Extended Press-Schechter Theory Research Articles

The mass accretion history of dark matter haloes down to Earth mass

ABSTRACT We take advantage of the unprecedented dynamical range provided by the ‘Cosmic-Zoom’ project to study the mass accretion history (MAH) of present-day dark matter haloes over the entire mass range present in the Lambda cold dark matter paradigm when the dark matter is made of weakly interacting massive particles of mass 100 GeV. In particular, we complement previous studies by exploring the MAHs of haloes with mass from $10^8\ h^{-1}\,\mathrm{{\rm M}_{\odot }}$ down to Earth mass, $10^{-6}\ h^{-1}\,\mathrm{{\rm M}_{\odot }}$. The formation redshift of low-mass haloes anticorrelates weakly with mass, peaking at z = 3 for haloes of mass $10^{-4}\ h^{-1}\,\mathrm{{\rm M}_{\odot }}$. Even lower masses are affected by the free-streaming cut-off in the primordial spectrum of density fluctuations and form at lower redshift. We compare MAHs in our simulations with predictions from two analytical models based on the extended Press–Schechter theory (EPS), and three empirical models derived by fitting and extrapolating either results from cosmological N-body simulations or Monte Carlo realizations of halo growth. All models fit our simulations reasonably well over the mass range for which they were calibrated. While the empirical models match better for more massive haloes, $M\gt 10^{10}\ h^{-1}\,\mathrm{{\rm M}_{\odot }}$, the analytical models do better when extrapolated down to Earth mass. At the higher masses, we explore the correlation between local environment density and MAH, finding that biases are relatively weak, with typical MAHs for haloes in extremely low-density and in typical regions differing by less than 20 per cent at high redshift. If this result can be extrapolated to lower halo masses, we conclude that EPS theory predicts the hierarchical build up of dark matter haloes quite well over the entire halo mass range.

The brightest galaxies at cosmic dawn

ABSTRACT Recent JWST observations suggest an excess of z ≳ 10 galaxy candidates above most theoretical models. Here, we explore how the interplay between halo formation time-scales, star formation efficiency, and dust attenuation affects the properties and number densities of galaxies observed in the early Universe. To guide intuition, we calculate the theoretical upper limit on the UV luminosity function (LF), assuming star formation is 100 per cent efficient and all gas in haloes is converted into stars, and that galaxies are at the peak age for UV emission (∼10 Myr). This upper limit is ∼4 orders of magnitude greater than current observations, implying no formal tension with star formation in Lambda cold dark matter cosmology. In a more realistic model, we use the distribution of halo formation time-scales derived from extended Press–Schechter theory as a proxy for star formation rate (SFR). We predict that the galaxies observed so far at z ≳ 10 are dominated by those with the fastest formation time-scales, and thus most extreme SFRs and young ages. These galaxies can be upscattered by ∼1.5 mag compared to the median UV magnitude versus halo mass relation. This likely introduces a selection effect at high redshift whereby only the youngest (≲10 Myr), most highly star-forming galaxies (specific SFR$\gtrsim 30\, \mathrm{Gyr}^{-1}$) have been detected so far. Furthermore, our modelling suggests that redshift evolution at the bright end of the UV LF is substantially affected by the build-up of dust attenuation. We predict that deeper JWST observations (reaching m ∼ 30) will reveal more typical galaxies with relatively older ages (∼100 Myr) and less extreme specific SFRs ($\sim 10\, \mathrm{Gyr}^{-1}$ for a MUV ∼ −20 galaxy at z ∼ 10).

Semi-analytical frameworks for subhaloes from the smallest to the largest scale

ABSTRACT Substructures of dark matter halo, called subhaloes, provide important clues to understand the nature of dark matter. We construct a useful model to describe the properties of subhalo mass functions based on the well-known analytical prescriptions, the extended Press–Schechter theory. The unevolved subhalo mass functions at arbitrary mass scales become describable without introducing free parameters. The different host halo evolution histories are directly recast to their subhalo mass functions. As applications, we quantify the effects from (i) the Poisson fluctuation, (ii) the host-mass scatter, and the (iii) different tidal evolution models on observables in the current Universe with this scheme. The Poisson fluctuation dominates in the number count of the mass ratio to the host of $\sim {\cal O}(10^{-2})$, where the intrinsic scatter is smaller by a factor of a few. The host-mass scatter around its mean does not affect the subhalo mass function. Different models of the tidal evolution predict a factor of ∼2 difference in numbers of subhaloes with $\lesssim {\cal O}(10^{-5})$, while the dependence of the Poisson fluctuation on the tidal evolution models is subtle. The scheme provides a new tool for investigating the smallest scale structures of our Universe which are to be observed in near future experiments.

