Modeling the Thermal Bulge of A Hot Jupiter with the Two-Stream Approximation. (arXiv:1911.12687v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Gu_P/0/1/0/all/0/1">Pin-Gao Gu</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Peng_D/0/1/0/all/0/1">Da-Kai Peng</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Yen_C/0/1/0/all/0/1">Chien-Chang Yen</a>
We revisit the problem of thermal bulge of asynchronous hot Jupiters, using
HD 209458 b as a fiducial study. We improve upon previous works by using a
double-gray atmosphere model and interior structure from MESA as the background
state, and then solve for the thermal bulge in response to the semidiurnal
component of stellar insolation. The atmosphere model is based on the radiative
transfer with Eddington’s two-stream approximation. Two opacity cases are
considered: the first introduces a greenhouse effect and the second exhibits a
strong temperature inversion. We find that for the predominant thermal bulges
excited by g-modes of lower orders, our results are qualitatively similar to
the adiabatic results from Arras and Socrates (2010). It arises because the
perturbed heating due to self-absorption of thermal emissions can be
significant (i.e., greenhouse effect) against Newtonian damping, thereby
leading to almost undamped thermal bulges. We also find that the contribution
to the thermal bulge from the evanescent waves in the convective zone is not
negligible, implying that the thermal bulge is not merely confined in the
atmosphere and radiative envelope. Assuming the torque balance between the
thermal and gravitational bulges, we estimate the tidal quality factor of the
planet for gravitational tides to match the observed radius. The limitations of
our model are also briefly discussed.
We revisit the problem of thermal bulge of asynchronous hot Jupiters, using
HD 209458 b as a fiducial study. We improve upon previous works by using a
double-gray atmosphere model and interior structure from MESA as the background
state, and then solve for the thermal bulge in response to the semidiurnal
component of stellar insolation. The atmosphere model is based on the radiative
transfer with Eddington’s two-stream approximation. Two opacity cases are
considered: the first introduces a greenhouse effect and the second exhibits a
strong temperature inversion. We find that for the predominant thermal bulges
excited by g-modes of lower orders, our results are qualitatively similar to
the adiabatic results from Arras and Socrates (2010). It arises because the
perturbed heating due to self-absorption of thermal emissions can be
significant (i.e., greenhouse effect) against Newtonian damping, thereby
leading to almost undamped thermal bulges. We also find that the contribution
to the thermal bulge from the evanescent waves in the convective zone is not
negligible, implying that the thermal bulge is not merely confined in the
atmosphere and radiative envelope. Assuming the torque balance between the
thermal and gravitational bulges, we estimate the tidal quality factor of the
planet for gravitational tides to match the observed radius. The limitations of
our model are also briefly discussed.
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