Press-Schechter Model Research Articles

Quantifying the Tension between Cosmological Models and JWST Red Candidate Massive Galaxies

We develop a Python tool to estimate the tail distribution of the number of dark matter halos beyond a mass threshold and in a given volume in a light-cone. The code is based on the extended Press–Schechter model and is computationally efficient, typically taking a few seconds on a personal laptop for a given set of cosmological parameters. The high efficiency of the code allows a quick estimation of the tension between cosmological models and the red candidate massive galaxies released by the James Webb Space Telescope, as well as scanning the theory space with the Markov Chain Monte Carlo method. As an example application, we use the tool to study the cosmological implication of the candidate galaxies presented in Labbé et al. The standard Λ cold dark matter (ΛCDM) model is well consistent with the data if the star formation efficiency can reach ∼0.3 at high redshift. For a low star formation efficiency ϵ ∼ 0.1, the ΛCDM model is disfavored at ∼2σ–3σ confidence level.

Implications of multi-axion dark matter on structure formation

Axions are candidates for dark matter in the universe.We develop an accurate Boltzmann code to calculate the linear growth of the plasma. As an interesting example, we investigate a mixed dark matter model consisting of cold dark matter (CDM) and two-axion dark matter. We analyze the growth of the structure numerically and analytically. We find that an effective single axion with an effective mass and an effective abundance is useful to characterize the two-axion cosmology. Moreover, we generalize the effective single axion description to multi-axion dark matter cosmology. We also compare the results with those of warm dark matter (WDM) model. Moreover, we calculate halo mass functions for the mixed model by using the Press-Schechter model and linear perturbations and then determine the mass function as a function of masses and axion abundance.

A systematic search for galaxy proto-cluster cores at z ∼ 2

ABSTRACT A proto-cluster core is the most massive dark matter halo (DMH) in a given proto-cluster. To reveal the galaxy formation in core regions, we search for proto-cluster cores at z ∼ 2 in ${\sim}1.5\, \mathrm{deg}^{2}$ of the COSMOS field. Using pairs of massive galaxies [log (M*/M⊙) ≥ 11] as tracers of cores, we find 75 candidate cores, among which 54 per cent are estimated to be real. A clustering analysis finds that these cores have an average DMH mass of $2.6_{-0.8}^{+0.9}\times 10^{13}\, \mathrm{M}_{\odot }$, or $4.0_{-1.5}^{+1.8}\, \times 10^{13} \, \mathrm{M}_{\odot }$ after contamination correction. The extended Press–Schechter model shows that their descendant mass at z = 0 is consistent with Fornax-like or Virgo-like clusters. Moreover, using the IllustrisTNG simulation, we confirm that pairs of massive galaxies are good tracers of DMHs massive enough to be regarded as proto-cluster cores. We then derive the stellar mass function (SMF) and the quiescent fraction for member galaxies of the 75 candidate cores. We find that the core galaxies have a more top-heavy SMF than field galaxies at the same redshift, showing an excess at log (M*/M⊙) ≳ 10.5. The quiescent fraction, $0.17_{-0.04}^{+0.04}$ in the mass range 9.0 ≤ log (M*/M⊙) ≤ 11.0, is about three times higher than that of field counterparts, giving an environmental quenching efficiency of $0.13_{-0.04}^{+0.04}$. These results suggest that stellar mass assembly and quenching are accelerated as early as z ∼ 2 in proto-cluster cores.

Void Formation: Does the Void-in-Cloud Process Matter?

Abstract We investigate the basic properties of voids from high resolution, cosmological N-body simulations of Λ–dominated cold dark matter (ΛCDM) models, in order to compare with the analytical model of Sheth and van de Weygaert (SvdW) for void statistics. For the subsample of five dark matter simulations in the ΛCDM cosmology with box sizes ranging from 1000h−1Mpc to 8 h−1Mpc, we find that the standard void–in–cloud effect is too simplified to explain several properties of identified small voids in simulations. (i) The number density of voids is found to be larger than the prediction of the analytical model up to 2 orders of magnitude below 1h−1Mpc scales. The Press-Schechter model with the linear critical threshold of void δv = −2.71, or a naive power law, is found to provide an excellent agreement with the void size function, suggesting that the void-in-cloud effect does not suppress as much voids as predicted by the SvdW model. (ii) We then measured the density and velocity profiles of small voids, and find that they are mostly partially collapsing underdensities, instead of being completely crushed in the standard void–in–cloud scenario. (iii) Finally, we measure the void distributions in four different tidal environments, and find that the void–in-void effect alone can explain the correlation between distribution and environments, whereas the void–in–cloud effect is only weakly influencing the abundance of voids, even in filaments and clusters.

