We construct merger trees based on the extended Press-Schechter theory (EPS) in order to study the merger rates of dark matter haloes over a range of present day mass ($10^{10}M_{\sun}\leq M_0 \leq10^{15}M_{\sun}$), progenitor mass $(5\times10^{-3}\leq ξ\leq1$) and redshift ($0\leq z\leq 3$). We used the first crossing distribution of a moving barrier of the form $B(S,z)=p(z)+q(z)S^γ$, proposed by Sheth & Tormen, to take into account the ellipsoidal nature of collapse. We find that the mean merger rate per halo $B_m/n$ depends on the halo mass $M$ as $M^{0.2}$ and on the redshift as $(\mathrm{d}δ_c(z)/\mathrm{d}z)^{1.1}$. Our results are in agreement with the predictions of N-body simulations and this shows the ability of merger-trees based on EPS theory to follow with a satisfactory agreement the results of N-body simulations and the evolution of structures in a hierarchical Universe.
Structure formation provides a strong test of any cosmic acceleration model because a successful dark energy model must not inhibit {\black or overpredict} the development of observed large-scale structures. Traditional approaches to studies of structure formation in the presence of dark energy or a modified gravity implement a modified Press-Schechter formalism, which relates the linear overdensities to the abundance of dark matter haloes it at the same time. We critically examine the universality of the Press-Schechter formalism for different cosmologies, and show that the halo abundance is …
Aims.We study the dependence of the halo abundance function (AF) on different environments in a whole-sky $Λ$CDM light-cone halo catalogue extending to z < 0.65, using a simple and well-defined halo isolation criterion. Methods. The isolation status of each individual dark matter halo is determined by the distance to its nearest neighbour, which defines the maximum spherical region devoid of halos above a threshold mass around it (although the true size of such region may be much larger since it is not necessarily spherical). A versatile double power-law Schechter function is used to fit the d…
We study the halo mass function and inner halo structure at high redshifts ($z\geq5$) for a suite of simulations within the structure formation ETHOS framework. Scenarios such as cold dark matter (CDM), thermal warm dark matter (WDM), and dark acoustic oscillations (DAO) of various strengths are contained in ETHOS with just two parameters $h_{\rm peak}$ and $k_{\rm peak}$, the amplitude and scale of the first DAO peak. The Extended Press-Schechter (EPS) formalism with a smooth-$k$ filter is able to predict the cut-off in the halo mass function created by the suppression of small scale power in…
Dark matter haloes have long been recognized as one of the fundamental building blocks of large scale structure formation models. Despite their importance -- or perhaps because of it! -- halo definitions continue to evolve towards more physically motivated criteria. Here, we propose a new definition that is physically motivated, and effectively unique and parameter-free: ''A dark matter halo is comprised of the collection of particles orbiting in their own self-generated potential.'' This definition is enabled by the fact that, even with as few as $\approx 300$ particles per halo, nearly every…
We study halo mass functions with the Press-Schechter formalism for interacting dark matter models, where matter power spectra are damped due to dark acoustic oscillations in the early universe. After adopting a smooth window function, we calibrate the analytical model with numerical simulations from the "effective theory of structure formation" (ETHOS) project and fix the model parameters in the high mass regime, $M_{\rm h}\gtrsim3\times10^{10}\;{\rm M}_{\odot}$. We also perform high-resolution cosmological simulations with halo masses down to $M_{\rm h}\sim10^8\;{\rm M}_{\odot}$ to cover a w…
Lagrangian algorithms to simulate the evolution of cold dark matter (CDM) are invaluable tools to generate large suites of mock halo catalogues. In this paper, we first show that the main limitation of current semi-analytical schemes to simulate the displacement of CDM is their inability to model the evolution of overdensities in the initial density field, a limit that can be circumvented by detecting halo particles in the initial conditions. We thus propose `MUltiscale Spherical Collapse Lagrangian Evolution Using Press-Schechter' (muscle-ups), a new scheme that reproduces the results from La…
We derive an estimate of the rate of formation of dark matter halos per unit volume as a function of the halo mass and redshift of formation. Analytical estimates of the number density of dark matter halos are useful in modeling several cosmological phenomena. We use the excursion set formalism for computing the formation rate of dark matter halos. We use an approach that allows us to differentiate between major and minor mergers, as this is a pertinent issue for semi-analytic models of galaxy formation. We compute the formation rate for the Press-Schechter and the Sheth-Tormen mass function. …
We use path integrals in order to estimate merger rates of dark matter haloes using the Extended Press-Schechter approximation (EPS) for the Spherical Collapse (SC) and the Ellipsoidal Collapse (EC) models. Merger rates have been calculated for masses in the range $10^{10}M_{\odot}\mathrm{h}^{-1}$ to $10^{14}M_{\odot}\mathrm{h}^{-1}$ and for redshifts $z$ in the range 0 to 3. A detailed comparison between these models is presented. Path approach gives a better agreement with the exact solutions for constrained distributions than the approach of \cite{shto02}. Although this improvement seems no…
