We present and test a new numerical method to determine second-order Lagrangian displacement fields in the context of modified gravity (MG) theories. We start from the extension of Lagrangian Perturbation Theory to a class of MG models that can be described by a parametrized Poisson equation, with the introduction of a scale-dependent function. We exploit fast Fourier transforms to compute the full source term of the differential equation for the second-order Lagrangian displacement field. We compare its mean to the source term computed for specific configurations for which a k-dependent solution can be found numerically. We choose the configuration that best matches the full source term, thus obtaining an approximate factorization of the second-order displacement field as the space term valid for standard gravity times a k-dependent, second-order growth factor $D_2(k,t)$. This approximation is used to compute second order displacements for particles. The method is tested against N-body simulations run with standard and $f(R)$ gravity: we rely on the results of a friends-of-friends code run on the N-body snapshots to assign particles to halos, then compute the halo power spectrum. We find very consistent results for the two gravity theories: second-order LPT (2LPT) allows to recover the halo power spectrum of N-body simulations within $\sim 10\%$ precision to $k\sim 0.2-0.4\ h\ {\rm Mpc}^{-1}$, as well as halo positions, with an error that is a fraction of the inter-particle distance. We show that, when considering the same level of non-linearity in the density field, the performance of 2LPT with MG is the same (within $1\%$) as the one obtained for the standard $Λ$CDM model with General Relativity. When implemented in a computer code, this formulation of 2LPT can quickly generate dark matter distributions with $f(R)$ gravity, and can easily be extended to other MG theories.
Virtually any investigation involving dark matter halos relies on a definition of their radius, mass, and of whether they are a subhalo. The halo boundary is most commonly defined to include a spherical overdensity contrast (such as R200c, Rvir, and R200m), but different thresholds lead to significant differences in radius and mass. The splashback radius has recently been suggested as a more physically motivated (and generally larger) halo boundary, adding to the range of definitions. It is often difficult to assess the impact of a particular choice because most halo catalogs contain only one …
We delineate the conditions under which the consistency relation for the non-Gaussian bias and the universality of the halo mass function hold in the context of microscopic Lagrangian descriptions of halos. The former is valid provided that the collapse barrier depends only on the physical fields (instead of fields normalized by their variance for example) and explicitly includes the effect of {\it all} physical fields such as the tidal shear. The latter holds provided that the response of the halo number density to a long-wavelength density fluctuation is equivalent to the response induced by…
Using a mapping from dark matter halos to galaxy properties based on hydrodynamical simulations, we explore the impact of galaxy properties on the void size function and the void-galaxy correlation function. We replicate the properties of galaxies from Illustris on MassiveNus halos, to perform both luminosity and star formation rate cuts on MassiveNus halos. We compare the impact of such cuts on voids properties with respect to cuts on halo mass (as usually performed on halo catalogs driven from N-body simulations). We find that void catalogs built from luminosity-selected galaxies and halos a…
We apply a new galaxy group finder to the Main Galaxy Sample of the SDSS. This algorithm introduces new freedom to assign halos to galaxies that is self-calibrated by comparing the catalog to complementary data. These include galaxy clustering data and measurements of the total satellite luminosity from deep imaging data. We present constraints on the galaxy-halo connection for star-forming and quiescent populations. The results of the self-calibrated group catalog differ in several key ways from previous group catalogs and halo occupation analyses. The transition halo mass scale, where half o…
