We extend the Halo Occupation Distribution (HOD) framework to generate mock galaxy catalogs exhibiting varying levels of galactic conformity, which has emerged as a potentially powerful probe of environmental effects in galaxy evolution. Our model co
rrelates galaxy colours in a group with the concentration of the common parent dark halo through a group quenching efficiency $rho$ which makes older, more concentrated halos $textit{at fixed mass}$ preferentially host redder galaxies. We find that, for a specific value of $rho$, this 1-halo conformity matches corresponding measurements in a group catalog based on the Sloan Digital Sky Survey. Our mocks also display conformity at large separations from isolated objects, potentially an imprint of halo assembly bias. A detailed study - using mocks with assembly bias erased while keeping 1-halo conformity intact - reveals a rather nuanced situation, however. At separations $lesssim 4$Mpc, conformity is mainly a 1-halo effect dominated by the largest halos and is $textit{not}$ a robust indicator of assembly bias. Only at very large separations ($gtrsim 8$Mpc) does genuine 2-halo conformity, driven by the assembly bias of small halos, manifest distinctly. We explain all these trends in standard Halo Model terms. Our model opens the door to parametrized HOD analyses that self-consistently account for galactic conformity at all scales.
We investigate potential systematic effects in constraining the amplitude of primordial fluctuations sigma_8 arising from the choice of halo mass function in the likelihood analysis of current and upcoming galaxy cluster surveys. We study the widely
used N-body simulation fit of Tinker et al. (T08) and, as an alternative, the recently proposed analytical model of Excursion Set Peaks (ESP). We first assess the relative bias between these prescriptions when constraining sigma_8 by sampling the ESP mass function to generate mock catalogs and using the T08 fit to analyse them, for various choices of survey selection threshold, mass definition and statistical priors. To assess the level of absolute bias in each prescription, we then repeat the analysis on dark matter halo catalogs in N-body simulations designed to mimic the mass distribution in the current data release of Planck SZ clusters. This N-body analysis shows that using the T08 fit without accounting for the scatter introduced when converting between mass definitions (alternatively, the scatter induced by errors on the parameters of the fit) can systematically over-estimate the value of sigma_8 by as much as 2sigma for current data, while analyses that account for this scatter should be close to unbiased in sigma_8. With an increased number of objects as expected in upcoming data releases, regardless of accounting for scatter, the T08 fit could over-estimate the value of sigma_8 by ~1.5sigma. The ESP mass function leads to systematically more biased but comparable results. A strength of the ESP model is its natural prediction of a weak non-universality in the mass function which closely tracks the one measured in simulations and described by the T08 fit. We suggest that it might now be prudent to build new unbiased ESP-based fitting functions for use with the larger datasets of the near future.
We investigate the problem of predicting the halo mass function from the properties of the Lagrangian density field. We focus on a perturbation spectrum with a small-scale cut-off (as in warm dark matter cosmologies). This cut-off results in a strong
suppression of low mass objects, providing additional leverage to rigorously test which perturbations collapse and to what mass. We find that all haloes are consistent with forming near peaks of the initial density field, with a strong correlation between proto-halo density and ellipticity. We demonstrate that, while standard excursion set theory with correlated steps completely fails to reproduce the mass function, the inclusion of the peaks constraint leads to the correct number of haloes but significantly underpredicts the masses of low-mass objects (with the predicted halo mass function at low masses behaving like dn/dln m ~ m^{2/3}). This prediction is very robust and cannot be easily altered within the framework of a single collapse barrier. The nature of collapse in the presence of a small-scale cut-off thus reveals that excursion set calculations require a more detailed understanding of the collapse-time of a general ellipsoidal perturbation to predict the ultimate collapsed mass of a peak -- a problem that has been hidden in the large abundance of small-scale structure in CDM. We demonstrate how this problem can be resolved within the excursion set framework.
