Anisotropic Extinction Distortion of the Galaxy Correlation Function

Similar to the magnification of the galaxies' fluxes by gravitational lensing, the extinction of the fluxes by comic dust, whose existence is recently detected by Menard et al (2009), also modify the distribution of a flux-selected galaxy sample. We study the anisotropic distortion by dust extinction to the 3D galaxy correlation function, including magnification bias and redshift distortion at the same time. We find the extinction distortion is most significant along the line of sight and at large separations, similar to that by magnification bias. The correction from dust extinction is negative except at sufficiently large transverse separations, which is almost always opposite to that from magnification bias (we consider a number count slope s > 0.4). Hence, the distortions from these two effects tend to reduce each other. At low z (~<1), the distortion by extinction is stronger than that by magnification bias, but at high z, the reverse holds. We also study how dust extinction affects probes in real space of the baryon acoustic oscillations (BAO) and the linear redshift distortion parameter beta. We find its effect on BAO is negligible. However, it introduces a positive scale-dependent correction to beta that can be as large as a few percent. At the same time, we also find a negative scale-dependent correction from magnification bias, which is up to percent level at low z, but to ~40% at high z. These corrections are non-negligible for precision cosmology, and should be considered when testing General Relativity through the scale-dependence of beta.