128 research outputs found
Evolution of eccentricity and orbital inclination of migrating planets in 2:1 mean motion resonance
We determine, analytically and numerically, the conditions needed for a
system of two migrating planets trapped in a 2:1 mean motion resonance to enter
an inclination-type resonance. We provide an expression for the asymptotic
equilibrium value that the eccentricity of the inner planet reaches
under the combined effects of migration and eccentricity damping. We also show
that, for a ratio of inner to outer masses below unity, has to
pass through a value of order 0.3 for the system to enter an
inclination-type resonance. Numerically, we confirm that such a resonance may
also be excited at another, larger, value , as found
by previous authors. A necessary condition for onset of an inclination-type
resonance is that the asymptotic equilibrium value of is larger
than . We find that, for , the system cannot enter an
inclination-type resonance if the ratio of eccentricity to semimajor axis
damping timescales is smaller than 0.2. This result still holds if
only the eccentricity of the outer planet is damped and . As the
disc/planet interaction is characterized by , we conclude
that excitation of inclination through the type of resonance described here is
very unlikely to happen in a system of two planets migrating in a disc.Comment: 22 pages, 10 figures, accepted for publication in MNRA
Orbital evolution of a planet on an inclined orbit interacting with a disc
We study the dynamics of a planet on an orbit inclined with respect to a
disc. If the initial inclination of the orbit is larger than some critical
value, the gravitational force exerted by the disc on the planet leads to a
Kozai cycle in which the eccentricity of the orbit is pumped up to large values
and oscillates with time in antiphase with the inclination. On the other hand,
both the inclination and the eccentricity are damped by the frictional force
that the planet is subject to when it crosses the disc. We show that, by
maintaining either the inclination or the eccentricity at large values, the
Kozai effect provides a way of delaying alignment with the disc and
circularization of the orbit. We find the critical value to be
characteristically as small as about 20 degrees. Typically, Neptune or lower
mass planets would remain on inclined and eccentric orbits over the disc
lifetime, whereas orbits of Jupiter or higher mass planets would align and
circularize. This could play a significant role in planet formation scenarios.Comment: 28 pages, 8 figures, accepted for publication in MNRA
Pulsed Disc Accretion Driven by Hot Jupiters
We present 2D hydrodynamical simulations of hot Jupiters orbiting near the
inner edge of protoplanetary discs. We systemically explore how the accretion
rate at the inner disc edge is regulated by a giant planet of different mass,
orbital separation and eccentricity. We find that a massive (with
planet-to-star mass ratio ) eccentric () planet
drives a pulsed accretion at the inner edge of the disc, modulated at one or
two times the planet's orbital frequency. The amplitude of accretion
variability generally increases with the planet mass and eccentricity, although
some non-monotonic dependences are also possible. Applying our simulation
results to the T Tauri system CI Tau, where a young hot Jupiter candidate has
been detected, we show that the observed luminosity variability in this system
can be explained by pulsed accretion driven by an eccentric giant planet.Comment: 10 pages, 12 figures, submitted to MNRA
Extreme orbital evolution from hierarchical secular coupling of two giant planets
Observations of exoplanets over the last two decades have revealed a new
class of Jupiter-size planets with orbital periods of a few days, the so-called
"hot Jupiters". Recent measurements using the Rossiter-McLaughlin effect have
shown that many (~ 50%) of these planets are misaligned; furthermore, some (~
15%) are even retrograde with respect to the stellar spin axis. Motivated by
these observations, we explore the possibility of forming retrograde orbits in
hierarchical triple configurations consisting of a star-planet inner pair with
another giant planet, or brown dwarf, in a much wider orbit. Recently Naoz et
al. (2011) showed that in such a system, the inner planet's orbit can flip back
and forth from prograde to retrograde, and can also reach extremely high
eccentricities. Here we map a significant part of the parameter space of
dynamical outcomes for these systems. We derive strong constraints on the
