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Register a new userAccurate and Efficient Halo-based Galaxy Clustering Modelling with Simulations
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Zheng Zheng University of Utah
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Small- and intermediate-scale galaxy clustering can be used to establish the galaxy-halo connection to study galaxy formation and evolution and to tighten constraints on cosmological parameters. With the increasing precision of galaxy clustering measurements from ongoing and forthcoming large galaxy surveys, accurate models are required to interpret the data and extract relevant information. We introduce a method based on high-resolution N-body simulations to accurately and efficiently model the galaxy two-point correlation functions (2PCFs) in projected and redshift spaces. The basic idea is to tabulate all information of haloes in the simulations necessary for computing the galaxy 2PCFs within the framework of halo occupation distribution or conditional luminosity function. It is equivalent to populating galaxies to dark matter haloes and using the mock 2PCF measurements as the model predictions. Besides the accurate 2PCF calculations, the method is also fast and therefore enables an efficient exploration of the parameter space. As an example of the method, we decompose the redshift-space galaxy 2PCF into different components based on the type of galaxy pairs and show the redshift-space distortion effect in each component. The generalizations and limitations of the method are discussed.
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We perform an ensemble of $N$-body simulations with $2048^3$ particles for 101 flat $w$CDM cosmological models sampled based on a maximin-distance Sliced Latin Hypercube Design. By using the halo catalogs extracted at multiple redshifts in the range of $z=[0,1.48]$, we develop Dark Emulator, which enables fast and accurate computations of the halo mass function, halo-matter cross-correlation, and halo auto-correlation as a function of halo masses, redshift, separations and cosmological models, based on the Principal Component Analysis and the Gaussian Process Regression for the large-dimensional input and output data vector. We assess the performance of the emulator using a validation set of $N$-body simulations that are not used in training the emulator. We show that, for typical halos hosting CMASS galaxies in the Sloan Digital Sky Survey, the emulator predicts the halo-matter cross correlation, relevant for galaxy-galaxy weak lensing, with an accuracy better than $2%$ and the halo auto-correlation, relevant for galaxy clustering correlation, with an accuracy better than $4%$. We give several demonstrations of the emulator. It can be used to study properties of halo mass density profiles such as the mass-concentration relation and splashback radius for different cosmologies. The emulator outputs can be combined with an analytical prescription of halo-galaxy connection such as the halo occupation distribution at the equation level, instead of using the mock catalogs, to make accurate predictions of galaxy clustering statistics such as the galaxy-galaxy weak lensing and the projected correlation function for any model within the $w$CDM cosmologies, in a few CPU seconds.
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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 galaxy surveys. Our method relies on low-resolution approximate gravity solvers to simulate the large scale dark matter field, which we then populate with halos according to a flexible nonlinear and stochastic bias model. In particular, we extend the textsc{patchy} code with an efficient particle mesh algorithm to simulate the dark matter field (the textsc{FastPM} code), and with a robust MCMC method relying on the textsc{emcee} code for constraining the parameters of the bias model. Using the halos in the BigMultiDark high-resolution $N$-body simulation as a reference catalog, we demonstrate that our technique can model the bivariate probability distribution function (counts-in-cells), power spectrum, and bispectrum of halos in the reference catalog. Specifically, we show that the new ingredients permit us to reach percentage accuracy in the power spectrum up to $ksim 0.4; ,h,{rm Mpc}^{-1}$ (within 5% up to $ksim 0.6; ,h,{rm Mpc}^{-1}$) with accurate bispectra improving previous results based on Lagrangian perturbation theory.
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