标题： 中子星诞生与死亡时普遍关系的扩展 显示英文标题

标题： The broadening of universal relations at the birth and death of a neutron star

摘要： 已知某些中子星观测量之间的特定关系对状态方程不敏感。这些普适关系已被证明适用于冷且静止的中子星。在这里，我们研究这些关系在更动态的情形下：即原中子星和超大质量中子星。首先，我们研究原中子星。我们使用从三维核心坍缩超新星模拟中提取的有效状态方程来获得球对称原中子星的结构。然后我们考虑非径向振荡以计算其 $f$- 模式频率（$f$），以及缓慢旋转和小潮汐变形，以计算其转动惯量（$I$）、自旋诱导的四极矩（$Q$）和洛夫数。 我们发现，涉及这些可观测量（$I$-Love-$Q$和$f$-Love关系）的冷中子星普遍关系对于新生中子星也近似成立，在考虑八个不同的超新星前身天体以及SFHo状态方程的情况下，反弹时间超过$\approx$0.5秒时，偏差低于$\approx$10$\%$。 接下来，我们研究超质量中子星。 我们利用总体量得到冷且非旋转中子星的$f$模频率与紧凑性的新的普遍关系。 我们展示了这种关系具有$\approx$$3\%$的物态方程变化，考虑了一组十个物态方程。利用双中子星并合模拟的结果，我们在$f$-$C$平面上研究了超大质量中子星的演化，考虑了两种不同的质量比和SFHo物态方程。 我们发现，当引力波信号的峰值频率直接作为 $f$- 模式代理时，这些超大质量中子星的峰值频率与紧凑性之间的关系偏离了普遍的 $f$-$C$ 关系约 70 $-$至 80 $\%$。 显示英文摘要

摘要： Certain relations among neutron-star observables that are insensitive to the equation of state are known to exist. Such universal relations have been shown to be valid for cold and stationary neutron stars. Here, we study these relations in more dynamic scenarios: protoneutron stars and hypermassive neutron stars. First, we study protoneutron stars. We use an effective equation of state, extracted from three-dimensional core-collapse supernova simulations, to obtain the structure of spherically symmetric protoneutron stars. We then consider nonradial oscillations to compute their $f$-mode frequency ($f$), as well as slow rotation and small tidal deformation, to compute their moment of inertia ($I$), spin-induced quadrupole moment ($Q$), and Love number. We find that well-established universal relations for cold neutron stars involving these observables ($I$-Love-$Q$ and $f$-Love relations) are approximately valid for protoneutron stars, with a deviation below $\approx$ 10$\%$ for a postbounce time above $\approx$ 0.5 s, considering eight different supernova progenitors and the SFHo equation of state. Next, we study hypermassive neutron stars. We obtain a new universal relation between the $f$-mode frequency and the compactness of cold and nonrotating neutron stars, using bulk quantities. We show that this relation has an equation-of-state-variation of $\approx$ $3\%$, considering a set of ten equations of state. Using results from binary neutron star merger simulations, we study the evolution of hypermassive neutron stars on the $f$-$C$ plane, considering two different mass ratios and the SFHo equation of state. We find that the relation between the peak frequency of the gravitational-wave signal and the compactness from these hypermassive neutron stars deviates from the universal $f$-$C$ relation by 70 $-$ 80$\%$, when the peak frequency is taken directly as a proxy for the $f$-mode.