The impact of baryons on the sparsity of simulated galaxy clusters from "The three hundred project". Astrophysical and cosmological implications

Context. Measurements of the sparsity of galaxy clusters can be used to probe the cosmological information encoded in the host dark matter halo profile, and infer constraints on the cosmological model parameters. Key to the success of these analyses is the control of potential sources of systematic uncertainties. As an example, the presence of baryons can alter the cluster sparsity with respect to predictions from N-body simulations. Similarly, a radial-dependent mass bias, as in the case of cluster masses inferred under the hydrostatic equilibrium (HE) hypothesis, can affect sparsity estimates. Aims. First, we examined the imprint of baryonic processes on the sparsity statistics. Then, we investigated the relation between cluster sparsities and the gas mass fraction. Finally, we performed a study of the impact of HE mass bias on sparsity measurements and the implication on cosmological parameter inference analyses. Methods. We used catalogues of simulated galaxy clusters from THE THREE HUNDRED project and ran a comparative analysis of the sparsity of clusters from hydrodynamical N-body simulations implementing different feedback model scenarios. Results. Sparsities that probe the mass profile across a large radial range are affected by the presence of baryons in a way that is particularly sensitive to astrophysical feedback, whereas those exclusively probing external cluster regions are less affected. In the former case, we find the sparsities to be moderately correlated with measurements of the gas fraction in the inner cluster regions. We inferred constraints on S8 using synthetic average sparsity measurements generated to evaluate the impact of baryons, selection effects and HE bias. In the case of multiple sparsities (s200, 500, s200, 2500, and s500, 2500), these lead to highly biased results. Hence, we calibrated linear bias models that enabled us to correct for these effects and recover unbiased constraints that are significantly tighter than those inferred from the analysis of s200, 500 only.