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Many studies point out that there exists some tight correlations between darkmatter and baryonic matter at different radii in galaxies. However, similartight correlations can only be found in galaxy clusters for large radii. Herewe report extremely tight correlations between the gravitational mass $M_{\rmgrav}$ and hot gas mass $M_{\rm gas}$ in galaxy clusters at the hot gas coreradius $r_c$ and at $2r_c$ (i.e. $M_{\rm grav}(r_c)$ vs $M_{\rm gas}(r_c)$ and$M_{\rm grav}(2r_c)$ vs $M_{\rm gas}(2r_c)$). By using the X-ray data of 64large galaxy clusters with different sizes and masses, we find that thecorrelations can be described by a single relation $\log(M_{\rmgrav}/M_{\odot})=(0.74 \pm 0.02) \log(M_{\rm gas}/M_{\odot})+(4.47 \pm 0.23)$for a wide range of hot gas mass ($10^{11}M_{\odot}-10^{14}M_{\odot}$). Thecorresponding correlation coefficient and scatter are 0.97 and 0.10 dexrespectively. This would be the first tight correlation with very small scatterbetween the enclosed gravitational mass and hot gas mass for galaxy clusterswithin intermediate radii ($\sim 100-1000$ kpc) and it provides a new kind ofobservational evidence to support the universality of correlation between darkmatter and baryons.

A tight correlation between the enclosed gravitational mass and hot gas mass in galaxy clusters at intermediate radii