A systematic search for galaxy proto-cluster cores at z ∼ 2

AbstractA proto-cluster core is the most massive dark matter halo (DMH) in a given proto-cluster. To reveal the galaxy formation in core regions, we search for proto-cluster cores at z ˜ 2 in ˜1.5deg2 of the COSMOS field. Using pairs of massive galaxies (log (M*/Mʘ) ≥ 11) as tracers of cores, we find 75 candidate cores. A clustering analysis and the extended Press-Schechter model show that their descendant mass at z = 0 is consistent with Fornax-like or Virgo-like clusters. Moreover, using the IllustrisTNG simulation, we confirm that pairs of massive galaxies are good tracers of DMHs massive enough to be regarded as proto-cluster cores. We then derive the stellar mass function and the quiescent fraction for member galaxies of the 75 candidate cores. We find that stellar mass assembly and quenching are accelerated as early as z ˜ 2 in proto-cluster cores.

The mass function of dark halos in superclusters and voids

A modification of the Press-Schechter model for the mass function of the dark halos, whose population develops in the presence of a supercluster or a cosmological void, is proposed. The large-scale structure is specified as a set of statistical constraints in the form of linear functionals that are applied to the initial overdensity field. The parameters and values of these functionals are related to properties of the large-scale structure: its mean density, spatial scales, and shape. The model is applied to the simple case of a spherically symmetric background structure to demonstrate a procedure for recovering these parameters by fitting the halo mass function.

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 cutoff have been performed with cosmological particle-based simulations, but they all suffer from spurious structure formation at scales below their respective free streaming scales -- i.e. where the physics of halo formation is most affected by free streaming. We perform a series of high resolution numerical simulations of different WDM models, and develop an approximate method to subtract artificial 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 significantly under-predicts the halo abundance at high redshifts. By taking into account the ellipticity of the initial patches and connecting the characteristic filter 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 first quantitative prediction of the mass function over the full range of scales of CDM structure formation.

Dark matter halo growth - II. Diffuse accretion and its environmental dependence

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. This behaviour is independent of the mass cuts used to define haloes vs non-haloes. For galaxy-scale haloes, these two opposite correlations largely cancel out, but a weak environmental dependence remains that results in a slightly lower mean total growth rate, and hence an earlier mean formation redshift, for haloes in denser regions. The mean formation redshift of the ~5000 cluster-mass haloes, on the other hand, appears to have no correlation with halo environment. The origin of the positive correlation of dM_mer/dt with local density can be traced to the surrounding mass reservoir outside the haloes, where more progenitor haloes are available in denser regions. The negative correlation of dM_dif/dt with density, however, is not explained by the available diffuse mass in the reservoir, which is in fact larger in denser regions. The non-halo component may therefore be partially comprised of truly diffuse dark matter particles that are dynamically hotter and are accreted at a suppressed rate in denser regions. We also discuss the implications of these results for how to modify the Extended Press-Schechter model of halo growth, which in its original form does not predict environmental dependence.

Tidal effects and the environment dependence of halo assembly

We explore a possible origin for the puzzling anti-correlation between the formation epoch of galactic dark-matter haloes and their environment density. This correlation has been revealed from cosmological N-body simulations and is in conflict with the Extended Press-Schechter model of halo clustering. Using similar simulations, we first quantify the straightforward association of an early formation epoch with a reduced mass growth rate at late times. We then find that a primary driver of suppressed growth, by accretion and mergers, is tidal effects dominated by a neighbouring massive halo. The tidal effects range from a slowdown of the assembly of haloes due to the shear along the large-scale filaments that feed the massive halo to actual mass loss in haloes that pass through the massive halo. Using the restricted three-body problem, we show that haloes are prone to tidal mass loss within 1.5 virial radii of a larger halo. Our results suggest that the dependence of formation epoch on environment density is a secondary effect induced by the enhanced density of haloes in filaments near massive haloes where the tides are strong. Our measures of assembly rate are particularly correlated with the tidal field at high redshifts z~1.

