Modelling Circumbinary Gas Flows in Close T Tauri Binaries

Young close binaries open central gaps in the surrounding circumbinary accretion disc, but the stellar components may still gain mass from gas crossing through the gap. It is not well understood how this process operates and how the stellar components are affected by such inflows. Our main goal is to investigate how gas accretion takes place and evolves in close T Tauri binary systems. In particular, we model the accretion flows around two close T Tauri binaries, V4046 Sgr and DQ Tau, both showing periodic changes in emission lines, although their orbital characteristics are very different. In order to derive the density and velocity maps of the circumbinary material, we employ two-dimensional hydrodynamic simulations with a locally isothermal equation of state. The flow patterns become quasi-stable after a few orbits in the frame co-rotating with the system. Gas flows across the circumbinary gap through the co-rotating Lagrangian points, and local circumstellar discs develop around both components. Spiral density patterns develop in the circumbinary disc that transport angular momentum efficiently. Mass is preferentially channelled towards the primary and its circumstellar disc is more massive than the disc around the secondary. We also compare the derived density distribution to observed line profile variability. The line profile variability tracing the gas flows in the central cavity shows clear similarities with the corresponding observed line profile variability in V4046 Sgr, but only when the local circumstellar disc emission was excluded. Closer to the stars normal magnetospheric accretion may dominate while further out the dynamic accretion process outlined here dominates. Periodic changes in the accretion rates onto the stars can explain the outbursts of line emission observed in eccentric systems such as DQ Tau.Comment: Accepted for publication in MNRA

Giant planet migration during FU Orionis outbursts: 1D disc models

I present the results of semi-analytic calculations of migrating planets in young, outbursting circumstellar discs. Formed far out in the disc via gravitational fragmentation early on in its lifetime, these planets typically migrate at very slow rates and are therefore mostly expected to remain at large radii (such as is the case in HR 8799). I show that changes in the disc structure during FUor outbursts affect the planet’s ability to maintain a gap and can allow a massive giant planet’s semimajor axis to reduce by almost 5 per cent in a single outburst under the most optimistic conditions. Given that a single disc will likely undergo ∼ 10 such outbursts this process can significantly alter the expected radial distribution for GI-formed planets

Modelling Circumbinary Gas Flows in Close T Tauri Binaries

Young close binaries open central gaps in the surrounding circumbinary accretion disc, but the stellar components may still gain mass from gas crossing through the gap. It is not well understood how this process operates and how the stellar components are affected by such inflows. Our main goal is to investigate how gas accretion takes place and evolves in close T Tauri binary systems. In particular, we model the accretion flows around two close T Tauri binaries, V4046 Sgr and DQ Tau, both showing periodic changes in emission lines, although their orbital characteristics are very different. In order to derive the density and velocity maps of the circumbinary material, we employ two-dimensional hydrodynamic simulations with a locally isothermal equation of state. The flow patterns become quasi-stable after a few orbits in the frame co-rotating with the system. Gas flows across the circumbinary gap through the co-rotating Lagrangian points, and local circumstellar discs develop around both components. Spiral density patterns develop in the circumbinary disc that transport angular momentum efficiently. Mass is preferentially channelled towards the primary and its circumstellar disc is more massive than the disc around the secondary. We also compare the derived density distribution to observed line profile variability. The line profile variability tracing the gas flows in the central cavity shows clear similarities with the corresponding observed line profile variability in V4046 Sgr, but only when the local circumstellar disc emission was excluded. Closer to the stars normal magnetospheric accretion may dominate while further out the dynamic accretion process outlined here dominates. Periodic changes in the accretion rates onto the stars can explain the outbursts of line emission observed in eccentric systems such as DQ Tau.Comment: Accepted for publication in MNRA

Planet migration: self-gravitating radiation hydrodynamical models of protoplanets with surfaces

We calculate radial migration rates of protoplanets in laminar minimum mass solar nebula discs using three-dimensional self-gravitating radiation hydrodynamical (RHD) models. The protoplanets are free to migrate, whereupon their migration rates are measured. For low mass protoplanets (10-50 M_\oplus) we find increases in the migration timescales of up to an order of magnitude between locally-isothermal and RHD models. In the high-mass regime the migration rates are changed very little. These results are arrived at by calculating migration rates in locally-isothermal models, before sequentially introducing self-gravity, and radiative transfer, allowing us to isolate the effects of the additional physics. We find that using a locally-isothermal equation of state, without self-gravity, we reproduce the migration rates obtained by previous analytic and numerical models. We explore the impact of different protoplanet models, and changes to their assumed radii, upon migration. The introduction of self-gravity gives a slight reduction of the migration rates, whilst the inertial mass problem, which has been proposed for high mass protoplanets with circumplanetary discs, is reproduced. Upon introducing radiative transfer to models of low mass protoplanets (\approx 10 M_\oplus), modelled as small radius accreting point masses, we find outward migration with a rate of approximately twice the analytic inward rate. However, when modelling such a protoplanet in a more realistic manner, with a surface which enables the formation of a deep envelope, this outward migration is not seen.Comment: 21 pages, 21 figure

