  The inflated radii observed in hundreds of Hot Jupiters represent a
long-standing open issue. The observed correlation between radii and
irradiation strength, and the occasional extreme cases, nearly double the size
of Jupiter, remain without a comprehensive quantitative explanation. In this
investigation, we delve into this issue within the framework of Ohmic
dissipation, one of the most promising mechanisms for explaining the radius
anomaly. Using the evolutionary code MESA, we simulate the evolution of
irradiated giant planets, spanning the range 1 to 8 Jupiter masses,
incorporating an internal source of Ohmic dissipation located beneath the
radiative-convective boundary. Our modeling is based on physical parameters,
and accounts for the approximated conductivity and the evolution of the
magnetic fields, utilizing widely-used scaling laws. We compute the radius
evolution across a spectrum of masses and equilibrium temperatures, considering
varying amounts of Ohmic dissipation, calculated with the internal conductivity
profile and an effective parametrization of the currents, based on the typical
radius of curvature of the field lines. Our analysis reveals that this internal
Ohmic dissipation can broadly reproduce the range of observed radii using
values of radius of curvature up to about one order of magnitude lower than
what we estimate from the Juno measurements of the Jovian magnetosphere and
from MHD dynamo simulations presented herein. The observed trend with
equilibrium temperature can be explained if the highly-irradiated planets have
more intense and more small-scale magnetic fields. This suggests the
possibility of an interplay between atmospherically induced currents and the
interior, via turbulence, in agreement with recent box simulations of turbulent
MHD in atmospheric columns.
