发表机构
Niels Bohr International Academy, The Niels Bohr Institute; Center of Gravity, Niels Bohr Institute; Institute of Science and Technology Austria (ISTA)（尼尔斯·玻尔国际学院，尼尔斯·玻尔研究所; 引力中心，尼尔斯·玻尔研究所; 奥地利科学与技术研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将钱德拉塞卡脉动稳定性判据推广至带表面压力边界条件的相对论恒星，应用于快速吸积超大质量恒星模型，发现压力约束可延迟广义相对论不稳定性并显著提高临界质量，最终可能导致超大质量黑洞形成。
AI 中文摘要
我们推导了钱德拉塞卡脉动稳定性判据在具有表面压力边界条件的相对论恒星中的推广形式。随后，我们将这一新判据应用于hylotropes模型，该模型描述了具有核-包层结构的快速吸积超大质量恒星。我们发现，约束通常使恒星趋于稳定，当表面外部压力约为恒星流体静压力尺度的$\sim10^{-3}$时，广义相对论不稳定性的起始被延迟。超过该值后，边际稳定性处的临界质量迅速增加，比孤立$n=3$多方球（用于氦燃烧）的临界质量$\sim 10^5$ M$_\odot$高出数个数量级。我们讨论了吸积流在组装超大质量恒星时提供的冲压压力与磁压相结合如何产生所需的压力边界条件，并给出了坍缩前最终质量的拟合公式。作为粗略估计，假设标准$\alpha$盘中磁压与热压之间满足均分，我们发现当吸积率约为$\dot M\sim100\\,{\rm M_\odot}\\,{\rm yr}^{-1}$时临界质量加倍，此后再次迅速增加。我们的结果表明，在何种条件下（可能在高红移暗物质晕的子集中实现），非旋转超大质量恒星可能坍缩成超过重种子典型尺度的黑洞。
英文摘要
We derive an extension of Chandrasekhar's pulsational stability criterion for relativistic stars with a pressure boundary condition at the surface. We then apply the new criterion to hylotropes, a model describing rapidly accreting supermassive stars with a core-envelope structure. We find that confinement typically stabilises stars, delaying the onset of the general relativistic instability when the external pressure at the surface is roughly $\sim10^{-3}$ of the stars' hydrostatic pressure scale. Beyond this value, the critical mass at marginal stability increases rapidly, exceeding the value of $\sim 10^5$ M$_{\odot}$ for helium burning, isolated $n=3$ polytropes by orders of magnitude. We discuss how the required pressure boundary conditions may be produced by the combined ram and magnetic pressure supplied by the accretion flow as it assembles the supermassive star, and provide a fitting formula for the final mass before collapse. As a rough estimate assuming equipartition between magnetic and thermal pressures in a standard $α$-disk, we find that the critical mass doubles at accretion rates of order $\dot M\sim100\,{\rm M_\odot}\,{\rm yr}^{-1}$, again increasing rapidly after this value. Our results show under what conditions, potentially realized in a subset of high redshift halos, non-rotating SMS may collapse into black holes beyond the typical scale of heavy seeds.
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