Euclid preparation. Simulating thousands of Euclid spectroscopic skies

The joint probability distribution of matter overdensity and galaxy counts in cells is a powerful probe of cosmology, and the extent to which variance in galaxy counts at fixed matter density deviates from Poisson shot noise is not fully understood. The lack of informed bounds on this stochasticity is currently the limiting factor in constraining cosmology with the galaxy–matter probability distribution function (PDF). We investigate stochasticity in the conditional distribution of galaxy counts along lines of sight with fixed matter density, and we present a halo occupation distribution (HOD)-based approach for obtaining plausible ranges for stochasticity parameters. To probe the high-dimensional space of possible galaxy–matter connections, we derive a set of HODs that conserve the galaxies’ linear bias and number density to produce REDMAGIC-like galaxy catalogs within the ABACUSSUMMIT suite of N-body simulations. We study the impact of individual HOD parameters and cosmology on stochasticity and perform a Monte Carlo search in HOD parameter space subject to the constraints on bias and density. In mock catalogs generated by the selected HODs, shot noise in galaxy counts spans both sub-Poisson and super-Poisson values, ranging from 80% to 133% of Poisson variance for cells with mean matter density. Nearly all of the derived HODs show a positive relationship between local matter density and stochasticity. For galaxy catalogs with higher stochasticity, modeling galaxy bias to second order is required for an accurate description of the conditional PDF of galaxy counts at fixed matter density. The presence of galaxy assembly bias also substantially extends the range of stochasticity in the super-Poisson direction. This HOD-based approach leverages degrees of freedom in the galaxy–halo connection to obtain informed bounds on nuisance model parameters and can be adapted to study other parametrizations of shot noise in galaxy counts, in particular to motivate prior ranges on stochasticity for cosmological analyses.

We present measurements of the redshift-space three-point correlation function of 50 967 luminous red galaxies (LRGs) from Data Release 3 (DR3) of the Sloan Digital Sky Survey (SDSS). We have studied the shape dependence of the reduced three-point correlation function (Qz(s, q, θ)) on three different scales, s= 4, 7 and 10 h−1 Mpc, and over the range of 1 < q < 3 and 0° < θ < 180°. On small scales (s= 4 h−1 Mpc), Qz is nearly constant, with little change as a function of q and θ. However, there is evidence for a shallow U-shaped behaviour (with θ) which is expected from theoretical modelling of Qz(s, q, θ). On larger scales (s= 7 and 10 h−1 Mpc), the U-shaped anisotropy in Qz (with θ) is more clearly detected. We compare this shape dependence in Qz(s, q, θ) with that seen in mock galaxy catalogues which were generated by populating the dark matter haloes in large N-body simulations with mock galaxies using various halo occupation distributions (HOD). We find that the combination of the observed number density of LRGs, the (redshift-space) two-point correlation function and Qz(s, q, θ) provides a strong constraint on the allowed HOD parameters (Mmin, M1, α) and breaks key degeneracies between these parameters. For example, our observed Qz(s, q, θ) disfavours mock catalogues that overpopulate massive dark matter haloes with many LRG satellites. We also estimate the linear bias of LRGs to be b= 1.87 ± 0.07 in excellent agreement with other measurements.

Cosmic voids are a promising environment to characterize neutrino-induced effects on the large-scale distribution of matter in the universe. We perform a comprehensive numerical study of the statistical properties of voids, identified both in the matter and galaxy distributions, in massive and massless neutrino cosmologies. The matter density field is obtained by running several independent N-body simulations with cold dark matter and neutrino particles, while the galaxy catalogs are modeled by populating the dark matter halos in simulations via a halo occupation distribution (HOD) model to reproduce the clustering properties observed by the Sloan Digital Sky Survey (SDSS) II Data Release 7. We focus on the impact of massive neutrinos on the following void statistical properties: number density, ellipticities, two-point statistics, density and velocity profiles. Considering the matter density field, we find that voids in massive neutrino cosmologies are less evolved than those in the corresponding massless neutrinos case: there is a larger number of small voids and a smaller number of large ones, their profiles are less evacuated, and they present a lower wall at the edge. Moreover, the degeneracy between σ8 and Ων is broken when looking at void properties. In terms of the galaxy density field, we find that differences among cosmologies are difficult to detect because of the small number of galaxy voids in the simulations. Differences are instead present when looking at the matter density and velocity profiles around these voids.