Public Release of A-SLOTH: Ancient Stars and Local Observables by Tracing Halos

The semianalytical model a-sloth (Ancient Stars and Local Observables by Tracing Halos) is the first public code that connects the formation of the first stars and galaxies to observables. After several successful projects with this model, we publish the source code (https://gitlab.com/thartwig/asloth) and describe the public version in this paper. The model is based on dark matter merger trees that can either be generated based on Extended Press–Schechter theory or be imported from dark matter simulations. On top of these merger trees, a-sloth applies analytical recipes for baryonic physics to model the formation of both metal-free and metal-poor stars and the transition between them with unprecedented precision and fidelity. a-sloth samples individual stars and includes radiative, chemical, and mechanical feedback. It is calibrated based on six observables, such as the optical depth to Thomson scattering, the stellar mass of the Milky Way and its satellite galaxies, the number of extremely metal-poor stars, and the cosmic star formation rate density at high redshift. a-sloth has versatile applications with moderate computational requirements. It can be used to constrain the properties of the first stars and high-z galaxies based on local observables, predicts properties of the oldest and most metal-poor stars in the Milky Way, can serve as a subgrid model for larger cosmological simulations, and predicts next-generation observables of the early universe, such as supernova rates or gravitational wave events.

A fully Lagrangian, non-parametric bias model for dark matter halos

We present a non-parametric Lagrangian biasing model and fit the ratio of the halo and mass densities at the field level using the mass-weighted halo field in the AbacusSummit simulations at z=0.5. Unlike the perturbative halo bias model that has been widely used in interpreting the observed large-scale structure traced by galaxies, we find a non-negative halo-to-mass ratio that increases monotonically with the linear overdensity δ1 in the initial Lagrangian space. The bias expansion, however, does not guarantee non-negativity of the halo counts, and may lead to rising halo number counts at negative overdensities. The shape of the halo-to-mass ratio is unlikely to be described by a polynomial function of δ1 and other quantities. Especially for massive halos with 6×1012 h-1 M⊙, the halo-to-mass ratio starts soaring up at δ1>0, substantially different from the predictions of the bias expansion. We show that for the halo masses we consider (M>3×1011 h-1 M⊙) a non-parametric halo-to-mass ratio as a function of δ1 and its local derivative ∇^2δ1 can recover the halo power spectra to sub-percent level accuracy for wavenumbers k=0.01-0.1 h Mpc-1 given a proper smoothing scale to filter the initial density field, even though we do not fit the power spectrum directly. However, there is mild dependence of the recovery of the halo power spectrum on the smoothing scale and other input parameters. At k<0.01 h Mpc-1 and for massive halos with M>6×1012 h-1 M⊙, our non-parametric model leads to a few percent overestimation of the halo power spectrum, indicating the need for larger or multiple smoothing scales. The halo-to-mass ratios obtained qualitatively agree with intuitions from extended Press-Schechter theory. We compare our framework to the bias expansion and discuss possible extensions.

Machine learning cosmological structure formation

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 mass range, based on spherical overdensities. We show that the resulting predictions match those of spherical collapse approximations such as extended Press-Schechter theory. Additional information on the shape of the local gravitational potential is not able to improve halo collapse predictions; the linear density field contains sufficient information for the algorithm to also reproduce ellipsoidal collapse predictions based on the Sheth-Tormen model. We investigate the algorithm's performance in terms of halo mass and radial position and perform blind analyses on independent initial conditions realisations to demonstrate the generality of our results.