Environmental dependence of dark matter halo growth - I. Halo merger rates

In an earlier paper, we quantified the mean merger rate of dark matter haloes as a function of redshift z, descendant halo mass M 0 , and progenitor halo mass ratio ξ using the Millennium simulation of the A cold dark matter cosmology. Here, we broaden that study and investigate the dependence of the merger rate of haloes on their surrounding environment. A number of local mass overdensity variables, both including and excluding the halo mass itself, are tested as measures of a halo's environment. The simple functional dependence on z, M 0 , and ξ of the merger rate found in our earlier work, is largely preserved in different environments, but we find that the overall amplitude of the merger rate has a strong positive correlation with the environmental densities. For galaxy-mass haloes, we find mergers to occur ∼2.5 times more frequently in the densest regions than in voids at both z = 0 and higher redshifts. Higher mass haloes show similar trends. We present a fitting form for this environmental dependence that is a function of both mass and local density and valid out to z = 2. The amplitude of the progenitor (or conditional) mass function shows a similar correlation with local overdensity, suggesting that the extended Press-Schechter model for halo growth needs to be modified to incorporate environmental effects.

The nearly universal merger rate of dark matter haloes in ΛCDM cosmology

We construct merger trees from the largest data base of dark matter haloes to date provided by the Millennium Simulation to quantify the merger rates of haloes over a broad range of descendant halo mass (10 12 ≤ M 0 ≤ 1015 M ⊙ ), progenitor mass ratio (10 -3 ≤ ξ ≤ 1), and redshift (0 ≤ z ≤ 6). We find the mean merger rate per halo, Bin, to have very simple dependence on M 0 , ξ, and z, and propose a universal fitting form for B/n that is accurate to 10-20 per cent. Overall, B/n depends very weakly on the halo mass (oc M 0 0 .08) and scales as a power law in the progenitor mass ratio (oc ξ -2 ) for minor mergers (ξ ≤ 0.1) with a mild upturn for major mergers. As a function of time, we find the merger rate per Gyr to evolve roughly as (1 + z) nm with r m = 2-2.3, while the rate per unit redshift is nearly independent of z. Several tests are performed to assess how our merger rates are affected by e.g. the time interval between Millennium outputs, binary versus multiple progenitor mergers, and mass conservation and diffuse accretion during mergers. In particular, we find halo fragmentations to be a general issue in merger tree construction from N-body simulations and compare two methods for handling these events. We compare our results with predictions of two analytical models for halo mergers based on the extended Press-Schechter (EPS) model and the coagulation theory. We find that the EPS model overpredicts the major merger rates and underpredicts the minor merger rates by up to a factor of a few.

The halo mass function from the dark ages through the present day

We use an array of high-resolution N-body simulations to determine the mass function of dark matter haloes at redshifts 10-30. We develop a new method for compensating for the effects of finite simulation volume that allows us to find an approximation to the true 'global' mass function. By simulating a wide range of volumes at different mass resolution, we calculate the abundance of haloes of mass 10 5-12 h -1 M ⊙ . This enables us to predict accurately the abundance of the haloes that host the sources that reionize the Universe. In particular, we focus on the small mass haloes (≥10 5.5-6 h -1 M ⊙ ) likely to harbour Population III stars where gas cools by molecular hydrogen emission, early galaxies in which baryons cool by atomic hydrogen emission at a virial temperature of ∼10 4 K (∼10 7.5-8 h -1 M ⊙ ), and massive galaxies that may be observable at redshift ∼10. When we combine our data with simulations that include high-mass haloes at low redshift, we find that the best fit to the halo mass function depends not only on the linear overdensity, as is commonly assumed in analytic models, but also on the slope of the linear power spectrum at the scale of the halo mass. The Press-Schechter model gives a poor fit to the halo mass function in the simulations at all epochs; the Sheth-Tormen model gives a better match, but still overpredicts the abundance of rare objects at all times by up to 50 per cent. Finally, we consider the consequences of the recently released WMAP 3-yr cosmological parameters. These lead to much less structure at high redshift, reducing the number of z = 10 'mini-haloes' by more than a factor of two and the number of z=30 galaxy hosts by nearly four orders of magnitude. Code to generate our best-fitting halo mass function may be downloaded from http://icc.dur.ac.uk/Research/PublicDownloads/genmf.readme.html.

