The Mass Function and Average Mass Loss Rate of Dark Matter Subhaloes

We present a simple, semi-analytical model to compute the mass functions of dark matter subhaloes. The masses of subhaloes at their time of accretion are obtained from a standard merger tree. During the subsequent evolution, the subhaloes experience mass loss due to the combined effect of dynamical friction, tidal stripping, and tidal heating. Rather than integrating these effects along individual subhalo orbits, we consider the average mass loss rate, where the average is taken over all possible orbital configurations. This allows us to write the average mass loss rate as a simple function that depends only on redshift and on the instantaneous mass ratio of subhalo and parent halo. After calibrating the model by matching the subhalo mass function (SHMF) of cluster-sized dark matter haloes obtained from numerical simulations, we investigate the predicted mass and redshift dependence of the SHMF.We find that, contrary to previous claims, the subhalo mass function is not universal. Instead, both the slope and the normalization depend on the ratio of the parent halo mass, M, and the characteristic non-linear mass M*. This simply reflects a halo formation time dependence; more massive parent haloes form later, thus allowing less time for mass loss to operate. We analyze the halo-to-halo scatter, and show that the subhalo mass fraction of individual haloes depends most strongly on their accretion history in the last Gyr. Finally we provide a simple fitting function for the average SHMF of a parent halo of any mass at any redshift and for any cosmology, and briefly discuss several implications of our findings.Comment: Replaced to match version accepted for publication in MNRAS. Small section added that discusses higher-order moments of subhalo occupation distribution (including a new figure). Otherwise, few small change

Can giant radio halos probe the merging rate of galaxy clusters?

Radio and X-ray observations of galaxy clusters probe a direct link between cluster mergers and giant radio halos (RH), suggesting that these sources can be used as probes of the cluster merging rate with cosmic time. In this paper we carry out an explorative study that combines the observed fractions of merging clusters (fm) and RH (fRH) with the merging rate predicted by cosmological simulations and attempt to infer constraints on merger properties of clusters that appear disturbed in X-rays and of clusters with RH. We use morphological parameters to identify merging systems and analyze the currently largest sample of clusters with radio and X-ray data (M500>6d14 Msun, and 0.2<z<0.33, from the Planck SZ cluster catalogue). We found that in this sample fm~62-67% while fRH~44-51%. The comparison of the theoretical f_m with the observed one allows to constrain the combination (xi_m,tau_m), where xi_m and tau_m are the minimum merger mass ratio and the timescale of merger-induced disturbance. Assuming tau_m~ 2-3 Gyr, as constrained by simulations, we find that the observed f_m matches the theoretical one for xi_m~0.1-0.18. This is consistent with optical and near-IR observations of clusters in the sample (xi_m~0.14-0.16). The fact that RH are found only in a fraction of merging clusters may suggest that merger events generating RH are characterized by larger mass ratio; this seems supported by optical/near-IR observations of RH clusters in the sample (xi_min~0.2-0.25). Alternatively, RH may be generated in all mergers but their lifetime is shorter than \tau_m (by ~ fRH/fm). This is an explorative study, however it suggests that follow up studies using the forthcoming radio surveys and adequate numerical simulations have the potential to derive quantitative constraints on the link between cluster merging rate and RH at different cosmic epochs and for different cluster masses.Comment: 10 pages, 3 figures, accepted for publication in A&

Selecting background galaxies in weak-lensing analysis of galaxy clusters

In this paper, we present a new method to select the faint, background galaxies used to derive the mass of galaxy clusters by weak lensing. The method is based on the simultaneous analysis of the shear signal, that should be consistent with zero for the foreground, unlensed galaxies, and of the colors of the galaxies: photometric data from the COSMic evOlution Survey are used to train the color selection. In order to validate this methodology, we test it against a set of state-of-the-art image simulations of mock galaxy clusters in different redshift [$0.23-0.45$] and mass [$0.5-1.55\times10^{15}M_\odot$] ranges, mimicking medium-deep multicolor imaging observations (e.g. SUBARU, LBT). The performance of our method in terms of contamination by unlensed sources is comparable to a selection based on photometric redshifts, which however requires a good spectral coverage and is thus much more observationally demanding. The application of our method to simulations gives an average ratio between estimated and true masses of $\sim 0.98 \pm 0.09$. As a further test, we finally apply our method to real data, and compare our results with other weak lensing mass estimates in the literature: for this purpose we choose the cluster Abell 2219 ($z=0.228$), for which multi-band (BVRi) data are publicly available.Comment: MNRAS, Accepted 2016 February 2