The halo occupation distribution (HOD) describes the bias between galaxies and dark matter by specifying (a) the probability P(N|M) that a halo of virial mass M contains N galaxies of a particular class and (b) the relative distributions of galaxies and dark matter within halos. We calculate predicted HODs for a Lambda-CDM cosmological model using an SPH hydrodynamic simulation and a semi-analytic (SA) galaxy formation model. Although the two methods predict different galaxy mass functions, their HOD predictions agree remarkably well. For mass-selected samples, the mean occupation <N(M)> exhibits a sharp cutoff at low halo masses, a slowly rising plateau for <N>~1-2, and a more steeply rising high occupancy regime. At low <N>, the mean pair and triple counts are well below Poisson expectations, with important consequences for small scale behavior of 2- and 3-point correlation functions. The HOD depends strongly on galaxy age, with high mass halos populated mainly by old galaxies and low mass halos by young galaxies. The SPH simulation supports several simplifying assumptions about HOD bias: the most massive galaxy in a halo usually lies close to the center and moves near the halo's mean velocity; satellite galaxies have the same radial profile and velocity dispersion as the dark matter; and the mean occupation at fixed halo mass is independent of the halo's larger scale environment. By applying the SPH and SA HODs to a large volume N-body simulation, we show that both methods predict slight, observable departures from a power-law galaxy correlation function. The predicted HODs are closely tied to the underlying galaxy formation physics, they offer useful guidance to theoretical models of galaxy clustering, and they will be tested empirically by ongoing analyses of galaxy redshift surveys. (Shortened)

We present measurements of the luminosity-dependent redshift-space three-point correlation functions (3PCFs) for the Sloan Digital Sky Survey Data Release 7 Main galaxy sample. We compare the 3PCF measurements to the predictions from three different halo and subhalo models. One is the halo occupation distribution (HOD) model and the other two are extensions of the subhalo abundance matching model by allowing the central and satellite galaxies to have different occupation distributions in the host halos and subhalos. Parameters in all the models are chosen to best describe the projected and redshift-space two-point correlation functions (2PCFs) of the same set of galaxies. All three model predictions agree well with the 3PCF measurements for the most luminous galaxy sample, while the HOD model better performs in matching the 3PCFs of fainter samples (with luminosity threshold below L*), which is similar in trend to the case of fitting the 2PCFs. The decomposition of the model 3PCFs into contributions from different types of galaxy triplets shows that on small scales the dependence of the 3PCFs on triangle shape is driven by nonlinear redshift-space distortion (and not by the intrinsic halo shape) while on large scales it reflects the filamentary structure. The decomposition also reveals more detailed differences in the three models, which are related to the radial distribution, the mean occupation function, and the velocity distribution of satellite galaxies inside halos. The results suggest that galaxy 3PCFs can further help constrain the above galaxy–halo relation and test theoretical models.

Halo models provide a simple and computationally inexpensive way to investigate the connection between galaxies and their dark matter haloes. However, these models rely on the assumption that the role of baryons can easily be parametrized in the modelling procedure. We aim to examine the ability of halo occupation distribution (HOD) modelling to reproduce the galaxy clustering found in two different hydrodynamic simulations, Illustris and EAGLE. For each simulation, we measure several galaxy clustering statistics on two different luminosity threshold samples. We then apply a simple five parameter HOD, which was fit to each simulation separately, to the corresponding dark matter-only simulations, and measure the same clustering statistics. We find that the halo mass function is shifted to lower masses in the hydrodynamic simulations, resulting in a galaxy number density that is too high when an HOD is applied to the dark matter-only simulation. However, the exact way in which baryons alter the mass function is remarkably different in the two simulations. After applying a correction to the halo mass function in each simulation, the HOD is able to accurately reproduce all clustering statistics for the high luminosity sample of galaxies. For the low luminosity sample, we find evidence that in addition to correcting the halo mass function, including spatial, velocity, and assembly bias parameters in the HOD is necessary to accurately reproduce clustering statistics.

