Controlling and leveraging small-scale information in tomographic galaxy–galaxy lensing

Abstract

The tangential shear signal receives contributions from physical scales in the galaxymatter correlation function well below the transverse scale at which it is measured.Since small scales are difficult to model, this non-locality has generally required stringent scale cuts or new statistics for cosmological analyses. Using the fact that uncertainty in these contributions corresponds to an uncertainty in the enclosed projected mass around the lens, we provide an analytic marginalization scheme to account for this. Our approach enables the inclusion of measurements on smaller scales without requiring numerical sampling over extra free parameters. We extend the analytic marginalization formalism to retain cosmographic ("shear-ratio") information from small-scale measurements that would otherwise be removed due to modeling uncertainties, again without requiring the addition of extra sampling parameters. We test the methodology using simulated likelihood analysis of a DES Year 5-like galaxygalaxy lensing and galaxy clustering datavector. We demonstrate that we can remove parameter biases due to the presence of an un-modeled 1-halo contamination of the galaxy-galaxy lensing signal, and use the shear-ratio information on small scales to improve cosmological parameter constraints.

Dark Energy Survey Year 3 results: Galaxy-halo connection from galaxy-galaxy lensing

“…When let to vary, it accounts for any imperfect modeling of the galaxy-matter crosscorrelation on scales smaller than the smallest measured scale used in the model fit. This is similar to the point-mass term derived in MacCrann et al (2020a) and used in Krause et al (2021).…”

Dark Energy Survey Year 3 Results: Exploiting small-scale information with lensing shear ratios

“…The grey bands show the size of the data uncertainties on the ratios, for reference. Prat et al 2021 andMacCrann et al 2019) the scales between 6-8 ℎ −1 Mpc do not add significant information. Regardless, we use the large-scale ratios purely as validation for the small-scale ratios, as detailed in Section VII.…”

“…The correlation of the SR likelihood with the (3×)2pt likelihood will come mostly from the galaxy-galaxy lensing 2pt measurements. Since we do not leave any gap between the minimum scale used for 2pt measurements (6ℎ −1 Mpc) and the small-scale ratios, this can in principle be worrying since the tangential shear is non-local, and therefore it receives contributions from physical scales in the galaxy-matter correlation function that are below the scale at which it is measured (Baldauf et al 2010, MacCrann et al 2019, Park et al 2020). However, for the large scales 2pt galaxy-galaxy lensing used in the DES Y3 3×2pt analysis, we follow the approach of MacCrann et al ( 2019) and marginalize analytically over the unknown enclosed mass, which effectively removes any cor-relation with scales smaller than the small-scale limit of 6 ℎ −1 Mpc, ensuring that the information from the 3×2pt measurements is independent from the small-scale ratios used in this work, which use scales smaller than 6 ℎ −1 Mpc.…”

Perturbation theory for modeling galaxy bias: Validation with simulations of the Dark Energy Survey

“…The tangential shear γ t ðθÞ is nonlocal and depends on the correlation function at all scales smaller than the transverse distance χθ [Eq. (18); see MacCrann et al [45] and Baldauf et al [46] for a detailed analysis]. Perturbation theory is not adequate for modeling these small scales.…”