We develop a new, simple, fast and parameter-free method to construct dark matter halo catalogues. This method requires as inputs only the linear matter power spectrum and the threshold density for halo formation in linear theory. It directly uses excursion set ideas and Lagrangian perturbation theory to produce halo catalogues with the correct abundance, large scale power spectrum, bispectrum and velocity field. These halo catalogues can be used for the fast construction of mock galaxy catalogues, allowing for the evaluation of covariance matrices for multiple observables. Because of its robu…
We present a detailed description and validation of our massively-parallel update to the mass-Peak Patch method, a fully predictive initial-space algorithm to quickly generate dark matter halo catalogues in very large cosmological volumes. We perform an extensive systematic comparison to a suite of N-body simulations covering a broad range of redshifts and simulation resolutions, and find that, without any parameter fitting, our method is able to generally reproduce N-body results while typically using over 3 orders of magnitude less CPU time, and a fraction of the memory cost. Instead of calc…
We present the latest version of Pinocchio, a code that generates catalogues of DM haloes in an approximate but fast way with respect to an N-body simulation. This code version extends the computation of particle and halo displacements up to 3rd-order Lagrangian Perturbation Theory (LPT), in contrast with previous versions that used Zeldovich approximation (ZA). We run Pinocchio on the same initial configuration of a reference N-body simulation, so that the comparison extends to the object-by-object level. We consider haloes at redshifts 0 and 1, using different LPT orders either for halo cons…
Towards precision cosmology with Voids x CMB correlations (I): Roman-Agora mock catalogs and pipeline validation
Instituto de Astrofísica de Canarias（加那利天体物理学研究所）；Universidad de La Laguna（拉古纳大学）；MTA–CSFK Lendület “Momentum” Large-Scale Structure (LSS) Research Group（马塔-匈牙利科学院技术研究中心“动量”大尺度结构研究组）；Konkoly Observatory, HUN-REN Research Centre for Astronomy and Earth Sciences（孔科利天文台，匈牙利研究与创新地球与天文学研究中心）；CPPM, Aix-Marseille Université, CNRS/IN2P3（马赛物理中心，艾克斯-马赛大学，法国国家科学研究中心/法国国家核与粒子物理研究所）；Princeton University（普林斯顿大学）
Optimal linear reconstruction of dark matter from halo catalogs
我们推导出适用于暗物质晕的加权函数w（M），它使加权晕分布与其底层质量密度场之间的随机性最小化。最佳w（M）取决于估计量中使用的质量范围。在N体模拟中，Poisson估计量的噪音比最佳估计量高出15倍。实施的最佳权重产生显着较低的随机性比加权晕的质量，偏差或相等。最佳加权可以使基于物质功率谱或互相关的宇宙学测试更加强大和/或具有成本效益。在z <1 universe could ideally be done using only 6 million redshifts of halos with mass M>=0（z=1）时，对整个z 6 \times 10^{13}h^{-1}M_ \odot（1 \times 10^{13}）在k= 0.2 h/Mpc处的质量功率谱进行体积限制测量;这比泊松模型预测的少5倍。使用晕占有率分布（HOD），我们发现均匀加权的明亮红色星系表需要比最佳加权晕表多3倍的红移才能重建相同精度的质量。虽然在阈值光度以上的星系的平均HOD类似于最佳w（M），晕占据的随机性降低了质量估计。蓝色或发射线星系在重建质量方面的效率比最佳加权方案低100倍。这表明一种有效的观测方法，在进行光谱调查之前，用深光-Z调查来识别和加权晕。当M>10^{12}h^{-1}M_ \odot时，由标准晕模型预测的最佳w（M）和质量估计随机性与我们的测量结果相当一致，但重要…
Predictions of the next-to-leading order, i.e. one-loop, halo power spectra depend on local and non-local bias parameters up to cubic order. The linear bias parameter can be estimated from the large scale limit of the halo-matter power spectrum, and the second order bias parameters from the large scale, tree-level, bispectrum. Cubic operators would naturally be quantified using the tree-level trispectrum. As the latter is computationally expensive, we extent the quadratic field method proposed in Schmittfull et al. 2014 to cubic fields in order to estimate cubic bias parameters. We cross-corre…
The ELUCID project aims to build a series of realistic cosmological simulations that reproduce the spatial and mass distribution of the galaxies as observed in the Sloan Digital Sky Survey (SDSS). This requires powerful reconstruction techniques to create constrained initial conditions. We test the reconstruction method by applying it to several $N$-body simulations. We use 2 medium resolution simulations from each of which three additional constrained $N$-body simulations were produced. We compare the resulting friend of friend catalogs by using the particle indexes as tracers, and quantify t…
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 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 $δ_1$ in the initial Lagrangian space. The bias expansion, however, does not guarantee non-negativity of the halo counts, and may give rising halo number counts at negative overd…