The formation of cold dark matter haloes – II. Collapse time and tides

We use two cosmological simulations of structure formation in the LambdaCDM scenario to study the evolutionary histories of dark-matter haloes and to characterize the Lagrangian regions from which they form. We focus on haloes identified at redshift z_id=0 and show that the classic ellipsoidal collapse model systematically overestimates their collapse times. If one imposes that halo collapse takes place at z_id, this model requires starting from a significantly lower linear density contrast than what is measured in the simulations at the locations of halo formation. We attempt to explain this discrepancy by testing two key assumptions of the model. First, we show that the tides felt by collapsing haloes due to the surrounding large-scale structure evolve non-linearly. Although this effect becomes increasingly important for low-mass haloes, accounting for it in the ellipsoidal collapse model only marginally improves the agreement with N-body simulations. Second, we track the time evolution of the physical volume occupied by forming haloes and show that, after turnaround, it generally stabilizes at a well-defined redshift, z_c>z_id, contrary to the basic assumption of extended Press-Schechter theory based on excursion sets. We discuss the implications of this result for understanding the origin of the mass-dependence and scatter in the linear threshold for halo formation. Finally, we show that, when tuned for collapse at z_c, a modified version of the ellipsoidal collapse model that also accounts for the triaxial nature of protohaloes predicts their linear density contrast in an unbiased way.

EXTREMELY METAL-POOR STARS AND A HIERARCHICAL CHEMICAL EVOLUTION MODEL

Early phases of the chemical evolution and formation history of extremely metal poor (EMP) stars are investigated using hierarchical galaxy formation models. We build a merger tree of the Galaxy according to the extended Press-Schechter theory. We follow the chemical evolution along the tree, and compare the model results to the metallicity distribution function (MDF) and abundance ratio distribution of the Milky Way halo. We adopt three different initial mass functions (IMFs). In a previous studies, we argue that typical mass of EMP stars should be high-mass(~10Msun) based on studies of binary origin carbon-rich EMP stars. In this study, we show that only the high-mass IMF can explain a observed small number of EMP stars. For relative element abundances, the high-mass IMF and the Salpeter IMF predict similar distributions. We also investigate dependence on nucleosynthetic yields of supernovae (SNe). The theoretical SN yields by Kobayashi et al.(2006) and Chieffi & Limonge (2004) show reasonable agreement with observations for $\alpha$-elements. Our model predicts significant scatter of element abundances at [Fe/H]<-3. Best fit yields for one zone chemical evolution model by Francois et al.(2004) well reproduces the trend of the typical abundances of EMP stars but our model with their yield predicts much larger scatter of abundances than the observations. The model with hypernovae predicts Zn abundance in agreement with observations but other models predict lower [Zn/Fe]. Ejecta from the hypernovae with large explosion energy is mixed in large mass and decreases scatter of the element abundances.

GECO: Galaxy Evolution COde – A new semi-analytical model of galaxy formation

We present a new semi-analytical model of galaxy formation, GECO (Galaxy Evolution COde), aimed at a better understanding of when and how the two processes of star formation and galaxy assembly have taken place. Our model is structured into a Monte Carlo algorithm based on the Extended Press-Schechter theory, for the representation of the merging hierarchy of dark matter halos, and a set of analytic algorithms for the treatment of the baryonic physics, including classical recipes for the gas cooling, the star formation time-scales, galaxy mergers and SN feedback. Together with the galaxies, the parallel growth of BHs is followed in time and their feedback on the hosting galaxies is modelled. We set the model free parameters by matching with data on local stellar mass functions and the BH-bulge relation at z=0. Based on such local boundary conditions, we investigate how data on the high-redshift universe constrain our understanding of the physical processes driving the evolution, focusing in particular on the assembly of stellar mass and on the star formation history. Since both processes are currently strongly constrained by cosmological near- and far-IR surveys, the basic physics of the Lambda CDM hierarchical clustering concept of galaxy formation can be effectively tested by us by comparison with the most reliable set of observables. Our investigation shows that when the time-scales of the stellar formation and mass assembly are studied as a function of dark matter halo mass and the single galaxy stellar mass, the 'downsizing' fashion of star formation appears to be a natural outcome of the model, reproduced even in the absence of the AGN feedback. On the contrary, the stellar mass assembly history turns out to follow a more standard hierarchical pattern progressive in cosmic time, with the more massive systems assembled at late times mainly through dissipationless mergers.

