Dependency of high-mass satellite galaxy abundance on cosmology in Magneticum simulations

Context. Observational studies carried out to calibrate the masses of galaxy clusters often use mass-richness relations to interpret galaxy number counts.
Aims: Here, we aim to study the impact of the richness-mass relation modelled with cosmological parameters on mock mass calibrations.
Methods: We build a Gaussian process regression emulator of high-mass satellite abundance normalisation and log-slope based on cosmological parameters Ω_m, Ω_b, σ₈, h₀, and redshift z. We train our emulator using Magneticum hydrodynamic simulations that span different cosmologies for a given set of feedback scheme parameters.
Results: We find that the normalisation depends, albeit weakly, on cosmological parameters, especially on Ω_m and Ω_b, and that their inclusion in mock observations increases the constraining power of these latter by 10%. On the other hand, the log-slope is ≈1 in every setup, and the emulator does not predict it with significant accuracy. We also show that satellite abundance cosmology dependency differs between full-physics simulations, dark-matter only, and non-radiative simulations.
Conclusions: Mass-calibration studies would benefit from modelling of the mass-richness relations with cosmological parameters, especially if the satellite abundance cosmology dependency.