We investigate various phenomenological schemes for the rapid generation of 3D mock galaxy catalogues with a given power spectrum and bispectrum. We apply the fast bispectrum estimator \MODALLSS{} to these mock galaxy catalogues and compare to $N$-body simulation data analysed with the halo-finder \texttt{ROCKSTAR} (our benchmark data). We propose an assembly bias model for populating parent halos with subhalos by using a joint lognormal-Gaussian probability distribution for the subhalo occupation number and the halo concentration. This prescription enabled us to recover the benchmark power sp…
We investigate the viability of producing galaxy mock catalogues with COmoving Lagrangian Acceleration (COLA) simulations in Modified Gravity (MG) models employing the Halo Occupation Distribution (HOD) formalism. In this work, we focus on two theories of MG: $f(R)$ gravity with the chameleon mechanism, and a braneworld model (nDGP) that incorporates the Vainshtein mechanism. We use a suite of full $N$-body simulations in MG as a benchmark to test the accuracy of COLA simulations. At the level of Dark Matter (DM), we show that COLA accurately reproduces the matter power spectrum up to $k \sim …
Lagrangian algorithms to simulate the evolution of cold dark matter (CDM) are invaluable tools to generate large suites of mock halo catalogues. In this paper, we first show that the main limitation of current semi-analytical schemes to simulate the displacement of CDM is their inability to model the evolution of overdensities in the initial density field, a limit that can be circumvented by detecting halo particles in the initial conditions. We thus propose `MUltiscale Spherical Collapse Lagrangian Evolution Using Press-Schechter' (muscle-ups), a new scheme that reproduces the results from La…
We present a method for generating suites of dark-matter halo catalogs with only a few $N$-body simulations, focusing on making small changes to the underlying cosmology of a simulation with high precision. In the context of blind challenges, this allows us to reuse a simulation by giving it a new cosmology after the original cosmology is revealed. Starting with full $N$-body realizations of an original cosmology and a target cosmology, we fit a transfer function that displaces halos in the original so that the galaxy/HOD power spectrum matches that of the target cosmology. This measured trans…
This paper introduces SMACC -- Subhalo Mass-loss Analysis using Core Catalogs. SMACC adds a mass model to substructure merger trees based on halo "core tracking." Our approach avoids the need for running expensive subhalo finding algorithms and instead uses subhalo mass-loss modeling to assign masses to halo cores. We present details of the SMACC methodology and demonstrate its excellent performance in describing halo substructure and its evolution. Validation of the approach is carried out using cosmological simulations at significantly different resolutions. We apply SMACC to the 1.24 trilli…
We study the relations among the parameters of the hybrid Lagrangian bias expansion model, fitting biased auto and cross power spectra up to $k_{\rm max} = 0.7 \, h \, \mathrm{Mpc}^{-1}$. We consider $\sim 8000$ halo and galaxy samples, with different halo masses, redshifts, galaxy number densities, and varying the parameters of the galaxy formation model. Galaxy samples are obtained through state-of-the-art extended subhalo abundance matching techniques and include both stellar-mass and star-formation-rate selected galaxies. All of these synthetic galaxies samples are publicly available at ht…
The protohalo patches from which halos form are defined by a number of constraints imposed on the Lagrangian dark matter density field. Each of these constraints contributes to biasing the spatial distribution of the protohalos relative to the matter. We show how measurements of this spatial distribution -- linear combinations of protohalo bias factors -- can be used to make inferences about the physics of halo formation. Our analysis exploits the fact that halo bias factors satisfy consistency relations which encode this physics, and that these relations are the same even for sub-populations …
