(No) dimming of X-ray clusters beyond z~1 at fixed mass: crude redhshifts and masses from raw X-ray and SZ data

Scaling relations in the LCDM Cosmology predict that for a given mass the clusters formed at larger redshift are hotter, denser and therefore more luminous in X-rays than their local z~0 counterparts. This effect overturns the decrease in the observable X-ray flux so that it does not decrease at z > 1, similar to the SZ signal. Provided that scaling relations remain valid at larger redshifts, X-ray surveys will not miss massive clusters at any redshift, no matter how far they are. At the same time, the difference in scaling with mass and distance of the observable SZ and X-ray signals from galaxy clusters at redshifts $z\lesssim 2$ offers a possibility to crudely estimate the redshift and the mass of a cluster. This might be especially useful for preselection of massive high-redshift clusters and planning of optical follow-up for overlapping surveys in X-ray (e.g., by SRG/eRosita) and SZ (e.g. Planck, SPT and ACT).