Title: Tidal Dissipation in WASP-12,
Abstract: WASP-12 is a hot Jupiter system with an orbital period of $P= 1.1\textrm{
day}$, making it one of the shortest-period giant planets known. Recent transit
timing observations by Maciejewski et al. (2016) and Patra et al. (2017) find a
decreasing period with $P/|\dot{P}| = 3.2\textrm{ Myr}$. This has been
interpreted as evidence of either orbital decay due to tidal dissipation or a
long term oscillation of the apparent period due to apsidal precession. Here we
consider the possibility that it is orbital decay. We show that the parameters
of the host star are consistent with either a $M_\ast \simeq 1.3 M_\odot$ main
sequence star or a $M_\ast \simeq 1.2 M_\odot$ subgiant. We find that if the
star is on the main sequence, the tidal dissipation is too inefficient to
explain the observed $\dot{P}$. However, if it is a subgiant, the tidal
dissipation is significantly enhanced due to nonlinear wave breaking of the
dynamical tide near the star's center. The subgiant models have a tidal quality
factor $Q_\ast'\simeq 2\times10^5$ and an orbital decay rate that agrees well
with the observed $\dot{P}$. It would also explain why the planet survived for
$\simeq 3\textrm{ Gyr}$ while the star was on the main sequence and yet is now
inspiraling on a 3 Myr timescale. Although this suggests that we are witnessing
the last $\sim 0.1\%$ of the planet's life, the probability of such a detection
is a few percent given the observed sample of $\simeq 30$ hot Jupiters in
$P<3\textrm{ day}$ orbits around $M_\ast>1.2 M_\odot$ hosts.