Effects of Turbulence, Eccentricity Damping, and Migration Rate on the Capture of Planets into Mean Motion Resonance

Pairs of migrating extrasolar planets often lock into mean motion resonance as they drift inward. This paper studies the convergent migration of giant planets (driven by a circumstellar disk) and determines the probability that they are captured into mean motion resonance. The probability that such planets enter resonance depends on the type of resonance, the migration rate, the eccentricity damping rate, and the amplitude of the turbulent fluctuations. This problem is studied both through direct integrations of the full 3-body problem, and via semi-analytic model equations. In general, the probability of resonance decreases with increasing migration rate, and with increasing levels of turbulence, but increases with eccentricity damping. Previous work has shown that the distributions of orbital elements (eccentricity and semimajor axis) for observed extrasolar planets can be reproduced by migration models with multiple planets. However, these results depend on resonance locking, and this study shows that entry into -- and maintenance of -- mean motion resonance depends sensitively on migration rate, eccentricity damping, and turbulence.Comment: 43 pages including 14 figures; accepted for publication in The Astrophysical Journa

Origin and Detectability of coorbital planets from radial velocity data

We analyze the possibilities of detection of hypothetical exoplanets in coorbital motion from synthetic radial velocity (RV) signals, taking into account different types of stable planar configurations, orbital eccentricities and mass ratios. For each nominal solution corresponding to small-amplitude oscillations around the periodic solution, we generate a series of synthetic RV curves mimicking the stellar motion around the barycenter of the system. We then fit the data sets obtained assuming three possible different orbital architectures: (a) two planets in coorbital motion, (b) two planets in a 2/1 mean-motion resonance, and (c) a single planet. We compare the resulting residuals and the estimated orbital parameters. For synthetic data sets covering only a few orbital periods, we find that the discrete radial velocity signal generated by a coorbital configuration could be easily confused with other configurations/systems, and in many cases the best orbital fit corresponds to either a single planet or two bodies in a 2/1 resonance. However, most of the incorrect identifications are associated to dynamically unstable solutions. We also compare the orbital parameters obtained with two different fitting strategies: a simultaneous fit of two planets and a nested multi-Keplerian model. We find that the nested models can yield incorrect orbital configurations (sometimes close to fictitious mean-motion resonances) that are nevertheless dynamically stable and with orbital eccentricities lower than the correct nominal solutions. Finally, we discuss plausible mechanisms for the formation of coorbital configurations, by the interaction between two giant planets and an inner cavity in the gas disk. For equal mass planets, both Lagrangian and anti-Lagrangian configurations can be obtained from same initial condition depending on final time of integration.Comment: 14 pages, 16 figures.2012. MNRAS, 421, 35

Recent developments in planet migration theory

Planetary migration is the process by which a forming planet undergoes a drift of its semi-major axis caused by the tidal interaction with its parent protoplanetary disc. One of the key quantities to assess the migration of embedded planets is the tidal torque between the disc and planet, which has two components: the Lindblad torque and the corotation torque. We review the latest results on both torque components for planets on circular orbits, with a special emphasis on the various processes that give rise to additional, large components of the corotation torque, and those contributing to the saturation of this torque. These additional components of the corotation torque could help address the shortcomings that have recently been exposed by models of planet population syntheses. We also review recent results concerning the migration of giant planets that carve gaps in the disc (type II migration) and the migration of sub-giant planets that open partial gaps in massive discs (type III migration).Comment: 52 pages, 18 figures. Review article to be published in "Tidal effects in Astronomy and Astrophysics", Lecture Notes in Physic

The dynamical role of the circumplanetary disc in planetary migration

Numerical simulations of planets embedded in protoplanetary gaseous discs are a precious tool for studying the planetary migration ; however, some approximations have to be made. Most often, the selfgravity of the gas is neglected. In that case, it is not clear in the literature how the material inside the Roche lobe of the planet should be taken into account. Here, we want to address this issue by studying the influence of various methods so far used by different authors on the migration rate. We performed high-resolution numerical simulations of giant planets embedded in discs. We compared the migration rates with and without gas selfgravity, testing various ways of taking the circum-planetary disc (CPD) into account. Different methods lead to significantly different migration rates. Adding the mass of the CPD to the perturbing mass of the planet accelerates the migration. Excluding a part of the Hill sphere is a very touchy parameter that may lead to an artificial suppression of the type III, runaway migration. In fact, the CPD is smaller than the Hill sphere. We recommend excluding no more than a 0.6 Hill radius and using a smooth filter. Alternatively, the CPD can be given the acceleration felt by the planet from the rest of the protoplanetary disc. The gas inside the Roche lobe of the planet should be very carefully taken into account in numerical simulations without any selfgravity of the gas. The entire Hill sphere should not be excluded. The method used should be explicitly given. However, no method is equivalent to computing the full selfgravity of the gas.Comment: 15 pages, 19 figures (most in color), in press in Astronomy and Astrophysic

