Local Axisymmetric Instability Criterion in the Thin, Rotating, Multicomponent Disk

Purely gravitational perturbations are considered in a thin rotating disk composed of several gas and stellar components. The dispersion relation for the axisymmetric density waves propagating through the disk is found and the criterion for the local axisymmetric stability of the whole system is formulated. In the appropriate limit of two-component gas we confirm the findings of Jog & Solomon (1984) and extend consideration to the case when one component is collisionless. Gravitational stability of the Galactic disk in the Solar neighborhood based on the multicomponent instability condition is explored using recent measurements of the stellar composition and kinematics in the local Galactic disk obtained by Hipparcos satellite.Comment: 8 pages, 5 figures, 1 table, to be submitted to MNRA

How to build Tatooine: reducing secular excitation in Kepler circumbinary planet formation

Circumbinary planetary systems recently discovered by Kepler represent an important testbed for planet formation theories. Planetesimal growth in disks around binaries has been expected to be inhibited interior to ~10 AU by secular excitation of high relative velocities between planetesimals, leading to their collisional destruction (rather than agglomeration). Here we show that gravity of the gaseous circumbinary disk in which planets form drives fast precession of both the planetesimal and binary orbits, resulting in strong suppression of planetesimal eccentricities beyond 2-3 AU and making possible growth of 1-100 km objects in this region. The precise location of the boundary of accretion-friendly region depends on the size of the inner disk cavity cleared by the binary torques and on the disk mass (even 0.01 M_Sun disk strongly suppresses planetesimal excitation), among other things. Precession of the orbit of the central binary, enhanced by the mass concentration naturally present at the inner edge of a circumbinary disk, plays key role in this suppression, which is a feature specific to the circumbinary planet formation.Comment: 6 pages, 2 figures, submitted to ApJ

Supersonic Shear Instabilities in Astrophysical Boundary Layers

Disk accretion onto weakly magnetized astrophysical objects often proceeds via a boundary layer that forms near the object's surface, in which the rotation speed of the accreted gas changes rapidly. Here we study the initial stages of formation for such a boundary layer around a white dwarf or a young star by examining the hydrodynamical shear instabilities that may initiate mixing and momentum transport between the two fluids of different densities moving supersonically with respect to each other. We find that an initially laminar boundary layer is unstable to two different kinds of instabilities. One is an instability of a supersonic vortex sheet (implying a discontinuous initial profile of the angular speed of the gas) in the presence of gravity, which we find to have a growth rate of order (but less than) the orbital frequency. The other is a sonic instability of a finite width, supersonic shear layer, which is similar to the Papaloizou-Pringle instability. It has a growth rate proportional to the shear inside the transition layer, which is of order the orbital frequency times the ratio of stellar radius to the boundary layer thickness. For a boundary layer that is thin compared to the radius of the star, the shear rate is much larger than the orbital frequency. Thus, we conclude that sonic instabilities play a dominant role in the initial stages of nonmagnetic boundary layer formation and give rise to very fast mixing between disk gas and stellar fluid in the supersonic regime.Comment: 35 pages, 6 figures, submitted to Ap

Disk-satellite interaction in disks with density gaps

Gravitational coupling between a gaseous disk and an orbiting perturber leads to angular momentum exchange between them which can result in gap opening by planets in protoplanetary disks and clearing of gas by binary supermassive black holes (SMBHs) embedded in accretion disks. Understanding the co-evolution of the disk and the orbit of the perturber in these circumstances requires knowledge of the spatial distribution of the torque exerted by the latter on a highly nonuniform disk. Here we explore disk-satellite interaction in disks with gaps in linear approximation both in Fourier and in physical space, explicitly incorporating the disk non-uniformity in the fluid equations. Density gradients strongly displace the positions of Lindblad resonances in the disk (which often occur at multiple locations), and the waveforms of modes excited close to the gap edge get modified compared to the uniform disk case. The spatial distribution of the excitation torque density is found to be quite different from the existing prescriptions: most of the torque is exerted in a rather narrow region near the gap edge where Lindblad resonances accumulate, followed by an exponential fall-off with the distance from the perturber. Despite these differences, for a given gap profile the full integrated torque exerted on the disk agrees with the conventional uniform disk theory prediction at the level of ~10%. The nonlinearity of the density wave excited by the perturber is shown to decrease as the wave travels out of the gap, slowing down its nonlinear evolution and damping. Our results suggest that gap opening in protoplanetary disks and gas clearing around SMBH binaries can be more efficient than the existing theories predict. They pave the way for self-consistent calculations of the gap structure and the orbital evolution of the perturber using accurate prescription for the torque density behavior.Comment: corrected typos in reference