Abundance Of Dark Matter Halos Research Articles

Deep learning insights into non-universality in the halo mass function

ABSTRACT The abundance of dark matter haloes is a key cosmological probe in forthcoming galaxy surveys. The theoretical understanding of the halo mass function (HMF) is limited by our incomplete knowledge of the origin of non-universality and its cosmological parameter dependence. We present a deep-learning model which compresses the linear matter power spectrum into three independent factors which are necessary and sufficient to describe the $z=0$ HMF from the state-of-the-art Aemulus emulator to sub-per cent accuracy in a wCDM$+N_\mathrm{eff}$ parameter space. Additional information about growth history does not improve the accuracy of HMF predictions if the matter power spectrum is already provided as input, because required aspects of the former can be inferred from the latter. The three factors carry information about the universal and non-universal aspects of the HMF, which we interrogate via the information-theoretic measure of mutual information. We find that non-universality is captured by recent growth history after matter-dark-energy equality and $N_{\rm eff}$ for $M\sim 10^{13} \, \mathrm{M_\odot }\, h^{-1}$ haloes, and by $\Omega _{\rm m}$ for $M\sim 10^{15} \, \mathrm{M_\odot }\, h^{-1}$. The compact representation learnt by our model can inform the design of emulator training sets to achieve high emulator accuracy with fewer simulations.

Early Structure Formation from Primordial Density Fluctuations with a Blue, Tilted Power Spectrum: High-redshift Galaxies

Recent observations by the James Webb Space Telescope (JWST) discovered unexpectedly abundant luminous galaxies at high redshift, posing possibly a severe challenge to popular galaxy formation models. We study early structure formation in a cosmological model with a blue, tilted power spectrum (BTPS) given by P(k)∝kms with m s > 1 at small length scales. We run a set of cosmological N-body simulations and derive the abundance of dark matter halos and galaxies under simplified assumptions on star formation efficiency. The enhanced small-scale power allows rapid nonlinear structure formation at z > 7, and galaxies with stellar mass exceeding 1010 M ⊙ can be formed by z = 9. Because of frequent mergers, the structure of galaxies and galaxy groups appears clumpy. The BTPS model reproduces the observed stellar mass density at z = 7–9, and thus eases the claimed tension between galaxy formation theory and recent JWST observations. The large-scale structure of the present-day Universe is largely unaffected by the modification of the small-scale power spectrum. We conduct a systematic study by varying the slope of the small-scale power spectrum to derive constraints on the BTPS model from a set of observations of high-redshift galaxies.

The abundance of dark matter haloes down to Earth mass

ABSTRACT We use the voids-within-voids-within-voids (VVV) simulations, a suite of successive nested N-body simulations with extremely high resolution (denoted, from low to high resolution, by L0 to L7), to test the Press–Schechter (PS), Sheth–Tormen (ST), and extended Press–Schechter (EPS) formulae for the halo abundance over the entire mass range, from minihaloes of 10−6 M⊙, to cluster haloes of 1015 M⊙, at different redshifts, from z = 30 to the present. We find that at z = 0 and z = 2, ST best reproduces the results of L0, which has the mean cosmic density (overdensity δ = 0), at 1011−15 M⊙. The higher resolution levels (L1–L7) are biased underdense regions (δ < −0.6). The EPS formalism takes this into account since it gives the mass function of a region conditioned, in this case, on having a given underdensity. EPS provides good matches to these higher levels, with deviations ≲20 per cent, at 10−6−12.5 M⊙. At z ∼ 7−15, the ST predictions for L0 and the EPS for L1–L7 show somewhat larger deviations from the simulation results. However, at even higher redshifts, z ∼ 30, EPS fits the simulations well again. We confirm our results by picking more subvolumes from the L0 simulation, finding that our conclusions depend only weakly on the size and overdensity of the region. The good agreement of EPS with the higher level simulations implies that PS (or ST) gives an accurate description of the total halo mass function in representative regions of the universe.

