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Three-Dimensional Atmospheric Circulation Models of HD 189733b and HD 209458b with Consistent Magnetic Drag and Ohmic Dissipation

We present the first three-dimensional circulation models for extrasolar gas giant atmospheres with geometrically and energetically consistent treatments of magnetic drag and ohmic dissipation. Atmospheric resistivities are continuously updated and calculated directly from the flow structure, strongly coupling the magnetic effects with the circulation pattern. We model the hot Jupiters HD 189733b (Teq \approx 1200 K) and HD 209458b (Teq \approx 1500 K) and test planetary magnetic field strengths from 0 to 30 G. We find that even at B = 3 G the atmospheric structure and circulation of HD 209458b are strongly influenced by magnetic effects, while the cooler HD 189733b remains largely unaffected, even in the case of B = 30 G and super-solar metallicities. Our models of HD 209458b indicate that magnetic effects can substantially slow down atmospheric winds, change circulation and temperature patterns, and alter observable properties. These models establish that longitudinal and latitudinal hot spot offsets, day-night flux contrasts, and planetary radius inflation are interrelated diagnostics of the magnetic induction process occurring in the atmospheres of hot Jupiters and other similarly forced exoplanets. Most of the ohmic heating occurs high in the atmosphere and on the day side of the planet, while the heating at depth is strongly dependent on the internal heat flux assumed for the planet, with more heating when the deep atmosphere is hot. We compare the ohmic power at depth in our models, and estimates of the ohmic dissipation in the bulk interior (from general scaling laws), to evolutionary models that constrain the amount of heating necessary to explain the inflated radius of HD 209458b. Our results suggest that deep ohmic heating can successfully inflate the radius of HD 209458b for planetary magnetic field strengths of B \geq 3 - 10 G.