  Recent simulations show that giant planets of about one Jupiter mass migrate
inward at a rate that differs from the Type II prediction. Here we show that at
higher masses, planets migrate outward. Our result differs from previous ones
because of our longer simulation times, lower viscosity, and our boundary
conditions that allow the disk to reach viscous steady state. We show that, for
planets on circular orbits, the transition from inward to outward migration
coincides with the known transition from circular to eccentric disks that
occurs for planets more massive than a few Jupiters. In an eccentric disk, the
torque on the outer disk weakens due to two effects: the planet launches weaker
waves, and those waves travel further before damping. As a result, the torque
on the inner disk dominates, and the planet pushes itself outward. Our results
suggest that the many super-Jupiters observed by direct-imaging at large
distances from the star may have gotten there by outward migration.
