The Three Hundred Project: Validating $H_0$ inference from mock X-ray and millimetre analyses of galaxy clusters
Measurements of thermodynamical quantities in galaxy clusters are differently affected by simplified modelling of radially averaged observables in the X-ray and millimetre bands. This includes assumptions about the cosmological model and the morphology of the cluster intracluster medium (ICM). Within a large sample of clusters extracted from The Three Hundred hydrodynamical simulations, we assess the systematic differences expected from the morphological assumptions between ICM temperatures as inferred from X-ray spectroscopy or joint X-ray and millimetre imaging. We find that these differences show a well-defined statistical behaviour that correlates with the cluster dynamical and morphological indicators. We then investigate how joint inferences of cluster temperature profiles, a priori informed by this statistical behaviour, allow us to constrain cosmological parameters inferred from the apparent cluster sizes. Assuming a flat $\Lambda$ cold dark matter ($\Lambda$CDM) cosmology and priors on $\Omega_\mathrm{m}$ and the helium abundance, this method provides us with unbiased estimates of the Hubble constant, $H_0$, characterised with a precision of about $4\%$ and $1.5\%$ for samples of 100 and 1000 clusters, respectively, and ultimately limited by systematic uncertainties of about $0.6$--$0.8\, {\rm km\, s^{-1} Mpc^{-1}}$. This work highlights the potential of joint X-ray and millimetre observations of galaxy cluster samples to place tight constraints on $H_0$.