Halo mass function in scale invariant models

ABSTRACTSheth–Tormen mass function has been widely used to quantify the abundance of dark matter haloes. It is a significant improvement over the Press–Schechter mass function as it uses ellipsoidal collapse in place of spherical collapse. Both of these mass functions can be written in a form that is universal, i.e. independent of cosmology and power spectrum when scaled in suitable variables. However, cosmological simulations have shown that this universality is approximate. In this paper, we investigate the power spectrum dependence of halo mass function through a suite of dark-matter-only N-body simulations of seven power-law models in an Einstein–de Sitter cosmology. This choice of cosmology and a power-law power spectrum ensures the self-similar evolution of dark matter distribution, allowing us to isolate the power spectrum dependence of mass function. We find that the mass function shows a clear non-universality. We present fits for the parameters of the Sheth–Tormen mass function for a range of power-law power spectrum indices. We find a mild evolution in the overall shape of the mass function with the epoch. Finally, we extend our result to LCDM cosmology. We show that the Sheth–Tormen mass function with parameter values derived from a matched power-law Einstein–de Sitter cosmology provides a better fit to the LCDM mass function than the standard Sheth–Tormen mass function. Our results indicate that an improved analytical theory is required to provide better fits to the mass function.

Non-universality of the mass function: dependence on the growth rate and power spectrum shape

ABSTRACT The abundance of dark matter haloes is one of the key probes of the growth of structure and expansion history of the Universe. Theoretical predictions for this quantity usually assume that, when expressed in a certain form, it depends only on the mass variance of the linear density field. However, cosmological simulations have revealed that this assumption breaks, leading to 10–20 per cent systematic effects. In this paper, we employ a specially designed suite of simulations to further investigate this problem. Specifically, we carry out cosmological N-body simulations where we systematically vary growth history at a fixed linear density field, or vary the power spectrum shape at a fixed growth history. We show that the halo mass function generically depends on these quantities, thus showing a clear signal of non-universality. Most of this effect can be traced back to the way in which the same linear fluctuation grows differently into the non-linear regime depending on details of its assembly history. With these results, we propose a parameterization with explicit dependence on the linear growth rate and power spectrum shape. Using an independent suite of simulations, we show that this fitting function accurately captures the mass function of haloes over cosmologies spanning a vast parameter space, including massive neutrinos and dynamical dark energy. Finally, we employ this tool to improve the accuracy of so-called cosmology-rescaling methods and show they can deliver 2 per cent accurate predictions for the halo mass function over the whole range of currently viable cosmologies.

HIKER: a halo-finding method based on kernel-shift algorithm

We introduce a new halo/subhalo finder, HIKER (a Halo fInder based on KERnel-shift algorithm), which takes advantage of a machine learning method – the mean-shift algorithm combined with the Plummer kernel function, to effectively locate density peaks corresponding to halos/subhalos in density field. Based on these density peaks, dark matter halos are identified as spherical overdensity structures, and subhalos are bound substructures with boundaries at their tidal radius. By testing HIKER code with mock halos, we show that HIKER performs excellently in recovering input halo properties. In particular, HIKER has higher accuracy in locating halo/subhalo centres than most halo finders. With cosmological simulations, we further show that HIKER reproduces the abundance of dark matter halos and subhalos quite accurately, and the HIKER halo/subhalo mass functions and Vmax functions are in good agreement with two widely used halo finders, SUBFIND and AHF.

Effects of long-wavelength fluctuations in large galaxy surveys

ABSTRACT In order to capture as much information as possible large galaxies surveys have been increasing their volume and redshift depth. To face this challenge theory has responded by making cosmological simulations of huge computational volumes with equally increasing numbers of dark matter particles and supercomputing resources. Thus, it is taken for granted that the ideal situation is when a single computational box encompasses the whole volume of the observational survey, e.g. $\sim 50\, h^{-3}\,{\rm Gpc}^3$ for the DESI and Euclid surveys. Here we study the effects of missing long waves in a finite volume using several relevant statistics: the abundance of dark matter haloes, the probability distribution function (PDF), the correlation function and power spectrum, and covariance matrices. Finite volume effects can substantially modify the results if the computational volumes are less than $\sim (500\mbox{$\, h^{-1}$Mpc})^3$. However, the effects become extremely small and practically can be ignored when the box size exceeds ∼1 Gpc3. We find that the average power spectra of dark matter fluctuations show remarkable lack of dependence on the computational box size with less than 0.1 per cent differences between $1$ and $4\mbox{$\, h^{-1}\,$Gpc}$ boxes. No measurable differences are expected for the halo mass functions for these volumes. The covariance matrices are scaled trivially with volume, and small corrections due to supersample modes can be added. We conclude that there is no need to make those extremely large simulations when a box size of $1-1.5\mbox{$\, h^{-1}$Gpc}$ is sufficient to fulfil most of the survey science requirements.

