The vertical structure of the boundary layer around compact objects

Context. Mass transfer due to Roche lobe overflow leads to the formation of an accretion disk around a weakly magnetized white dwarf (WD) in cataclysmic variables. At the inner edge of the disk, the gas comes upon the surface of the WD and has to get rid of its excess kinetic energy in order to settle down on the more slowly rotating outer stellar layers. This region is known as the boundary layer (BL). Aims. In this work we investigate the vertical structure of the BL, which is still poorly understood. We shall provide details of the basic structure of the two-dimensional (2D) BL and how it depends on parameters such as stellar mass and rotation rate, as well as the mass-accretion rate. We further investigate the destination of the disk material and compare our results with previous one-dimensional (1D) simulations. Methods. We solve the 2D equations of radiation hydrodynamics in a spherical geometry using a parallel grid-based code that employs a Riemann solver. The radiation energy is considered in the two-temperature approach with a radiative flux given by the flux-limited diffusion approximation. Results. The BL around a non-rotating WD is characterized by a steep drop in angular velocity over a width of only 1% of the stellar radius, a heavy depletion of mass, and a high temperature (500 000 K) as a consequence of the strong shear. Variations in Om_star, M_star, and M_dot influence the extent of the changes of the variables in the BL but not the general structure. Depending on Om_star, the disk material travels up to the poles or is halted at a certain latitude. The extent of mixing with the stellar material also depends on Om_star. We find that the 1D approximation matches the 2D data well, apart from an underestimated temperature.Comment: 15 pages, 9 figures, accepted for publication in Astronomy & Astrophysic

Evolution of circumbinary planets around eccentric binaries: The case of Kepler-34

The existence of planets orbiting a central binary star system immediately raises questions regarding their formation and dynamical evolution. Recent discoveries of circumbinary planets by the Kepler space telescope has shown that some of these planets reside close to the dynamical stability limit where it is very difficult to form planets in situ. For binary systems with nearly circular orbits, such as Kepler-38, the observed proximity of planetary orbits to the stability limit can be understood by an evolutionary process in which planets form farther out in the disk and migrate inward to their observed position. The Kepler-34 system has a high orbital eccentricity of 0.52. Here, we analyse evolutionary scenarios for the planet observed around this system using two-dimensional hydrodynamical simulations. The highly eccentric binary opens a wide inner hole in the disk which is also eccentric, and displays a slow prograde precession. As a result of the large, eccentric inner gap, an embedded planet settles in a final equilibrium position that lies beyond the observed location of Kepler-34 b, but has the correct eccentricity. In this configuration the planetary orbit is aligned with the disk in a state of apsidal corotation.To account for the closer orbit of Kepler-34 b to the central binary, we considered a two-planet scenario and examined the evolution of the system through joint inward migration and capture into mean-motion resonances. When the inner planet orbits inside the gap of the disk, planet-planet scattering ensues. While often one object is thrown into a large, highly eccentric orbit, at times the system is left with a planet close to the observed orbit, suggesting that Kepler 34 might have had two circumbinary planets where one might have been scattered out of the system or into an orbit where it did not transit the central binary during the operation of Kepler.Comment: 11 pages, 13 figures, accepted by Astronomy & Astrophysics. arXiv admin note: text overlap with arXiv:1401.764