Comparative statistics and origin of triple and quadruple stars

The statistics of catalogued quadruple stars consisting of two binaries (hierarchy 2+2) is studied in comparison with triple stars, with respective sample sizes of 81 and 724. Seven representative quadruple systems are discussed in greater detail. The properties of multiple stars do not correspond to the products of dynamical decay of small clusters, hence the N-body dynamics is not the dominant process of their formation. On the other hand, rotationally-driven (cascade) fragmentation possibly followed by migration of inner and/or outer orbits to shorter periods is a promising scenario to explain the origin of triple and quadruple stars. Our main results are: (i) Quadruple systems of Epsilon Lyr type with similar masses and inner periods are common. (ii) The distributions of the inner periods in triple and quadruple stars are similar and bimodal. The inner mass ratios do not correlate with the inner periods. (iii) The statistics of outer periods and mass ratios in triples and quadruples are different. The median outer mass ratio in triples is 0.39 independently of the outer period, which has a smooth distribution. In contrast, the outer periods of 25% quadruples concentrate in the narrow range from 10yr to 100yr, the outer mass ratios of these tight quadruples are above 0.6 and their two inner periods are similar to each other. (iv) The outer and inner mass ratios in triple and quadruple stars are not mutually correlated. (v) The inner and outer orbital angular momenta and periods in triple and quadruple systems with inner periods above 30d show some correlation, the ratio of outer-to-inner periods is mostly comprised between 5 and 10^4. In the systems with small period ratios the directions of the orbital spins are correlated, while in the systems with large ratios they are not.Comment: Accepted by MNRAS, 14 pages, 12 figures. Two electronic tables at http://www.ctio.noao.edu/ftp/pub/tokovinin/quadruples

Numerical simulations of type III planetary migration: III. Outward migration of massive planets

We present a numerical study of rapid, so called type III migration for Jupiter-sized planets embedded in a protoplanetary disc. We limit ourselves to the case of outward migration, and study in detail its evolution and physics, concentrating on the structure of the co-rotation and circumplanetary regions, and processes for stopping migration. We also consider the dependence of the migration behaviour on several key parameters. We perform this study using global, two-dimensional hydrodynamical simulations with adaptive mesh refinement. We find that the outward directed type III migration can be started if the initial conditions support $Z > 1$, that corresponds to initial value M_\rmn{\Delta} \ga 1.5. Unlike the inward directed migration, in the outward migration the migration rate increases due to the growing of the volume of the co-orbital region. We find the migration to be strongly dependent on the rate of the mass accumulation in the circumplanetary disc, leading to two possible regimes of migration, fast and slow. The structure of the co-orbital region and the stopping mechanism differ between these two regimes.Comment: 18 pages, 13 figures, submitted to MNRA

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

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

From Grains to Planetesimals: Les Houches Lecture

This pedagogical review covers an unsolved problem in the theory of protoplanetary disks: the growth of dust grains into planetesimals, solids at least a kilometer in size. I summarize timescale constraints imposed on planetesimal formation by circumstellar disk observations, analysis of meteorites, and aerodynamic radial migration. The infall of ~meter-sized solids in a hundred years is the most stringent constraint. I review proposed mechanisms for planetesimal formation. Collisional coagulation models are informed by laboratory studies of microgravity collisions. The gravitational collapse (or Safronov-Goldreich-Ward) hypothesis involves detailed study of the interaction between solid particles and turbulent gas. I cover the basics of aerodynamic drag in protoplanetary disks, including radial drift and vertical sedimentation. I describe various mechanisms for particle concentration in gas disks -- including turbulent pressure maxima, drag instabilities and long-lived anticylonic vortices. I derive a general result for the minimum size for a vortex to trap particles in a sub-Keplerian disk. Recent numerical simulations demonstrate that particle clumping in turbulent protoplanetary disks can trigger gravitational collapse. I discuss several outstanding issues in the field.Comment: 20 pages, 3 figures, to appear in the proceedings of the Les Houches Winter School "Physics and Astrophysics of Planetary Systems" (EDP Sciences: EAS Publications Series). Version 2 is the same paper, simply adds above publisher inf

Two phase, inward-then-outward migration of Jupiter and Saturn in the gaseous Solar Nebula

It has recently been shown that the terrestrial planets and asteroid belt can be reproduced if the giant planets underwent an inward-then-outward migration (the "Grand Tack"; Walsh et al 2011). Inward migration occurs when Jupiter opens a gap and type II migrates inward. The planets "tack" and migrate outward when Saturn reaches the gap-opening mass and is caught in the 3:2 resonance with Jupiter. The aim is to test the viability of the Grand Tack model and to study the dynamical evolution of Jupiter and Saturn during their growth from 10 Earth masses cores. We have performed numerical simulations using a grid-based hydrodynamical code. Most of our simulations assume an isothermal equation of state for the disk but a subset use a fully-radiative version of the code. For an isothermal disk the two phase migration of Jupiter and Saturn is very robust and independent of the mass-growth history of these planets provided the disk is cool enough. For a radiative disk the we find some outcomes with two phase migrations and others with more complicated behavior. We construct a simple, 1-D model of an evolving viscous disk to calculate the evolution of the disk's radiative properties: the disk transitions from radiative to isothermal from its outermost regions inward in time. We show that a two-phase migration is a natural outcome at late times even under the limiting assumption that isothermal conditions are required. Thus, our simulations provide strong support for the Grand Tack scenario.Comment: 16 pages, 21 figures, accepted in Astronomy and Astrophysic