The traditional approximation of rotation for rapidly rotating stars and planets. II. Deformation and differential rotation. (arXiv:2110.03619v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Dhouib_H/0/1/0/all/0/1">Hachem Dhouib</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Prat_V/0/1/0/all/0/1">Vincent Prat</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Reeth_T/0/1/0/all/0/1">Timothy Van Reeth</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Mathis_S/0/1/0/all/0/1">Stéphane Mathis</a>
We examine the dynamics of low-frequency gravito-inertial waves (GIWs) in
differentially rotating deformed radiation zones in stars and planets by
generalising the traditional approximation of rotation (TAR). The TAR treatment
was built on the assumptions that the star is spherical and uniformly rotating.
However, it has been generalised in our previous work by including the effects
of the centrifugal deformation using a non-perturbative approach in the
uniformly rotating case. We aim to carry out a new generalisation of the TAR
treatment to account for the differential rotation and the strong centrifugal
deformation simultaneously. We generalise our previous work by taking into
account the differential rotation in the derivation of our complete analytical
formalism that allows the study of the dynamics of GIWs in differentially and
rapidly rotating stars. We derived the complete set of equations that
generalises the TAR, simultaneously taking the full centrifugal acceleration
and the differential rotation into account. Within the validity domain of the
TAR, we derived a generalised Laplace tidal equation for the horizontal
eigenfunctions and asymptotic wave periods of the GIWs, which can be used to
probe the structure and dynamics of differentially rotating deformed stars with
asteroseismology. A new generalisation of the TAR, which simultaneously takes
into account the differential rotation and the centrifugal acceleration in a
non-perturbative way, was derived. This generalisation allowed us to study the
detectability and the signature of the differential rotation on GIWs in rapidly
rotating deformed stars and planets. We found that the effects of the
differential rotation in early-type deformed stars on GIWs is theoretically
largely detectable in modern space photometry using observations from
$textit{Kepler}$ and TESS.
We examine the dynamics of low-frequency gravito-inertial waves (GIWs) in
differentially rotating deformed radiation zones in stars and planets by
generalising the traditional approximation of rotation (TAR). The TAR treatment
was built on the assumptions that the star is spherical and uniformly rotating.
However, it has been generalised in our previous work by including the effects
of the centrifugal deformation using a non-perturbative approach in the
uniformly rotating case. We aim to carry out a new generalisation of the TAR
treatment to account for the differential rotation and the strong centrifugal
deformation simultaneously. We generalise our previous work by taking into
account the differential rotation in the derivation of our complete analytical
formalism that allows the study of the dynamics of GIWs in differentially and
rapidly rotating stars. We derived the complete set of equations that
generalises the TAR, simultaneously taking the full centrifugal acceleration
and the differential rotation into account. Within the validity domain of the
TAR, we derived a generalised Laplace tidal equation for the horizontal
eigenfunctions and asymptotic wave periods of the GIWs, which can be used to
probe the structure and dynamics of differentially rotating deformed stars with
asteroseismology. A new generalisation of the TAR, which simultaneously takes
into account the differential rotation and the centrifugal acceleration in a
non-perturbative way, was derived. This generalisation allowed us to study the
detectability and the signature of the differential rotation on GIWs in rapidly
rotating deformed stars and planets. We found that the effects of the
differential rotation in early-type deformed stars on GIWs is theoretically
largely detectable in modern space photometry using observations from
$textit{Kepler}$ and TESS.
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