We present a physically motivated model for the early coevolution of massive spheroidal galaxies and active nuclei at their centers. Within dark matter halos, forming at the rate predicted by the canonical hierarchical clustering scenario, the gas evolution is controlled by gravity, radiative cooling, and heating by feedback from supernovae and from the growing active nucleus. Supernova heating is increasingly effective with decreasing binding energy in slowing down the star formation and in driving gas outflows. The more massive protogalaxies virializing at earlier times are thus the sites of the faster star formation. The correspondingly higher radiation drag fastens the angular momentum loss by the gas, resulting in a larger accretion rate onto the central black hole. In turn, the kinetic energy carried by outflows driven by active nuclei can unbind the residual gas, thus halting both the star formation and the black hole growth, in a time again shorter for larger halos. For the most massive galaxies the gas unbinding time is short enough for the bulk of the star formation to be completed before Type Ia supernovae can substantially increase the Fe abundance of the interstellar medium, thus accounting for the -enhancement seen in the largest galaxies. The feedback from supernovae and from the active nucleus also determines the relationship between the black hole mass and the mass, or the velocity dispersion, of the host galaxy, as well as the black hole mass function. In both cases the model predictions are in excellent agreement with the observational data. Coupling the model with GRASIL (Silva et al. 1998), the code computing in a selfconsistent way the chemical and spectrophotometric evolution of galaxies over a very wide wavelength interval, we have obtained predictions in excellent agreement with observations for a number of observables that proved to be extremely challenging for all the current semianalytic models, including the submillimeter counts and the corresponding redshift distributions, and the epoch-dependent K-band luminosity function of spheroidal galaxies.

Context. Feedback from accreting supermassive black holes is often identified as the main mechanism responsible for regulating star-formation in AGN host galaxies. However, the relationships between AGN activity, radiation, winds, and star-formation are complex and still far from being understood. Aims. We study scaling relations between AGN properties, host galaxy properties and AGN winds. We then evaluate the wind mean impact on the global star-formation history, taking into account the short AGN duty cycle with respect to that of star-formation. Methods. We first collect AGN wind observations for 94 AGN with detected massive winds at sub-pc to kpc spatial scales. We then fold AGN wind scaling relations with AGN luminosity functions, to evaluate the average AGN wind mass-loading factor as a function of cosmic time. Results. We find strong correlations between the AGN molecular and ionised wind mass outflow rates and the AGN bolometric luminosity. The power law scaling is steeper for ionised winds (slope 1.29±0.38) than for molecular winds (0.76±0.06), meaning that the two rates converge at high bolometric luminosities. The molecular gas depletion timescale and the molecular gas fraction of galaxies hosting powerful AGN driven winds are 3-10 times shorter and smaller than those of main-sequence galaxies with similar star-formation rate, stellar mass and redshift. These findings suggest that, at high AGN bolometric luminosity, the reduced molecular gas fraction may be due to the destruction of molecules by the wind, leading to a larger fraction of gas in the atomic ionised phase. The AGN wind mass-loading factor η =ṀOF /SFR is systematically higher than that of starburst driven winds. Conclusions. Our analysis shows that AGN winds are, on average, powerful enough to clean galaxies from their molecular gas only in massive systems at z < ∼ 2, i.e. a strong form of co-evolution between SMBHs and galaxies appears to break down for the least massive galaxies.

We construct evolutionary models of the populations of active galactic nuclei (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 luminosity in Eddington units. 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. We discuss observational uncertainties in the local black hole mass function, which remain substantial, with estimates of the integrated black hole mass density ρ • spanning the range 3 − 5.5 × 10 5 M ⊙ Mpc −3 . We find good agreement with estimates of the local mass function for a reference model where all active black holes have a fixed efficiency ǫ = 0.065 and L bol /L Edd ≈ 0.4 (shifting to ǫ = 0.09, L bol /L Edd ≈ 0.9 for the Hopkins et al. luminosity function). In our reference model, the duty cycle of 10 9 M ⊙ black holes declines from 0.07 at z = 3 to 0.004 at z = 1 and 10 −4 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. Models with reduced Eddington ratios at low redshift or black hole mass predict fewer low mass black holes (M • 10 8 M ⊙ ) in the local universe, while models with black hole mergers predict more black holes at M • > 10 9 M ⊙ . Matching the integrated AGN emissivity to the local black hole mass density implies ǫ = 0.075 × (ρ • /4.5 × 10 5 M ⊙ Mpc −3 ) −1 for our standard luminosity function estimate, or 25% higher for Hopkins et al.'s estimate. It is difficult to reconcile current observations with a model in which most black holes have the high efficiencies ǫ ≈ 0.16−0.20 predicted by MHD simulations of disk accretion. We provide electronic tabulations of our bolometric luminosity function and our reference model predictions for black hole mass functions and duty cycles as a function of redshift.

