Darren S. Reed

Halo mass function and the free streaming scale

The nature of structure formation around the particle free streaming scale is still far from understood. Many attempts to simulate hot, warm, and cold dark matter cosmologies with a free streaming cuto have been performed with cosmological particlebased simulations, but they all suer from spurious structure formation at scales below their respective free streaming scales { i.e. where the physics of halo formation is most aected by free streaming. We perform a series of high resolution numerical simulations of dierent warm dark matter (WDM) models, and develop an approximate method to subtract articial structures in the measured halo mass function. The corrected measurements are then used to construct and calibrate an extended Press-Schechter (EPS) model with sharp-k window function and adequate mass assignment. The EPS model gives accurate predictions for the low redshift halo mass function of CDM and WDM models, but it signicantly under-predicts the halo abundance at high redshifts. By taking into account the ellipticity of the initial patches and connecting the characteristic lter scale to the smallest ellipsoidal axis, we are able to eliminate this inconsistency and obtain an accurate mass function over all redshifts and all dark matter particle masses covered by the simulations. As an additional application we use our model to predict the microhalo abundance of the standard neutralino-CDM scenario and we give the rst quantitative prediction of the mass function over the full range of scales of CDM structure formation.

Dark matter subhaloes in numerical simulations

We use cosmologicalCDM numerical simulations to model the evolution of the substructure population in sixteen dark matter haloes with resolutions of up to seven million particles within the virial radius. The combined substructure circular velocity distribution function (VDF) for hosts of 10 11 to 10 14 M⊙ at redshifts from zero to two or higher has a self-similar shape, is independent of host halo mass and redshift, and follows the relation dn/dv = (1/8)(vcmax/vcmax,host) −4 . Halo to halo variance in the VDF is a factor of roughly two to four. At high redshifts, we find preliminary evidence for fewer large substructure haloes (subhaloes). Specific angular momenta are significantly lower for subhaloes nearer the host halo centre where tidal stripping is more effective. The radial distribution of subhaloes is marginally consistent with the mass profile for r > � 0.3rvir, where the possibility of artificial numerical disruption of subhaloes can be most reliably excluded by our convergence study, although a subhalo distribution that is shallower than the mass profile is favoured. Subhalo masses but not circular velocities decrease toward the host centre. Subhalo velocity dispersions hint at a positive velocity bias at small radii. There is a weak bias toward more circular orbits at lower redshift, especially at small radii. We additionally model a cluster in several power law cosmologies of P / k n , and demonstrate that a steeper spectral index, n, results in significantly less substructure.

The Structure of Halos: Implications for Group and Cluster Cosmology

The dark matter halo mass function is a key repository of cosmological information over a wide range of mass scales, from individual galaxies to galaxy clusters. N-body simulations have established that the friends-of-friends (FOF) mass function has a universal form to a surprising level of accuracy (10%). The high-mass tail of the mass function is exponentially sensitive to the amplitude of the initial density perturbations, the mean matter density parameter, Ω m , and to the dark energy controlled late-time evolution of the density field. Observed group and cluster masses, however, are usually stated in terms of a spherical overdensity (SO) mass which does not map simply to the FOF mass. Additionally, the widely used halo models of structure formation—and halo occupancy distribution descriptions of galaxies within halos—are often constructed exploiting the universal form of the FOF mass function. This again raises the question of whether FOF halos can be simply related to the notion of a spherical overdensity mass. By employing results from Monte Carlo realizations of ideal Navarro-Frenk-White (NFW) halos and N-body simulations, we study the relationship between the two definitions of halo mass. We find that the vast majority of halos (80%-85%) in the mass-range 1012.5-1015.5 h –1 M ☉ indeed allow for an accurate mapping between the two definitions (~5%), but only if the halo concentrations are known. Nonisolated halos fall into two broad classes: those with complex substructure that are poor fits to NFW profiles and those bridged by the (isodensity-based) FOF algorithm. A closer investigation of the bridged halos reveals that the fraction of these halos and their satellite mass distribution is cosmology dependent. We provide a preliminary discussion of the theoretical and observational ramifications of these results.

