arXiv 1609.047242016-09astro-ph.COgr-qchep-th

轴子星的黑洞形成

Black hole formation from axion stars

Thomas Helfer, David J. E. Marsh, Katy Clough, Malcolm Fairbairn, Eugene A. Lim, Ricardo Becerril

备注：: 19 pages, 11 figures, link to movies: http://www.grchombo.org/publications
DOI：: 10.1088/1475-7516/2017/03/055

摘要：

具有势$V(ϕ)=m_a^2f_a^2 [1-\cos (ϕ/f_a)]$的轴子的经典运动方程具有准稳定的、定域的、振荡的解，我们称之为“轴子星”。我们研究，第一次，使用完整的非线性广义相对论爱因斯坦方程和完整的非微扰余弦势的数值，轴子星的崩溃。我们映射区域上的“轴子星稳定图”，参数化的初始ADM质量，$M_{\rm ADM}$，和轴子衰变常数，$f_a$。我们确定了三个区域的参数空间：i）长寿命的振荡轴子星的解决方案，与一个基本频率，$m_a$，调制的自相互作用，ii）崩溃BH和iii）由于引力冷却和相互作用的完全分散。我们定位这三个区域的边界和一个近似的“三相点“$(M_{\rm TP},f_{\rm TP})\sim (2.4 M_{pl}^2/m_a,0.3 M_{pl})$。对于$f_a$低于三相点BH形成过程中进行缠绕（在复杂的$U(1)$图片）的轴子场附近的分散阶段。这可能会阻止天体物理BH的形成从轴子星与$f_a\ll M_{pl}$。对于较大的$f_a\gtrsim f_{\rm TP}$，BH的形成发生通过稳定的分支，我们估计的BH的质量比的稳定状态在相边界是$\mathcal{O}(1)$内的数值不确定性。我们讨论了我们的研究结果的观测相关性的轴子星BH种子，这是超大质量的超轻轴子的情况下。对于QCD轴子，由轴子星坍缩形成的典型BH质量是$M_{\rm BH}\sim 3.4 (f_a/0.6 M_{pl})^{1.2} M_\odot$。

英文摘要：

The classical equations of motion for an axion with potential $V(ϕ)=m_a^2f_a^2 [1-\cos (ϕ/f_a)]$ possess quasi-stable, localized, oscillating solutions, which we refer to as "axion stars". We study, for the first time, collapse of axion stars numerically using the full non-linear Einstein equations of general relativity and the full non-perturbative cosine potential. We map regions on an "axion star stability diagram", parameterized by the initial ADM mass, $M_{\rm ADM}$, and axion decay constant, $f_a$. We identify three regions of the parameter space: i) long-lived oscillating axion star solutions, with a base frequency, $m_a$, modulated by self-interactions, ii) collapse to a BH and iii) complete dispersal due to gravitational cooling and interactions. We locate the boundaries of these three regions and an approximate "triple point" $(M_{\rm TP},f_{\rm TP})\sim (2.4 M_{pl}^2/m_a,0.3 M_{pl})$. For $f_a$ below the triple point BH formation proceeds during winding (in the complex $U(1)$ picture) of the axion field near the dispersal phase. This could prevent astrophysical BH formation from axion stars with $f_a\ll M_{pl}$. For larger $f_a\gtrsim f_{\rm TP}$, BH formation occurs through the stable branch and we estimate the mass ratio of the BH to the stable state at the phase boundary to be $\mathcal{O}(1)$ within numerical uncertainty. We discuss the observational relevance of our findings for axion stars as BH seeds, which are supermassive in the case of ultralight axions. For the QCD axion, the typical BH mass formed from axion star collapse is $M_{\rm BH}\sim 3.4 (f_a/0.6 M_{pl})^{1.2} M_\odot$.

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