Stability of the viscously spreading ring

We study analytically and numerically the stability of the pressure-less, viscously spreading accretion ring. We show that the ring is unstable to small non-axisymmetric perturbations. To perform the perturbation analysis of the ring we use a stretching transformation of the time coordinate. We find that to 1st order, one-armed spiral structures, and to 2nd order additionally two-armed spiral features may appear. Furthermore, we identify a dispersion relation determining the instability of the ring. The theoretical results are confirmed in several simulations, using two different numerical methods. These computations prove independently the existence of a secular spiral instability driven by viscosity, which evolves into persisting leading and trailing spiral waves. Our results settle the question whether the spiral structures found in earlier simulations of the spreading ring are numerical artifacts or genuine instabilities.Comment: 13 pages, 12 figures; A&A accepte

Formation of massive planets in binary star systems

As of today over 40 planetary systems have been discovered in binary star systems. In all cases the configuration appears to be circumstellar, where the planets orbit around one of the stars, the secondary acting as a perturber. The formation of planets in binary star systems is more difficult than around single stars due to the gravitational action of the companion on the dynamics of the protoplanetary disk. In this contribution we first briefly present the relevant observational evidence for planets in binary systems. Then the dynamical influence that a secondary companion has on a circumstellar disk will be analyzed through fully hydrodynamical simulations. We demonstrate that the disk becomes eccentric and shows a coherent precession around the primary star. Finally, fully hydrodynamical simulations of evolving protoplanets embedded in disks in binary star systems are presented. We investigate how the orbital evolution of protoplanetary embryos and their mass growth from cores to massive planets might be affected in this very dynamical environment. We consider, in particular, the planet orbiting the primary in the system Gamma Cephei.Comment: To appear in Proceedings: Extrasolar Planets in Multi-body Systems: Theory and Observations Eds. K. Gozdziewski, A. Niedzielski and J. Schneide

Migration and Accretion of Protoplanets in 2D and 3D Global Hydrodynamical Simulations

Planet evolution is tightly connected to the dynamics of both distant and close disk material. Hence, an appropriate description of disk-planet interaction requires global and high resolution computations, which we accomplish by applying a Nested-Grid method. Through simulations in two and three dimensions, we investigate how migration and accretion are affected by long and short range interactions. For small mass objects, 3D models provide longer growth and migration time scales than 2D ones do, whereas time lengths are comparable for large mass planets.Comment: 4 pages, 4 figures; to appear in the Conference Proceedings of "Scientific Frontiers in Research on Extrasolar Planets

Modelling the evolution of planets in disks

To explain important properties of extrasolar planetary systems (eg. close-in hot Jupiters, resonant planets) an evolutionary scenario which allows for radial migration of planets in disks is required. During their formation protoplanets undergo a phase in which they are embedded in the disk and interact gravitationally with it. This planet-disk interaction results in torques (through gravitational forces) acting on the planet that will change its angular momentum and result in a radial migration of the planet through the disk. To determine the outcome of this very important process for planet formation, dedicated high resolution numerical modeling is required. This contribution focusses on some important aspects of the numerical approach that we found essential for obtaining successful results. We specifically mention the treatment of Coriolis forces, Cartesian grids, and the FARGO method.Comment: Talk given at JENAM meeting, Vienna 200

Modelling Accretion in Transitional Disks

Transitional disks are protoplanetary disk around young stars that display inner holes in the dust distribution within a few AU, which is accompanied nevertheless by some gas accretion onto the central star. These cavities could possibly be created by the presence of one or more massive planets. If the gap is created by planets and gas is still present in it, then there should be a flow of gas past the planet into the inner region. It is our goal to study the mass accretion rate into the gap and in particular the dependency on the planet's mass and the thermodynamic properties of the disk. We performed 2D hydro simulations for disks with embedded planets. We added radiative cooling from the disk surfaces, radiative diffusion in the disk midplane, and stellar irradiation to the energy equation to have more realistic models. The mass flow rate into the gap region depends, for given disk thermodynamics, non-monotonically on the mass of the planet. Generally, more massive planets open wider and deeper gaps which would tend to reduce the mass accretion into the inner cavity. However, for larger mass planets the outer disk becomes eccentric and the mass flow rate is enhanced over the low mass cases. As a result, for the isothermal disks the mass flow is always comparable to the expected mass flow of unperturbed disks M_d, while for more realistic radiative disks the mass flow is very small for low mass planets (<= 4 M_jup) and about 50% for larger planet masses. For the radiative disks that critical planet mass for the disk to become eccentric is much larger that in the isothermal case. Massive embedded planets can reduce the mass flow across the gap considerably, to values of about an order of magnitude smaller than the standard disk accretion rate, and can be responsible for opening large cavities. The remaining mass flow into the central cavity is in good agreement with the observations.Comment: 10 pages, 29 figures, accepted for publication in Astronomy & Astrophysic

