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ABSTRACT  The X‐ray properties of groups and clusters of galaxies obey scaling relations that provide insight into the physics of their formation and evolution. In this paper, we constrain gas and dark matter parameters of these systems, by comparing the observed relations to theoretical expectations, obtained assuming that the gas is in hydrostatic equilibrium with the dark matter and follows a polytropic relation. In this exercise, we vary four parameters: the gas polytropic index Γ, its temperature at large radii, the dark matter logarithmic slope at large radii ζ and its concentration. When comparing the model to the observed mass–temperature relation of local high‐mass systems, we find our results to be independent of both the gas temperature at large radii and of the dark matter concentration. We thus obtain constraints on Γ, by fixing the dark matter profile, and on ζ, by fixing the gas profile. For a Navarro–Frenk–White dark matter profile, we find that Γ must lie between 6/5 and 13/10. This value is consistent with numerical simulations and observations of individual clusters. Taking 6/5 ≲Γ≲ 13/10 allows the dark matter profile to be slightly steeper than the Navarro–Frenk–White profile at large radii. Upon including local low‐mass systems, we obtain constraints on the mass dependence of Γ and on the value of the gas temperature at large radii. Interestingly, by fixing Γ= 6/5 and ζ=−3, we reproduce the observed steepening/breaking of the mass–temperature relation at low masses if the temperature of the intercluster medium is between 10 6  and 10 7  K, consistent with numerical simulations and observations of the warm–hot intergalactic medium. When extrapolated to high redshift, the model with a constant Γ reproduces the expected self‐similar behaviour. Given our formulation, we can also naturally account for the observed, non‐self‐similar relations provided by some high‐redshift clusters, as they simply provide constraints on the evolution of Γ. In addition, comparing our model to the observed luminosity–temperature relation, we are able to discriminate between different mass–concentration relations and find that a weak dependence of concentration on mass is currently preferred by data. In summary, this simple theoretical model can still account for much of the complexity of recent, improved X‐ray scaling relations, provided that we allow for a mild dependence of the polytropic index on mass or for a gas temperature at large radii consistent with intercluster values.

The polytropic approximation and X‐ray scaling relations: constraints on gas and dark matter profiles for galaxy groups and clusters