Bispectrum and Nonlinear Biasing of Galaxies: Perturbation Analysis, Numerical Simulation, and SDSS Galaxy Clustering

Abstract

Abstract We consider nonlinear biasing models of galaxies with particular attention to a correlation between the linear and quadratic biasing coefficients, $b_1$ and $b_2$. We first derive perturbative expressions for $b_1$ and $b_2$ in halo and peak biasing models. We then discuss our computations of the power spectra and bispectra of dark matter particles and halos using $N$-body simulation data and of volume-limited subsamples of Sloan Digital Sky Survey (SDSS) galaxies, and determine their $b_1$ and $b_2$. We find that the values of those coefficients at linear regimes ($k<0.2$$h$ Mpc$^{-1}$) are fairly insensitive to the redshift-space distortion and the survey volume shape. The resulting normalized amplitudes of the bispectra, $Q$, for equilateral triangles are insensitive to the values of $b_1$, implying that $b_2$ indeed correlates with $b_1$. The present results explain the previous finding of Kayo et al. (2004, PASJ, 56, 415) for the hierarchical relation of three-point correlation functions of SDSS galaxies. While the relations between $b_1$ and $b_2$ are quantitatively different for specific biasing models, their approximately similar correlations indicate a fairly generic outcome of the biasing due to the gravity in primordial Gaussian density fields.