Anisotropic magnification distortion of the 3D galaxy correlation. I. Real space

Abstract

It has long been known that gravitational lensing, primarily via magnification bias, modifies the observed galaxy (or quasar) clustering. Such discussions have largely focused on the 2D angular correlation function. Here and in paper II [L. Hui, E. Gazta\~naga, and M. LoVerde, arXiv:0710.4191] we explore how magnification bias distorts the 3D correlation function and power spectrum, as first considered by Matsubara [Astrophys. J. Lett. 537, L77 (2000).]. The interesting point is that the distortion is anisotropic. Magnification bias in general preferentially enhances the observed correlation in the line-of-sight (LOS) orientation, especially on large scales. For instance, at a LOS separation of $\ensuremath{\sim}100\text{ }\text{ }\mathrm{Mpc}/\mathrm{h}$, where the intrinsic galaxy-galaxy correlation is rather weak, the observed correlation can be enhanced by lensing by a factor of a few, even at a modest redshift of $z\ensuremath{\sim}0.35$. This effect presents an interesting opportunity as well as a challenge. The opportunity: this lensing anisotropy is distinctive, making it possible to separately measure the galaxy-galaxy, galaxy-magnification, and magnification-magnification correlations, without measuring galaxy shapes. The anisotropy is distinguishable from the well-known distortion due to peculiar motions, as will be discussed in paper II. The challenge: the magnification distortion of the galaxy correlation must be accounted for in interpreting data as precision improves. For instance, the $\ensuremath{\sim}100\text{ }\text{ }\mathrm{Mpc}/\mathrm{h}$ baryon acoustic oscillation scale in the correlation function is shifted by up to $\ensuremath{\sim}3%$ in the LOS orientation, and up to $\ensuremath{\sim}0.6%$ in the monopole, depending on the galaxy bias, redshift, and number count slope. The corresponding shifts in the inferred Hubble parameter and angular diameter distance, if ignored, could significantly bias measurements of the dark energy equation of state. Lastly, magnification distortion offers a plausible explanation for the well-known excess correlations seen in pencil beam surveys.