究了通过核塌陷超新星提供的来自原子质子星（PNS）的引力波的本征频率，重点研究了频率如何取决于数值模拟的维数，特别是对于核弹后的早期阶段。正如预期的那样，我们发现引力波频率的时间演化在很大程度上取决于数值模拟的维数以及高密度物质的状态方程。即使这样，我们发现作为PNS平均密度的函数的基频以及作为PNS特性的函数的比本征频率与基频的比值也与数值模拟的尺寸无关，其中，在反弹后的早期阶段，状态也很弱。从而，即使使用一维模拟获得的频率，也可以安全地讨论PNS的重力波频率与PNS平均密度或紧密度的关系。我们还提供了紧密度和平均密度之间的现象学关系，以及之间的关系。$F$-， $p$-和 $G$-模式频率。