Tidal Oscillations of Rotating Hot Jupiters. (arXiv:2004.03094v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Lee_U/0/1/0/all/0/1">Umin Lee</a>

We calculate small amplitude gravitational and thermal tides of uniformly
rotating hot Jupiters composed of a nearly isentropic convective core and a
geometrically thin radiative envelope. We treat the fluid in the convective
core as a viscous fluid and solve linearized Navier Stokes equations to obtain
tidal responses of the core, assuming that the Ekman number ${rm Ek}$ is a
constant parameter. In the radiative envelope, we take account of the effects
of radiative dissipations on the responses. The properties of tidal responses
depend on thermal timescales $tau_*$ in the envelope and Ekman number Ek in
the core and on weather the forcing frequency $omega$ is in the inertial range
or not, where the inertial range is defined by $|omega|le2Omega$ for the
rotation frequency $Omega$. If ${rm Ek}gtrsim 10^{-7}$, the viscous
dissipation in the core is dominating the thermal contributions in the envelope
for $tau_*gtrsim 1$ day. If ${rm Ek}lesssim 10^{-7}$, however, the viscous
dissipation is comparable to or smaller than the thermal contributions and the
envelope plays an important role to determine the tidal torques. If the forcing
is in the inertial range, frequency resonance of the tidal forcing with core
inertial modes significantly affects the tidal torques, producing numerous
resonance peaks of the torque. Depending on the sign of the torque in the
peaks, we suggest that there exist cases in which the resonance with core
inertial modes hampers the process of synchronization between the spin and
orbital motion of the planets.

We calculate small amplitude gravitational and thermal tides of uniformly
rotating hot Jupiters composed of a nearly isentropic convective core and a
geometrically thin radiative envelope. We treat the fluid in the convective
core as a viscous fluid and solve linearized Navier Stokes equations to obtain
tidal responses of the core, assuming that the Ekman number ${rm Ek}$ is a
constant parameter. In the radiative envelope, we take account of the effects
of radiative dissipations on the responses. The properties of tidal responses
depend on thermal timescales $tau_*$ in the envelope and Ekman number Ek in
the core and on weather the forcing frequency $omega$ is in the inertial range
or not, where the inertial range is defined by $|omega|le2Omega$ for the
rotation frequency $Omega$. If ${rm Ek}gtrsim 10^{-7}$, the viscous
dissipation in the core is dominating the thermal contributions in the envelope
for $tau_*gtrsim 1$ day. If ${rm Ek}lesssim 10^{-7}$, however, the viscous
dissipation is comparable to or smaller than the thermal contributions and the
envelope plays an important role to determine the tidal torques. If the forcing
is in the inertial range, frequency resonance of the tidal forcing with core
inertial modes significantly affects the tidal torques, producing numerous
resonance peaks of the torque. Depending on the sign of the torque in the
peaks, we suggest that there exist cases in which the resonance with core
inertial modes hampers the process of synchronization between the spin and
orbital motion of the planets.

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