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It has been recently shown that any halo velocity bias present in the initial conditions does not decay to unity, in agreement with predictions from peak theory. However, this is at odds with the standard formalism based on the coupled fluids approximation for the coevolution of dark matter and halos. Starting from conservation laws in phase space, we discuss why the fluid momentum conservation equation for the biased tracers needs to be modified in accordance with the change advocated in Baldauf, Desjacques & Seljak (2014). Our findings indicate that a correct description of the halo properties should properly take into account peak constraints when starting from the Vlasov-Boltzmann equation.
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Dark matter halo clustering depends not only on halo mass, but also on other properties such as concentration and shape. This phenomenon is known broadly as assembly bias. We explore the dependence of assembly bias on halo definition, parametrized by spherical overdensity parameter, $Delta$. We summarize the strength of concentration-, shape-, and spin-dependent halo clustering as a function of halo mass and halo definition. Concentration-dependent clustering depends strongly on mass at all $Delta$. For conventional halo definitions ($Delta sim 200mathrm{m}-600mathrm{m}$), concentration-dependent clustering at low mass is driven by a population of haloes that is altered through interactions with neighbouring haloes. Concentration-dependent clustering can be greatly reduced through a mass-dependent halo definition with $Delta sim 20mathrm{m}-40mathrm{m}$ for haloes with $M_{200mathrm{m}} lesssim 10^{12}, h^{-1}mathrm{M}_{odot}$. Smaller $Delta$ implies larger radii and mitigates assembly bias at low mass by subsuming altered, so-called backsplash haloes into now larger host haloes. At higher masses ($M_{200mathrm{m}} gtrsim 10^{13}, h^{-1}mathrm{M}_{odot}$) larger overdensities, $Delta gtrsim 600mathrm{m}$, are necessary. Shape- and spin-dependent clustering are significant for all halo definitions that we explore and exhibit a relatively weaker mass dependence. Generally, both the strength and the sense of assembly bias depend on halo definition, varying significantly even among common definitions. We identify no halo definition that mitigates all manifestations of assembly bias. A halo definition that mitigates assembly bias based on one halo property (e.g., concentration) must be mass dependent. The halo definitions that best mitigate concentration-dependent halo clustering do not coincide with the expected average splashback radii at fixed halo mass.
The simplest analyses of halo bias assume that halo mass alone determines halo clustering. However, if the large scale environment is fixed, then halo clustering is almost entirely determined by environment, and is almost completely independent of halo mass. We show why. Our analysis is useful for studies which use the environmental dependence of clustering to constrain cosmological and galaxy formation models. It also shows why many correlations between galaxy properties and environment are merely consequences of the underlying correlations between halos and their environments, and provides a framework for quantifying such inherited correlations.
If the formation of central galaxies in dark matter haloes traces the assembly history of their host haloes, in haloes of fixed mass, central galaxy clustering may show dependence on properties indicating their formation history. Such a galaxy assembly bias effect has been investigated by Lin et al. 2016, with samples of central galaxies constructed in haloes of similar mass and with mean halo mass verified by galaxy lensing measurements, and no significant evidence of assembly bias is found from the analysis of the projected two-point correlation functions of early- and late-forming central galaxies. In this work, we extend the the investigation of assembly bias effect from real space to redshift (velocity) space, with an extended construction of early- and late-forming galaxies. We carry out halo occupation distribution modelling to constrain the galaxy-halo connection to see whether there is any sign of the effect of assembly bias. We find largely consistent host halo mass for early- and late-forming central galaxies, corroborated by lensing measurements. The central velocity bias parameters, which are supposed to characterise the mutual relaxation between central galaxies and their host haloes, are inferred to overlap between early- and late-forming central galaxies. However, we find a large amplitude of velocity bias for early-forming central galaxies (e.g. with central galaxies moving at more than 50% that of dark matter velocity dispersion inside host haloes), which may signal an assembly bias effect. A large sample with two-point correlation functions and other clustering measurements and improved modelling will help reach a conclusive result.
We study the impact of theoretical uncertainty in the dark matter halo mass function and halo bias on dark energy constraints from imminent galaxy cluster surveys. We find that for an optical cluster survey like the Dark Energy Survey, the accuracy required on the predicted halo mass function to make it an insignificant source of error on dark energy parameters is ~ 1%. The analogous requirement on the predicted halo bias is less stringent (~ 5%), particularly if the observable-mass distribution can be well constrained by other means. These requirements depend upon survey area but are relatively insensitive to survey depth. The most stringent requirements are likely to come from a survey over a significant fraction of the sky that aims to observe clusters down to relatively low mass, Mth ~ 10^13.7 Msun/h; for such a survey, the mass function and halo bias must be predicted to accuracies of ~ 0.5% and ~ 1%, respectively. These accuracies represent a limit on the practical need to calibrate ever more accurate halo mass and bias functions. We find that improving predictions for the mass function in the low-redshift and low-mass regimes is the most effective way to improve dark energy constraints.
We derive a simple prescription for including beyond-linear halo bias within the standard, analytical halo-model power spectrum calculation. This results in a corrective term that is added to the usual two-halo term. We measure this correction using data from $N$-body simulations and demonstrate that it can boost power in the two-halo term by a factor of $sim2$ at scales $ksim0.7,h Mpc^{-1}$, with the exact magnitude of the boost determined by the specific pair of fields in the two-point function. How this translates to the full power spectrum depends on the relative strength of the one-halo term, which can mask the importance of this correction to a greater or lesser degree, again depending on the fields. Generally we find that our correction is more important for signals that arise from lower-mass haloes. When comparing our calculation to simulated data we find that the under-prediction of power in the transition region between the two- and one-halo terms, which typically plagues halo-model calculations, is almost completely eliminated when including the full non-linear halo bias. We show improved results for the auto and cross spectra of galaxies, haloes and matter. In the specific case of matter-matter or matter-halo power we note that a large fraction of the improvement comes from the non-linear biasing between low- and high-mass haloes. We envisage our model being useful in the analytical modelling of cross correlation signals. Our non-linear bias halo-model code is available at https://github.com/alexander-mead/BNL
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