Large Scale Structure and Galaxies
large scale structures
Physical Sciences and Mathematics
These notes sketch the motivation for and ingredients of the Halo Model of nonlinear and biased structures in the Universe. A key part of this approach is the relation between halo abundances and their large scale clustering. These come from the excursion set approach, so I have taken the opportunity to collect together all the formulae associated with this approach into one place. These include expressions for: the unconditional mass function, the conditional mass function, the environmental dependence of the mass function, halo bias, merger rates, creation anddestruction rates, the distribution of half-mass assembly times, masses and mass at fixed assembly time. In addition, I discuss how the approach can be used to describe voids, filaments and sheets, as well as the nonlinear counts in cells distribution, and provide analytic formulae for a number of these statistics. Together these formulae show that, in hierarchical models: massive halos assemble their mass later than low mass halos; halos which assemble their mass abnormally late for their mass will tend to have experienced a recent major merger; if one is interested in the mass assembled in pieces which are above some mininum mass, then this happens earlier for the more massive halos; for similar reasons, the mass fraction in pieces which are between a fixed mass range reaches a maximum at higher redshifts for halos which are more massive today. The first trend may explain why the oldest stars tend to sit in massive objects; the second may be why star formation in massive objects ended earlier. This approach also shows that the mass function in dense regions should be ‘top-heavy’, and that more massive halos should be more strongly clustered. If galaxy properties are determined primarily by the mass of their parent halo, then many observed correlations with environment are a simple consequence of these trends. Finally, I summarize the Halo Model of galaxy clustering. I discuss how it describes typedependent clustering, particularly dependence on luminosity and color, and sketch how to use it to build accurate mock catalogs which include information about stellar mass, dust, and star formation history.