FORMATION HISTORY OF METAL-POOR HALO STARS WITH THE HIERARCHICAL MODEL AND THE EFFECT OF INTERSTELLAR MATTER ACCRETION ON THE MOST METAL-POOR STARS

We investigate the star formation and chemical evolution in the early universe by considering the merging history of the Galaxy in the {\Lambda}CDM scenario according to the extended Press-Schechter theory. We give some possible constraints from comparisons with observation of extremely metal-poor (EMP) stars. We demonstrate that (1) The hierarchical structure formation can explain the characteristics of the observed metallicity distribution function (MDF) including a break around [Fe/H]~-4. (2) A high mass IMF of peak mass ~10Msun with the contribution of binaries, derived from the statistics of carbon enhanced EMP stars (Komiya et al. 2007), predicts the frequency of low-mass survivors consistent with the number of EMP stars observed for -4~<[Fe/H]~<-2.5. (3) The stars formed from primordial gas before the first supernova explosions in their host mini-halos are assigned to the HMP stars with [Fe/H]~-5. (4) There is no indication of significant changes in the IMF and the binary contribution at metallicity -4~<[Fe/H]~<-2.5, or even larger as long as the field stars of Galactic halo are concerned. We further study the effects of the surface pollution through the accretion of ISM along the chemical and dynamical evolution of the Galaxy for low-mass Pop.III and EMP survivors. Because of shallower potential of smaller halos, the accretion of ISM in the mini-halos in which these stars were born dominates the surface metal pollution. This can account for the surface iron abundances as observed for the HMP stars if the cooling and concentration of gas in their birth mini-halos is taken into account. We also study the feedback effect from the very massive Pop. III stars. The metal pre-pollution by PISNe is shown to be compatible with the observed lack of their nucleosynthetic signatures when some positive feedback on gas cooling works and changes IMF from being very massive to being high mass.

Spherical collapse in quintessence models with zero speed of sound

We study the spherical collapse model in the presence of quintessence with negligible speed of sound. This case is particularly motivated for w < −1 as it is required by stability. As pressure gradients are negligible, quintessence follows dark matter during the collapse. The spherical overdensity behaves as a separate closed FLRW universe, so that its evolution can be studied exactly. We derive the critical overdensity for collapse and we use the extended Press-Schechter theory to study how the clustering of quintessence affects the dark matter mass function. The effect is dominated by the modification of the linear dark matter growth function. A larger effect occurs on the total mass function, which includes the quintessence overdensities. Indeed, here quintessence constitutes a third component of virialized objects, together with baryons and dark matter, and contributes to the total halo mass by a fraction ∼ (1+w)ΩQ/Ωm. This gives a distinctive modification of the total mass function at low redshift.

THE MASS FUNCTION OF VOID GROUPS AS A PROBE OF PRIMORDIAL NON-GAUSSIANITY

The primordial non-Gaussianity signal, if measured accurately, will allow us to distinguish between different candidate models for cosmic inflation. Since the galaxy groups located in void regions are rare events, their abundance may be a sensitive probe of primordial non-Gaussianity. We construct an analytic model for the mass function of void groups in the framework of the extended Press-Schechter theory with non-Gaussian initial conditions and investigate how it depends on the primordial non-Gaussianity parameter. A feasibility study is conducted by fitting the analytic mass function of void groups to the observational results from the galaxy group catalog of the Sloan Digital Sky Survey Data Release 4 by adjusting the primordial non-Gaussianity parameter.

Erratum: Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture [Phys. Rev. D78, 083519 (2008)

