102 research outputs found
Puzzling out the coexistence of terrestrial planets and giant exoplanets. The 2/1 resonant periodic orbits
Hundreds of giant planets have been discovered so far and the quest of
exo-Earths in giant planet systems has become intriguing. In this work, we aim
to address the question of the possible long-term coexistence of a terrestrial
companion on an orbit interior to a giant planet, and explore the extent of the
stability regions for both non-resonant and resonant configurations. Our study
focuses on the restricted three-body problem, where an inner terrestrial planet
(massless body) moves under the gravitational attraction of a star and an outer
massive planet on a circular or elliptic orbit. Using the Detrended Fast
Lyapunov Indicator as a chaotic indicator, we constructed maps of dynamical
stability by varying both the eccentricity of the outer giant planet and the
semi-major axis of the inner terrestrial planet, and identify the boundaries of
the stability domains. Guided by the computation of families of periodic
orbits, the phase space is unravelled by meticulously chosen stable periodic
orbits, which buttress the stability domains. We provide all possible stability
domains for coplanar symmetric configurations and show that a terrestrial
planet, either in mean-motion resonance or not, can coexist with a giant
planet, when the latter moves on either a circular or an (even highly)
eccentric orbit. New families of symmetric and asymmetric periodic orbits are
presented for the 2/1 resonance. It is shown that an inner terrestrial planet
can survive long time spans with a giant eccentric outer planet on resonant
symmetric orbits, even when both orbits are highly eccentric. For 22 detected
single-planet systems consisting of a giant planet with high eccentricity, we
discuss the possible existence of a terrestrial planet. This study is
particularly suitable for the research of companions among the detected systems
with giant planets, and could assist with refining observational data.Comment: Accepted for publication in A&
Origin and continuation of 3/2, 5/2, 3/1, 4/1 and 5/1 resonant periodic orbits in the circular and elliptic restricted three-body problem
We consider a planetary system consisting of two primaries, namely a star and
a giant planet, and a massless secondary, say a terrestrial planet or an
asteroid, which moves under their gravitational attraction. We study the
dynamics of this system in the framework of the circular and elliptic
restricted TBP, when the motion of the giant planet describes circular and
elliptic orbits, respectively. Originating from the circular family, families
of symmetric periodic orbits in the 3/2, 5/2, 3/1, 4/1 and 5/1 mean-motion
resonances are continued in the circular and the elliptic problems. New
bifurcation points from the circular to the elliptic problem are found for each
of the above resonances and thus, new families, continued from these points are
herein presented. Stable segments of periodic orbits were found at high
eccentricity values of the already known families considered as whole unstable
previously. Moreover, new isolated (not continued from bifurcation points)
families are computed in the elliptic restricted problem. The majority of the
new families mainly consist of stable periodic orbits at high eccentricities.
The families of the 5/1 resonance are investigated for the first time in the
restricted three-body problems. We highlight the effect of stable periodic
orbits on the formation of stable regions in their vicinity and unveil the
boundaries of such domains in phase space by computing maps of dynamical
stability. The long-term stable evolution of the terrestrial planets or
asteroids is dependent on the existence of regular domains in their dynamical
neighbourhood in phase space, which could host them for long time spans. This
study, besides other celestial architectures that can be efficiently modelled
by the circular and elliptic restricted problems, is particularly appropriate
for the discovery of terrestrial companions among the single-giant planet
systems discovered so far.Comment: Accepted for publication in Celestial Mechanics and Dynamical
Astronom
Predicting links in ego-networks using temporal information
Link prediction appears as a central problem of network science, as it calls
for unfolding the mechanisms that govern the micro-dynamics of the network. In
this work, we are interested in ego-networks, that is the mere information of
interactions of a node to its neighbors, in the context of social
relationships. As the structural information is very poor, we rely on another
source of information to predict links among egos' neighbors: the timing of
interactions. We define several features to capture different kinds of temporal
information and apply machine learning methods to combine these various
features and improve the quality of the prediction. We demonstrate the
efficiency of this temporal approach on a cellphone interaction dataset,
pointing out features which prove themselves to perform well in this context,
in particular the temporal profile of interactions and elapsed time between
contacts.Comment: submitted to EPJ Data Scienc
On the 3D secular dynamics of radial-velocity-detected planetary systems
Aims. To date, more than 600 multi-planetary systems have been discovered.