Implications for the missing low-mass galaxies (satellites) problem from cosmic shear

ABSTRACT The number of observed dwarf galaxies, with dark matter mass ≲1011 M⊙ in the Milky Way or the Andromeda galaxy does not agree with predictions from the successful ΛCDM paradigm. To alleviate this problem, a suppression of dark matter clustering power on very small scales has been conjectured. However, the abundance of dark matter halos outside our immediate neighbourhood (the Local Group) seem to agree with the ΛCDM–expected abundance. Here we connect these problems to observations of weak lensing cosmic shear, pointing out that cosmic shear can make significant statements about the missing satellites problem in a statistical way. As an example and pedagogical application, we use recent constraints on small-scale power suppression from measurements of the CFHTLenS data. We find that, on average, in a region of ∼Gpc3 there is no significant small-scale power suppression. This implies that suppression of small-scale power is not a viable solution to the ‘missing satellites problem’ or, alternatively, that on average in this volume there is no ‘missing satellites problem’ for dark matter masses ≳5 × 109 M⊙. Further analysis of current and future weak lensing surveys will probe much smaller scales, k > 10h Mpc−1 corresponding roughly to masses M < 109M⊙.

Spherical collapse model in agegraphic dark energy cosmologies

Under the commonly used spherical collapse model, we study how dark energy affects the growth of large scale structures of the Universe in the context of agegraphic dark energy models. The dynamics of the spherical collapse of dark matter halos in nonlinear regimes is determined by the properties of the dark energy model. We show that the main parameters of the spherical collapse model are directly affected by the evolution of dark energy in the agegraphic dark energy models. We compute the spherical collapse quantities for different values of agegraphic model parameter $\alpha$ in two different scenarios: first, when dark energy does not exhibit fluctuations on cluster scales, and second, when dark energy inside the overdense region collapses similar to dark matter. Using the Sheth-Tormen and Reed mass functions, we investigate the abundance of dark matter halos in the framework of agegraphic dark energy cosmologies. The model parameter $\alpha$ is a crucial parameter in order to count the abundance of dark matter halos. Specifically, the present analysis suggests that the agegraphic dark energy model with bigger (smaller) value of $\alpha$ predicts less (more) virialized halos with respect to that of $\Lambda$CDM cosmology. We also show that in agegraphic dark energy models, the number of halos strongly depends on clustered or uniformed distributions of dark energy.

Halo and subhalo demographics with Planck cosmological parameters: Bolshoi–Planck and MultiDark–Planck simulations

We report and provide fitting functions for the abundance of dark matter halos and subhalos as a function of mass, circular velocity, and redshift from the new Bolshoi-Planck and MultiDark-Planck $\Lambda$CDM cosmological simulations, based on the Planck cosmological parameters. We also report the halo mass accretion rates, which may be connected with galaxy star formation rates. We show that the higher cosmological matter density of the Planck parameters compared with the WMAP parameters leads to higher abundance of massive halos at high redshifts. We find that the median halo spin parameter $\lambda_{\rm B} = J(2M_{\rm vir}R_{\rm vir}V_{\rm vir})^{-1}$ is nearly independent of redshift, leading to predicted evolution of galaxy sizes that is consistent with observations, while the significant decrease with redshift in median $\lambda_{\rm P} = J|E|^{-1/2}G^{-1}M^{-5/2}$ predicts more decrease in galaxy sizes than is observed. Using the Tully-Fisher and Faber-Jackson relations between galaxy velocity and mass, we show that a simple model of how galaxy velocity is related to halo maximum circular velocity leads to increasing overprediction of cosmic stellar mass density as redshift increases beyond redshifts $z\sim1$, implying that such velocity-mass relations must change at redshifts $z>1$. By making a realistic model of how observed galaxy velocities are related to halo circular velocity, we show that recent optical and radio observations of the abundance of galaxies are in good agreement with our $\Lambda$CDM simulations. Our halo demographics are based on updated versions of the \rockstar\ and \ctrees\ codes, and this paper includes appendices explaining all of their outputs. This paper is an introduction to a series of related papers presenting other analyses of the Bolshoi-Planck and MultiDark-Planck simulations.