Masses of high-z galaxy hosting haloes from angular clustering and their evolution in the cold dark matter model★

We examine masses of hosting haloes of two photometrically selected high-z galaxy samples: the old passively evolving galaxies (OPEGs) at z ∼ 1 and Lyman break galaxies (LBGs) at z ∼ 4 both taken from the Subaru/XMM-Newton Deep Survey (SXDS). The large survey area of the SXDS (1 deg 2 ) allows us to measure the angular two-point correlation functions to a wide separation of >10 arcmin with a good statistical quality. We utilize the halo model prescription for estimating characteristic masses of hosting haloes from the measured large-scale clustering amplitudes. It is found that the hosting halo mass positively correlates with the luminosity of galaxies. Then, adopting the extended Press-Schechter (EPS) model, we compute the predictions for the mass evolution of the hosting haloes in the framework of the cold dark matter (CDM) cosmology in order to make an evolutionary link between the two galaxy samples at different redshifts and to identify their present-day descendants by letting their haloes evolve forward in time. It is found that, in the view of the mass evolution of hosting haloes in the CDM model, bright (i'? i'* + 1) LBGs are consistent with being the progenitor of the OPEGs, whereas it is less likely that the LBG population, as a whole, has evolved into the OPEG population. It is also found that the present-day descendants of both the bright LBGs and OPEGs are likely to be located in massive systems such as groups of galaxies or clusters of galaxies. Finally, we estimate the hosting halo mass of local early-type galaxy samples from the 2dF and Sloan Digital Sky Survey (SDSS) based on the halo model, and it turns out that their expected characteristic mass of hosting haloes is in good agreement with the EPS predictions for the descendant's mass of both the bright LBGs and OPEGs.

Numerical Galaxy Catalog. I. A Semianalytic Model of Galaxy Formation withN‐Body Simulations

We construct the Numerical Galaxy Catalog (νGC), based on a semianalytic model of galaxy formation combined with high-resolution N-body simulations in a Λ-dominated flat cold dark matter (ΛCDM) cosmological model. The model includes several essential ingredients for galaxy formation, such as merging histories of dark halos taken directly from N-body simulations, radiative gas cooling, star formation, heating by supernova explosions (supernova feedback), mergers of galaxies, population synthesis, and extinction by internal dust and intervening H I clouds. As the first paper in a series using this model, we focus on basic photometric, structural, and kinematical properties of galaxies at present and at high redshift. Two sets of model parameters are examined, strong and weak supernova feedback models, which are in good agreement with observational luminosity functions of local galaxies within observational uncertainties. Both models agree well with many observations of, e.g., cold gas mass-to-stellar luminosity ratios of spiral galaxies, H I mass functions, galaxy sizes, faint galaxy number counts and photometric redshift distributions in optical passbands, isophotal angular sizes, and cosmic star formation rates. In particular, the strong supernova feedback model is in much better agreement with near-infrared (K'-band) faint galaxy number counts and redshift distribution than the weak-feedback model and our previous semianalytic models based on the extended Press-Schechter formalism. Observed Tully-Fisher relations for bright galaxies and color-magnitude relations for dwarf elliptical galaxies in clusters of galaxies are broadly reproduced, but no agreement with observations is obtained over whole ranges. Nevertheless, they show improvements over results produced by other semianalytic models. A direction to be pursued in overcoming the remaining problems is also discussed. We find that the resolution of N-body simulations, which is down to 3 × 109 M☉ for the minimum mass of dark halos consisting of 10 dark matter particles in our model, plays a significant role in galaxy formation, and that merging histories of dark halos directly taken from N-body simulations produce results different from models based on the extended Press-Schechter model even if the mass function of dark halos at present is set to be the same as that obtained by the same N-body simulations used here.

The Mass Function of Void Galaxies in the Sloan Digital Sky Survey Data Release 2

We estimate the mass function of void galaxies in the second public data release of the Sloan Digital Sky Survey from a sample of 1000 galaxies with local density contrasts of ?v < -0.6. The galaxy sample is split into ellipticals and spirals using a color-S?rsic index criterion. We estimate the virial masses of ellipticals using the measured spectral line widths along with the observed size. Projection effects and uncertainties in halo properties make mass estimates of spirals more difficult. We use an inversion of the Tully-Fisher relation to estimate the isothermal rotational velocity and introduce a scaling factor to estimate the halo extent. We then fit the measured mass function against a theoretical Press-Schechter model and find that the distribution of galaxies in voids appears to be nearly unbiased compared to the mass.

