We consider the astrophysical consequences of the self-interacting dark matter (SIDM) scenario for a general velocity-dependent cross section per unit mass that varies as some power of velocity: σ_(DM) = σ_0(v/v_0)~(-a) Accretion of SIDM onto seed black holes can produce supermassive black holes that are too large for certain combinations of σ_0v_0~a and a, a fact that is used to obtain a new constraint on the dark matter interaction. Constraints due to other astrophysical considerations are presented and previous constraints for a constant cross section are generalized. The black hole constraint is extremely sensitive to the cusp slope, α, of the inner density profile ρ～ r~(-α) of dark halps. For the most probable value of α = 1.3, we find that there exists a tiny region in the parameter space for SIDM properties, with a ≈ 0.5 and (σ_0/1 cm~2 g~(-1)（v_o/100 km s~(-1))~a ≈ 0.5, such that all constraints are satisfies. However, the adiabatic compression of the dark halo by baryons as they cool and contract in normal galaxies yields a steeper cusp, ρ～ r~(-α′). We find that in both the highly collisional and collisionless limits invariance arguments require α′= (6 - α) (4 - α), where α and α′ are the (4α) inner profile slope of the dark halo before and after compression, respectively. This gives the tighter constraint (σ_0/1 cm~2 g~(-1))(v_0/100 km s~(-1))~a approx<0.02, which would exclude SIDM as a possible solution to the purported problems with cold dark matter (CDM) on subgalactic scales in the absence of other dynamical processes. Nevertheless, SIDM with parameters consistent with this stronger constraint, can explain the ubiquity of supermassive black holes in the centers of galaxies. A " best-fit" model is presented with a = 0 and (σ_0/1 cm~2 g~(-1)) = 0.02, which reproduces the supermassive black hole masses and their observed correlations with the velocity dispersion of the host bulges. Specifically, the approximately fourth-power dependence of black hole mass on galactic velocity dispersion is a direct consequence of the power spectrum of primeval perturbations having an index of n ≈ -2 and the value of a. Although the dark matter collision rates for this model are too small to directly remedy problems with CDM, mergers between dark halos harboring supermassive black holes at high redshift could ameliorate the cuspy halo problem. This scenario also explains the lack of comparable supermassive black holes in bulgeless galaxies like M33.
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机译：我们考虑了自相互作用暗物质（SIDM）情景的天体物理后果，即单位质量的一般速度相关截面随速度的变化而变化：σ_（DM）=σ_0（v / v_0）〜（-a SIDM在种子黑洞上的积聚会产生对于σ_0v_0〜a和a的某些组合而言太大的超大质量黑洞，这一事实用于获得对暗物质相互作用的新约束。提出了由于其他天体物理学考虑而产生的约束，并概括了以前对于恒定横截面的约束。黑洞约束对暗半茎内部密度分布ρ〜r〜（-α）的尖点斜率α非常敏感。对于最可能的α= 1.3值，我们发现SIDM属性的参数空间中存在一个微小区域，其≈0.5和（σ_0/ 1 cm〜2 g〜（-1）（v_o / 100 km s 〜（-1））〜a≈0.5，因此所有约束都满足。但是，重子在正常星系中冷却和收缩时，其对暗晕的绝热压缩会产生更陡峭的尖端ρ〜r〜（-α'）。我们发现，在高度碰撞和无碰撞极限中，不变性均要求α'=（6-α）（4-α），其中α和α'是压缩前后暗晕的（4α）内轮廓斜率，分别。这给出了更严格的约束（σ_0/ 1 cm〜2 g〜（-1））（v_0 / 100 km s〜（-1））〜约<0.02，这将SIDM排除为解决所称问题的可能解决方案在没有其他动力学过程的情况下，银河系下的暗暗物质（CDM）。然而，具有与该更强约束一致的参数的SIDM可以解释星系中心超大质量黑洞的普遍性。提出了一个“最佳拟合”模型，其中a = 0且（σ_0/ 1 cm〜2 g〜（-1））= 0.02，它再现了超大质量黑洞质量及其观察到的与主凸起速度散布的相关性。 。具体而言，黑洞质量对银河速度弥散的大约四次方的依赖性是原始扰动的功率谱的直接结果，其原始指数为n≈-2并且值为a。尽管此模型的暗物质碰撞率太小，无法直接解决CDM的问题，但是在高红移下具有超大质量黑洞的暗光晕之间的合并可以缓解尖锐的光晕问题。这种情况也说明了像M33这样的无凸出星系缺乏可比的超大质量黑洞。
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