Effect of supersonic relative motion between baryons and dark matter on collapsed objects

Great attention is given to the first star formation and the epoch of reionization as main targets of planned large radio interferometries (e.g. Square Kilometre Array). Recently, it is claimed that the supersonic relative velocity between baryons and cold dark matter can suppress the abundance of first stars and impact the cosmological reionization process. Therefore, in order to compare observed results with theoretical predictions it is important to examine the effect of the supersonic relative motion on the small-scale structure formation. In this paper, we investigate this effect on the nonlinear structure formation in the context of the spherical collapse model in order to understand the fundamental physics in a simple configuration. We show the evolution of the dark matter sphere with the relative velocity by both using N-body simulations and numerically calculating the equation of motion for the dark matter mass shell. The effects of the relative motion in the spherical collapse model appear as the delay of the collapse time of dark matter halos and the decrease of the baryon mass fraction within the dark matter sphere. Based on these results, we provide the fitting formula of the critical density contrast for collapses with the relative motion effect and calculate the mass function of dark matter halos in the Press-Schechter formalism. As a result, the relative velocity decreases the abundance of dark matter halos whose mass is smaller than $10^8~M_\odot/h$.

WEIGHING NEUTRINOS WITH COSMIC NEUTRAL HYDROGEN

We investigate the signatures left by massive neutrinos on the spatial distribution of neutral hydrogen (HI) in the post-reionization era by running hydrodynamic simulations that include massive neutrinos as additional collisionless particles. We find that halos in massive/massless neutrino cosmologies host a similar amount of neutral hydrogen, although for a fixed halo mass, on average, the HI mass increases with the sum of the neutrino masses. Our results show that HI is more strongly clustered in cosmologies with massive neutrinos, while its abundance, $\Omega_{\rm HI}(z)$, is lower. These effects arise mainly from the impact of massive neutrinos on cosmology: they suppress both the amplitude of the matter power spectrum on small scales and the abundance of dark matter halos. Modelling the HI distribution with hydrodynamic simulations at $z > 3$, and a simple analytic model at $z<3$, we use the Fisher matrix formalism to conservatively forecast the constraints that Phase 1 of the Square Kilometre Array (SKA) will place on the sum of neutrino masses, $M_\nu\equiv \Sigma m_{\nu}$. We find that with 10,000 hours of interferometric observations at $3 \lesssim z \lesssim 6$ from a deep and narrow survey with SKA1-LOW, the sum of the neutrino masses can be measured with an error $\sigma(M_\nu)\lesssim0.3$ eV (95% CL). Similar constraints can be obtained with a wide and deep SKA1-MID survey at $z \lesssim 3$, using the single-dish mode. By combining data from MID, LOW, and Planck, plus priors on cosmological parameters from a Stage IV spectroscopic galaxy survey, the sum of the neutrino masses can be determined with an error $\sigma(M_\nu)\simeq0.06$ eV (95% CL).

SCORCH. I. THE GALAXY–HALO CONNECTION IN THE FIRST BILLION YEARS

SCORCH (Simulations and Constructions of the Reionization of Cosmic Hydrogen) is a new project to study the Epoch of Reionization (EoR). In this first paper, we probe the connection between observed high-redshift galaxies and simulated dark matter halos to better understand the abundance and evolution of the primary source of ionizing radiation. High-resolution N-body simulations are run to quantify the abundance of dark matter halos as a function of mass $M$, accretion rate $\dot{M}$, and redshift $z$. A new fit for the halo mass function $dn/dM$ is $\approx 20\%$ more accurate at the high-mass end where bright galaxies are expected to reside. A novel approach is used to fit the halo accretion rate function $dn/d\dot{M}$ in terms of the halo mass function. Abundance matching against the observed galaxy luminosity function is used to estimate the luminosity-mass relation and the luminosity-accretion-rate relation. The inferred star formation efficiency is not monotonic with $M$ nor $\dot{M}$, but reaches a maximum value at a characteristic mass $\sim 2 \times 10^{11}\ M_\odot$ and a characteristic accretion rate $\sim 6 \times 10^2\ M_\odot/{\rm yr}$ at $z \approx 6$. We find a universal EoR luminosity-accretion-rate relation and construct a fiducial model for the galaxy luminosity function. The Schechter parameters evolve such that $\phi_\star$ decreases, $M_\star$ is more positive (fainter), and $\alpha$ is more negative (steeper) at higher redshifts. We forecast for the upcoming James Webb Space Telescope and show that with apparent magnitude limit $m_{\rm AB} \approx 31\ (32)$, it can observe $\gtrsim 11\ (24)$ unlensed galaxies per square degree per unit redshift at least down to $M_\star$ at $z \lesssim 13\ (14)$.