The Distribution of Two‐dimensional Eccentricity of Sunyaev‐Zel'dovich Effect and X‐Ray Surface Brightness Profiles

With the triaxial density profile of dark matter halos and the corresponding equilibrium gas distribution, we derive two-dimensional Sunyaev-Zel'dovich (SZ) effect and X-ray surface brightness profiles for clusters of galaxies. It is found that the contour map of these observables can be well approximated by a series of concentric ellipses with scale-dependent eccentricities. The statistical distribution of their eccentricities (or, equivalently, axial ratios) is analyzed by taking into account the orientation of clusters with respect to the line of sight and the distribution of the axial ratios and the concentration parameters of dark matter halos. For clusters of mass 1013 h-1 M☉ at redshift z = 0, the axial ratio is peaked at η ~ 0.9 for both SZ and X-ray profiles. For larger clusters, the deviation from circular distributions is more apparent, with η peaked at η ~ 0.85 for M = 1015 h-1 M☉. To be closer to observations, we further study the axial-ratio distribution for mass-limited cluster samples with the number distribution of clusters at different redshifts described by a modified Press-Schechter model. For a mass limit of value Mlim = 1014 h-1 M☉, the average axial ratio is η ~ 0.84, with a tail extended to η ~ 0.6. With the fast advance of high-quality imaging observations of both SZ effect and X-ray emissions, our analyses provide a useful way to probe cluster halo profiles and therefore to test theoretical halo formation models.

Formation time-distribution of dark matter haloes: theories versus N-body simulations

In this paper we use numerical simulations to test the formation time distribution of dark matter haloes predicted by the analytical excursion set approaches. The formation time distribution is closely linked to the conditional mass function and this test is therefore an indirect probe of this distribution. The excursion set models tested are the extended Press-Schechter (EPS) model, the ellipsoidal collapse model, and the non-spherical collapse boundary model. Three sets of simulations (six realizations) have been used to investigate the halo formation time distribution for halo masses ranging from dwarf-galaxy-like haloes (M = 10 - 3 M * , where M * is the characteristic non-linear mass scale) to massive haloes of M = 8.7M * . None of the models can match the simulation results at both high and low redshift. In particular, dark matter haloes formed generally earlier in our simulations than predicted by the EPS model. This discrepancy might help explain why semi-analytical models of galaxy formation, based on EPS merger trees, underpredict the number of high redshift galaxies compared with recent observations.

Modelling peculiar velocities of dark matter haloes

We present a simple model that accurately describes various statistical properties of peculiar velocities of dark matter haloes. We pay particular attention to the following two effects. First, the evolution of the halo peculiar velocity depends on the local matter density, instead of the global density. Secondly, dark matter haloes are biased tracers of the underlying mass distribution, thus haloes tend to be located preferentially at high density regions. For the former, we develop an empirical model calibrated with N-body simulations while, for the latter, we use a conventional halo bias model based on the extended Press–Schechter model combined with an empirical lognormal probability distribution function of the mass density distribution. We find that, compared with linear theory, the present model significantly improves the accuracy of predictions of statistical properties of the halo peculiar velocity field including the velocity dispersion, the probability distribution function, and the pairwise velocity dispersion at large separations. Thus, our model predictions may be useful in analysing future observations of the peculiar velocities of galaxy clusters.

Major mergers of haloes, the growth of massive black holes and the evolving luminosity function of quasars

We construct a physically motivated analytical model for the quasar luminosity function, based on the joint star formation and feeding of massive black holes suggested by the observed correlation between the black hole mass and the stellar mass of the hosting spheroids. The parallel growth of massive black holes and host galaxies is assumed to be triggered by major mergers of haloes. The halo major merger rate is computed within the framework of the extended Press-Schechter model. The evolution of black holes on cosmological time-scales is achieved by the integration of the governing set of differential equations, established from a few reasonable assumptions that account for the distinct (Eddington-limited or supply-limited) accretion regimes. Finally, the typical light curves of the reactivated quasars are obtained under the assumption that, in such accretion episodes, the fall of matter on to the black hole is achieved in a self-regulated stationary way. The predicted quasar luminosity function is compared with the luminosity functions of the 2dF quasi-stellar object sample and other, higher-redshift data. We find good agreement in all cases, except for z < 1 where the basic assumption of our model is likely to break down.

Testing the modified Press-Schechter model against N-body simulations

A modified version of the extended Press–Schechter model for the growth of dark-matter haloes was introduced in two previous papers, with the aim of explaining the mass–density relation shown by haloes in high-resolution cosmological simulations. In this model, major mergers are well separated from accretion, thereby allowing a natural definition of halo formation and destruction. This makes it possible to derive analytic expressions for halo formation and destruction rates, the mass accretion rate and the probability distribution functions of halo formation times and progenitor masses. The stochastic merger histories of haloes can be readily derived and easily incorporated into semi-analytical models of galaxy formation, thus avoiding the usual problems encountered in the construction of Monte Carlo merger trees from the original extended Press–Schechter formalism. Here we show that the predictions of the modified Press–Schechter model are in good agreement with the results of N-body simulations for several scale-free cosmologies.