Cosmological Evolution of the Duty Cycle of Quasars Jian-Min Wang, Yan-Mei Chen & Fan Zhang

1. BH birth today active dormant active active dormant a single episodic phase Mass distribution Total: triple power law Mass function in each redshift z-bin Cosmological Evolution of the Duty Cycle of Quasars Jian-Min Wang, Yan-Mei Chen & Fan Zhang Institute of High Energy Physics, CAS, China, chenym@mail.ihep.ac.cn Abstract: The problem of the duty cycle related to the episodic activity of the black holes remains one of the major questions of the cosmological evolution of quasars. In this work, we obtain quasar mass function based on analyses of a large sample of quasars from SDSS with z ≤ 2.1. We then get the duty cycle based on Sołtan’s argument, using quasar mass function and luminosity function. We find that the duty cycle has a strong evolution which follows the history of the cosmic star formation rate (SFR) density in the universe. • Motivation • During entire evolution, how many times and how many black holes are triggered ? • What is the trigger mechanism and why do quasars switch off ? • 2. The definition of duty cycle • For a single black hole, • In statistic, duty cycle can be defined as the fraction of active BHs to their total number • 3. Method & Calculation • According to the definition of duty cycle,we have • duty cycle in terms of their number density, • (1) • Multiplying by the black hole mass and integrating • equation (1) over all black hole masses, we have the • mass averaged duty cycle, • (2) • where • In the assumption of multiple episodic growth of • black holes, it can be easily understood that • So we have • According to Sołtan’s argument, we have • Once we get the luminosity function and mass function, we can calculate out the duty cycle. • 4. Mass function • 5. Result • Using the luminosity function given by Richards et al. (2006) & the mass function calculated from the SDSS sample, we get the duty cycle as a function of redshift. In figure 2(a), we plot the duty cycle. The evolution of star formation rate density is plot in figure 2(b). From these two figures, we can see that the duty cycle δ have the following properties: • δ∈ (10-3, 1) • strong evolution • consistent with • history of SFR density (Fig. 1) (Fig. 2) • Reference: • McLure, R., & Dunlop, J. S. 2001, MNRAS, 327, 199 Richards, G. T., et al. 2006, AJ, 131, 2766 • Pe´re´z-Gonza´lez, P. G., et al. 2005, ApJ, 630, 82 Sołtan, A. 1982, MNRAS, 200, 115