Anisotropic redshift distributions in photometric galaxy clustering and their cosmological impact

Photometric galaxy clustering is a major probe of large-scale structure. Its interpretation rests on an accurate treatment of the redshift distribution, n(z), of the galaxy sample. Standard analyses assume the n(z) of a selected lens galaxy sample to be isotropic, whereas observational systematics imprint a variation of it across the sky. The cosmological impact of this n(z) anisotropy has not yet been studied end-to-end at survey-level realism. We quantified how it biases the angular two-point correlations w(þeta), the internal consistency of a cosmological analysis of these data, and the inferred cosmological parameters. We developed an analytical formalism of angular galaxy clustering under spatially varying n(z) and forward-modeled the full observation chain from realistic maps of observational systematics, a machine-learning emulated galaxy selection function, to tomographic binning. We computed the resulting observed w(þeta) and propagated the impact of anisotropic n(z) to a joint analysis of galaxy clustering and galaxy--galaxy lensing for a KiDS-like survey. We extended the analysis to configurations that adopt the larger DES- and LSST-sized tiles together with each survey's area and number density. For our fiducial magnitude-limited sample, modeling w(þeta) with a single global bar n (z) underestimates the true clustering signal by up to ∼10% at small scales in the highest tomographic bin, falling to a few percent at intermediate redshifts and vanishing at low redshifts. When propagated to cosmology, the parameter shifts remain below 1σ for the KiDS-like and DES-like setups. However, for the LSST-like setup, σ_8 is biased low by 1.7σ and Ω_m is biased high by 1.4σ along their degeneracy. The contamination is preferentially absorbed by the high-redshift galaxy bias, which shifts by up to ∼4σ. The anisotropy also affects whether the probes are consistent enough to combine: a calibrated posterior-predictive internal-consistency test determines the contaminated angular clustering to be improbable given the joint cosmic-shear and galaxy--galaxy-lensing constraints (median calibrated tilde p under LSST-like noise). -4 Anisotropic redshift distributions have a small but non-negligible effect in our KiDS-like and DES-like configurations and a significant effect in our LSST-like configuration, which retains KiDS-like selection and observing-condition variation. Because our forward model is predictive and independent of cosmology, the same machinery that quantifies the effect could be inverted to mitigate it given a realistic selection function and galaxy population model.