The nonlinear perturbation theory of gravitational instability is extended to include effects of both biasing and redshift-space distortions, which are inevitable in predicting observable quantities in galaxy surveys. The precise determination of scales of baryon acoustic oscillations is crucial to investigate the nature of dark energy by galaxy surveys. We find that a local Lagrangian bias and redshift-space distortions are naturally incorporated in our formalism of perturbation theory with a resummation technique via the Lagrangian picture. Our formalism is applicable to any biasing scheme which is local in Lagrangian space, including the halo bias as a special case. Weakly nonlinear effects on halo clustering in redshift space are analytically given.We assume only a fundamental idea of the halo model: haloes form according to the extended Press-Schechter theory, and the spatial distributions are locally biased in Lagrangian space. There is no need for assuming the spherical collapse model to follow the dynamical evolution, which is additionally assumed in standard halo prescriptions. One-loop corrections to the power spectrum and correlation function of haloes in redshift space are explicitly derived and presented. Instead of relying on expensive numerical simulations, our approach provides an analytic way of investigating the weakly nonlinear effects, simultaneously including the nonlinear biasing and nonlinear redshift-space distortions. Nonlinearity introduces a weak scale dependence in the halo bias. The scale dependence is a smooth function in Fourier space, and the bias does not critically change the feature of baryon acoustic oscillations in the power spectrum. The same feature in the correlation function is less affected by nonlinear effects of biasing.

Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture

The nonlinear perturbation theory of gravitational instability is extended to include effects of both biasing and redshift-space distortions, which are inevitable in predicting observable quantities in galaxy surveys. Weakly nonlinear effects in galaxy clustering on large scales recently attracted great interest, since the precise determination of scales of baryon acoustic oscillations is crucial to investigate the nature of dark energy by galaxy surveys. We find that a local Lagrangian bias and redshift-space distortions are naturally incorporated in our formalism of perturbation theory with a resummation technique via the Lagrangian picture. Our formalism is applicable to any biasing scheme which is local in Lagrangian space, including the halo bias as a special case. Weakly nonlinear effects on halo clustering in redshift space are analytically given. We assume only a fundamental idea of the halo model: haloes form according to the extended Press-Schechter theory, and the spatial distributions are locally biased in Lagrangian space. There is no need for assuming the spherical collapse model to follow the dynamical evolution, which is additionally assumed in standard halo prescriptions. One-loop corrections to the power spectrum and correlation function of haloes in redshift space are explicitly derived and presented. Instead of relying on expensive numerical simulations, our approach provides an analytic way of investigating the weakly nonlinear effects, simultaneously including the nonlinear biasing and nonlinear redshift-space distortions. Nonlinearity introduces a weak scale dependence in the halo bias. The scale dependence is a smooth function in Fourier space, and the bias does not critically change the feature of baryon acoustic oscillations in the power spectrum. The same feature in the correlation function is less affected by nonlinear effects of biasing.

On the spin distributions of ΛCDM haloes

We used merger trees realizations, predicted by the extended Press-Schechter theory, in order to study the growth of angular momentum of dark matter haloes. Our results showed that: 1) The spin parameter $\lambda'$ resulting from the above method, is an increasing function of the present day mass of the halo. The mean value of $\lambda'$ varies from 0.0343 to 0.0484 for haloes with present day masses in the range of $ 10^9\mathrm{h}^{-1}M_{\odot}$ to $10^{14}\mathrm{h}^{-1}M_{\odot}$. 2)The distribution of $\lambda'$ is close to a log-normal, but, as it is already found in the results of N-body simulations, the match is not satisfactory at the tails of the distribution. A new analytical formula that approximates the results much more satisfactorily is presented. 3) The distribution of the values of $\lambda'$ depends only weakly on the redshift. 4) The spin parameter of an halo depends on the number of recent major mergers. Specifically the spin parameter is an increasing function of this number.

Cosmic Variance and Its Effect on the Luminosity Function Determination in Deep High‐zSurveys

We study cosmic variance in deep high redshift surveys and its influence on the determination of the luminosity function for high redshift galaxies. For several survey geometries relevant for HST and JWST instruments, we characterize the distribution of the galaxy number counts. This is obtained by means of analytic estimates via the two point correlation function in extended Press-Schechter theory as well as by using synthetic catalogs extracted from N-body cosmological simulations of structure formation. We adopt a simple luminosity - dark halo mass relation to investigate the environment effects on the fitting of the luminosity function. We show that in addition to variations of the normalization of the luminosity function, a steepening of its slope is also expected in underdense fields, similarly to what is observed within voids in the local universe. Therefore, to avoid introducing artificial biases, caution must be taken when attempting to correct for field underdensity, such as in the case of HST UDF i-dropout sample, which exhibits a deficit of bright counts with respect to the average counts in GOODS. A public version of the cosmic variance calculator based on the two point correlation function integration is made available on the web.