Due to the limitations of the detection methods, our knowledge of the systems
is usually far from complete. In particular, for planetary systems discovered
with the radial velocity (RV) technique, the inclinations of the orbital
planes, and thus the mutual inclinations and planetary masses, are unknown. Our
work aims to constrain the spatial configuration of several RV-detected
extrasolar systems that are not in a mean-motion resonance. Methods. Through an
analytical study based on a first-order secular Hamiltonian expansion and
numerical explorations performed with a chaos detector, we identified ranges of
values for the orbital inclinations and the mutual inclinations, which ensure
the long-term stability of the system. Our results were validated by comparison
with n-body simulations, showing the accuracy of our analytical approach up to
high mutual inclinations (approx. 70{\deg}-80{\deg}). Results. We find that,
given the current estimations for the parameters of the selected systems,
long-term regular evolution of the spatial configurations is observed, for all
the systems, i) at low mutual inclinations (typically less than 35{\deg}) and
ii) at higher mutual inclinations, preferentially if the system is in a
Lidov-Kozai resonance. Indeed, a rapid destabilisation of highly mutually
inclined orbits is commonly observed, due to the significant chaos that
develops around the stability islands of the Lidov-Kozai resonance. The extent
of the Lidov-Kozai resonant region is discussed for ten planetary systems (HD
11506, HD 12661, HD 134987, HD 142, HD 154857, HD 164922, HD 169830, HD 207832,
HD 4732, and HD 74156).Comment: Accepted for publication in A&
Highly inclined and eccentric massive planets I: Planet-disc interactions
In the Solar System, planets have a small inclination with respect to the
equatorial plane of the Sun, but there is evidence that in extrasolar systems
the inclination can be very high. This spin-orbit misalignment is unexpected,
as planets form in a protoplanetary disc supposedly aligned with the stellar
spin. Planet-planet interactions are supposed to lead to a mutual inclination,
but the effects of the protoplanetary disc are still unknown. We investigate
therefore planet-disc interactions for planets above 1M_Jup. We check the
influence of the inclination i, eccentricity e, and mass M_p of the planet. We
perform 3D numerical simulations of protoplanetary discs with embedded
high-mass planets. We provide damping formulae for i and e as a function of i,
e, and M_p that fit the numerical data. For highly inclined massive planets,
the gap opening is reduced, and the damping of i occurs on time-scales of the
order of 10^-4 deg/yr M_disc/(0.01 M_star) with the damping of e on a smaller
time-scale. While the inclination of low planetary masses (<5M_Jup) is always
damped, large planetary masses with large i can undergo a Kozai-cycle with the
disc. These Kozai-cycles are damped in time. Eccentricity is generally damped,
except for very massive planets (M_p = 5M_Jup) where eccentricity can increase
for low inclinations. The dynamics tends to a final state: planets end up in
midplane and can then, over time, increase their eccentricity as a result of
interactions with the disc. The interactions with the disc lead to damping of i
and e after a scattering event of high-mass planets. If i is sufficiently
reduced, the eccentricity can be pumped up because of interactions with the
disc. If the planet is scattered to high inclination, it can undergo a
Kozai-cycle with the disc that makes it hard to predict the exact movement of
the planet and its orbital parameters at the dispersal of the disc.Comment: accepted for publication in Astronomy and Astrophysic
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
Kozai resonance in extrasolar systems
Aims. We study the possibility that extrasolar two-planet systems, similar to the ones that are observed, can be in a stable Kozairesonant state, assuming a mutual inclination of the orbital planes of order Imut - 40-60°. Methods. Five known multi-planet systems that are not in mean motion resonance were selected, according to defined criteria, as "possible prototypes" (v Andromedae, HD 12661, HD 169830, HD 741.56, HD 1.55358). We performed a parametric study, integrating several sets of orbits of the two planets, obtained by varying the (unknown) inclination of their orbital planes and their nodal longitudes, thus changing the values of their masses and mutual inclination. We also take into account the reported observational errors on the orbital elements. These numerical results are characterized using analytical secular theory and frequency analysis. Surface of section techniques are also used to distinguish between stable and chaotic motions. Results. Frequency analysis offers a reliable way of identifying the Kozai resonance in a general reference frame, where the argument of the pericenter of the inner planet does not necessarily librate around ±90° as in the frame of the Laplace plane, through the non-coupling of the eccentricities of the two planets. We find that four of the five selected systems (v Andromedae, HD 12661, HD 169830 and HD 741.56) could in principle be in Kozai resonance, as their eccentricities and apsidal orientations are such that the system, enters in the stability region of the Kozai resonance in 20-70% of the cases, provided that their mutual inclination is at least 45°. Thus, a large fraction of the observed multi-planet systems has observed orbital characteristics that are consistent with stable, Kozai-type, motion in 3D. Unstable sets of orbits are also found, due to the chaos that develops around the stability islands of the Kozai resonance. A variety of physical mechanisms that could generate the necessary large mutual, inclinations are discussed, including (a) planet formation; (b) type II migration and resonant interactions during the gas-dominated phase; (c) planetesimal-driven migration and resonance crossing during the gas-free era; (d) multi-planet scattering, caused by the presence of an additional planet.</p
RankMerging: A supervised learning-to-rank framework to predict links in large social network
Uncovering unknown or missing links in social networks is a difficult task
because of their sparsity and because links may represent different types of
relationships, characterized by different structural patterns. In this paper,
we define a simple yet efficient supervised learning-to-rank framework, called
RankMerging, which aims at combining information provided by various
unsupervised rankings. We illustrate our method on three different kinds of
social networks and show that it substantially improves the performances of
unsupervised metrics of ranking. We also compare it to other combination
strategies based on standard methods. Finally, we explore various aspects of
RankMerging, such as feature selection and parameter estimation and discuss its
area of relevance: the prediction of an adjustable number of links on large
networks.Comment: 43 pages, published in Machine Learning Journa
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