Constraints on precipitation-limited hot halos from massive galaxies to galaxy clusters

We present constraints on a simple analytical model for hot diffuse halo gas, derived from a fit spanning two orders of magnitude in halo mass ($M_{500} \sim 10^{12.5}-10^{14.5} M_{\odot}$). The model is motivated by the observed prevalence of a precipitation limit, and its main free parameter is the central ratio of gas cooling timescale to free-fall timescale ($t_{\rm cool}/t_{\rm ff}$). We use integrated X-ray and thermal Sunyaev-Zel'dovich observations of the environments around massive galaxies, galaxy groups and clusters, averaged in halo mass bins, and obtain the best-fitting model parameters. We find $t_{\rm cool}/t_{\rm ff} \sim 50-110$, depending on the model extrapolation beyond the halo virial radius and possibly on biases present in the data-sets used in the fitting analysis. The model adequately describes the entire mass range, except for intermediate mass halos ($M_{500} \sim 10^{13.5} M_{\odot}$) which systematically fall below the model predictions. However, the best fits for $t_{\rm cool}/t_{\rm ff}$ substantially exceed the values typically derived from X-ray observations of individual systems ($t_{\rm cool}/t_{\rm ff} \sim 10-30$). We consider several explanations for those discrepancies, including X-ray selection biases and a potential anti-correlation between X-ray luminosity and the central galaxy's stellar mass.