Using the numerical simulation data for two-dimensional core-collapse supernova, we examine the protoneutron star (PNS) asteroseismology with the relativistic Cowling approximation. As shown in the previous study, e.g., [H. Sotani and T. Takiwaki, Mon. Not. R. Astron. Soc. 498, 3503 (2020).], the gravitational wave signals appearing in the numerical simulation can be well identified with the gravity (fundamental) oscillation in the early (later) phase before (after) the avoided crossing between the gravity and fundamental oscillations. On the other hand, the time evolution of supernova gravitational waves strongly depends on the PNS models, such as the progenitor mass and the equation of state for dense matter. Nevertheless, we find that the fundamental and gravity mode frequencies according to the gravitational wave signals appearing in the numerical simulations can be expressed as a function of the protoneutron star average density independently of the PNS models. Using the average density, we derive the empirical formula for supernova gravitational wave frequency. In addition, we confirm that the dependence of the PNS surface density on the PNS average density is almost independent of the PNS models, and we also discuss how the different treatment of the nonuniform matter in the equation of state affects the observables.

中文翻译：

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超新星引力波的普遍关系

使用二维核心坍缩超新星的数值模拟数据，我们用相对论 Cowling 近似检查了原中子星 (PNS) 星震学。如之前的研究所示，例如，[H. Sotani 和 T. Takiwaki，周一。不是。R. 阿斯特朗。社会。 498, 3503 (2020).]，数值模拟中出现的引力波信号可以很好地与早期（后期）阶段的重力（基本）振荡识别，之前（之后）避免了重力和基本振荡之间的交叉。另一方面，超新星引力波的时间演化强烈依赖于 PNS 模型，例如前身质量和致密物质的状态方程。尽管如此，我们发现根据出现在数值模拟中的引力波信号的基本和重力模式频率可以独立于 PNS 模型表示为质子星平均密度的函数。使用平均密度，我们推导出超新星引力波频率的经验公式。此外，