orbital configurations for the outer perturber that could lead to the formation
of hot Jupiters with misaligned or retrograde orbits. We focus only on the
secular evolution, neglecting other dynamical effects such as mean-motion
resonances, as well as all dissipative forces. For example, with an inner
Jupiter-like planet initially on a nearly circular orbit at 5 AU, we show that
a misaligned hot Jupiter is likely to be formed in the presence of a more
massive planetary companion (> 2 MJ) within 140 AU of the inner system, with
mutual inclination 50 degrees and eccentricity above 0.25. This is in striking
contrast to the test-particle approximation, where an almost perpendicular
configuration can still cause large eccentricity excitations, but flips of an
inner Jupiter-like planet are much less likely to occur. The constraints we
derive can be used to guide future observations, and, in particular, searches
for more distant companions in systems containing a hot Jupiter.Comment: To appear in the Astrophysical Journa
Transit-Timing Variation Signature of Planet Migration: The Case of K2-24
The convergent migration of two planets in a gaseous disc can lead to capture
in mean motion resonance (MMR). In addition, pairs of planets in or near MMRs
are known to produce strong transit timing variations (TTVs). In this paper we
study the impact of disc-induced migrations on the TTV signal of pairs of
planets that enter a resonant configuration. We show that disc-induced
migration creates a correlation between the amplitude and the period of the
TTVs. We study the case of K2-24, a system of two planets whose period ratio
indicates that they are in or near the 2:1 MMR, with non-zero eccentricities
and large-amplitude TTVs. We show that a simple disc-induced migration cannot
reproduce the observed TTVs, and we propose a formation scenario in which the
capture in resonance occurring during migration in a disc with strong
eccentricity damping is followed by eccentricity excitation during the
dispersal of the disc, assisted by a third planet whose presence has been
suggested by radial velocity observations. This scenario accounts for the
eccentricities of the two planets and their period ratio, and accurately
reproduces the amplitude and period of the TTVs. It allows for a unified view
of the formation and evolution history of K2-24, from disc-induced migration to
its currently observed properties.Comment: 9 pages, 7 figures. Accepted for publication in Astronomy and
Astrophysic
Tidal interactions shape period ratios in planetary systems with three-body resonant chains
These last years several Systems with Tightly packed Inner Planets in the
super-Earth mass regime have been discovered harboring chains of resonances. It
is generally believed that planet pairs get trapped in MMR during the migration
phase in the protoplanetary disk, while the tides raised by the host star
provide a source of dissipation on very long timescales. In this work, we aim
to study the departure from exact commensurabilities observed among the STIPs
which harbor 3-planet resonances and analyze how tides play an important role
in shaping the resonance offsets for the STIPs. We analyzed the resonance
offsets between adjacent pairs for five multi-planetary systems, namely
Kepler-80, Kepler-223, K2-138, TOI-178, and TRAPPIST-1, highlighting the
existence of different trends in the offsets. On the one hand, we derived
analytical estimates for the offsets, which confirm that the departure of the
planetary pairs from the nominal MMRs are due to the 3-planet resonant
dynamics. On the other hand, we performed N-body simulations including both
orbital migration and tidal dissipation from the host star with simple
prescriptions in order to test the effectiveness of this mechanism at shaping
the observed trend in the offsets, focusing our study on the preservation of
the resonant patterns in the different systems with the same general setup. We
found that the trends in the offsets of the five detected systems can be
produced by tidal damping effects, regardless of the considered value for the
tidal factor. It is a robust mechanism that relaxes the system towards
equilibrium while efficiently moving it along 3-planet resonances, which
induces the observed resonance offset for each planet pair. In addition, we
showed that for Kepler-80, K2-138, and TOI-178, the amplitudes of the resonant
offsets can also be reproduced with appropriate tidal factor, for the estimated
age of the systems.Comment: Accepted for publication in A&
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