The Importance of Disk Structure in Stalling Type I Migration

As planets form they tidally interact with their natal disks. Though the tidal perturbation induced by Earth and super-Earth mass planets is generally too weak to significantly modify the structure of the disk, the interaction is potentially strong enough to cause the planets to undergo rapid type I migration. This physical process may provide a source of short-period super-Earths, though it may also pose a challenge to the emergence and retention of cores on long-period orbits with sufficient mass to evolve into gas giants. Previous numerical simulations have shown that the type I migration rate sensitively depends upon the circumstellar disk's properties, particularly the temperature and surface density gradients. Here, we derive these structure parameters for 1) a self-consistent viscous-disk model based on a constant \alpha-prescription, 2) an irradiated disk model that takes into account heating due to the absorption of stellar photons, and 3) a layered-accretion disk model with variable \alpha-parameter. We show that in the inner viscously-heated regions of typical protostellar disks, the horseshoe and corotation torques of super-Earths can exceed their differential Lindblad torque and cause them to undergo outward migration. However, the temperature profile due to passive stellar irradiation causes type I migration to be inwards throughout much of the disk. For disks in which there is outwards migration, we show that location and the mass range of the "planet traps" depends on some uncertain assumptions adopted for these disk models. Competing physical effects may lead to dispersion in super-Earths' mass-period distribution.Comment: 12 pages, Submitted to Ap

A torque formula for non-isothermal Type I planetary migration - I. Unsaturated horseshoe drag

We study the torque on low-mass planets embedded in protoplanetary discs in the two-dimensional approximation, incorporating non-isothermal effects. We couple linear estimates of the Lindblad (or wave) torque to a simple, but non-linear, model of adiabatic corotation torques (or horseshoe drag), resulting in a simple formula that governs Type I migration in non-isothermal discs. This formula should apply in optically thick regions of the disc, where viscous and thermal diffusion act to keep the horseshoe drag unsaturated. We check this formula against numerical hydrodynamical simulations, using three independent numerical methods, and find good agreement.Comment: 17 pages, 17 figures, accepted for publication in MNRA

Disk Planet Interactions and Early Evolution in Young Planetary Systems

We study and review disk protoplanet interactions using local shearing box simulations. These suffer the disadvantage of having potential artefacts arising from periodic boundary conditions but the advantage, when compared to global simulations, of being able to capture much of the dynamics close to the protoplanet at high resolution for low computational cost. Cases with and without self sustained MHD turbulence are considered. The conditions for gap formation and the transition from type I migration are investigated and found to depend on whether the single parameter M_p R^3/(M_* H^3), with M_p, M_*, R and H being the protoplanet mass, the central mass, the orbital radius and the disk semi-thickness respectively exceeds a number of order unity. We also investigate the coorbital torques experienced by a moving protoplanet in an inviscid disk. This is done by demonstrating the equivalence of the problem for a moving protoplanet to one where the protoplanet is in a fixed orbit which the disk material flows through radially as a result of the action of an appropriate external torque. For sustainable coorbital torques to be realized a quasi steady state must be realized in which the planet migrates through the disk without accreting significant mass. In that case although there is sensitivity to computational parameters, in agreement with earlier work by Masset & Papaloizou (2003) based on global simulations, the coorbital torques are proportional to the migration speed and result in a positive feedback on the migration, enhancing it and potentially leading to a runaway. This could lead to a fast migration for protoplanets in the Saturn mass range in massive disks and may be relevant to the mass period correlation for extrasolar planets which gives a preponderance of sub Jovian masses at short orbital period.Comment: To appear in Celestial Mechanics and Dynamical Astronomy (with higher resolution figures

Do low surface brightness galaxies have dense disks?

The disk masses of four low surface brightness galaxies (LSB) were estimated using marginal gravitational stability criterion and the stellar velocity dispersion data which were taken from Pizzella et al., 2008 [1]. The constructed mass models appear to be close to the models of maximal disk. The results show that the disks of LSB galaxies may be significantly more massive than it is usually accepted from their brightnesses. In this case their surface densities and masses appear to be rather typical for normal spirals. Otherwise, unlike the disks of many spiral galaxies, the LSB disks are dynamically overheated.Comment: 14 pages, 10 figures, submitted to Astronomy Report

Ferromagnetism and large negative magnetoresistance in Pb doped Bi-Sr-Co-O misfit-layer compound

Ferromagnetism and accompanying large negative magnetoresistance in Pb-substituted Bi-Sr-Co-O misfit-layer compound are investigated in detail. Recent structural analysis of (Bi,Pb)${}_2$Sr${}_{3}$Co${}_2$O${}_9$, which has been believed to be a Co analogue of Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta}$, revealed that it has a more complex structure including a CoO${}_2$ hexagonal layer [T. Yamamoto {\it et al.}, Jpn. J. Appl. Phys. {\bf 39} (2000) L747]. Pb substitution for Bi not only introduces holes into the conducting CoO${}_2$ layers but also creates a certain amount of localized spins. Ferromagnetic transition appears at $T$ = 3.2 K with small spontaneous magnetization along the $c$ axis, and around the transition temperature large and anisotropic negative magnetoresistance was observed. This compound is the first example which shows ferromagnetic long-range order in a two-dimensional metallic hexagnonal CoO${}_2$ layer.Comment: 8 pages including eps figures. To be published in J. Phys. Soc. Jp

Metal insulator transition in TlSr2CoO5 from orbital degeneracy and spin disproportionation

To describe the metal insulator transition in the new oxide TlSr2CoO5 we investigate its electronic structure by LDA and model Hartree-Fock calculations. Within LDA we find a homogeneous metallic and ferromagnetic ground state, but when including the Coulomb interaction more explicitly within the Hartree-Fock approximation, we find an insulating state of lower energy with both spin and orbital order. We also interpret our results in terms of a simple model.Comment: 8 pages, 9 figure