We provide fits to the distribution of galaxy luminosity, size, velocity dispersion and stellar mass as a function of concentration index C r and morphological type in the Sloan Digital Sky Survey (SDSS). (Our size estimate, a simple analogue of the SDSS cmodel magnitude, is new: it is computed using a combination of seeing-corrected quantities in the SDSS data base, and is in substantially better agreement with results from more detailed bulge/disc decompositions.) We also quantify how estimates of the fraction of 'early'-or 'late'-type galaxies depend on whether the samples were cut in colour, concentration or light profile shape, and compare with similar estimates based on morphology. Our fits show that ellipticals account for about 20 per cent of the r-band luminosity density, ρ L r , and 25 per cent of the stellar mass density, ρ * ; including S0s and Sas increases these numbers to 33 per cent and 40 per cent, and 50 per cent and 60 per cent, respectively. The values of ρ L r and ρ * , and the mean sizes, of E, E+S0 and E+S0+Sa samples are within 10 per cent of those in the Hyde & Bernardi, C r ≥ 2.86 and C r ≥ 2.6 samples, respectively. Summed over all galaxy types, we find ρ * ∼ 3 × 10 8 M Mpc −3 at z ∼ 0. This is in good agreement with expectations based on integrating the star formation history. However, compared to most previous work, we find an excess of objects at large masses, up to a factor of ∼10 at M * ∼ 5 × 10 11 M . The stellar mass density further increases at large masses if we assume different initial mass functions for elliptical and spiral galaxies, as suggested by some recent chemical evolution models, and results in a better agreement with the dynamical mass function.We also show that the trend for ellipticity to decrease with luminosity is primarily because the E/S0 ratio increases at large L. However, the most massive galaxies, M * ≥ 5 × 10 11 M , are less concentrated and not as round as expected if one extrapolates from lower L, and they are not well fit by pure deVaucouleur laws. This suggests formation histories with recent radial mergers. Finally, we show that the age-size relation is flat for ellipticals of fixed dynamical mass, but, at fixed M dyn , S0s and Sas with large sizes tend to be younger. Hence, samples selected on the basis of colour or C r will yield different scalings. Explaining this difference between E and S0 formation is a new challenge for models of early-type galaxy formation.

In addition to the large systematic differences arising from assumptions about the stellar mass-to-light ratio, the massive end of the stellar mass function is rather sensitive to how one fits the light profiles of the most luminous galaxies. We quantify this by comparing the luminosity and stellar mass functions based on SDSS cmodel magnitudes, and PyMorph single-Sersic and Sersic-Exponential fits to the surface brightness profiles of galaxies in the SDSS. The PyMorph fits return more light, so that the predicted masses are larger than when cmodel magnitudes are used. As a result, the total stellar mass density at z ∼ 0.1 is about 1.2× larger than in our previous analysis of the SDSS. The differences are most pronounced at the massive end, where the measured number density of objects having M * ≥ 6 × 10 11 M ⊙ is ∼ 5× larger. Alternatively, at number densities of 10 −6 Mpc −3 , the limiting stellar mass is 2× larger. The differences with respect to fits by other authors, typically based on Petrosian-like magnitudes, are even more dramatic, although some of these differences are due to sky-subtraction problems, and are sometimes masked by large differences in the assumed M * /L (even after scaling to the same IMF). Our results impact studies of the growth and assembly of stellar mass in galaxies, and of the relation between stellar and halo mass, so we provide simple analytic fits to these new luminosity and stellar mass functions and quantify how they depend on morphology, as well as the binned counts in electronic format. While these allow one to quantify the differences which arise because of the assumed light profile, and we believe our Sersic-Exponential based results to be the most realistic of the models we have tested, we caution that which profile is the most appropriate at the high mass end is still debated.