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Register a new userVirial halo mass function in the ${it Planck}$ cosmology
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We study halo mass functions with high-resolution $N$-body simulations under a $Lambda$CDM cosmology. Our simulations adopt the cosmological model that is consistent with recent measurements of the cosmic microwave backgrounds with the ${it Planck}$ satellite. We calibrate the halo mass functions for $10^{8.5} lower.5exhbox{$; buildrel < over sim ;$} M_mathrm{vir} / (h^{-1}M_odot) lower.5exhbox{$; buildrel < over sim ;$} 10^{15.0 - 0.45 , z}$, where $M_mathrm{vir}$ is the virial spherical overdensity mass and redshift $z$ ranges from $0$ to $7$. The halo mass function in our simulations can be fitted by a four-parameter model over a wide range of halo masses and redshifts, while we require some redshift evolution of the fitting parameters. Our new fitting formula of the mass function has a 5%-level precision except for the highest masses at $zle 7$. Our model predicts that the analytic prediction in Sheth $&$ Tormen would overestimate the halo abundance at $z=6$ with $M_mathrm{vir} = 10^{8.5-10}, h^{-1}M_odot$ by $20-30%$. Our calibrated halo mass function provides a baseline model to constrain warm dark matter (WDM) by high-$z$ galaxy number counts. We compare a cumulative luminosity function of galaxies at $z=6$ with the total halo abundance based on our model and a recently proposed WDM correction. We find that WDM with its mass lighter than $2.71, mathrm{keV}$ is incompatible with the observed galaxy number density at a $2sigma$ confidence level.
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Luminous matter produces very energetic events, such as active galactic nuclei and supernova explosions, that significantly affect the internal regions of galaxy clusters. Although the current uncertainty in the effect of baryonic physics on cluster statistics is subdominant as compared to other systematics, the picture is likely to change soon as the amount of high-quality data is growing fast, urging the community to keep theoretical systematic uncertainties below the ever-growing statistical precision. In this paper, we study the effect of baryons on galaxy clusters, and their impact on the cosmological applications of clusters, using the Magneticum suite of cosmological hydrodynamical simulations. We show that the impact of baryons on the halo mass function can be recast in terms on a variation of the mass of the halos simulated with pure N-body, when baryonic effects are included. The halo mass function and halo bias are only indirectly affected. Finally, we demonstrate that neglecting baryonic effects on halos mass function and bias would significantly alter the inference of cosmological parameters from high-sensitivity next-generations surveys of galaxy clusters.
Studies of flux anomalies statistics and perturbations in stellar streams have the potential to constrain models of warm dark matter (WDM), including sterile neutrinos. Producing these constraints requires a parametrization of the WDM mass function relative to that of the cold dark matter (CDM) equivalent. We use five WDM models with half-mode masses, $M_mathrm{hm}=[1.3,35]times10^{8}$~$M_{odot}$, spread across simulations of the Local Group, lensing ellipticals and the $z=2$ universe, to generate such a parametrization: we fit parameters to a functional form for the WDM-to-CDM halo mass function ratio, $n_mathrm{WDM}(M_{X})/n_mathrm{CDM}(M_{X})$, of ($1+(alpha M_mathrm{hm}/M_{X})^{beta})^{gamma}$. For $M_{X}equiv$ virial mass of central halos we obtain $alpha=2.3$, $beta=0.8$, and $gamma=-1.0$, and this fit is steeper than the extended Press-Schechter formalism predicts. For $M_{X}equiv$ mass of subhalos we instead obtain $alpha=4.2$, $beta=2.5$ and $gamma=-0.2$; in both mass definitions the scatter is $sim20$~per~cent. The second fit typically underestimates the relative abundance of $z=2$ WDM subhaloes at the tens of per cent level. We caution that robust constraints will require bespoke simulations and a careful definition of halo mass, particularly for subhalos of mass $<10^{8}M_{odot}$.
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 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 present a new theory for the hierarchical clustering of dark matter (DM) halos based on stochastic differential equations, that constitutes a change of perspective with respect to existing frameworks (e.g., the excursion set approach); this work is specifically focused on the halo mass function. First, we present a stochastic differential equation that describes fluctuations in the mass growth of DM halos, as driven by a multiplicative white (Gaussian) noise dependent on the spherical collapse threshold and on the power spectrum of DM perturbations. We demonstrate that such a noise yields an average drift of the halo population toward larger masses, that quantitatively renders the standard hierarchical clustering. Then, we solve the Fokker-Planck equation associated to the stochastic dynamics, and obtain the Press & Schechter mass function as a (stationary) solution. Moreover, generalizing our treatment to a mass-dependent collapse threshold, we obtain an exact analytic solution capable of fitting remarkably well the N-body mass function over a wide range in mass and redshift. All in all, the new perspective offered by the theory presented here can contribute to better understand the gravitational dynamics leading to the formation, evolution and statistics of DM halos across cosmic times.
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