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 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. Then we compute 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<0.2h/Mpc) are fairly insensitive to the redshift-space distortion and the survey volume shape. The resulting normalized amplitudes of 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) 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. 
Takahiro Nishimichi, Issha Kayo, Chiaki Hikage, Kazuhiro Yahata,   Atsushi Taruya, Y. P. Jing, Ravi K. Sheth, and Yasushi Suto