71 research outputs found
Compact planetary systems perturbed by an inclined companion: II. Stellar spin-orbit evolution
The stellar spin orientation relative to the orbital planes of multiplanet
systems are becoming accessible to observations. Here, we analyze and classify
different types of spin-orbit evolution in compact multiplanet systems
perturbed by an inclined outer companion. Our study is based on classical
secular theory, using a vectorial approach developed in a separate paper. When
planet-planet perturbations are truncated at the second order in eccentricity
and mutual inclination, and the planet-companion perturbations are developed at
the quadrupole order, the problem becomes integrable. The motion is composed of
a uniform precession of the whole system around the total angular momentum, and
in the rotating frame, the evolution is periodic. Here, we focus on the
relative motion associated to the oscillations of the inclination between the
planet system and the outer orbit, and of the obliquities of the star with
respect to the two orbital planes. The solution is obtained using a powerful
geometric method. With this technique, we identify four different regimes
characterized by the nutation amplitude of the stellar spin-axis relative to
the orbital plane of the planets. In particular, the obliquity of the star
reaches its maximum when the system is in the Cassini regime where planets have
more angular momentum than the star, and where the precession rate of the star
is similar to that of the planets induced by the companion. In that case,
spin-orbit oscillations exceed twice the inclination between the planets and
the companion. Even if mutual inclination is only ~ 20 deg, this resonant case
can cause the spin-orbit angle to oscillate between perfectly aligned and
retrograde values.Comment: 29 pages, 15 figures, accepted for publication in Ap
Speed limit on Neptune migration imposed by Saturn tilting
In this Letter, we give new constraints on planet migration. They were
obtained under the assumption that Saturn's current obliquity is due to a
capture in resonance with Neptune's ascending node. If planet migration is too
fast, then Saturn crosses the resonance without being captured and it keeps a
small obliquity. This scenario thus gives a lower limit on the migration time
scale tau. We found that this boundary depends strongly on Neptune's initial
inclination. For two different migration types, we found that tau should be at
least greater than 7 Myr. This limit increases rapidly as Neptune's initial
inclination decreases from 10 to 1 degree. We also give an algorithm to know if
Saturn can be tilted for any migration law.Comment: 5 pages, 4 figures, published in ApJ
AMD-stability in presence of first order Mean Motion Resonances
The AMD-stability criterion allows to discriminate between a-priori stable
planetary systems and systems for which the stability is not granted and needs
further investigations. AMD-stability is based on the conservation of the
Angular Momentum Deficit (AMD) in the averaged system at all orders of
averaging. While the AMD criterion is rigorous, the conservation of the AMD is
only granted in absence of mean-motion resonances (MMR). Here we extend the
AMD-stability criterion to take into account mean-motion resonances, and more
specifically the overlap of first order MMR. If the MMR islands overlap, the
system will experience generalized chaos leading to instability. The
Hamiltonian of two massive planets on coplanar quasi-circular orbits can be
reduced to an integrable one degree of freedom problem for period ratios close
to a first order MMR. We use the reduced Hamiltonian to derive a new overlap
criterion for first order MMR. This stability criterion unifies the previous
criteria proposed in the literature and admits the criteria obtained for
initially circular and eccentric orbits as limit cases. We then improve the
definition of AMD-stability to take into account the short term chaos generated
by MMR overlap. We analyze the outcome of this improved definition of
AMD-stability on selected multi-planet systems from the Extrasolar Planets
Encyclopeadia.Comment: Accepted by A and A 07/10/1
Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology
In this paper we present a new approach to tidal theory. Assuming a Maxwell
viscoelastic rheology, we compute the instantaneous deformation of celestial
bodies using a differential equation for the gravity field coefficients. This
method allows large eccentricities and it is not limited to quasi-periodic
perturbations. It can take into account an extended class of perturbations,
including chaotic motions and transient events. We apply our model to some
already detected eccentric hot Jupiters and super-Earths in planar
configurations. We show that when the relaxation time of the deformation is
larger than the orbital period, spin-orbit equilibria arise naturally at
half-integers of the mean motion, even for gaseous planets. In the case of
super-Earths, these equilibria can be maintained for very low values of
eccentricity. Our method can also be used to study planets with complex
internal structures and other rheologies.Comment: 16 pages, 13 figures, 2 table
Thermal tides in neutrally stratified atmospheres: Revisiting the Earth's Precambrian rotational equilibrium
Rotational dynamics of the Earth, over geological timescales, have profoundly
affected local and global climatic evolution, probably contributing to the
evolution of life. To better retrieve the Earth's rotational history, and
motivated by the published hypothesis of a stabilized length of day during the
Precambrian, we examine the effect of thermal tides on the evolution of
planetary rotational motion. The hypothesized scenario is contingent upon
encountering a resonance in atmospheric Lamb waves, whereby an amplified
thermotidal torque cancels the opposing torque of the oceans and solid
interior, driving the Earth into a rotational equilibrium. With this scenario
in mind, we construct an ab initio model of thermal tides on rocky planets
describing a neutrally stratified atmosphere. The model takes into account
dissipative processes with Newtonian cooling and diffusive processes in the
planetary boundary layer. We retrieve from this model a closed-form solution
for the frequency-dependent tidal torque which captures the main spectral
features previously computed using 3D general circulation models. In
particular, under longwave heating, diffusive processes near the surface and
the delayed thermal response of the ground prove to be responsible for
attenuating, and possibly annihilating, the accelerating effect of the
thermotidal torque at the resonance. When applied to the Earth, our model
prediction suggests the occurrence of the Lamb resonance in the Phanerozoic,
but with an amplitude that is insufficient for the rotational equilibrium.