The window function for protohalos in Lagrangian space is often assumed to be a tophat in real space. We measure this profile directly and find that it is more extended than a tophat but less extended than a Gaussian; its shape is well-described by rounding the edges of the tophat by convolution with a Gaussian that has a scale length about 5 times smaller. This effective window $W_{\rm eff}$ is particularly simple in Fourier space, and has an analytic form in real space. Together with the excursion set bias parameters, $W_{\rm eff}$ describes the scale-dependence of the Lagrangian halo-matter…
Large-scale sky surveys require companion large volume simulated mock catalogs. To ensure precision cosmology studies are unbiased, the correlations in these mocks between galaxy properties and their large-scale environments must be realistic. Since galaxies are embedded in dark matter halos, an important first step is to include such correlations -- sometimes called assembly bias -- for dark matter halos. However, galaxy properties correlate with smaller scale physics in halos which large simulations struggle to resolve. We describe an algorithm which addresses and largely mitigates this prob…
Reliable extraction of cosmological information from clustering measurements of galaxy surveys requires estimation of the error covariance matrices of observables. The accuracy of covariance matrices is limited by our ability to generate sufficiently large number of independent mock catalogs that can describe the physics of galaxy clustering across a wide range of scales. Furthermore, galaxy mock catalogs are required to study systematics in galaxy surveys and to test analysis tools. In this investigation, we present a fast and accurate approach for generation of mock catalogs for the upcoming…
Fitting half-integer generalized Laguerre functions to the evolved, real-space dark matter and halo correlation functions provides a simple way to reconstruct their initial shapes. We show that this methodology also works well in a wide variety of realistic, assembly biased, velocity biased and redshift-space distorted mock galaxy catalogs. We use the linear point feature in the monopole of the redshift-space distorted correlation function to quantify the accuracy of our approach. We find that the linear point estimated from the mock galaxy catalogs is insensitive to the details of the biasing…
We present several methods to accurately estimate Lagrangian bias parameters and substantiate them using simulations. In particular, we focus on the quadratic terms, both the local and the non local ones, and show the first clear evidence for the latter in the simulations. Using Fourier space correlations, we also show for the first time, the scale dependence of the quadratic and non-local bias coefficients. For the linear bias, we fit for the scale dependence and demonstrate the validity of a consistency relation between linear bias parameters. Furthermore we employ real space estimators, usi…
Associating the formation sites of haloes with the maxima of the smoothed linear density field, we present non-perturbative predictions for the Lagrangian and evolved halo correlation functions that are valid at all separations. In Lagrangian space, we find significant deviations from the perturbative bias calculation at small scales, in particular, a pronounced exclusion region where $ξ=-1$ for maxima of unequal height. Our predictions are in good agreement with the Lagrangian clustering of dark matter proto-haloes reconstructed from N-body simulations. Our predictions for the mean infall and…
We present rotation curve fits to 175 late-type galaxies from the Spitzer Photometry & Accurate Rotation Curves (SPARC) database using seven dark matter (DM) halo profiles: pseudo-isothermal (pISO), Burkert, Navarro-Frenk-White (NFW), Einasto, Di Cintio (2014, DC14), coreNFW, and a new semi-empirical profile named Lucky13. We marginalize over stellar mass-to-light ratio, galaxy distance, disk inclination, halo concentration and halo mass (and an additional shape parameter for Einasto) using a Markov Chain Monte Carlo method. We find that cored halo models such as the DC14 and Burkert profiles …
