RASS-MCMF: A full-sky X-ray selected galaxy cluster catalog

We present the RASS-MCMF catalog of 8,465 X-ray selected galaxy clusters over 25,000 deg$^2$ of extragalactic sky. The accumulation of deep, multiband optical imaging data, the development of the Multi-Component Matched Filter cluster confirmation algorithm (MCMF), and the release of the DESI Legacy Survey DR10 catalog makes it possible -- for the first time, more than 30 years after the launch of the ROSAT X-ray satellite -- to identify the majority of the galaxy clusters detected in the second ROSAT All-Sky-Survey (RASS) source catalog (2RXS). The resulting 90\% pure RASS-MCMF catalog is the largest ICM-selected cluster sample to date. RASS-MCMF probes a large dynamic range in cluster mass spanning from galaxy groups to the most massive clusters. The cluster redshift distribution peaks at $z\sim0.1$ and extends to redshifts $z\sim1$. Out to $z\sim0.4$, the RASS-MCMF sample contains more clusters per redshift interval ($dN/dz$) than any other ICM-selected sample. In addition to the main sample, we present two subsamples with 6,924 and 5,516 clusters, exhibiting 95\% and 99\% purity, respectively.. We forecast the utility of the sample for a cluster cosmological study, using realistic mock catalogs that incorporate most observational effects, including the X-ray exposure time and background variations, the existence likelihood selection and the impact of the optical cleaning with the algorithm MCMF. Using realistic priors on the observable-mass relation parameters from a DES-based weak lensing analysis, we estimate the constraining power of the RASS-MCMF$\times$DES sample to be of 0.026, 0.033 and 0.15 ($1\sigma$) on the parameters $\Omega_\mathrm{m}$, $\sigma_8$ and $w$, respectively.