The simple, conventional dark matter halo mass definitions commonly used in cosmological simulations ("virial" mass, FoF mass, $M_{50,100,200,...}$) only capture part of the collapsed material and are therefore inconsistent with the halo mass concept used in analytical treatments of structure formation. Simulations have demonstrated that typical dark matter particle orbits extend out to about 90 per cent of their turnaround radius, which results in apocenter passages outside of the current "virial" radius on the first and also on the second orbit. Here we describe how the formation history of …
We calculate merger rates of dark matter haloes using the Extended Press-Schechter approximation (EPS) for the Spherical Collapse (SC) and the Ellipsoidal Collapse (EC) models. Merger rates have been calculated for masses in the range $10^{10}M_{\odot}\mathrm{h}^{-1}$ to $10^{14}M_{\odot}\mathrm{h}^{-1}$ and for redshifts $z$ in the range 0 to 3 and they have been compared with merger rates that have been proposed by other authors as fits to the results of N-body simulations. The detailed comparison presented here shows that the agreement between the analytical models and N-body simulations de…
Press-Schechter theory gives a simple, approximate functional form of the mass function of dark matter haloes. Sheth and Tormen (ST) refined this mass function to give an improved analytical fit to results of N-body simulations. These forms of the halo mass function are universal (independent of cosmology and power spectrum) when scaled in suitable variables. Using large suites of LCDM N-body simulations, studies in the last few years have shown that this universality is only approximate. We explore whether some of the deviations from universality can be attributed to the power spectrum by com…
Dark matter haloes in Lambda CDM simulations grow by mergers with other haloes as well as accretion of "diffuse" non-halo material. We quantify the mass growth rates via these two processes, dM_mer/dt and dM_dif/dt, and their dependence on halo environment using the ~500,000 haloes in the Millennium simulation. Adopting a local mass density parameter as a measure of halo environment, we find the two rates show strong but opposite environmental dependence, with mergers playing an increasingly important role for halo growths in overdense regions and diffuse accretion dominating growth in voids. …
The nature of dark matter (DM) is still under intense debate. Sub-galactic scales are particularly critical, as different, currently viable DM models make diverse predictions on the expected abundance and density profile of DM haloes on these scales. We investigate the ability of sub-galactic DM haloes to act as strong lenses on background compact sources, producing gravitational lensing events on milli-arcsecond scales (milli-lenses), for different DM models. For each DM scenario, we explore whether a sample of $\sim$ 5000 distant sources is sufficient to detect at least one milli-lens. We de…
Galaxy clusters are luminous tracers of the most massive dark matter haloes in the Universe. To use them as a cosmological probe, a detailed description of the properties of dark matter haloes is required. We characterize how the dynamical state of haloes impacts the halo mass function at the high-mass end. We used the dark matter-only MultiDark suite of simulations and the high-mass objects M > 2.7e13 M/h therein. We measured mean relations of concentration, offset, and spin as a function of halo mass and redshift. We investigated the distributions around the mean relations. We measured the h…
Halo merger trees describe the hierarchical mass assembly of dark matter haloes, and are the backbone for modeling galaxy formation and evolution. Merger trees constructed using Monte Carlo algorithms based on the extended Press-Schechter (EPS) formalism are complementary to those extracted from N-body simulations, and have the advantage that they are not trammeled by limited numerical resolution and uncertainties in identifying (sub)haloes and linking them between snapshots. This paper compares multiple EPS-based merger tree algorithms to simulation results using four diagnostics: progenitor …
Several independent cosmological tests have shown evidences that the energy density of the Universe is dominated by a dark energy component, which cause the present accelerated expansion. The large scale structure formation can be used to probe dark energy models, and the mass function of dark matter haloes is one of the best statistical tools to perform this study. We present here a statistical analysis of mass functions of galaxies under a homogeneous dark energy model, proposed in the work of Percival (2005), using an observational flux-limited X-ray cluster survey, and CMB data from WMAP. …
We present a modification of the Press-Schechter (PS) formalism to derive general mass functions for primordial black holes (PBHs), considering their formation as being associated to the amplitude of linear energy density fluctuations. To accommodate a wide range of physical relations between the linear and non-linear conditions for collapse, we introduce an additional parameter to the PS mechanism, and that the collapse occurs at either a given cosmic time, or as fluctuations enter the horizon. We study the case where fluctuations obey Gaussian statistics and follow a primordial power spectru…
We present results of a study of the virial state of high redshift dark matter haloes in an N-body simulation. We find that the majority of collapsed, bound haloes are not virialized at any redshift slice in our study ($z=15-6$) and have excess kinetic energy. At these redshifts, merging is still rampant and the haloes cannot strictly be treated as isolated systems. To assess if this excess kinetic energy arises from the environment, we include the surface pressure term in the virial equation explicitly and relax the assumption that the density at the halo boundary is zero. Upon inclusion of t…
