Detecting Scale‐Dependence of Bias from APM‐BGC Galaxies

We present an investigation of the scale-dependence of bias described by thelinear model: $(\delta \rho({\bf x})/\bar{\rho})_{g} = b (\delta\rho(x)/\bar{\rho})_{m}$, $b$ being the bias parameter, and $\rho({\bf x})_{g}$and $\rho({\bf x})_{m}$ are the galaxy number density and mass density,respectively. Using a discrete wavelet decomposition, we show that the behaviorof bias scale-dependence cannot be described by one parameter $b$. In thelinear bias model the scale-dependence should be measured by the $j$-spectra ofwavelet-coefficient-represented bias parameters $\tilde{b}^{(n)}_j$ and$b_j^{(n)}$, $n$ being positive integers. Because $\tilde{b}^{(n)}_j$ withdifferent $n$ are independent from each other, a systematic analysis of the$j$-spectra of $\tilde{b}^{(n)}_j$ and $b_j^{(n)}$ 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 catalog. We found that, forstatistics of two-point correlation functions or DWT power spectrum, thescale-independence holds within 1 $\sigma$. However, the bias scale-dependencebecomes substantial when phase-sensitive statistics (e.g. $\tilde{b}^{(n)}_j$with $n>2$ or $b_j^{(n)}$) are applied. These results indicate that the biasscale-dependence has the same origin as the non-Gaussianity of galaxydistributions. This is generally consistent with the explanation that the biasscale-dependence originated from non-linear and non-local relationship betweengalaxy formation and their environment.Comment: AAS Latex file, 25 pages with 9 figures included, accepted for publication in Ap