Bispectrum and nonlinear biasing of galaxies: Perturbation analysis, numerical simulation, and SDSS galaxy clustering

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.