Scalar Field Dark Matter (SFDM) comprised of ultralight bosons has attracted great interest as an alternative to standard, collisionless Cold Dark Matter (CDM) because of its novel structure-formation dynamics, described by the coupled Schrödinger-Poisson equations. In the free-field ("fuzzy") limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength, but resembles CDM on larger scales. Virialized haloes have "solitonic" cores of radius $\simλ_\text{deB}$, surrounded by CDM-like envelopes. When a strong enough repulsive self-interaction (SI) is also present, structure can be …
We introduce a simple analytic model of galaxy formation that links the growth of dark matter haloes in a cosmological background to the build-up of stellar mass within them. The model aims to identify the physical processes that drive the galaxy-halo co-evolution through cosmic time. The model restricts the role of baryonic astrophysics to setting the relation between galaxies and their haloes. Using this approach, galaxy properties can be directly predicted from the growth of their host dark matter haloes. We explore models in which the effective star formation efficiency within haloes is a …
The claimed detection of large amounts of substructure in lensing flux anomalies, and in Milky Way stellar stream gaps statistics, has lead to a step change in constraints on simple warm dark matter models. In this study we compute predictions for the halo mass function both for these simple models and also for comprehensive particle physics models of sterile neutrinos and dark acoustic oscillations. We show that the mass function fit of Lovell et al. underestimates the number of haloes less massive than the half-mode mass, $M_\mathrm{hm}$ by a factor of 2, relative to the extended Press-Schec…
We use the Extended-Press-Schechter (EPS) formalism to study halo assembly histories in a standard $Λ$CDM cosmology. A large ensemble of Monte Carlo random walks provides the {\it entire} halo membership histories of a representative set of dark matter particles, which we assume to be neutralinos. The first generation halos of most particles do not have a mass similar to the free-streaming cut-off $M_{f.s.}$ of the neutralino power spectrum, nor do they form at high redshift. Median values are $M_1 = 10^5$ to $10^7M_{f.s.}$ and $z_1 = 13$ to 8 depending on the form of the collapse barrier assu…
We present a theoretical analysis of some unexplored aspects of relaxed Bose-Einstein condensate dark matter (BECDM) haloes. This type of ultralight bosonic scalar field dark matter is a viable alternative to the standard cold dark matter (CDM) paradigm, as it makes the same large-scale predictions as CDM and potentially overcomes CDM's small-scale problems via a galaxy-scale de Broglie wavelength. We simulate BECDM halo formation through mergers, evolved under the Schrödinger-Poisson equations. The formed haloes consist of a soliton core supported against gravitational collapse by the quantum…
Any successful model of galaxy formation needs to explain the low rate of star formation in the small progenitors of today's galaxies. This inefficiency is necessary for reproducing the low stellar-to-virial mass fractions, suggested by current abundance matching models. A possible driver of this low efficiency is the radiation pressure exerted by ionizing photons from massive stars. The effect of radiation pressure in cosmological, zoom-in galaxy formation simulations is modeled as a non-thermal pressure that acts only in dense and optically thick star-forming regions. We also include photoio…
A modification of the Press-Schechter theory allowing for presence of a background large-scale structure (LSS) - a supercluster or a void, is proposed. The LSS is accounted as the statistical constraints in form of linear functionals of the random overdensity field. The deviation of the background density within the LSS is interpreted in a pseudo-cosmological sense. Using the constraints formalism may help us to probe non-trivial spatial statistics of haloes, e.g. edge and shape effects on boundaries of the superclusters and voids. Parameters of the constraints are connected to features of the…
We train a machine learning algorithm to learn cosmological structure formation from N-body simulations. The algorithm infers the relationship between the initial conditions and the final dark matter haloes, without the need to introduce approximate halo collapse models. We gain insights into the physics driving halo formation by evaluating the predictive performance of the algorithm when provided with different types of information about the local environment around dark matter particles. The algorithm learns to predict whether or not dark matter particles will end up in haloes of a given mas…
Modelling the growth histories of specific galaxies often involves generating the entire population of objects that arise in a given cosmology and selecting systems with appropriate properties. This approach is highly inefficient when targeting rare systems such as the extremely luminous high-redshift galaxy candidates detected by JWST. Here, we present a novel framework for generating merger trees with branches that are guaranteed to achieve a desired halo mass at a chosen redshift. This method augments extended Press Schechter theory solutions with constrained random processes known as Brown…