The accretion of migrating giant planets

Most studies concerning the growth and evolution of massive planets focus either on their accretion or their migration only. In this work we study both processes concurrently to investigate how they might mutually affect each other. We modeled a 2-dimensional disk with a steady accretion flow onto the central star and embed a Jupiter mass planet at 5.2 au. The disk is locally isothermal and viscosity is modeled using a constant $\alpha$. The planet is held on a fixed orbit for a few hundred orbits to allow the disk to adapt and carve a gap. After this period, the planet is released and free to move according to the gravitational interaction with the gas disk. The mass accretion onto the planet is modeled by removing a fraction of gas from the inner Hill sphere, and the removed mass and momentum can be added to the planet. Our results show that a fast migrating planet is able to accrete more gas than a slower migrating planet. Utilizing a tracer fluid we analyzed the origin of the accreted gas which comes predominantly originating from the inner disk for a fast migrating planet. In case of slower migration the fraction of gas from the outer disk increases. We also found that even for very high accretion rates in some cases gas crosses the planetary gap from the inner to the outer disk. Our simulations show that the crossing of gas changes during the migration process as the migration rate slows down. Therefore classical type II migration where the planet migrates with the viscous drift rate and no gas crosses the gap is no general process but may only occur for special parameters and at a certain time during the orbital evolution of the planet.Comment: 9 pages, 14 figures, accepted for publication in A&

Modelling Circumbinary Planets: The case of Kepler-38

Recently, a number of planets orbiting binary stars have been discovered by the Kepler space telescope. In a few systems the planets reside close to the dynamical stability limit. Due to the difficulty of forming planets in such close orbits, it is believed that they have formed further out in the disk and migrated to their present locations. Our goal is to construct more realistic models of planet migration in circumbinary disks, and to determine the final position of these planets. In our work, we focus on the system Kepler-38. The evolution of the circumbinary disk is studied using two-dimensional hydrodynamical simulations. We study locally isothermal disks as well as more realistic models with viscous heating, radiative cooling from the disk surfaces, and radiative diffusion in the disk mid plane. After the disk has been brought into equilibrium, a 115 Earth-mass planet is embedded and its evolution is followed. In all cases the planets stop inward migration near the inner edge of the disk. In isothermal disks with a typical disk scale height of H/r = 0.05, the final outcome agrees very well with the observed location of planet Kepler-38b. For the radiative models, the disk thickness and location of the inner edge is determined by the mass in the system. For surface densities in the order of 3000 g/cm^2 at 1 AU, the inner gap lies close to the binary and planets stop in the region between the 5:1 and 4:1 mean-motion resonances with the binary. A model with a disk with approximately a quarter of the mass yields a final position very close to the observed one. For planets migrating in circumbinary disks, the final position is dictated by the structure of the disk. Knowing the observed orbits of circumbinary planets, radiative disk simulations with embedded planets can provide important information on the physical state of the system during the final stages of its evolution.Comment: 14 pages, accepted by Astronomy & Astrophysics, Animations available under: http://www.tat.physik.uni-tuebingen.de/~kley/projects/kep38

Wave mediated angular momentum transport in astrophysical boundary layers

Context. Disk accretion onto weakly magnetized stars leads to the formation of a boundary layer (BL) where the gas loses its excess kinetic energy and settles onto the star. There are still many open questions concerning the BL, for instance the transport of angular momentum (AM) or the vertical structure. Aims. It is the aim of this work to investigate the AM transport in the BL where the magneto-rotational instability (MRI) is not operating owing to the increasing angular velocity $\Omega(r)$ with radius. We will therefore search for an appropriate mechanism and examine its efficiency and implications. Methods. We perform 2D numerical hydrodynamical simulations in a cylindrical coordinate system $(r, \varphi)$ for a thin, vertically inte- grated accretion disk around a young star. We employ a realistic equation of state and include both cooling from the disk surfaces and radiation transport in radial and azimuthal direction. The viscosity in the disk is treated by the {\alpha}-model; in the BL there is no viscosity term included. Results. We find that our setup is unstable to the sonic instability which sets in shortly after the simulations have been started. Acoustic waves are generated and traverse the domain, developing weak shocks in the vicinity of the BL. Furthermore, the system undergoes recurrent outbursts where the activity in the disk increases strongly. The instability and the waves do not die out for over 2000 orbits. Conclusions. There is indeed a purely hydrodynamical mechanism that enables AM transport in the BL. It is efficient and wave mediated; however, this renders it a non-local transport method, which means that models of a effective local viscosity like the {\alpha}-viscosity are probably not applicable in the BL. A variety of further implications of the non-local AM transport are discussed.Comment: 18 pages, 15 figures, accepted for publication in Astronomy & Astrophysic

