We construct evolutionary models of the populations of AGN and supermassive black holes, in which the black hole mass function grows at the rate implied by the observed luminosity function, given assumptions about the radiative efficiency and the Eddington ratio. We draw on a variety of recent X-ray and optical measurements to estimate the bolometric AGN luminosity function and compare to X-ray background data and the independent estimate of Hopkins et al. (2007) to assess remaining systematic uncertainties. The integrated AGN emissivity closely tracks the cosmic star formation history, suggesting that star formation and black hole growth are closely linked at all redshifts. Observational uncertainties in the local black hole mass function remain substantial, with estimates of the integrated black hole mass density ρ_BH spanning the range 3-5.5x10^5 Msun/Mpc^3. We find good agreement with estimates of the local mass function for a reference model where all active black holes have efficiency \eps=0.065 and L_bol/L_Edd~0.4. In this model, the duty cycle of 10^9 Msun black holes declines from 0.07 at z=3 to 0.004 at z=1 and 0.0001 at z=0. The decline is shallower for less massive black holes, a signature of "downsizing" evolution in which more massive black holes build their mass earlier. The predicted duty cycles and AGN clustering bias in this model are in reasonable accord with observational estimates. If the typical Eddington ratio declines at z<2, then the "downsizing" of black hole growth is less pronounced. Matching the integrated AGN emissivity to the local black hole mass density implies \eps=0.075 (ρ_BH/4.5x10^5 Msun/Mpc^3)^{-1} for our standard luminosity function estimate (25% higher for Hopkins et al.'s), lower than the values \eps=0.16-0.20 predicted by MHD simulations of disk accretion.
我们使用一个体积和通量有限的本地（$0.03 \leq z \leq 0.1$）的射电星系与光学对应的样本来解决一个典型的星系花了多长时间在放射性活跃和静止状态的问题。活跃期的长度与宿主星系的恒星质量有很强的依赖性。最大规模主机中的无线电源也更频繁地被重新触发。在活跃阶段所花费的时间与气体冷却速率一样依赖于恒星质量，这表明静止阶段的开始是由于燃料耗尽。我们发现射电和发射线活动星系核的活动是独立的，与这些对应于不同的吸积状态。
活动星系核的吸积速率在短时间尺度上可能变化很大;比椭圆星系和星系团中X射线发射气体的典型冷却时间要短得多。使用Langevin方法，它示出，对于一个简单的反馈系统，这可以引起AGN功率输出的变化，是更大的幅度，并持续更长的时间尺度，比初始波动。这意味着，丰富的星系团预计将显示出最大和最长寿命的波动。吸积率的随机变化也意味着活动星系核在很宽的时间尺度上注入能量。这使得活动星系核与其周围环境保持着比周期性激活时更紧密的平衡。如果瞬时吸积率（按喷流功率换算）对数正态变化，则可以解释Allen等人在2006年发现的Bondi吸积率与喷流功率之间可能存在的非线性相关性。这一解释也意味着活动星系核活动的占空比随着周围环境的辐射损失而增加，与Best et al 2005定性一致。
