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In the ellipsoidal collapse model, the critical density for the collapse of a gravitationally bound object is a function of its mass. In the excursion set formalism, this translates into a moving barrier problem such that the mass function of dark matter haloes is given by the first crossing probability of a random walker across the barrier. In this paper, we study this first crossing probability analytically. Complete solutions are obtained for barriers that vary as square root of time and square of time. Large and small time asymptotic behaviour is derived. For arbitrary power-law barriers, the large time behaviour is determined. The solutions allow us to derive useful inferences about the scaling of the conditional mass function in terms of present day halo masses and look back redshifts. As an application of our results, we compare the estimates of major merger rates of haloes in constant and moving barrier models and find that for massive haloes ($10^{12-13} M_\odot$) the latter predicts significantly higher merger rates towards high redshifts ($z \gtrsim 4$), Comment: 12 pages, 12 figures

An empirically motivated model is presented for accretion-dominated growth of the super massive black holes (SMBH) in galaxies, and the implications are studied for the evolution of the quasar population in the universe. We investigate the core aspects of the quasar population, including space density evolution, evolution of the characteristic luminosity, plausible minimum masses of quasars, the mass function of SMBH and their formation epoch distribution. Our model suggests that the characteristic luminosity in the quasar luminosity function arises primarily as a consequence of a characteristic mass scale above which there is a systematic separation between the black hole and the halo merging rates. At lower mass scales, black hole merging closely tracks the merging of dark halos. When combined with a declining efficiency of black hole formation with redshift, the model can reproduce the quasar luminosity function over a wide range of redshifts. The observed space density evolution of quasars is well described by formation rates of SMBH above $\sim 10^8 M_\odot$. The inferred mass density of SMBH agrees with that found independently from estimates of the SMBH mass function derived empirically from the quasar luminosity function., Comment: 15 pages, 16 figures

Observations on galactic scales seem to be in contradiction with recent high resolution N-body simulations. This so-called cold dark matter (CDM) crisis has been addressed in several ways, ranging from a change in fundamental physics by introducing self-interacting cold dark matter particles to a tuning of complex astrophysical processes such as global and/or local feedback. All these efforts attempt to soften density profiles and reduce the abundance of satellites in simulated galaxy halos. In this contribution we are exploring the differences between a Warm Dark Matter model and a CDM model where the power on a certain scale is reduced by introducing a narrow negative feature (''dip''). This dip is placed in a way so as to mimic the loss of power in the WDM model: both models have the same integrated power out to the scale where the power of the Dip model rises to the level of the unperturbed CDM spectrum again. Using N-body simulations we show that that the new Dip model appears to be a viable alternative to WDM while being based on different physics: where WDM requires the introduction of a new particle species the Dip stems from a non-standard inflationary period. If we are looking for an alternative to the currently challenged standard LCDM structure formation scenario, neither the LWDM nor the new Dip model can be ruled out with respect to the analysis presented in this contribution. They both make very similar predictions and the degeneracy between them can only be broken with observations yet to come., Comment: 4 pages, 3 figures; to appear in "The Evolution of Galaxies III. From Simple Approaches to Self-Consistent Models", proceedings of the 3rd EuroConference on the evolution of galaxies, held in Kiel, Germany, July 16-20, 2002

Observations on galactic scales seem to be in contradiction with recent high resolution N-body simulations. This so-called cold dark matter (CDM) crisis has been addressed in several ways, ranging from a change in fundamental physics by introducing self-interacting cold dark matter particles to a tuning of complex astrophysical processes such as global and/or local feedback. All these efforts attempt to soften density profiles and reduce the abundance of satellites in simulated galaxy halos. In this paper, we explore a somewhat different approach which consists of filtering the dark matter power spectrum on small scales, thereby altering the formation history of low mass objects. The physical motivation for damping these fluctuations lies in the possibility that the dark matter particles have a different nature i.e. are warm (WDM) rather than cold. We show that this leads to some interesting new results in terms of the merger history and large-scale distribution of low mass halos, as compared to the standard CDM scenario. However, WDM does not appear to be the ultimate solution, in the sense that it is not able to fully solve the CDM crisis, even though one of the main drawbacks, namely the abundance of satellites, can be remedied. Indeed, the cuspiness of the halo profiles still persists, at all redshifts, and for all halos and sub-halos that we investigated. Despite the persistence of the cuspiness problem of DM halos, WDM seems to be still worth taking seriously, as it alleviates the problems of overabundant sub-structures in galactic halos and possibly the lack of angular momentum of simulated disk galaxies. WDM also lessens the need to invoke strong feedback to solve these problems, and may provide a natural explanation of the clustering properties and ages of dwarfs., Comment: 11 pages, 17 figures, MNRAS submitted, high-res figures can be found at http://www-thphys.physics.ox.ac.uk/users/AlexanderKnebe/publications.html, replaced with accepted version (warmon masses corrected!)