Computation of the halo mass function using physical collapse parameters: application to non-standard cosmologies

In this article we compare the halo mass function predicted by the excursion set theory with a drifting diffusive barrier against the results of N-body simulations for several cosmological models. This includes the standard ΛCDM case for a large range of halo masses, models with different types of primordial non-Gaussianity, and the Ratra-Peebles quintessence model of Dark Energy. We show that in all those cosmological scenarios, the abundance of dark matter halos can be described by a drifting diffusive barrier, where the two parameters describing the barrier have physical content. In the case of the Gaussian ΛCDM, the statistics are precise enough to actually predict those parameters at different redshifts from the initial conditions. Furthermore, we found that the stochasticity in the barrier is non-negligible making the simple deterministic spherical collapse model a bad approximation even at very high halo masses. We also show that using the standard excursion set approach with a barrier inspired by peak patches leads to inconsistent predictions of the halo mass function.

Testing the Self-Consistency of the Excursion Set Approach to Predicting the Dark Matter Halo Mass Function

The excursion set approach provides a framework for predicting how the abundance of dark matter halos depends on the initial conditions. A key ingredient of this formalism is the specification of a critical overdensity threshold (barrier) which protohalos must exceed if they are to form virialized halos at a later time. However, to make its predictions, the excursion set approach explicitly averages over all positions in the initial field, rather than the special ones around which halos form, so it is not clear that the barrier has physical motivation or meaning. In this Letter we show that once the statistical assumptions which underlie the excursion set approach are considered a drifting diffusing barrier model does provide a good self-consistent description both of halo abundance as well as of the initial overdensities of the protohalo patches.

The ratio of CO to total gas mass in high-redshift galaxies

Walter et al. (20012) have recently identified the J=6-5, 5-4, and 2-1 CO rotational emission lines, and [C_{II}] fine-structure emission line from the star-forming interstellar medium in the high-redshift submillimeter source HDF 850.1, at z = 5.183. We employ large velocity gradient (LVG) modeling to analyze the spectra of this source assuming the [C_{II}] and CO emissions originate from (i) separate unvirialized regions, (ii) separate virialized regions, (iii) uniformly mixed unvirialized region, and (iv) uniformly mixed virialized regions. We present the best fit set of parameters, including for each case the ratio $\alpha$ between the total hydrogen/helium gas mass and the CO(1-0) line luminosity. We also present computations of the ratio of H_{2} mass to [C_{II}] line-luminosity for optically thin conditions, for a range of gas temperatures and densities, for direct conversion of [C_{II}] line-luminosities to "dark-H_{2}" masses. For HDF 850.1 we find that a model in which the CO and C^{+} are uniformly mixed in gas that is shielded from UV radiation, requires a cosmic-ray or X-ray ionization rate of $\zeta \approx$ 10^{-13} s^{-1}, plausibly consistent with the large star-formation rate ($\sim$ 10^{3} M$_{\odot}$ yr^{-1}) observed in this source. Enforcing the cosmological constraint posed by the abundance of dark matter halos in the standard $\Lambda$CDM cosmology and taking into account other possible contributions to the total gas mass, we find that three of these four models are less likely at the 2$\sigma$ level. We conclude that modeling HDF 850.1's ISM as a collection of unvirialized molecular clouds with distinct CO and C^{+} layers, for which $\alpha$ = 0.6 M$_{\odot}$ (K km s^{-1} pc^{2})^{-1} for the CO to H_{2} mass-to-luminosity ratio, (similar to the standard ULIRG value), is most consistent with the $\Lambda$CDM cosmology.

