Reconstructing the Cosmic Evolution of Quasars from the Age Distribution of Local Early-Type Galaxies

We use the spectra of 22,000 nearby early-type galaxies from the Sloan Digital Sky Survey (SDSS) to determine the age distribution of these galaxies as a function of their velocity dispersion sigma_v in the range 100 km/s < sigma_v < 280 km/s. We then combine the inferred age-distributions with the local abundance of spheroids, including early-type galaxies and late-type bulges, to predict the evolution of the quasar luminosity function (LF) in the redshift range 0<z<6. We make the following simple assumptions: (i) the formation of stars in each galaxy, at the epoch identified with the mean mass-weighted stellar age, is accompanied by the prompt assembly of the nuclear supermassive black hole (SMBH); (ii) the mass of the SMBH obeys the M_bh-sigma_v correlation observed in nearby galaxies; (iii) the SMBH radiates at a fraction f_Edd of the Eddington limit for a fixed duration t_Q, and is identified as a luminous quasar during this epoch, (iv) the intrinsic dispersions in the Eddington ratio and the M_bh-sigma_v relation produce a combined scatter of Delta(log L_Q) around the mean logarithmic quasar luminosity <log L_Q> at fixed sigma_v. These assumptions require that the SMBH remnants of quasars with bolometric luminosity below L_bol=10^{12.5} f_Edd L_sun reside predominantly in bulges of late type galaxies. We find that evolution of the observed quasar LF can be fit over the entire redshift range in this simple model, 0<z<6 with the choices of Delta(log L_Q)=0.6-0.9, t_Q= (6-8)x10^7 yr, and <f_Edd>=0.3-0.5. We find no evidence that any of the model parameters evolves with redshift, supporting the strong connection between the formation of stars and nuclear SMBHs in spheroids.