Reconstructing the cosmic evolution of quasars from the age distribution of local early-type galaxies

We use the spectra of approximate to 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 less than or similar to sigma(v)less than or similar to 280 km s(-1). 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 less than or similar to 6. We make the following simple assumptions: ( 1) 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); (2) the mass of the SMBH obeys the M-BH-sigma(v) correlation observed in nearby galaxies; (3) 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; and ( 4) 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 Lq log L-q at fixed sigma v. These assumptions require that the SMBH remnants of quasars with L-bol P10(12.5) f(Edd) L-circle dot 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 less than or similar to 6, with the choices of 0.6 less than or similar to Delta log L-q less than or similar to 0.9, 6x10(7) less than or similar to t(q) less than or similar to 8 x 10(7) yr, and 0.3 less than or similar to f(Edd)less than or similar to 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.