Influence of viscosity and the adiabatic index on planetary migration

The strength and direction of migration of low mass embedded planets depends on the disk's thermodynamic state, where the internal dissipation is balanced by radiative transport, and the migration can be directed outwards, a process which extends the lifetime of growing embryos. Very important parameters determining the structure of disks, and hence the direction of migration, are the viscosity and the adiabatic index. In this paper we investigate the influence of different viscosity prescriptions (alpha-type and constant) and adiabatic indices on disk structures and how this affects the migration rate of planets embedded in such disks. We perform 3D numerical simulations of accretion disks with embedded planets. We use the explicit/implicit hydrodynamical code NIRVANA that includes full tensor viscosity and radiation transport in the flux-limited diffusion approximation, as well as a proper equation of state for molecular hydrogen. The migration of embedded 20Earthmass planets is studied. Low-viscosity disks have cooler temperatures and the migration rates of embedded planets tend toward the isothermal limit. In these disks, planets migrate inwards even in the fully radiative case. The effect of outward migration can only be sustained if the viscosity in the disk is large. Overall, the differences between the treatments for the equation of state seem to play a more important role in disks with higher viscosity. A change in the adiabatic index and in the viscosity changes the zero-torque radius that separates inward from outward migration. For larger viscosities, temperatures in the disk become higher and the zero-torque radius moves to larger radii, allowing outward migration of a 20 Earth-mass planet to persist over an extended radial range. In combination with large disk masses, this may allow for an extended period of the outward migration of growing protoplanetary cores

Stability and Formation of the Resonant System HD 73526

Based on radial velocity measurements it has been found recently that the two giant planets detected around the star HD 73526 are in 2:1 resonance. However, as our numerical integration shows, the derived orbital data for this system result in chaotic behavior of the giant planets, which is uncommon among the resonant extrasolar planetary systems. We intend to present regular (non-chaotic) orbital solutions for the giant planets in the system HD 73526 and offer formation scenarios based on combining planetary migration and sudden perturbative effects such as planet-planet scattering or rapid dispersal of the protoplanetary disk. A comparison with the already studied resonant system HD 128311, exhibiting similar behavior, is also done. The new sets of orbital solutions have been derived by the Systemic Console (www.oklo.org). The stability of these solutions has been investigated by the Relative Lyapunov indicator, while the migration and scattering effects are studied by gravitational N-body simulations applying non-conservative forces as well. Additionally, hydrodynamic simulations of embedded planets in protoplanetary disks are performed to follow the capture into resonance. For the system HD 73526 we demonstrate that the observational radial velocity data are consistent with a coplanar planetary system engaged in a stable 2:1 resonance exhibiting apsidal corotation. We have shown that, similarly to the system HD 128311, the present dynamical state of HD 73526 could be the result of a mixed evolutionary process melting together planetary migration and a perturbative event.Comment: 12 pages, 14 figures, accepted in A&A, v2: technical change

Formation of the resonant system HD 60532

Among multi-planet planetary systems there are a large fraction of resonant systems. Studying the dynamics and formation of these systems can provide valuable informations on processes taking place in protoplanetary disks where the planets are thought have been formed. The recently discovered resonant system HD 60532 is the only confirmed case, in which the central star hosts a pair of giant planets in 3:1 mean motion resonance. We intend to provide a physical scenario for the formation of HD 60532, which is consistent with the orbital solutions derived from the radial velocity measurements. Observations indicate that the system is in an antisymmetric configuration, while previous theoretical investigations indicate an asymmetric equilibrium state. The paper aims at answering this discrepancy as well. We performed two-dimensional hydrodynamical simulations of thin disks with an embedded pair of massive planets. Additionally, migration and resonant capture are studied by gravitational N-body simulations that apply properly parametrized non-conservative forces. Our simulations suggest that the capture into the 3:1 mean motion resonance takes place only for higher planetary masses, thus favouring orbital solutions having relatively smaller inclination i=20 degrees. The system formed by numerical simulations qualitatively show the same behaviour as HD 60532. We also find that the presence of an inner disk (between the inner planet and the star) plays a very important role in determining the final configurations of resonant planetary systems. Its damping effect on the inner planet's eccentricity is responsible for the observed antisymmetric state of HD 60532.Comment: 7 pages, 7 figures, Accepted for publication in Astronomy & Astrophysic