We propose a simple estimator for the gravitational
potential of cluster-size halos using the temperature and density
profiles of the intracluster gas based on the assumptions of
hydrostatic equilibrium and spherical symmetry. Using high resolution
cosmological simulations of galaxy clusters, we show that the scaling
relation between this estimator and the gravitational potential has a
small intrinsic scatter of about 10%, and it is insensitive to baryon
physics outside the cluster core. The slope and the normalization of
the scaling relation vary weakly with redshift, and they are
relatively independent of the choice of radial range used and the
dynamical states of the clusters. The results presented here provide a
way for using the cluster potential function as an alternative to the
cluster mass function in constraining cosmology using galaxy clusters.
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