We present an efficient estimator for higher-order galaxy clustering using small groups of nearby galaxies, or multiplets. Using the Luminous Red Galaxy (LRG) sample from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2, we identify galaxy multiplets as discrete objects and measure their cross-correlations with the general galaxy field. Our results show that the multiplets exhibit stronger clustering bias as they trace more massive dark matter halos than individual galaxies. When comparing the observed clustering statistics with the mock catalogs generated from the N-body simulation AbacusSummit, we find that the mocks underpredict multiplet clustering despite reproducing the galaxy two-point auto-correlation reasonably well. This discrepancy indicates that the standard Halo Occupation Distribution (HOD) model is insufficient to describe the properties of galaxy multiplets, revealing the greater constraining power of this higher-order statistic on galaxy-halo connection and the possibility that multiplets are specific to additional assembly bias. We demonstrate that incorporating secondary biases into the HOD model improves agreement with the observed multiplet statistics, specifically by allowing galaxies to preferentially occupy halos in denser environments. Our results highlight the potential of utilizing multiplet clustering, beyond traditional two-point correlation measurements, to break degeneracies in models describing the galaxy-dark matter connection.

The halo occupation distribution (HOD) approach has proven to be an effective method for modeling galaxy clustering and bias. In this approach, galaxies of a given type are probabilistically assigned to individual halos in N-body simulations. In this paper, we present a fast emulator for predicting the fully nonlinear galaxy power spectrum over a range of freely specifiable HOD modeling parameters. The emulator is constructed using results from 100 HOD models run on a large LCDM N-body simulation, with Gaussian Process interpolation applied to a PCA-based representation of the galaxy power spectrum. The total error is currently ~3% (~2% in the simulation and ~1% in the emulation process) from z=1 to z=0, over the considered parameter range. We use the emulator to investigate parametric dependencies in the HOD model, as well as the behavior of galaxy bias as a function of HOD parameters. The emulator is publicly available at http://www.hep.anl.gov/cosmology/CosmicEmu/emu.html.

Perturbative, or effective field theory (EFT)-based, full-shape analyses of galaxy clustering data involve ``nuisance parameters'' to capture various observational effects such as the galaxy-dark matter connection (galaxy bias). We present an efficient approach to set informative physically motivated priors on these parameters. We extract these priors from simulated galaxy catalogs based on halo occupation distribution (HOD) models. First, we build a joint distribution between EFT galaxy bias and HOD parameters from a set of 10,500 HOD mock catalogs. We use the field level EFT technique that allows for cosmic variance cancellation, enabling a precision calibration of EFT parameters from computationally inexpensive small-volume simulations. Second, we use neural density estimators---normalizing flows---to model the marginal probability density of the EFT parameters, which can be used as a prior distribution in full shape analyses. As a first application, we use our HOD-based priors in a new analysis of galaxy power spectra and bispectra from the BOSS survey in the context of single field primordial non-Gaussianity. We find that our priors lead to a reduction of the posterior volume of bias parameters by an order of magnitude. We also find ${f}_{\mathrm{NL}}^{\text{equil}}=320\ifmmode\pm\else\textpm\fi{}300$ and ${f}_{\mathrm{NL}}^{\text{ortho}}=100\ifmmode\pm\else\textpm\fi{}130$ (at 68% CL) in a combined two-template analysis, representing a $\ensuremath{\approx}40%$ improvement in constraints on single field primordial non-Gaussianity, equivalent to doubling the survey volume.

We present the results of an halo occupation distribution (HOD) analysis of star-forming galaxies at $z \sim 2$. We obtained high-quality angular correlation functions based on a large sgzK sample, which enabled us to carry out the HOD analysis. The mean halo mass and the HOD mass parameters are found to increase monotonically with increasing $K$-band magnitude, suggesting that more luminous galaxies reside in more massive dark haloes. The luminosity dependence of the HOD mass parameters was found to be the same as in the local Universe; however, the masses were larger than in the local Universe over all ranges of magnitude. This implies that galaxies at $z \sim 2$ tend to form in more massive dark haloes than in the local Universe, a process known as downsizing. By analysing the dark halo mass evolution using the extended Press--Schechter formalism and the number evolution of satellite galaxies in a dark halo, we find that faint Lyman break galaxies at $z \sim 4$ could evolve into the faintest sgzKs $(22.0 < K \leq 23.0)$ at $z \sim 2$ and into the Milky-Way-like galaxies or elliptical galaxies in the local Universe, whereas the most luminous sgzKs $(18.0 \leq K \leq 21.0)$ could evolve into the most massive systems in the local Universe. The stellar-to-halo mass ratio (SHMR) of the sgzKs was found to be consistent with the prediction of the model, except that the SHMR of the faintest sgzKs was smaller than the prediction at $z \sim 2$. This discrepancy may be attributed that our samples are confined to star-forming galaxies.

