Anisotropic redshift distributions in photometric galaxy clustering and their cosmological impact

RESUMO

Photometric galaxy clustering is a major probe of large-scale structure whose interpretation relies on accurate characterization of the galaxy redshift distribution, $n(z)$. Standard analyses assume the $n(z)$ of a selected lens sample to be isotropic, whereas observational systematics can imprint spatial variations. We quantify how this anisotropy biases angular galaxy clustering, internal consistency, and cosmological inference. We develop an analytical formalism for clustering under spatially varying $n(z)$ and forward-model realistic observational systematics, galaxy selection, and tomographic binning. For a fiducial magnitude-limited sample, modeling $w(\theta)$ with a single global $\bar n(z)$ underestimates the clustering signal by up to $\sim10\%$ at small scales in the highest-redshift bin, decreasing towards lower redshift. In a $2\times2$pt analysis, cosmological parameter shifts remain below $1\sigma$ for KiDS-like and DES-like setups. For an LSST-like setup retaining KiDS-like selection and observing-condition variation, $\sigma_8$ is biased low by $1.7\sigma$ and $\Omega_m$ high by $1.4\sigma$, while the high-redshift galaxy bias shifts by up to $\sim4\sigma$. The anisotropy also affects whether the probes are consistent enough to combine: a calibrated posterior-predictive internal-consistency test finds the contaminated angular clustering improbable given the joint cosmic-shear and galaxy--galaxy-lensing constraints (median calibrated $\tilde p\approx8\times10^{-4}$ under LSST-like noise). Anisotropic redshift distributions are therefore a potentially significant systematic for future photometric clustering analyses. Our forward model can be used to mitigate it given a realistic selection function and galaxy population model.