Halo abundances within the cosmic web

We investigate the dependence of the mass function of dark-matter haloes on their environment within the cosmic web of large-scale structure. A dependence of the halo mass function on large-scale mean density is a standard element of cosmological theory, allowing mass-dependent biasing to be understood via the peak-background split. On the assumption of a Gaussian density field, this analysis can be extended to ask how the mass function depends on the geometrical environment: clusters, filaments, sheets and voids, as classified via the tidal tensor (the Hessian matrix of the gravitational potential). In linear theory, the problem can be solved exactly, and the result is attractively simple: the conditional mass function has no explicit dependence on the local tidal field, and is a function only of the local density on the filtering scale used to define the tidal tensor. There is nevertheless a strong implicit predicted dependence on geometrical environment, because the local density couples statistically to the derivatives of the potential. We compute the predictions of this model and study the limits of their validity by comparing them to results deduced empirically from $N$-body simulations. We have verified that, to a good approximation, the abundance of haloes in different environments depends only on their densities, and not on their tidal structure. In this sense we find relative differences between halo abundances in different environments with the same density which are smaller than 13%. Furthermore, for sufficiently large filtering scales, the agreement with the theoretical prediction is good, although there are important deviations from the Gaussian prediction at small, non-linear scales. We discuss how to obtain improved predictions in this regime, using the 'effective-universe' approach.Comment: 14 pages, 6 figures. Revision matching journal versio

Fourier analysis of luminosity-dependent galaxy clustering

We extend the Fourier transform based method for the analysis of galaxy redshift surveys of Feldman, Kaiser & Peacock (1994: FKP) to model luminosity-dependent clustering. In a magnitude limited survey, galaxies at high redshift are more luminous on average than galaxies at low redshift. Galaxy clustering is observed to increase with luminosity, so the inferred density field is effectively multiplied by an increasing function of radius. This has the potential to distort the shape of the recovered power spectrum. In this paper we present an extension of the FKP analysis method to incorporate this effect, and present revised optimal weights to maximize the precision of such an analysis. The method is tested and its accuracy assessed using mock catalogues of the 2-degree field galaxy redshift survey (2dFGRS). We also show that the systematic effect caused by ignoring luminosity-dependent bias was negligible for the initial analysis of the 2dFGRS of Percival et al. (2001). However, future surveys, sensitive to larger scales, or covering a wider range of galaxy luminosities will benefit from this refined method.Comment: 9 pages, 4 figures, accepted for publication in MNRA

Overmerging and M/L ratios in phenomenological galaxy formation models

We show that the discrepancy between the Tully-Fisher relation and the luminosity function predicted by most phenomenological galaxy formation models is mainly due to overmerging of galaxy haloes. We have circumvented this overmerging problem, which is inherent in both the Press-Schechter formalism and dissipationless N-body simulations, by including a specific galaxy halo formation recipe into an otherwise standard N-body code. This numerical technique provides the merger trees which, together with simplified gas dynamics and star formation physics, constitute our implementation of a phenomenological galaxy formation model. Resolving the overmerging problem provides us with the means to match both the I-band Tully-Fisher relation and the B and K band luminosity functions within an EdS sCDM structure formation scenario. It also allows us to include models for chemical evolution and starbursts, which improves the match to observational data and renders the modelling more realistic. We show that the inclusion of chemical evolution into the modelling requires a significant fraction of stars to be formed in short bursts triggered by merging events.Comment: 15 pages, 7 figures, to be published in MNRA

Extended Hernquist-Springel formalism for cosmic star formation

We present a revised and extended version of the analytic model for cosmic star formation originally given by Hernquist & Springel in 2003. The key assumption of this formalism is that star formation proceeds from cold gas, at a rate that is limited by an internal consumption timescale at early times, or by the rate of generation of gas via cooling at late times. These processes are analysed as a function of the mass of dark matter haloes and integrated over the halo population. We modify this approach in two main ways to make it more general: (1) halo collapse times are included explicitly, so that the behaviour is physically reasonable at late times; (2) allowance is made for a mass-dependent baryon fraction in haloes, which incorporates feedback effects. This model reproduces the main features of the observed baryonic Tully-Fisher relationship, and is consistent with observational estimates of the baryon mass fraction in the intergalactic medium. With minimal adjustment of parameters, our approach reproduces the observed history of cosmic star formation within a factor of two over the redshift range $0 < z < 10$. This level of agreement is comparable to that achieved by state-of-the-art cosmological simulations. Our simplified apparatus has pedagogical value in illuminating the results of such detailed calculations, and also serves as a means for rapid approximate exploration of non-standard cosmological models.Comment: submitted to MNRA