Aims. We extract groups of galaxies as flux-limited and volume-limited samples from the SDSS Data Release 7 (DR7) to study the supercluster-void network and environmental properties of groups therein. Volume-limited catalogues are particularly useful for a comparison of numerical simulations of dark matter halos and the large-scale structure with observations.Methods. The extraction of a volume-limited sample of galaxies and groups requires special care to avoid excluding too much observational data. We use a modified friends-of-friends (FoF) method with a slightly variable linking length to obtain a preliminary flux-limited sample. We take the flux-limited groups as the basic sample to include as many galaxies as possible in the volume-limited samples. To determine the scaling of the linking length we calibrated group sizes and mean galaxy number densities within groups by magnitude dilution of a nearby group sub-sample to follow the properties of groups with higher luminosity limits. Results. Our final flux-limited sample contains 78800 groups and volume-limited subsamples with absolute magnitude limits Mr = -18, -19, -20, and -21 contain 5463, 12 590, 18 973, and 9139 groups, respectively, in the DR7 main galaxy main area survey. The group catalogue is available at the CDS.Conclusions. The spatial number densities of our groups within the subsamples, as well as the mean sizes and rms velocities of our groups practically do not change from sub-sample to sub-sample. This means that the catalogues are homogeneous and well suited for a comparison with simulations.

We construct halo occupation distribution (HOD) models of high redshift ($z \gtrsim 7.5$) galaxies with $M_{*}>10^8~M_{\odot}/h$ using the BlueTides hydrodynamic simulation suite, with a particular emphasis on modelling the small scale / 1-halo clustering ($0.01\lesssim r \lesssim 1~ h^{-1}\rm{Mpc}$). Similar to low redshift studies, we find that the central and satellite mean HODs ($\left<N_{\mathrm{cen}}\right>$ and $\left<N_{\mathrm{sat}}\right>$) can be modeled by a smoothed step function and a power law respectively. The number density of satellite galaxies is however significantly suppressed compared to low redshift (satellite fractions drop from $\sim 50 \%$ at $z=0$ to $\lesssim 10 \%$ at $z=7.5$). The mean number of satellites, $\left<N_{\mathrm{sat}}\right> < 1$ for halo masses below $3 \times 10^{11} M_{\odot}/h$ (a rare halo at these redshifts). For the radial number density profiles, satellites with $10^8 \lesssim M^* \lesssim 10^{9} M_{\odot}/h$ in halos with $M_H \gtrsim 3 \times10^{11} M_{\odot}/h$ are consistent with NFW (with concentrations $c_{\mathrm{sat}} \sim 10-40$). Within halos of mass $M_H\lesssim 3 \times 10^{11} M_{\odot}/h$ satellites exhibit a power law profile with slope -3. Because these halos dominate the small scale clustering, the resulting 1-halo term is steeper than predicted using standard NFW profiles. Using this power-law profile for satellites, we can successfully reproduce the small-scale clustering exhibited by BlueTides galaxies using HOD modelling. We predict the highest probability of detecting satellites at $z>7.5$ is around centrals of $M^*\sim 3 \times 10^{10} M_{\odot}/h$ (with $M^{*}\gtrsim$ a few $10^{7} M_{\odot}/h$ ). This should be achievable with the James Webb Space Telescope (JWST).

