  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 ~8%-15%, 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 possible way for using the cluster potential
function as an alternative to the cluster mass function in constraining
cosmology using galaxy clusters.
