Detecting scale-dependence of bias from APM-BGC galaxies

We present an investigation of the scale-dependence of bias described by the linear model: [delta rho(x)/<(rho)over bar>](g) = b[delta rho(x)/<(rho)over bar>](m), b being the bias parameter, and rho(x)(g) and rho(x)(m) being the galaxy number density and mass density, respectively. Using a discrete wavelet decomposition, we show that the behavior of bias scale-dependence cannot be described by one parameter b. In the linear bias model, the scale-dependence should be measured by the j-spectra of wavelet-coefficient-represented bias parameters (b) over tilde(j)((n)) and b(j)((n)), n being positive integers. Because (b) over tilde(j)((n)) with different n are independent from each other, a systematic analysis of the j-spectra of (b) over tilde(j)((n)) and (b) over tilde(j)((n)) is necessary. We performed a j-spectrum analysis for samples of elliptical and lenticular (EL) and spiral (SP) galaxies listed in the APM Bright Galaxy Catalogue. We found that, for statistics of two-point correlation functions or discrete wavelet transform power spectrum, the scale-independence holds within 1 sigma. However, the bias scale-dependence becomes substantial when phase-sensitive statistics (e.g., (b) over tilde(j)((n)) with n > 2 or b(j)((n))) are applied. These results indicate that the bias scale-dependence has the same origin as the non-Gaussianity of galaxy distributions. This is generally consistent with the explanation that the bias scale-dependence originated from nonlinear and nonlocal relationship between galaxy formation and their environment.