On type-I migration near opacity transitions. A generalized Lindblad torque formula for planetary population synthesis

We give an expression for the Lindblad torque acting on a low-mass planet embedded in a protoplanetary disk that is valid even at locations where the surface density or temperature profile cannot be approximated by a power law, such as an opacity transition. At such locations, the Lindblad torque is known to suffer strong deviation from its standard value, with potentially important implications for type I migration, but the full treatment of the tidal interaction is cumbersome and not well suited to models of planetary population synthesis. The expression that we propose retains the simplicity of the standard Lindblad torque formula and gives results that accurately reproduce those of numerical simulations, even at locations where the disk temperature undergoes abrupt changes. Our study is conducted by means of customized numerical simulations in the low-mass regime, in locally isothermal disks, and compared to linear torque estimates obtained by summing fully analytic torque estimates at each Lindblad resonance. The functional dependence of our modified Lindblad torque expression is suggested by an estimate of the shift of the Lindblad resonances that mostly contribute to the torque, in a disk with sharp gradients of temperature or surface density, while the numerical coefficients of the new terms are adjusted to seek agreement with numerics. As side results, we find that the vortensity related corotation torque undergoes a boost at an opacity transition that can counteract migration, and we find evidence from numerical simulations that the linear corotation torque has a non-negligible dependency upon the temperature gradient, in a locally isothermal disk.Comment: Appeared in special issue of "Celestial Mechanics and Dynamical Astronomy" on Extrasolar Planetary System

The Migration and Growth of Protoplanets in Protostellar Discs

We investigate the gravitational interaction of a Jovian mass protoplanet with a gaseous disc with aspect ratio and kinematic viscosity expected for the protoplanetary disc from which it formed. Different disc surface density distributions have been investigated. We focus on the tidal interaction with the disc with the consequent gap formation and orbital migration of the protoplanet. Nonlinear hydrodynamic simulations are employed using three independent numerical codes. A principal result is that the direction of the orbital migration is always inwards and such that the protoplanet reaches the central star in a near circular orbit after a characteristic viscous time scale of approximately 10,000 initial orbital periods. This was found to be independent of whether the protoplanet was allowed to accrete mass or not. Inward migration is helped through the disappearance of the inner disc, and therefore the positive torque it would exert, because of accretion onto the central star.Our results indicate that a realistic upper limit for the masses of closely orbiting giant planets is approximately 5 Jupiter masses, because of the reduced accretion rates obtained for planets of increasing mass. Assuming some process such as termination of the inner disc through a magnetospheric cavity stops the migration, the range of masses estimated for a number of close orbiting giant planets (Marcy, Cochran, & Mayor 1999; Marcy & Butler 1998) as well as their inward orbital migration can be accounted for by consideration of disc--protoplanet interactions during the late stages of giant planet formation. Maximally accreting protoplanets reached about four Jovian masses on reaching the neighbourhood of the central star.Comment: 19 pages, 16 figures, submitted to MNRAS. A version of this paper that includes high resolution figures may be obtained from http://www.maths.qmw.ac.uk/~rpn/preprint.htm

Development of a PIGE-Detection System for In-situ Inspection and Quality Assurance in the Evolution of Fast Rotating Parts in High Temperature Environment Manufactured From TiAl

Intermetallic γ-titanium aluminides are a promising material in high temperature technologies. Their high specific strength at temperatures above 700°C offers the possibility for their use as components of aerospace and automotive industries. With a specific weight of 50% of that of the widely used Ni-based superalloys TiAl is very suitable as material for fast rotating parts like turbine blades in aircraft engines and land based power stations or turbocharger rotors. Thus lower mechanical stresses and a reduced fuel consumption and CO2-emission are expected. To overcome the insufficient oxidation protection the halogen effect offers an innovative way. After surface doping using F-implantation or liquid phase-treatment with an F-containing solution and subsequent oxidation at high temperatures the formation of a protective alumina scale can be achieved. By using non-destructive ion beam analyses (PIGE, RBS) F was found at the metal/oxide interface. For analysis of large scale components a new vacuum chamber at the IKF was installed and became operative. With this prototype of in-situ quality assurance system for the F-doping of manufactured parts from TiAl some performance test measurements were done and presented in this paper.Received: 01 March 2013; Revised: 24 April 2013; Accepted: 25 April 201

The Parker Instability in 3-D: Corrugations and Superclouds Along the Carina-Sagittarius Arm

Here we present three-dimensional MHD models for the Parker instability in a thick magnetized disk, including the presence of a spiral arm. The $B$-field is assumed parallel to the arm, and the model results are applied to the optical segment of the Carina-Sagittarius arm. The characteristic features of the undular and interchange modes are clearly apparent in the simulations. The undular mode creates large gas concentrations distributed along the arm. This results in a clear arm/inter-arm difference: the instability triggers the formation of large interstellar clouds inside the arms, but generates only small structures with slight density enhancements in the inter-arm regions. The resulting clouds are distributed in an antisymmetric way with respect to the midplane, creating an azimuthal corrugation along the arm. For conditions similar to those of the optical segment of the Carina-Sagittarius arm, it has a wavelength of about 2.4 kpc. This structuring can explain the origin of both HI superclouds and the azimuthal corrugations in spiral arms. The wavelength matches the corrugation length derived with the young stellar groups located in the optical segment of the Carina-Sagittarius arm. Keywords: Galaxy: kinematics and dynamics -- Galaxy: structure -- Instabilities -- ISM: clouds -- ISM: magnetic fields -- ISM: structure -- MHDComment: 29 pages, 12 figures, Latex, Accepted by the Astrophysical Journa

On disc driven inward migration of resonantly coupled planets with application to the system around GJ876

We consider two protoplanets gravitationally interacting with each other and a protoplanetary disc. The two planets orbit interior to a tidally maintained disc cavity while the disc interaction indices inward migration. When the migration is slow enough, the more rapidly migrating outer protoplanet approaches and becomes locked in a 2:1 commensurability with the inner one. This is maintained in subsequent evolution. We study this evolution using a simple anaytic model, full hydrodynamic 2D simulations of the disc planet system and longer time N body integrations incorporating simple prescriptions for the effect of the disc on the planet orbits. The eccentricity of the protoplanets are found to be determined by the migration rate induced in the outer planet orbit by the external disc. We apply our results to the recently discovered resonant planets around GJ876. Simulation shows that a disc with parameters expected for protoplanetary discs causes trapping in the 2:1 commensurability when the planets orbit in an inner cavity and that eccentricities in the observed range may be obtained.Comment: 8 pages, 5 figures, submitted to A&A on 30/03/200

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

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

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

A comparative study of disc-planet interaction

We perform numerical simulations of a disc-planet system using various grid-based and smoothed particle hydrodynamics (SPH) codes. The tests are run for a simple setup where Jupiter and Neptune mass planets on a circular orbit open a gap in a protoplanetary disc during a few hundred orbital periods. We compare the surface density contours, potential vorticity and smoothed radial profiles at several times. The disc mass and gravitational torque time evolution are analyzed with high temporal resolution. There is overall consistency between the codes. The density profiles agree within about 5% for the Eulerian simulations while the SPH results predict the correct shape of the gap although have less resolution in the low density regions and weaker planetary wakes. The disc masses after 200 orbital periods agree within 10%. The spread is larger in the tidal torques acting on the planet which agree within a factor 2 at the end of the simulation. In the Neptune case the dispersion in the torques is greater than for Jupiter, possibly owing to the contribution from the not completely cleared region close to the planet.Comment: 32 pages, accepted for publication in MNRA