黑洞与星系质量关系演化的经验约束：散射物质
Empirical Constraints on the Evolution of the Relationship between Black Hole and Galaxy Mass: Scatter Matters
摘要：
我调查是否有用的限制星系质量和黑洞（BH）质量之间的关系的演变可以从最近的测量星系恒星质量函数和类星体的热光度函数在高红移。我假设一个简单的幂律关系星系质量和BH质量，暗示BH质量测量在低红移，并考虑只在零点的关系的演变。我认为，人们可以通过假设每个星系都有一个BH，以其爱丁顿速率发光来获得零点演化的下限。人们可以通过要求在高红移的大质量BH的数量不超过当地观察到的数量来获得上限。我发现，在这些假设下，忽略BH-星系质量关系中的散射，BH在z=1时的质量一定是其宿主星系的2倍，在z=2时的质量一定是其宿主星系的5 ~ 6倍。然而，考虑到BH-星系质量关系中的内在散射，这些约束大大放松了。在星系质量固定的情况下，黑洞质量的对数散射为0.3到0.5 dex，类似于今天观测关系中的内在散射估计，即使没有任何零点演化，也有足够大质量的黑洞在z=2时产生观测到的发光类星体。采用更现实的估计，主机的星系活跃的BH和爱丁顿比的相关类星体的比例，我发现，在z=2的BH星系质量关系的零点不可能比现在的值大两倍以上的一个因素，因为发光类星体的数量预测将超过观察到的人口。
英文摘要：
I investigate whether useful constraints on the evolution of the relationship between galaxy mass and black hole (BH) mass can be obtained from recent measurements of galaxy stellar mass functions and QSO bolometric luminosity functions at high redshift. I assume a simple power-law relationship between galaxy mass and BH mass, as implied by BH mass measurements at low redshift, and consider only evolution in the zero-point of the relation. I argue that one can obtain a lower limit on the zero-point evolution by assuming that every galaxy hosts a BH, shining at its Eddington rate. One can obtain an upper limit by requiring that the number of massive BH at high redshift does not exceed that observed locally. I find that, under these assumptions, and neglecting scatter in the BH-galaxy mass relation, BH must have been a factor of about 2 times larger at z=1 and 5 to 6 times more massive relative to their host galaxies at z=2. However, accounting for intrinsic scatter in the BH-galaxy mass relationship considerably relaxes these constraints. With a logarithmic scatter of 0.3 to 0.5 dex in black hole mass at fixed galaxy mass, similar to estimates of the intrinsic scatter in the observed relation today, there are enough massive BH to produce the observed population of luminous QSOs at z=2 even in the absence of any zero-point evolution. Adopting more realistic estimates for the fraction of galaxies that host active BH and the Eddington ratios of the associated quasars, I find that the zero-point of the BH-galaxy mass relation at z=2 cannot be much more than a factor of two times larger than the present-day value, as the number of luminous quasars predicted would exceed the observed population.
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