Precision cosmology has recently triggered new attention on the topic of approximate methods for the clustering of matter on large scales, whose foundations date back to the period from late '60s to early '90s. Indeed, although the prospect of reaching sub-percent accuracy in the measurement of clustering poses a challenge even to full N-body simulations, an accurate estimation of the covariance matrix of clustering statistics, not to mention the sampling of parameter space, requires usage of a large number (hundreds in the most favourable cases) of simulated (mock) galaxy catalogs. Combinatio…
The halo mass function (HMF) is a critical element in cosmological analyses of galaxy cluster catalogs. We quantify the impact of uncertainties in HMF parameters on cosmological constraints from cluster catalogs similar to those from Planck, those expected from the Euclid, Roman and Rubin surveys, and from a hypothetical larger future survey. We analyse simulated catalogs in each case, gradually loosening priors on HMF parameters to evaluate the degradation in cosmological constraints. While current uncertainties on HMF parameters do not substantially impact Planck-like surveys, we find that t…
We calculate the dark matter halo correlation function in redshift space using the Gaussian streaming model (GSM). To determine the scale dependent functions entering the streaming model we use local Lagrangian bias together with Convolution Lagrangian perturbation theory (CLPT) which constitutes an approximation to the Post-Zel'dovich approximation. On the basis of N-body simulations we demonstrate that a smoothing of the initial conditions with the Lagrangian radius improves the Zel'dovich approximation and its ability to predict the displacement field of proto-halos. Based on this observati…
We present direct measurements of cubic bias parameters of dark matter halos from the halo-matter-matter-matter trispectrum. We measure this statistic efficiently by cross-correlating the halo field measured in N-body simulations with specific third-order nonlocal transformations of the initial density field in the same simulation. Together with the recent Abidi & Baldauf (2018), these are the first measurements of halo bias using the four-point function that have been reported to date. We also obtain constraints on the quadratic bias parameters. For all individual cubic parameters involving t…
We present 2000 mock galaxy catalogs for the analysis of baryon acoustic oscillations in the Emission Line Galaxy (ELG) sample of the Extended Baryon Oscillation Spectroscopic Survey Data Release 16 (eBOSS DR16). Each mock catalog has a number density of $6.7 \times 10^{-4} h^3 \rm Mpc^{-3}$, covering a redshift range from 0.6 to 1.1. The mocks are calibrated to small-scale eBOSS ELG clustering measurements at scales of around 10 $h^{-1}$Mpc. The mock catalogs are generated using a combination of GaLAxy Mocks (GLAM) simulations and the Quick Particle-Mesh (QPM) method. GLAM simulations are use…
The dark matter halos that host galaxies and clusters form out of initial high-density patches, providing a biased tracer of the linear matter density field. In the simplest local bias approximation, the halo field is treated as a perturbative series in the average overdensity of the Lagrangian patch. In more realistic models, however, additional quantities will affect the clustering of halo-patches, and this expansion becomes a function of several stochastic variables. In this paper, we present a general multivariate expansion scheme that can parametrize the clustering of any biased Lagrangia…
We construct an emulator for the halo mass function over group and cluster mass scales for a range of cosmologies, including the effects of dynamical dark energy and massive neutrinos. The emulator is based on the recently completed Mira-Titan Universe suite of cosmological $N$-body simulations. The main set of simulations spans 111 cosmological models with 2.1 Gpc boxes. We extract halo catalogs in the redshift range $z=[0.0, 2.0]$ and for masses $M_{200\mathrm{c}}\geq 10^{13}M_\odot/h$. The emulator covers an 8-dimensional hypercube spanned by {$Ω_\mathrm{m}h^2$, $Ω_\mathrm{b}h^2$, $Ω_νh^2$,…
Halo based reconstruction of the cosmic mass density field
我们提出了一个基于晕的方法重建宇宙质量密度场的实现。该方法利用宇宙学N体模拟计算的暗物质晕及其环境的质量密度分布，将其与晕星表卷积，重建由晕分布决定的暗物质密度场。我们将该方法应用于Yang et al（2007）根据SDSS数据Release 4构建的星表。因此，我们得到重建的宇宙质量密度场是独立的任何明确的假设的偏见。我们详细描述了该方法的实施，提出了一个详细的表征重建的密度场（平均质量密度分布，关联函数和细胞计数）和大规模的环境（细丝，空隙，峰和片）在我们的重建分类的结果。该方法的应用包括大尺度上的星系人口的形态学研究和约束模拟的实现。
