  We present the discovery of the transiting exoplanets HAT-P-65b and
HAT-P-66b, with orbital periods of 2.6055 d and 2.9721 d, masses of $0.527 \pm
0.083$ M$_{J}$ and $0.783 \pm 0.057$ M$_{J}$ and inflated radii of $1.89 \pm
0.13$ R$_{J}$ and $1.59^{+0.16}_{-0.10}$ R$_{J}$, respectively. They orbit
moderately bright ($V=13.145 \pm 0.029$, and $V=12.993 \pm 0.052$) stars of
mass $1.212 \pm 0.050$ M$_{\odot}$ and $1.255^{+0.107}_{-0.054}$ M$_{\odot}$.
The stars are at the main sequence turnoff. While it is well known that the
radii of close-in giant planets are correlated with their equilibrium
temperatures, whether or not the radii of planets increase in time as their
hosts evolve and become more luminous is an open question. Looking at the
broader sample of well-characterized close-in transiting giant planets, we find
that there is a statistically significant correlation between planetary radii
and the fractional ages of their host stars, with a false alarm probability of
only 0.0041%. We find that the correlation between the radii of planets and the
fractional ages of their hosts is fully explained by the known correlation
between planetary radii and their present day equilibrium temperatures, however
if the zero-age main sequence equilibrium temperature is used in place of the
present day equilibrium temperature then a correlation with age must also be
included to explain the planetary radii. This suggests that, after contracting
during the pre-main-sequence, close-in giant planets are re-inflated over time
due to the increasing level of irradiation received from their host stars.
Prior theoretical work indicates that such a dynamic response to irradiation
requires a significant fraction of the incident energy to be deposited deep
within the planetary interiors.

Earth and Planetary Astrophysics