Vertical shear instability in accretion disc models with radiation transport

The origin of turbulence in accretion discs is still not fully understood. While the magneto-rotational instability is considered to operate in sufficiently ionized discs, its role in the poorly ionized protoplanetary disc is questionable. Recently, the vertical shear instability (VSI) has been suggested as a possible alternative. Our goal is to study the characteristics of this instability and the efficiency of angular momentum transport, in extended discs, under the influence of radiative transport and irradiation from the central star. We use multi-dimensional hydrodynamic simulations to model a larger section of an accretion disc. First we study inviscid and weakly viscous discs using a fixed radial temperature profile in two and three spatial dimensions. The simulations are then extended to include radiative transport and irradiation from the central star. In agreement with previous studies we find for the isothermal disc a sustained unstable state with a weak positive angular momentum transport of the order of $\alpha \approx 10^{-4}$. Under the inclusion of radiative transport the disc cools off and the turbulence terminates. For discs irradiated from the central star we find again a persistent instability with a similar $\alpha$ value as for the isothermal case. We find that the VSI can indeed generate sustained turbulence in discs albeit at a relatively low level with $\alpha$ about few times $10^{-4}$Comment: 12 pages, 24 figures, accepted for publication in Astronomy & Astrophysic

Tensile & shear strength of porous dust agglomerates

Context.Within the sequential accretion scenario of planet formation, planets are build up through a sequence sticking collisions. The outcome of collisions between porous dust aggregates is very important for the growth from very small dust particles to planetesimals. In this work we determine the necessary material properties of dust aggregates as a function the porosity. Aims: Continuum models such as SPH that are capable of simulating collisions of macroscopic dust aggregates require a set of material parameters. Some of them such as the tensile and shear strength are difficult to obtain from laboratory experiments. The aim of this work is to determine these parameters from ab-initio molecular dynamics simulations. Methods: We simulate the behavior of porous dust aggregates using a detailed micro-physical model of the interaction of spherical grains that includes adhesion forces, rolling, twisting, and sliding. Using different methods of preparing the samples we study the strength behavior of our samples with varying porosity and coordination number of the material. Results: For the tensile strength, we can reproduce data from laboratory experiments very well. For the shear strength, there are no experimental data available. The results from our simulations differ significantly from previous theoretical models, which indicates that the latter might not be sufficient to describe porous dust aggregates. Conclusions: We have provided functional behavior of tensile and shear strength of porous dust aggregates as a function of the porosity that can be directly applied in continuum simulations of these objects in planet formation scenarios.Comment: Accepted for publication in A&

Erosion of dust aggregates

Aims: The aim of this work is to gain a deeper insight into how much different aggregate types are affected by erosion. Especially, it is important to study the influence of the velocity of the impacting projectiles. We also want to provide models for dust growth in protoplanetary disks with simple recipes to account for erosion effects. Methods: To study the erosion of dust aggregates we employed a molecular dynamics approach that features a detailed micro-physical model of the interaction of spherical grains. For the first time, the model has been extended by introducing a new visco-elastic damping force which requires a proper calibration. Afterwards, different sample generation methods were used to cover a wide range of aggregate types. Results: The visco-elastic damping force introduced in this work turns out to be crucial to reproduce results obtained from laboratory experiments. After proper calibration, we find that erosion occurs for impact velocities of 5 m/s and above. Though fractal aggregates as formed during the first growth phase are most susceptible to erosion, we observe erosion of aggregates with rather compact surfaces as well. Conclusions: We find that bombarding a larger target aggregate with small projectiles results in erosion for impact velocities as low as a few m/s. More compact aggregates suffer less from erosion. With increasing projectile size the transition from accretion to erosion is shifted to higher velocities. This allows larger bodies to grow through high velocity collisions with smaller aggregates.Comment: accepted for publication in Astronomy & Astrophysic