2022MNRAS.516..992S

Numerical simulations with varying realism indicate an emergent principle-multiphase condensation and large cavity power occur when the ratio of the cooling time to the free-fall time (t_cool/t_ff) falls below a threshold value close to 10. Observations indeed show cool-core signatures when this ratio falls below 20-30, but the prevalence of cores with t_cool/t_ff ratio below 10 is rare as compared to simulations. In X-ray observations, we obtain projected spectra from which we have to infer radial gas density and temperature profiles. Using idealized models of X-ray cavities and multiphase gas in the core and 3D hydro jet-ICM simulations, we quantify the biases introduced by deprojection based on the assumption of spherical symmetry in determining t_cool/t_ff. We show that while the used methods are able to recover the t_cool/t_ff ratio for relaxed clusters, they have an uncertainty of a factor of 2-3 in systems containing large cavities (≳ 20 kpc). We also show that the mass estimates from these methods, in the absence of X-ray spectra close to the virial radius, suffer from a degeneracy between the virial mass (M₂₀₀) and the concentration parameter (c) in the form of M₂₀₀c² ≈ constant. Additionally, the lack of soft-X-ray (≲ 0.5 keV) coverage and poor spatial resolution makes us overestimate min(t_cool/t_ff) by a factor of few in clusters with min(t_cool/t_ff) ≲ 5. This bias can largely explain the lack of cool-core clusters with min(t_cool/t_ff) ≲ 5.