The mass function and average mass-loss rate of dark matter subhaloes

We present a simple, semi-analytical model to compute the mass functions of dark matter subhaloes. The masses of subhaloes at their time of accretion are obtained from a standard merger tree. During the subsequent evolution, the subhaloes experience mass loss due to the combined effect of dynamical friction, tidal stripping, and tidal heating. Rather than integrating these effects along individual subhalo orbits, we consider the average mass-loss rate, where the average is taken over all possible orbital configurations. Under the Ansatz that the average distribution of orbits is independent of parent halo mass, this allows us to write the average mass-loss rate as a simple function that depends only on redshift and on the instantaneous mass ratio of subhalo and parent halo. After calibrating this model by matching the subhalo mass function (SHMF) of cluster-sized dark matter haloes obtained from high-resolution, numerical simulations, we investigate the predicted mass and redshift dependence of the SHMF. We find that, contrary to previous claims, the subhalo mass function is not universal. Instead, both the slope and the normalization depend on the ratio of the parent halo mass, M, and the characteristic non-linear mass M*. This simply reflects a halo formation time dependence; more massive parent haloes form later, thus allowing less time for mass loss to operate. We predict that galaxy-sized haloes, with a present-day mass of M≃ 1012 h−1 M⊙, have an average mass fraction of dark matter subhaloes that is a factor of 3 lower than for massive clusters with M≃ 1015 h−1 M⊙. We also analyse the halo-to-halo scatter in SHMFs, and show that the subhalo mass fraction of individual haloes depends most strongly on their accretion history in the last ∼1 Gyr. Finally we provide a simple fitting function for the average SHMF of a parent halo of any mass at any redshift and for any cosmology, and briefly discuss several implications of our finding

The Substructure Hierarchy in Dark Matter Haloes

We present a new algorithm for identifying the substructure within simulated dark matter haloes. The method is an extension of that proposed by Tormen et al. (2004) and Giocoli et al. (2008a), which identifies a subhalo as a group of self-bound particles that prior to being accreted by the main progenitor of the host halo belonged to one and the same progenitor halo (hereafter satellite). However, this definition does not account for the fact that these satellite haloes themselves may also have substructure, which thus gives rise to sub-subhaloes, etc. Our new algorithm identifies substructures at all levels of this hierarchy, and we use it to determine the mass function of all substructure (counting sub-haloes, sub-subhaloes, etc.). On average, haloes which formed more recently tend to have a larger mass fraction in substructure and to be less concentrated than average haloes of the same mass. We provide quantitative fits to these correlations. Even though our algorithm is very different from that of Gao et al. (2004), we too find that the subhalo mass function per unit mass at redshift z = 0 is universal. This universality extends to any redshift only if one accounts for the fact that host haloes of a given mass are less concentrated at higher redshifts, and concentration and substructure abundance are anti-correlated. This universality allows a simple parametrization of the subhalo mass function integrated over all host halo masses, at any given time. We provide analytic fits to this function which should be useful in halo model analyses which equate galaxies with halo substructure when interpreting clustering in large sky surveys. Finally, we discuss systematic differences in the subhalo mass function that arise from different definitions of (host) halo mass.Comment: 18 pages, 24 figures, accepted for publication on MNRA

Turbulent pressure support and hydrostatic mass-bias in the intracluster medium

The degree of turbulent pressure support by residual gas motions in galaxy clusters is not well known. Mass modelling of combined X-ray and Sunyaev Zel'dovich observations provides an estimate of turbulent pressure support in the outer regions of several galaxy clusters. Here, we test two different filtering techniques to disentangle bulk from turbulent motions in non-radiative high-resolution cosmological simulations of galaxy clusters using the cosmological hydro code ENZO. We find that the radial behavior of the ratio of non-thermal pressure to total gas pressure as a function of cluster-centric distance can be described by a simple polynomial function. The typical non-thermal pressure support in the centre of clusters is $\sim$5%, increasing to $\sim$15% in the outskirts, in line with the pressure excess found in recent X-ray observations. While the complex dynamics of the ICM makes it impossible to reconstruct a simple correlation between turbulent motions and hydrostatic bias, we find that a relation between them can be established using the median properties of a sample of objects. Moreover, we estimate the contribution of radial accelerations to the non-thermal pressure support and conclude that it decreases moving outwards from 40% (in the core) to 15% (in the cluster's outskirts). Adding this contribution to one provided by turbulence, we show that it might account for the entire observed hydrostatic bias in the innermost regions of the clusters, and for less than 80% of it at $r > 0.8 r_{200, m}$.Comment: 20 pages; 21 figures; Substantial Revision; MNRAS in pres

Cosmic degeneracies III: N-body simulations of Interacting Dark Energy with non-Gaussian initial conditions

