与大质量中心黑洞存在一致的暗物质晕中心密度的上限
An upper limit to the central density of dark matter haloes from consistency with the presence of massive central black holes
摘要：
我们研究了星系中心大质量黑洞的生长速率，这些黑洞是由周围晕圈中的暗物质吸积而来的。通过只考虑由于轨道上的暗物质粒子与中心黑洞的结合而产生的吸积，我们得到了吸积率的一个确定的下限。我们发现，一个失控的吸积制度发生在一个时间尺度上，这取决于三个特征参数的问题：黑洞的初始质量，体积密度和速度分散的暗物质粒子在其附近。吸积率的分析处理产生的结果意味着，对于最大的黑洞质量推断类星体的研究（$>10^{9} M_{\odot}$），失控制度将达到的时间尺度是短于中心暗物质密度超过$250 M_{\odot}$ pc $^{-3}$的问题的晕的寿命。由于达到失控吸积会强烈扭曲宿主暗物质晕，在这个质量范围内的类星体黑洞的推论导致其宿主晕中心暗物质密度的上限为$ρ_{0} < 250 M_{\odot} $ pc $^{-3}$。这个极限与假设的中心黑洞质量成反比。然而，考虑到宇宙学研究所暗示的暗物质分布在银河系中具有普遍性，我们得到了这种结构中暗物质中心密度的严格上限。
英文摘要：
We study the growth rates of massive black holes in the centres of galaxies from accretion of dark matter from their surrounding haloes. By considering only the accretion due to dark matter particles on orbits unbound to the central black hole, we obtain a firm lower limit to the resulting accretion rate. We find that a runaway accretion regime occurs on a timescale which depends on the three characteristic parameters of the problem: the initial mass of the black hole, and the volume density and velocity dispersion of the dark matter particles in its vicinity. An analytical treatment of the accretion rate yields results implying that for the largest black hole masses inferred from QSO studies ($>10^{9} M_{\odot}$), the runaway regime would be reached on time scales which are shorter than the lifetimes of the haloes in question for central dark matter densities in excess of $250 M_{\odot}$pc$^{-3}$. Since reaching runaway accretion would strongly distort the host dark matter halo, the inferences of QSO black holes in this mass range lead to an upper limit on the central dark matter densities of their host haloes of $ρ_{0} < 250 M_{\odot} $pc$^{-3}$. This limit scales inversely with the assumed central black hole mass. However, thinking of dark matter profiles as universal across galactic populations, as cosmological studies imply, we obtain a firm upper limit for the central density of dark matter in such structures.
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