  We present results for two-particle transverse momentum correlations, <dpt,i
dpt,j>, as a function of event centrality for Au+Au collisions at sqrt(sNN) =
20, 62, 130, and 200 GeV at the Relativistic Heavy Ion Collider. We observe
correlations decreasing with centrality that are similar at all four incident
energies. The correlations multiplied by the multiplicity density increase with
incident energy and the centrality dependence may show evidence of processes
such as thermalization, minijet production, or the saturation of transverse
flow. The square root of the correlations divided by the event-wise average
transverse momentum per event shows little or no beam energy dependence and
generally agrees with previous measurements at the Super Proton Synchrotron.
