Cosmology dependence of galaxy cluster scaling relations

The abundance of galaxy clusters as a function of mass and redshift is a well known powerful cosmological probe, which relies on underlying modelling assumptions on the mass-observable relations (MOR). Some of the MOR parameters can be constrained directly from multi-wavelength observations, as the normalization at some reference cosmology, the mass-slope, the redshift evolution and the intrinsic scatter. However, the cosmology dependence of MORs cannot be tested with multi-wavelength observations alone. We use {\tt Magneticum} simulations to explore the cosmology dependence of galaxy cluster scaling relations. We run fifteen hydro-dynamical cosmological simulations varying $\Omega_m$, $\Omega_b$, $h_0$ and $\sigma_8$ (around a reference cosmological model). The MORs considered are gas mass, baryonic mass, gas temperature, $Y$ and velocity dispersion as a function of virial mass. We verify that the mass and redshift slopes and the intrinsic scatter of the MORs are nearly independent of cosmology with variations significantly smaller than current observational uncertainties. We show that the gas mass and baryonic mass sensitively depends only on the baryon fraction, velocity dispersion and gas temperature on $h_0$, and $Y$ on both baryon fraction and $h_0$. We investigate the cosmological implications of our MOR parameterization on a mock catalog created for an idealized eROSITA-like experiment. We show that our parametrization introduces a strong degeneracy between the cosmological parameters and the normalization of the MOR. Finally, the parameter constraints derived at different overdensity ($\Delta_{500c}$), for X-ray bolometric gas luminosity, and for different subgrid physics prescriptions are shown in the appendix.