Unified dark matter models are appealing in that they describe the dark sector in terms of a single component. They however face problems when attempting to account for structure formation: in the linear regime, density fluctuations can become Jeans stable and oscillate rather than collapse, though it is possible that this difficulty may be circumvented by invoking nonlinear clustering. Here we examine the behaviour in the fully nonlinear regime, of collapsed objects that should mimic standard dark matter haloes. It is shown that the pressure gradient associated with the unified dark matter fl…
The thermal Sunyaev-Zel'dovich (tSZ) effect offers a means of probing the hot gas in and around massive galaxies and galaxy groups and clusters, which is thought to constitute a large fraction of the baryon content of the Universe. The Planck collaboration recently performed a stacking analysis of a large sample of `locally brightest galaxies' (LBGs) and, surprisingly, inferred an approximately self-similar relation between the tSZ flux and halo mass. At face value, this implies that the hot gas mass fraction is independent of halo mass, a result which is in apparent conflict with resolved X-r…
We study the effect of baryons on the abundance of structures and substructures in a Lambda-CDM cosmology, using a pair of high resolution cosmological simulations from the GIMIC project. Both simulations use identical initial conditions, but while one contains only dark matter, the other also includes baryons. We find that gas pressure, reionisation, supernova feedback, stripping, and truncated accretion systematically reduce the total mass and the abundance of structures below ~10^12 solar masses compared to the pure dark matter simulation. Taking this into account and adopting an appropriat…
The virial theorem prescribes the ratio of the globally-averaged equatorial to vertical velocity dispersion of a tracer population in spherical and flattened dark haloes. This gives sequences of physical models in the plane of global anisotropy and flattening. The tracer may have any density, though there are particularly simple results for power-laws and exponentials. We prove the flattening theorem: for a spheroidally stratified tracer density with axis ratio q in a dark density potential with axis ratio g, the ratio of globally averaged equatorial to vertical velocity dispersion depends onl…
$Λ$CDM-model predicts an excess of dark halos compared to the observations. The excess is seen from the estimates of the virialized mass inside the Local Supercluster and its surroundings. It is shown that account for cosmological velocity fluctuations in the process of formation of the population of dark halos it is possible to eliminate this contradiction remaining within the framework of the $Λ$CDM cosmology. Based on the formalism of Press and Schechter, we suggest a model of formation of dark halo population which takes into account the kinematic effects in the dark matter. The model allo…
Ultralight-axion (ULA) dark matter is one of the possible solutions to resolve small-scale problems, especially the core-cusp problem. This is because ULA dark matter can create a central soliton core in all dark matter haloes stemmed from the quantum pressure against gravity below the de Broglie wavelength, which becomes manifest on astrophysical scales with axion mass range $\sim10^{-22}$ eV. In this work, we apply our non-spherical dynamical models to the kinematic data of eight classical dwarf spheroidals (dSphs) to obtain more reliable and realistic limits on ULA particle mass. This is mo…
Analytical $f(R)$-gravity models introduce Yukawa-like corrections to the Newtonian potential in the weak field limit. These models can explain the dynamics of galaxies and cluster of galaxies without requiring dark matter. To test the model, we have computed the pressure profile of 579 X-ray galaxy clusters assuming the gas is in hydrostatic equilibrium within the potential well of the modified gravitational potential. We have compared those profiles with the ones measured in the foreground cleaned SMICA released by the Planck Collaboration. Our results show that Extended Theories of Gravity …
In the warm dark matter scenario, the Press-Schechter formalism is valid only for galaxy masses greater than the "velocity dispersion cut-off". In this work we extend the predictions to masses below the velocity dispersion cut-off, and thereby address the "Missing Satellites Problem", and the rest-frame ultra-violet luminosity cut-off required to not exceed the measured reionization optical depth. We find agreement between predictions and observations of these two phenomena. As a by-product, we obtain the empirical Tully-Fisher relation from first principles.
We introduce a modification of the Press-Schechter formalism aimed to derive general mass functions for primordial black holes (PBHs). In this case, we start from primordial power spectra (PPS) which include a monochromatic spike, typical of ultra slow-roll inflation models. We consider the PBH formation as being associated to the amplitude of the spike on top of the linear energy density fluctuations, coming from a PPS with a blue index. By modelling the spike with a log-normal function, we study the properties of the resulting mass function spikes, and compare these to the underlying extende…
We measure the stellar mass function (SMF) of galaxies in the COSMOS field up to $z\sim6$. We select them in the near-IR bands of the COSMOS2015 catalogue, which includes ultra-deep photometry from UltraVISTA-DR2, SPLASH, and Subaru/Hyper-SuprimeCam. At $z>2.5$ we use new precise photometric redshifts with error $σ_z=0.03(1+z)$ and an outlier fraction of $12\%$, estimated by means of the unique spectroscopic sample of COSMOS. The increased exposure time in the DR2, along with our panchromatic detection strategy, allow us to improve the stellar mass completeness at high $z$ with respect to prev…
