  Hot Jupiter atmospheres exhibit fast, weakly-ionized winds. The interaction
of these winds with the planetary magnetic field generates drag on the winds
and leads to ohmic dissipation of the induced electric currents. We study the
magnitude of ohmic dissipation in representative, three-dimensional atmospheric
circulation models of the hot Jupiter HD 209458b. We find that ohmic
dissipation can reach or exceed 1% of the stellar insolation power in the
deepest atmospheric layers, in models with and without dragged winds. Such
power, dissipated in the deep atmosphere, appears sufficient to slow down
planetary contraction and explain the typically inflated radii of hot Jupiters.
This atmospheric scenario does not require a top insulating layer or radial
currents that penetrate deep in the planetary interior. Circulation in the
deepest atmospheric layers may actually be driven by spatially non-uniform
ohmic dissipation. A consistent treatment of magnetic drag and ohmic
dissipation is required to further elucidate the consequences of magnetic
effects for the atmospheres and the contracting interiors of hot Jupiters.
