Equilibrium Tidal Response of Jupiter: Detectability by Juno. (arXiv:2001.03695v1 [astro-ph.EP])

Equilibrium Tidal Response of Jupiter: Detectability by Juno. (arXiv:2001.03695v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Wahl_S/0/1/0/all/0/1">Sean M Wahl</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Parisi_M/0/1/0/all/0/1">Marzia Parisi</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Folkner_W/0/1/0/all/0/1">William M Folkner</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Hubbard_W/0/1/0/all/0/1">William B Hubbard</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Militzer_B/0/1/0/all/0/1">Burkhard Militzer</a>

An observation of Jupiter’s tidal response is anticipated for the on-going
Juno spacecraft mission. We combine self-consistent, numerical models of
Jupiter’s equilibrium tidal response with observed Doppler shifts from the Juno
gravity science experiment to test the sensitivity of the spacecraft to tides
raised by the Galilean satellites and the Sun. The concentric Maclaurin
spheroid (CMS) method finds the equilibrium shape and gravity field of a
rotating, liquid planet with the tide raised by a satellite, expanded in Love
numbers ($k_{nm}$). We present improvements to CMS theory that eliminate an
unphysical center of mass offset and study in detail the convergence behavior
of the CMS approach. We demonstrate that the dependence of $k_{nm}$ with
orbital distance is important when considering the combined tidal response for
Jupiter. Conversely, the details of the interior structure have a negligible
influence on $k_{nm}$, for models that match the zonal harmonics $J_2$, $J_4$
and $J_6$, already measured to high precision by Juno. As the mission
continues, improved coverage of Jupiter’s gravity field at different phases of
Io’s orbit is expected to yield an observed value for the degree-2 Love number
($k_{22}$) and potentially select higher–degree $k_{nm}$. We present a test of
the sensitivity of the Juno Doppler signal to the calculated $k_{nm}$, which
suggests the detectability of $k_{33}$, $k_{42}$ and $k_{31}$, in addition to
$k_{22}$. A mismatch of a robust Juno observation with the remarkably small
range in calculated Io equilibrium $k_{22}=0.58976pm0.0001$, would indicate a
heretofore uncharacterized dynamic contribution to the tides.

An observation of Jupiter’s tidal response is anticipated for the on-going
Juno spacecraft mission. We combine self-consistent, numerical models of
Jupiter’s equilibrium tidal response with observed Doppler shifts from the Juno
gravity science experiment to test the sensitivity of the spacecraft to tides
raised by the Galilean satellites and the Sun. The concentric Maclaurin
spheroid (CMS) method finds the equilibrium shape and gravity field of a
rotating, liquid planet with the tide raised by a satellite, expanded in Love
numbers ($k_{nm}$). We present improvements to CMS theory that eliminate an
unphysical center of mass offset and study in detail the convergence behavior
of the CMS approach. We demonstrate that the dependence of $k_{nm}$ with
orbital distance is important when considering the combined tidal response for
Jupiter. Conversely, the details of the interior structure have a negligible
influence on $k_{nm}$, for models that match the zonal harmonics $J_2$, $J_4$
and $J_6$, already measured to high precision by Juno. As the mission
continues, improved coverage of Jupiter’s gravity field at different phases of
Io’s orbit is expected to yield an observed value for the degree-2 Love number
($k_{22}$) and potentially select higher–degree $k_{nm}$. We present a test of
the sensitivity of the Juno Doppler signal to the calculated $k_{nm}$, which
suggests the detectability of $k_{33}$, $k_{42}$ and $k_{31}$, in addition to
$k_{22}$. A mismatch of a robust Juno observation with the remarkably small
range in calculated Io equilibrium $k_{22}=0.58976pm0.0001$, would indicate a
heretofore uncharacterized dynamic contribution to the tides.

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