We use the ROSAT all sky survey X-ray cluster catalogs and the optical SDSS DR7 galaxy and group catalogs to cross-identify X-ray clusters with their optical counterparts , resulting in a sample of 201 X-ray clusters in the sky coverage of SDSS DR7 .
We investigate various correlations between the optical and X-ray properties of these X-ray clusters , and find that the following optical properties are correlated with the X-ray luminosity : the central galaxy luminosity , the central galaxy mass , the characteristic group luminosity ( \propto L _ { X } ^ { 0.43 } ) , the group stellar mass ( \propto L _ { X } ^ { 0.46 } ) , with typical 1- \sigma scatter of \sim 0.67 in \log L _ { X } .
Using the observed number distribution of X-ray clusters , we obtain an unbiased scaling relation between the X-ray luminosity , the central galaxy stellar mass and the characteristic satellite stellar mass as { \log L _ { X } } = -0.26 + 2.90 [ \log ( M _ { \ast,c } +0.26 M _ { sat } ) -12.0 ] ( and in terms of luminosities , as { \log L _ { X } } = -0.15 + 2.38 [ \log ( L _ { c } +0.72 L _ { sat } ) -12.0 ] ) .
We find that the systematic difference between different halo mass estimations , e.g. , using the ranking of characteristic group stellar mass or using the X-ray luminosity scaling relation can be used to constrain cosmology .
Comparing the properties of groups of similar stellar mass ( or optical luminosities ) and redshift that are X-ray luminous or under-luminous , we find that X-ray luminous groups have more faint satellite galaxies and higher red fraction in their satellites .
The cross-identified X-ray clusters together with their optical properties are provided in Appendix B .