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Self-gravitating systems such as elliptical galaxies appear to have aconstant integrated specific entropy and obey a scaling law relating theirpotential energy to their mass. These properties can be interpreted as due tothe physical processes involved in the formation and evolution of thesestructures. Dark matter halos obtained through numerical simulations have alsobeen found to obey a scaling law relating their potential energy to their masswith the same slope as for ellipticals, and very close to the expected valuepredicted by theory. Since the X-ray gas in clusters is weakly dissipative, wetest here the hypothesis that it verifies similar properties. Comparableproperties for the dark matter component are also investigated. With this aim,we have analyzed ROSAT-PSPC images of 24 clusters, and fit a S\'ersic law totheir X-ray surface brightness profiles. We found that: 1) the S\'ersic lawparameters (intensity, shape and scale) describing the X-ray gas emission arecorrelated two by two, with a strong correlation between the shape and scaleparameters; 2) the hot gas in all these clusters roughly has the sameintegrated specific entropy, although a second order correlation between thisintegrated specific entropy and both the gas mass and the dynamical mass isobserved; 3) a scaling law links the cluster potential energy to its totalmass, with the same slope as that derived for elliptical galaxies and for darkmatter halo simulations. Comparable relations are obtained for the dark mattercomponent. All these correlations are probably the consequence of the formationand evolution processes undergone by clusters of galaxies.Comment: Accepted for publication in A&

A study of dark matter halos and gas properties in clusters of galaxies from ROSAT data