We incorporate a simple scheme for the growth of supermassive black holes into semi‐analytic models that follow the formation and evolution of galaxies in a cold dark matter‐dominated Universe. We assume that supermassive black holes are formed and fuelled during major mergers. If two galaxies of comparable mass merge, their central black holes coalesce and a few per cent of the gas in the merger remnant is accreted by the new black hole over a time‐scale of a few times 107 yr. With these simple assumptions, our model not only fits many aspects of the observed evolution of galaxies, but also reproduces quantitatively the observed relation between bulge luminosity and black hole mass in nearby galaxies, the strong evolution of the quasar population with redshift, and the relation between the luminosities of nearby quasars and those of their host galaxies. The strong decline in the number density of quasars from z∼2 to z=0 is a result of the combination of three effects: (i) a decrease in the merging rate; (ii) a decrease in the amount of cold gas available to fuel black holes, and (iii) an increase in the time‐scale for gas accretion. The predicted decline in the total content of cold gas in galaxies is consistent with that inferred from observations of damped Lyα systems. Our results strongly suggest that the evolution of supermassive black holes, quasars and starburst galaxies is inextricably linked to the hierarchical build‐up of galaxies.

The matter power spectrum at comoving scales of (1−40) h −1 Mpc is very sensitive to the presence of Warm Dark Matter (WDM) particles with large free streaming lengths. We present constraints on the mass of WDM particles from a combined analysis of the matter power spectrum inferred from the large samples of high resolution high signal-to-noise Lyman-α forest data of Kim et al. (2004) and Croft et al. (2002) and the cosmic microwave background data of WMAP. We obtain a lower limit of mWDM ∼ > 550 eV (2σ) for early decoupled thermal relics and mWDM ∼ > 2.0 keV (2σ) for sterile neutrinos. We also investigate the case where in addition to cold dark matter a light thermal gravitino with fixed effective temperature contributes significantly to the matter density. In that case the gravitino density is proportional to its mass, and we find an upper limit m 3/2 ∼ < 16 eV (2σ).This translates into a bound on the scale of supersymmetry breaking, Λsusy ∼ < 260 TeV, for models of supersymmetric gauge mediation in which the gravitino is the lightest supersymmetric particle.

We present updated constraints on the free-streaming of warm dark matter (WDM) particles derived from an analysis of the Lyman-flux power spectrum measured from high-resolution spectra of 25 z > 4 quasars obtained with the Keck High Resolution Echelle Spectrometer and the Magellan Inamori Kyocera Echelle spectrograph. We utilize a new suite of high-resolution hydrodynamical simulations that explore WDM masses of 1, 2 and 4 keV (assuming the WDM consists of thermal relics), along with different physically motivated thermal histories. We carefully address different sources of systematic error that may affect our final results and perform an analysis of the Lyman-flux power with conservative error estimates. By using a method that samples the multidimensional astrophysical and cosmological parameter space, we obtain a lower limit m WDM * 3:3 keV (2) for warm dark matter particles in the form of early decoupled thermal relics. Adding the Sloan Digital Sky Survey Lyman-flux power spectrum does not improve this limit. Thermal relics of masses 1, 2 and 2.5 keV are disfavored by the data at about the 9, 4 and 3 C.L., respectively. Our analysis disfavors WDM models where there is a suppression in the linear matter power spectrum at (nonlinear) scales corresponding to k ¼ 10h=Mpc which deviates more than 10% from a Lambda cold dark matter model. Given this limit, the corresponding ''free-streaming mass'' below which the mass function may be suppressed is $2 Â 10 8 h À1 M . There is thus very little room for a contribution of the free-streaming of WDM to the solution of what has been termed the small scale crisis of cold dark matter.

A model of the density distribution in the intergalactic medium, motivated by that found in numerical simulations, is used to demonstrate the effect of a clumpy IGM and discrete sources on the reionization of the universe. In an inhomogeneous universe reionization occurs outside-in, starting in voids and gradually penetrating into overdense regions. Reionization should not be sudden but gradual, with a continuous rise of the photon mean free path over a fair fraction of the Hubble time as the emissivity increases. We show that a hydrogen Gunn-Peterson trough should be present at $z\simeq 6$ unless the emissivity increases with redshift at $z>4$. However, the epoch of overlap of cosmological \hii regions could have occurred at a higher redshift if sources of low luminosity reionized the IGM; the Gunn-Peterson trough at $z\sim 6$ would then appear because even the most underdense voids have a large enough neutral fraction in ionization equilibrium to be optically thick to \lya photons. Cosmological \hii regions near the epoch of overlap can produce gaps of transmitted flux only if luminous quasars contributed to the reionization. Despite the clumpiness of the matter distribution, recombinations are not very important during the reionization of hydrogen because the high density gas is not ionized until a late time. We show that the \heii reionization was most likely delayed relative to the hydrogen reionization, but should be completed by $z\sim 3$, the redshift where observations are available. The reported large optical depth fluctuations of \heii are probably not due to an incomplete \heii reionization, but arise from a combination of density fluctuations and the variations in the intensity of the ionizing background due to luminous QSO's.Comment: to be published in The Astrophysical Journa