The shape of the primordial matter power spectrum Plin(k) encodes critical information on cosmological parameters. At large scales, the observable galaxy power spectrum Pobs(k) is expected to follow the shape of Plin(k), but on smaller scales the effects of nonlinearity and galaxy bias make the ratio Pobs(k)/Plin(k) scale-dependent. We develop a method that can extend the dynamic range of the Plin(k) recovery by incorporating constraints on the galaxy halo occupation distribution (HOD) from the projected galaxy correlation function wp. We devise an analytic model to calculate Pobs(k) in real-space and redshift-space. Once HOD parameters are determined by matching wp for a given cosmological model, galaxy bias is completely specified, and our analytic model predicts both the shape and normalization of Pobs(k). Applying our method to SDSS main galaxy samples, we find that the real-space Pobs(k) follows the shape of the nonlinear matter power spectrum at the 1-2% level up to k=0.2 h/Mpc. When we apply our method to SDSS LRG samples, the linear bias approximation is accurate to 5% at k<0.08 h/Mpc, but the scale-dependence of LRG bias prevents the use of linear theory at k>0.08 h/Mpc. Our HOD model prediction is in good agreement with the recent SDSS LRG Pobs(k) measurements at all measured scales (k<0.2 h/Mpc), naturally explaining the shape of Pobs(k). The "Q-model" prescription is a poor description of galaxy bias for the LRG samples, and it can lead to biased cosmological parameter estimates when measurements at k>0.1 h/Mpc are included in the analysis. We quantify the potential bias and constraints on cosmological parameters that arise from applying linear theory and Q-model fitting, and we demonstrate the utility of HOD modeling of future high precision measurements of Pobs(k) on quasi-linear scales.

Context. Empirical models of galaxy-halo connection such as the halo occupation distribution (HOD) model have been widely used over the past decades to intensively test perturbative models on quasi-linear scales. However, these models fail to reproduce the galaxygalaxy lensing signal on non-linear scales, over-predicting the observed signal by up to 40%. Aims. With ongoing Stage-IV galaxy surveys such as DESI and Euclid that will measure cosmological parameters at sub-percent precision, it is now crucial to precisely model the galaxy-halo connection in order to accurately estimate the theoretical uncertainties of perturbative models. Methods. This paper compares a standard HOD (based on halo mass only) to an extended HOD that incorporates as additional features galaxy assembly bias and local environmental dependencies on halo occupation. These models were calibrated against the observed clustering and galaxy-galaxy lensing signal of eBOSS luminous red galaxies and emission line galaxies in the range 0.6 &lt; z &lt; 1.1. We performed a combined clustering-lensing cosmological analysis on the simulated galaxy samples of both HODs to quantify the systematic budget of perturbative models. Results. By considering not only the mass of the dark matter halos but also these secondary properties, the extended HOD offers a more comprehensive understanding of the connection between galaxies and their surroundings. In particular, we found that the luminous red galaxies preferentially occupy denser and more anisotropic environments. Our results highlight the importance of considering environmental factors in empirical models with an extended HOD that reproduces the observed signal within 20% on scales below 10 h−1 Mpc. Our cosmological analysis reveals that our perturbative model yields similar constraints regardless of the galaxy population, with a better goodness of fit for the extended HOD. These results suggest that the extended HOD should be used to quantify modelling systematics. This extended framework should also prove useful for forward modelling techniques.

We investigate machine learning (ML) techniques for predicting the number of galaxies (N_gal) that occupy a halo, given the halo's properties. These types of mappings are crucial for constructing the mock galaxy catalogs necessary for analyses of large-scale structure. The ML techniques proposed here distinguish themselves from traditional halo occupation distribution (HOD) modeling as they do not assume a prescribed relationship between halo properties and N_gal. In addition, our ML approaches are only dependent on parent halo properties (like HOD methods), which are advantageous over subhalo-based approaches as identifying subhalos correctly is difficult. We test 2 algorithms: support vector machines (SVM) and k-nearest-neighbour (kNN) regression. We take galaxies and halos from the Millennium simulation and predict N_gal by training our algorithms on the following 6 halo properties: number of particles, M_200, \sigma_v, v_max, half-mass radius and spin. For Millennium, our predicted N_gal values have a mean-squared-error (MSE) of ~0.16 for both SVM and kNN. Our predictions match the overall distribution of halos reasonably well and the galaxy correlation function at large scales to ~5-10%. In addition, we demonstrate a feature selection algorithm to isolate the halo parameters that are most predictive, a useful technique for understanding the mapping between halo properties and N_gal. Lastly, we investigate these ML-based approaches in making mock catalogs for different galaxy subpopulations (e.g. blue, red, high M_star, low M_star). Given its non-parametric nature as well as its powerful predictive and feature selection capabilities, machine learning offers an interesting alternative for creating mock catalogs.