Peaks theory and the excursion set approach

We describe a model of dark matter halo abundances and clustering which combines the two most widely used approaches to this problem: that based on peaks and the other based on excursion sets. Our approach can be thought of as addressing the cloud-in-cloud problem for peaks and/or modifying the excursion set approach so that it averages over a special subset, rather than all possible walks. In this respect, it seeks to account for correlations between steps in the walk as well as correlations between walks. We first show how the excursion set and peaks models can be written in the same formalism, and then use this correspondence to write our combined excursion set peaks model. We then give simple expressions for the mass function and bias, showing that even the linear halo bias factor is predicted to be k-dependent as a consequence of the nonlocality associated with the peak constraint. At large masses, our model has little or no need to rescale the variable delta_c from the value associated with spherical collapse, and suggests a simple explanation for why the linear halo bias factor appears to lie above that based on the peak-background split at high masses when such a rescaling is assumed. Although we have concentrated on peaks, our analysis is more generally applicable to other traditionally single-scale analyses of large-scale structure.

The non-Gaussian halo mass function with fNL, gNL and τNL

Primordial non-Gaussianity has emerged as one of the most promising probes of the inflationary epoch. While the cosmic microwave background and large-scale halo bias currently provide the most stringent constraints on the non-Gaussian parameter fNL, the abundance of dark matter halos is a complementary probe which may allow tests of Gaussianity which are independent of the precise form of non-Gaussian initial conditions. We study the halo mass function in N-body simulations with a range of non-Gaussian initial conditions. In addition to the usual fNL model, we consider gNLΦ3-type non-Gaussianity and models where the 4-point amplitude τNL is an independent parameter. We introduce a new analytic form for the halo mass function in the presence of primordial non-Gaussianity, the ``log-Edgeworth'' mass function, and find good agreement with the N-body simulations. The log-Edgeworth mass function introduces no free parameters and can be constructed from first principles for any model of primordial non-Gaussianity.

The statistics of the subhalo abundance of dark matter haloes

We study the population statistics of the surviving subhaloes of LCDM dark matter haloes using a set of very high resolution N-body simulations. These include both simulations of representative regions of the Universe and ultra-high resolution resimulations of individual dark matter haloes. We find that more massive haloes tend to have a larger mass fraction in subhaloes. For example, cluster size haloes typically have 7.5 percent of their mass within R200 in substructures of fractional mass larger than 1e-5, which is 25 percent higher than galactic haloes. There is, however, a large variance in the subhalo mass fraction from halo to halo, whereas the subhalo abundance shows much higher regularity. For dark matter haloes of fixed mass, the subhalo abundance decreases by 30 percent between redshift 2 and 0. The subhalo abundance function correlates with the host halo concentration parameter and formation redshift. However, the intrinsic scatter is not significantly reduced for narrow ranges of concentration parameter or formation redshift, showing that they are not the dominant parameters that determine the subhalo abundance in a halo.

Large-scale bias and the inaccuracy of the peak-background split

The peak-background split argument is commonly used to relate the abundance of dark matter halos to their spatial clustering. Testing this argument requires an accurate determination of the halo mass function. We present a Maximum Likelihood method for fitting parametric functional forms to halo abundances which differs from previous work because it does not require binned counts. Our conclusions do not depend on whether we use our method or more conventional ones. In addition, halo abundances depend on how halos are defined. Our conclusions do not depend on the choice of link length associated with the friends-of-friends halo-finder, nor do they change if we identify halos using a spherical overdensity algorithm instead. The large scale halo bias measured from the matter-halo cross spectrum b_x and the halo autocorrelation function b_xi (on scales k~0.03h/Mpc and r ~50 Mpc/h) can differ by as much as 5% for halos that are significantly more massive than the characteristic mass M*. At these large masses, the peak background split estimate of the linear bias factor b1 is 3-5% smaller than b_xi, which is 5% smaller than b_x. We discuss the origin of these discrepancies: deterministic nonlinear local bias, with parameters determined by the peak-background split argument, is unable to account for the discrepancies we see. A simple linear but nonlocal bias model, motivated by peaks theory, may also be difficult to reconcile with our measurements. More work on such nonlocal bias models may be needed to understand the nature of halo bias at this level of precision.