Supermassive stars, with masses greater than a million solar masses, are possible progenitors of supermassive black holes in galactic nuclei. Because of their short nuclear burning timescales, such objects can be formed only when matter is able to accumulate at a rate exceeding ~ 1 solar mass/yr. Here we revisit the structure and evolution of rotationally-stabilized supermassive stars, taking into account their continuous accumulation of mass and their thermal relaxation. We show that the outer layers of supermassive stars are not thermally relaxed during much of the star's main sequence lifetime. As a result, they do not resemble n=3 polytropes, as assumed in previous literature, but rather consist of convective (polytropic) cores surrounded by convectively stable envelopes that contain most of the mass. We compute the structures of these envelopes, in which the specific entropy is proportional to the enclosed mass M(R) to the 2/3-power. By matching the envelope solutions to convective cores, we calculate the core mass as a function of time. We estimate the initial black hole masses formed as a result of core-collapse, and their subsequent growth via accretion from the bloated envelopes ("quasistars") that result. The seed black holes formed in this way could have typical masses in the range ~ 10^4-10^5 solar masses, considerably larger than the remnants thought to be left by the demise of Population III stars. Supermassive black holes therefore could have been seeded during an epoch of rapid infall considerably later than the era of Pop III star formation.
Little Red Dots as self-gravitating discs accreting on supermassive stars: Spectral appearance and formation pathway of the progenitors to direct collapse black holes
Niels Bohr International Academy, The Niels Bohr Institute（尼尔斯·玻尔国际学院，尼尔斯·玻尔研究所）；Center of Gravity, Niels Bohr Institute（引力中心，尼尔斯·玻尔研究所）；Department of Astrophysics, University of Zurich（苏黎世大学天体物理学系）
Light or heavy supermassive black hole seeds: the role of internal rotation in the fate of supermassive stars
超大质量黑洞是星系演化的关键因素。然而，其起源仍有很大争议。在一个主要的形成场景中，$\sim100$ M $_{\odot}$黑洞是由超大质量恒星（$\gtrsim 10^{4-5}$ M $_{\odot}$）的内核坍塌造成的，该恒星是由原始气体在$z\sim 15$新形成的星系中心快速积累（$\gtrsim 0.1 $ M $_{\odot}$ yr $^{-1}$）而产生的。随后的演化仍然是推测性的：超大质量恒星中剩余的气体可以直接进入新生的黑洞，或者它的一部分可以形成一个中央吸积盘，其光度维持周围的大质量和几乎流体静力学的包络（称为“准星”的系统）。为了解决这一点，我们考虑了旋转对准恒星的影响，因为角动量不可避免地被积累的气体输送到星系核。使用一个模型的内部重新分配的角动量，定性匹配的结果从模拟旋转对流恒星信封，我们表明，准恒星的信封质量大于几个$10^{5}$ M $_{\odot} \times (\rm black~hole~mass/100 M_{\odot})^{0.82}$有高度次开普勒气体运动在其核心，防止气体循环外的黑洞的视界。质量较小的类恒星可能会形成，但在吸积光度解开包层之前，它们只能持续$\lesssim 10^4$年，从而抑制黑洞的生长。我们推测，这可能最终导致一个双黑洞种子人口：（i）大规模（$>10^{4}$ M $_{\odot}$）种子形成…
Multimessenger Constraints on Supermassive Dark Stars and Their Black Hole Remnants
International Center for Quantum-field Measurement Systems for Studies of the Universe and Particles (QUP,WPI), High Energy Accelerator Research Organization (KEK)（宇宙与粒子量子场测量系统国际中心（QUP,WPI），高能加速器研究机构（KEK））；Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK)（粒子与核研究研究所（IPNS），高能加速器研究机构（KEK））；Graduate University for Advanced Studies (SOKENDAI)（综合研究大学院大学（SOKENDAI））；Kavli Institute for the Physics and Mathematics of the Universe (WPI)（宇宙物理与数学卡弗里研究所（WPI））
Testing the evolutionary pathways of galaxies and their supermassive black holes and the impact of feedback from Active Galactic Nuclei via large multiwavelength datasets
Probing supermassive stars and massive black hole seeds through gravitational wave inspirals
我们提出了一个新的引力波发射源：原始超大质量恒星内部致密碎片的螺旋辐射。这样的系统被认为是超大质量黑洞（SMBH）形成过程中的一个重要通道，但人们对此知之甚少。一个模型表明，在原子冷却的原始晕中，$0.1$-1 M $_\odot$ /yr的高吸积率可能导致核燃烧SMS的形成。这最终将通过相对论不稳定性发生坍缩，留下巨大的BH残留物。最近的模拟表明，超大质量恒星很少单独形成，而伴星甚至形成的黑洞可能会被捕获/吸积，并由于气体动力学摩擦而螺旋进入SMS核心。在这里，我们探讨了从这样的吸气产生的GW发射，这可能会探测SMS的形成和演化和第一个超大质量黑洞的种子。我们使用一个半解析的气体动力学摩擦模型的吸气在SMS来表征其属性。我们发现这样的来源可能是潜在的观察到即将到来的空间出生的GW探测器在其形成的红移与引力透镜的好处。密切相关的准恒星合并可能会产生更强的信号，尽管从其他高z事件中消除这种事件可能具有挑战性。
An Alternate Pathway for H$_2$ Formation in the Early Universe: A physical process to account for the presence and coevolution of the luminous galaxies and supermassive black holes at the high redshifts
