Stochastic Biasing and Galaxy-Mass Density Relation in the Weakly Non-linear Regime

Abstract

It is believed that the biasing of the galaxies plays an important role for understanding the large-scale structure of the universe. In general, the biasing of galaxy formation could be stochastic. Furthermore, the future galaxy survey might allow us to explore the time evolution of the galaxy distribution. In this paper, the analytic study of the galaxy-mass density relation and its time evolution is presented within the framework of the stochastic biasing. In the weakly non-linear regime, we derive a general formula for the galaxy-mass density relation as a conditional mean using the Edgeworth expansion. The resulting expression contains the joint moments of the total mass and galaxy distributions. Using the perturbation theory, we investigate the time evolution of the joint moments and examine the influence of the initial stochasticity on the galaxy-mass density relation. The analysis shows that the galaxy-mass density relation could be well-approximated by the linear relation. Compared with the skewness of the galaxy distribution, we find that the estimation of the higher order moments using the conditional mean could be affected by the stochasticity. Therefore, the galaxy-mass density relation as a conditional mean should be used with a caution as a tool for estimating the skewness and the kurtosis.

22 pages, 7 Encapusulated Postscript Figures, aastex, The title and the structure of the paper has been changed, Results and conclusions unchanged, Accepted for publication in ApJ

References in corpus (5)

• The Bispectrum as a Signature of Gravitational Instability in Redshift-Space
• The time-evolution of bias
• On the spatial distribution of dark matter halos
• Old high-redshift galaxies and primordial density fluctuation spectra
• Quasi Non-linear Evolution of Stochastic Bias

Cited by in corpus (35)

• Large-Scale Galaxy Bias
• Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS
• Primordial non-Gaussianity: large-scale structure signature in the perturbative bias model
• Constraining Primordial non-Gaussianity with Bispectrum and Power Spectum from Upcoming Optical and Radio Surveys
• Modeling Biased Tracers at the Field Level
• Stochasticity of Bias and Nonlocality of Galaxy Formation: Linear Scales
• Observational evidence for stochastic biasing
• A halo bias function measured deeply into voids without stochasticity
• Testing one-loop galaxy bias: joint analysis of power spectrum and bispectrum
• On Combining Galaxy Clustering and Weak Lensing to Unveil Galaxy Biasing via the Halo Model
• Locally Biased Galaxy Formation and Large Scale Structure
• Cosmological parameters from the likelihood analysis of the galaxy power spectrum and bispectrum in real space
• Forecasts on Primordial non-Gaussianity from 21 cm Intensity Mapping experiments
• Scale-Dependent Galaxy Bias from Massive Particles with Spin during Inflation
• The Hunt for Primordial Interactions in the Large Scale Structures of the Universe
• Testing one-loop galaxy bias: Power spectrum
• Nonlinear stochastic biasing from the formation epoch distribution of dark halos
• Perturbation theory for modeling galaxy bias: validation with simulations of the Dark Energy Survey
• Lagrangian bias of generic large-scale structure tracers
• The Angular Three-Point Correlation Function in the Quasilinear Regime
• COMET: Clustering Observables Modelled by Emulated perturbation Theory
• Cosmological constraints from the power spectrum and bispectrum of 21cm intensity maps
• Probing primordial non-Gaussianity with the power spectrum and bispectrum of future 21cm intensity maps
• Multi-tracer power spectra and bispectra: Formalism
• Euclid preparation. XLI. Galaxy power spectrum modelling in real space
• Testing one-loop galaxy bias: cosmological constraints from the power spectrum
• Non-Gaussian gravitational clustering field statistics
• Nonlinear Stochastic Biasing of Peaks and Halos: Scale-Dependence, Time-Evolution, and Redshift-Space Distortion from Cosmological N-body Simulations
• Stochastic Biasing and Weakly Non-linear Evolution of Power Spectrum
• Renormalization of Lagrangian bias via spectral parameters
• Time evolution of the stochastic linear bias of interacting galaxies on linear scales
• A galaxy-halo model of large-scale structure
• $\text{PineTree}$: A generative, fast, and differentiable halo model for wide-field galaxy surveys
• The time evolution of bias
• Comparing the redshift-space density field to the real-space velocity field