Towards an accurate mass function for precision cosmology

Cosmological surveys aim to use the evolution of the abundance of galaxy clusters to accurately constrain the cosmological model. In the context of CDM, we show that it is possible to achieve the required percent level accuracy in the halo mass function with gravity-only cosmological simulations, and we provide simulation start and run parameter guidelines for doing so. Some previous works have had sucient statistical precision, but lacked robust verication of absolute accuracy. Convergence tests of the mass function with, for example, simulation start redshift can exhibit false convergence of the mass function due to counteracting errors, potentially misleading one to infer overly optimistic estimations of simulation accuracy. Percent level accuracy is possible if initial condition particle mapping uses second order Lagrangian Perturbation Theory, and if the start epoch is between 10 and 50 expansion factors before the epoch of halo formation of interest. The mass function for halos with fewer than 1000 particles is highly sensitive to simulation parameters and start redshift, implying a practical minimum mass resolution limit due to mass discreteness. The narrow range in converged start redshift suggests that it is not presently possible for a single simulation to capture accurately the cluster mass function while also starting early enough to model accurately the numbers of reionisation era galaxies, whose baryon feedback processes may aect later cluster properties. Ultimately, to fully exploit current and future cosmological surveys will require accurate modeling of baryon physics and observable properties, a formidable challenge for which accurate gravity-only simulations are just an initial step.

The first generation of star‐forming haloes

We model gas cooling in high-resolution N-body simulations in order to investigate the formation of the first generation of stars. We follow a region of a Lambda cold dark matter (�CDM) universe especially selected to contain a rich cluster by the present day. The properties of the dark haloes that form in these subsolar mass-resolution simulations are presented in a companion paper by Gao et al. The first gas clouds able to cool by molecular hydrogen (H2)-line emission collapse at extremely high redshift, z ≈ 47, when the mass of the dark halo is 2.4 × 10 5 h −1 M� .B yz ≈ 30, a substantial population of haloes are capable of undergoing molecular hydrogen cooling although their ability to form stars is dependent on the efficiency of feedback processes such as dissociating Lyman‐Werner radiation. The mass of the main halo grows extremely rapidly and, by z ≈ 36, its virial temperature has reached 10 4 K, at which point gas cooling becomes dominated by more effective atomic processes. By z ≈ 30, a small ‘group’ of such potential galaxies will have formed unless prevented from doing so by feedback processes. By this redshift, massive (100 M � ) Population III stars are able to ionize gas well beyond their own host halo and neighbouring H II regions can percolate to form an ionized superbubble. Such patches would be too widely separated to contribute significantly to reionization at this time. The large number density of early cooling haloes in the pre-reionized universe raises the exciting prospect that this ultra-early generation of stars may be observable as gamma-ray bursts or supernovae. Ke yw ords: methods: N-body simulations ‐ galaxies: formation ‐ galaxies: haloes ‐ cosmology: theory ‐ dark matter.

Matter power spectrum and the challenge of percent accuracy

Future galaxy surveys require one percent precision in the theoretical knowledge of the power spectrum over a large range including very nonlinear scales. While this level of accuracy is easily obtained in the linear regime with perturbation theory, it represents a serious challenge for small scales where numerical simulations are required. In this paper we quantify the precision of present-day

Hints against the cold and collisionless nature of dark matter from the galaxy velocity function

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Non‐universality of halo profiles and implications for dark matter experiments

-body methods, identifying main potential error sources from the set-up of initial conditions to the measurement of the final power spectrum. We directly compare three widely used

The clustering of the first galaxy haloes

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The age dependence of galaxy clustering

-body codes, Ramses, Pkdgrav3, and Gadget3 which represent three main discretisation techniques: the particle-mesh method, the tree method, and a hybrid combination of the two. For standard run parameters, the codes agree to within one percent at