We perform for the first time N-body simulations of interacting dark energy assuming non-Gaussian initial conditions, with the aim of investigating possible degeneracies of these two theoretically independent phenomena in different observational probes. We focus on the large-scale matter distribution, as well as on the statistical and structural properties of collapsed haloes and cosmic voids. On very large scales, we show that it is possible to choose the interaction and non-Gaussian parameters such that their effects on the halo power spectrum cancel, and the power spectrum is indistinguishable from a \u39b cold dark matter (\u2060\u39bCDM) model. On small scales, measurements of the non-linear matter power spectrum, halo-matter bias, halo and subhalo mass function, and cosmic void number function validate the degeneracy determined on large scales. However, the internal structural properties of haloes and cosmic voids, namely halo concentration\u2013mass relation and void density profile, are very different from those measured in the \u39bCDM model, thereby breaking the degeneracy. In practice, the values of fNL required to cancel the effect of interaction are already ruled by observations. Our results show in principle that the combination of large- and small-scale probes is needed to constrain interacting dark energy and primordial non-Gaussianity separately

Cosmic degeneracies III: N-body simulations of interacting dark energy with non-Gaussian initial conditions

We perform for the first time N-body simulations of interacting dark energy assuming non- Gaussian initial conditions, with the aim of investigating possible degeneracies of these two theoretically independent phenomena in different observational probes.We focus on the largescale matter distribution, as well as on the statistical and structural properties of collapsed haloes and cosmic voids. On very large scales, we show that it is possible to choose the interaction and non-Gaussian parameters such that their effects on the halo power spectrum cancel, and the power spectrum is indistinguishable from a \u39b cold dark matter (\u39bCDM) model. On small scales, measurements of the non-linear matter power spectrum, halo-matter bias, halo and subhalomass function, and cosmic void number function validate the degeneracy determined on large scales. However, the internal structural properties of haloes and cosmic voids, namely halo concentration-mass relation and void density profile, are very different from those measured in the \u39bCDM model, thereby breaking the degeneracy. In practice, the values of fNLrequired to cancel the effect of interaction are already ruled by observations. Our results show in principle that the combination of large- and small-scale probes is needed to constrain interacting dark energy and primordial non-Gaussianity separately

The Population of Dark Matter Subhaloes: Mass Functions and Average Mass Loss Rates

Using a cosmological N-Body simulation and a sample of re-simulated cluster-like haloes, we study the mass loss rates of dark matter subhaloes, and interpret the mass function of subhaloes at redshift zero in terms of the evolution of the mass function of systems accreted by the main halo progenitor. When expressed in terms of the ratio between the mass of the subhalo at the time of accretion and the present day host mass the unevolved subhalo mass function is found to be universal. However, the subhalo mass function at redshift zero clearly depends on $M_0$, in that more massive host haloes host more subhaloes. To relate the unevolved and evolved subhalo mass functions, we measure the subhalo mass loss rate as a function of host mass and redshift. We find that the average, specific mass loss rate of dark matter subhaloes depends mainly on redshift. These results suggest a pleasingly simple picture for the evolution and mass dependence of the evolved subhalo mass function. Less massive host haloes accrete their subhaloes earlier, which are thus subjected to mass loss for a longer time. In addition, their subhaloes are typically accreted by denser hosts, which causes an additional boost of the mass loss rate. To test the self-consistency of this picture, we use a merger trees constructed using the extended Press-Schechter formalism, and evolve the subhalo populations using the average mass loss rates obtained from our simulations, finding the subhalo mass functions to be in good agreement with the simulations. [abridged]Comment: 12 pages, 12 figures; submitted to MNRA

Cosmic voids in modified gravity models with massive neutrinos

Cosmic voids are progressively emerging as a new viable cosmological probe. Their abundance and density profiles are sensitive to modifications of gravity, as well as to dark energy and neutrinos. The main goal of this work is to investigate the possibility of exploiting cosmic void statistics to disentangle the degeneracies resulting from a proper combination of f(R) modified gravity and neutrino mass. We use N-body simulations to analyse the density profiles and size function of voids traced by both dark matter particles and haloes. We find clear evidence of the enhancement of gravity in f(R) cosmologies in the void density profiles at z = 1. However, these effects can be almost completely overridden by the presence of massive neutrinos because of their thermal free streaming. Despite the limited volume of the analysed simulations does not allow us to achieve a statistically relevant abundance of voids larger than 40 Mpc h-1, we find that the void size function at high redshifts and for large voids is potentially an effective probe to disentangle these degenerate cosmological models, which is key in the prospective of the upcoming wide-field redshift surveys