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Register a new userHalo mass function: Baryon impact, fitting formulae and implications for cluster cosmology
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We use a set of hydrodynamical (Hydro) and dark matter only (DMonly) simulations to calibrate the halo mass function (HMF). We explore the impact of baryons, propose an improved parametrization for spherical overdensity masses and identify differences between our DMonly HMF and previously published HMFs. We use the textit{Magneticum} simulations, which are well suited because of their accurate treatment of baryons, high resolution, and large cosmological volumes of up to $(3818~textrm{Mpc})^3$. Baryonic effects globally decrease the masses of galaxy clusters, which, at a given mass, results in a decrease of their number density. This effect vanishes at high redshift $zsim2$ and for high masses $M_{200textrm m}gtrsim10^{14}Modot$. We perform cosmological analyses of three idealized approximations to the cluster surveys by the South Pole Telescope (SPT), textit{Planck}, and eROSITA. We pursue two main questions: (1) What is the impact of baryons? -- For the SPT-like and the textit{Planck}-like samples, the impact of baryons on cosmological results is negligible. In the eROSITA-like case, however, neglecting the baryonic impact leads to an underestimate of $Omega_textrm m$ by about $0.01$, which is comparable to the expected uncertainty from eROSITA. (2) How does our DMonly HMF compare with previous work? -- For the textit{Planck}-like sample, results obtained using our DMonly HMF are shifted by $Delta(sigma_8)simeqDelta(sigma_8(Omega_textrm m/0.27)^{0.3})simeq0.02$ with respect to results obtained using the Tinker et al. (2008) fit. This suggests that using our HMF would shift results from textit{Planck} clusters toward better agreement with CMB anisotropy measurements. Finally, we discuss biases that can be introduced through inadequate HMF parametrizations that introduce false cosmological sensitivity.
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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.
The halo mass function (HMF) is a critical element in cosmological analyses of galaxy cluster catalogs. We quantify the impact of uncertainties in HMF parameters on cosmological constraints from cluster catalogs similar to those from Planck, those expected from the Euclid, Roman and Rubin surveys, and from a hypothetical larger future survey. We analyse simulated catalogs in each case, gradually loosening priors on HMF parameters to evaluate the degradation in cosmological constraints. While current uncertainties on HMF parameters do not substantially impact Planck-like surveys, we find that they can significantly degrade the cosmological constraints for a Euclid-like survey. Consequently, the current precision on the HMF will not be sufficient for Euclid (or Roman or Rubin) and possible larger surveys. Future experiments will have to properly account for uncertainties in HMF parameters, and it will be necessary to improve precision of HMF fits to avoid weakening constraints on cosmological parameters.
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 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.
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.
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