Interestingly, though our study was motivated by the Earth's history, the
generic tidal solution can be straightforwardly and efficiently applied in
exoplanetary settings.Comment: 20 pages (+14 for appendices), 6 figure
Can one hear supercontinents in the tides of ocean planets?
Recent observations and theoretical progress made about the history of the
Earth-Moon system suggest that tidal dissipation in oceans primarily drives the
long term evolution of orbital systems hosting ocean planets. Particularly,
they emphasise the key role played by the geometry of land-ocean distributions
in this mechanism. However, the complex way continents affect oceanic tides
still remains to be elucidated. In the present study, we investigate the impact
of a single supercontinent on the tidal response of an ocean planet and the
induced tidally dissipated energy. The adopted approach is based on the linear
tidal theory. By simplifying the continent to a spherical cap of given angular
radius and position on the globe, we proceed to a harmonic analysis of the
whole planet's tidal response including the coupling with the solid part due to
ocean loading and self-attraction variations. In this framework, tidal flows
are formulated analytically in terms of explicitly defined oceanic eigenmodes,
as well as the resulting tidal Love numbers, dissipated power, and torque. The
analysis highlights the symmetry breaking effect of the continent, which makes
the dependence of tidal quantities on the tidal frequency become highly
irregular. The metric introduced to quantify this continentality effect reveals
abrupt transitions between polar and non-polar configurations, and between
small-sized and medium-sized continents. Additionally, it predicts that a
continent similar to South America or smaller (30{\deg}-angular radius) does
not alter qualitatively the tidal response of a global ocean whatever its
position on the planet.Comment: 35 pages, 13 figures, 5 tables. Accepted for publication in Astronomy
& Astrophysic
Tilting Uranus via the migration of an ancient satellite
Context. The 98{\deg}-obliquity of Uranus is commonly attributed to giant
impacts that occurred at the end of the planetary formation. This picture,
however, is not devoid of weaknesses.
Aims. On a billion-year timescale, the tidal migration of the satellites of
Jupiter and Saturn has been shown to strongly affect their spin-axis dynamics.
We aim to revisit the scenario of tilting Uranus in light of this mechanism.
Methods. We analyse the precession spectrum of Uranus and identify the
candidate secular spin-orbit resonances that could be responsible for the
tilting. We determine the properties of the hypothetical ancient satellite
required for a capture and explore the dynamics numerically.
Results. If it migrates over 10 Uranus' radii, a single satellite with
minimum mass 4e-4 Uranus' mass is able to tilt Uranus from a small obliquity
and make it converge towards 90{\deg}. In order to achieve the tilting in less
than the age of the Solar System, the mean drift rate of the satellite must be
comparable to the Moon's current orbital expansion. Under these conditions,
simulations show that Uranus is readily tilted over 80{\deg}. Beyond this
point, the satellite is strongly destabilised and triggers a phase of chaotic
motion for the planet's spin axis. The chaotic phase ends when the satellite
collides into the planet, ultimately freezing the planet's obliquity in either
a prograde, or plainly retrograde state (as Uranus today). Spin states
resembling that of Uranus can be obtained with probabilities as large as 80%,
but a bigger satellite is favoured, with mass 1.7e-3 Uranus' mass or more. Yet,
a smaller ancient satellite is not categorically ruled out, and there is room
for improving this basic scenario in future studies. Interactions among several
pre-existing satellites is a promising possibility.Comment: Accepted for publication in Astronomy and Astrophysic
Did atmospheric thermal tides cause a daylength locking in the Precambrian? A review on recent results
After the initial suggestion by Zahnle and Walker (1987) that the torque
accelerating the spin rate of the Earth and produced by the heating of the
atmosphere by the Sun could counteract the braking lunir-solar gravitational
torque in the Precambrian, several authors have recently revisited this
hypothesis. In these studies, it is argued that the geological evidences of the
past spin state of the Earth play in favor of this atmospheric tidal locking of
the length of the day (LOD). In the present review of the recent literature, we
show that the drawn conclusions depend crucially on the consideration of the
stromatolite geological LOD estimates obtained by Pannella at 1.88 and 2.0 Ga,
which are subject to large uncertainties. When only the most robust
cyclostatigraphic estimates of the LOD are retained, the LOD locking hypothesis
is not supported. Moreover, the consideration of the published General
Circulation Model numerical simulations and of new analytical models for the
thermal atmospheric tides suggest that the atmospheric tidal resonance, which
is the crucial ingredient for the LOD locking in the Precambrian, was never of
sufficiently large amplitude to allow for this tidal LOD lock.Comment: 16 pages, 9 figure
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