The Halo Mass Function: High‐Redshift Evolution and Universality

We study the formation of dark matter halos in the concordance ΛCDM model over a wide range of redshifts, from -->z = 20 to the present. Our primary focus is the halo mass function, a key probe of cosmology. By performing a large suite of nested-box N-body simulations with careful convergence and error controls (60 simulations with box sizes from 4 to 256 h−1 Mpc), we determine the mass function and its evolution with excellent statistical and systematic errors, reaching a few percent over most of the considered redshift and mass range. Across the studied redshifts, the halo mass is probed over 6 orders of magnitude (107-1013.5 h−1 M☉). Historically, there has been considerable variation in the high-redshift mass function as obtained by different groups. We have made a concerted effort to identify and correct possible systematic errors in computing the mass function at high redshift and to explain the discrepancies between some of the previous results. We discuss convergence criteria for the required force resolution, simulation box size, halo mass range, initial and final redshifts, and time stepping. Because of conservative cuts on the mass range probed by individual boxes, our results are relatively insensitive to simulation volume, the remaining sensitivity being consistent with extended Press-Schechter theory. Previously obtained mass function fits near -->z = 0, when scaled by linear theory, are in good agreement with our results at all redshifts, although a mild redshift dependence consistent with that found by Reed et al. may exist at low redshifts. Overall, our results are consistent with a universal form for the mass function at high redshifts.

Generating dark matter halo merger trees

We present a new Monte-Carlo algorithm to generate merger trees describing the formation history of dark matter halos. The algorithm is a modification of the algorithm of Cole et al (2000) used in the GALFORM semi-analytic galaxy formation model. As such, it is based on the Extended Press-Schechter theory and so should be applicable to hierarchical models with a wide range of power spectra and cosmological models. It is tuned to be in accurate agreement with the conditional mass functions found in the analysis of merger trees extracted from the LCDM Millennium N-body simulation. We present a comparison of its predictions not only with these conditional mass functions, but also with additional statistics of the Millennium Simulation halo merger histories. In all cases we find it to be in good agreement with the Millennium Simulation and thus it should prove to be a very useful tool for semi-analytic models of galaxy formation and for modelling hierarchical structure formation in general. We have made our merger tree generation code and code to navigate the trees available at this http URL .

Semi-analytical predictions of density profiles for ΛCDM haloes

We combine the results of merger trees realizations, predicted by the extended Press-Schechter theory, to the assumption of “stable clustering” in order to calculate density profiles of dark matter haloes. Our results show that: 1) Haloes of different masses have different concentrations. More specifically, concentration is a decreasing function of the mass. The relation between concentration and virial mass predicted by our results is in good agreement with the predictions of large cosmological N-body simulations. 2) The slope of the density profile of dark matter haloes is flatter at the inner regions and steepens outwards. At a given fraction of the virial radius the slope (defined as minus the derivative of the logarithm of the density with respect to the logarithm of the radial distance) is a decreasing function of the virial mass of the halo. At 0.01 of the virial radius Rvir the slope ranges from 0.4 to 1.5 for masses in the range to . At distance Rvir the values of the slope are in the range 2.5 to 5.5. We note that the small values of the inner slope predicted in this paper are closer to the predictions of observations than the results of N-body simulations. 3) Comparing haloes of the same present day mass we found that: a) Haloes with large rate of recent mass increase, show flatter outer density profiles than those with small recent mass increase. b) The concentration becomes larger for increasing recent mass growth rate.

Source mergers and bubble growth during reionization

The recently introduced models of reionization bubbles based on extended Press-Schechter theory (Furlanetto, Zaldarriaga & Hernquist 2004) are generalized to include mergers of ionization sources. Sources with a recent major merger are taken to have enhanced photon production due to star formation, and accretion onto a central black hole if a black hole is present. This produces a scatter in the number of ionized photons corresponding to a halo of a given mass and a change in photon production over time for any given halo mass. Photon production histories, bubble distributions, and ionization histories are computed for several different parameter and recombination assumptions; the resulting distributions interpolate between previously calculated limiting cases.