The infall region as a complementary probe to cluster abundance

Abstract

ABSTRACT Galaxy cluster abundance measurements provide a classic test of cosmology. They are most sensitive to the evolved amplitude of fluctuations, usually expressed as $S_8 = \sigma _8\sqrt{\Omega _{\rm m}/0.3}$. Thus, abundance constraints exhibit a strong degeneracy between $\sigma _8$ and $\Omega _{\rm m}$, as do other similar low-redshift tests such as cosmic shear. The mass distribution in the infall region around galaxy clusters, where material is being accreted from the surrounding field, also exhibits a cosmological dependence, but in this case it is nearly orthogonal to the $S_8$ direction in the $\Omega _{\rm m}$–$\sigma _8$ plane, making it highly complementary to halo abundance or cosmic shear studies. We explore how weak-lensing measurements of the infall region might be used to complement abundance studies, considering three different tests. The splashback radius is a prominent feature of the infall region; we show that detection of this feature in lensing data from the Euclid survey could independently constrain $\Omega _{\rm m}$ and $\sigma _8$ to $\pm 0.05$. Another feature, the depletion radius where the bias reaches a minimum, also shows cosmological dependence, though it is challenging to observe in practice. The strongest constraints come from direct measurements of the shear profile in the infall region at 2–$4\, r_{200{\rm c}}$. Combining the latter with abundance constraints such as those reported from SRG$/$eROSITA should reduce the area of the error contours by an estimated factor of 1.2 using a sample of clusters observed by the UNIONS survey, or a factor of 3 using clusters observed by the Euclid Wide survey over a broader range of redshift.