  Large-scale convective flows called giant cells were once thought to
transport the Sun's luminosity in the solar convection zone, but recent
observations have called their existence into question. In place of large-scale
flows, some authors have suggested the solar luminosity may instead be
transported by small droplets of rapidly falling, low entropy fluid. This
"entropy rain" could propagate as dense vortex rings, analogous to rising
buoyant thermals in the Earth's atmosphere. In this work, we develop an
analytical theory describing the evolution of dense, negatively buoyant
thermals. We verify the theory with 2D cylindrical and 3D cartesian simulations
of laminar, axisymmetric thermals in highly stratified atmospheres. Our results
show that dense thermals fall in two categories: a stalling regime in which the
droplets slow down and expand, and a falling regime in which the droplets
accelerate and shrink as they propagate downwards. We estimate that solar
downflows are in the falling regime and maintain their entropy perturbation
against diffusion until they reach the base of the convection zone. This
suggests that entropy rain may be an effective nonlocal mechanism for
transporting the solar luminosity.
