Shapes of star-gas waves in spiral galaxies

Density-wave profile shapes are influenced by several effects. By solving viscous fluid equations, the nonlinear effects of the gas and its gravitational interaction with the stars can be analyzed. The stars are treated through a linear theory developed by Lin and coworkers. Short wavelength gravitational forces are important in determining the gas density profile shape. With the inclusion of disk finite thickness effects, the gas gravitational field remains important, but is significantly reduced at short wavelengths. Softening of the gas equation of state results in an enhanced response and a smoothing of the gas density profile. A Newtonian stress relation is marginally acceptable for HI gas clouds, but not acceptable for giant molecular clouds

The effect of planetary migration on the corotation resonance

The migration of a planet through a gaseous disc causes the locations of their resonant interactions to drift and can alter the torques exerted between the planet and the disc. We analyse the time-dependent dynamics of a non-coorbital corotation resonance under these circumstances. The ratio of the resonant torque in a steady state to the value given by Goldreich & Tremaine (1979) depends essentially on two dimensionless quantities: a dimensionless turbulent diffusion time-scale and a dimensionless radial drift speed. When the drift speed is comparable to the libration speed and the viscosity is small, the torque can become much larger than the unsaturated value in the absence of migration, but is still proportional to the large-scale vortensity gradient in the disc. Fluid that is trapped in the resonance and drifts with it acquires a vortensity anomaly relative to its surroundings. If the anomaly is limited by viscous diffusion in a steady state, the resulting torque is inversely proportional to the viscosity, although a long time may be required to achieve this state. A further, viscosity-independent, contribution to the torque comes from fluid that streams through the resonant region. In other cases, torque oscillations occur before the steady value is achieved. We discuss the significance of these results for the evolution of eccentricity in protoplanetary systems. We also describe the possible application of these findings to the coorbital region and the concept of runaway (or type III) migration. [Abridged]Comment: 15 pages, 6 figures, to be published in MNRA

Polar Alignment of a Protoplanetary Disc around an Eccentric Binary - II. Effect of Binary and Disc Parameters

In a recent paper Martin & Lubow showed that a circumbinary disc around an eccentric binary can undergo damped nodal oscillations that lead to the polar (perpendicular) alignment of the disc relative to the binary orbit. The disc angular momentum vector aligns to the eccentricity vector of the binary. We explore the robustness of this mechanism for a low-mass disc (0.001 of the binary mass) and its dependence on system parameters by means of hydrodynamic disc simulations. We describe how the evolution depends upon the disc viscosity, temperature, size, binary mass ratio, orbital eccentricity, and inclination. We compare results with predictions of linear theory. We show that polar alignment of a low-mass disc may occur over a wide range of binary-disc parameters. We discuss the application of our results to the formation of planetary systems around eccentric binary stars

Jet launching from accretion discs in the local approximation

The acceleration of an outflow along inclined magnetic field lines emanating from an accretion disc can be studied in the local approximation, as employed in the computational model known as the shearing box. By including the slow magnetosonic point within the computational domain, the rate of mass loss in the outflow can be calculated. The accretion rates of mass and magnetic flux can also be determined, although some effects of cylindrical geometry are omitted. We formulate a simple model for the study of this problem and present the results of one-dimensional numerical simulations and supporting calculations. Quasi-steady solutions are obtained for relatively strong poloidal magnetic fields for which the magnetorotational instability is suppressed. In this regime the rate of mass loss decreases extremely rapidly with increasing field strength, or with decreasing surface density or temperature. If the poloidal magnetic field in an accretion disc can locally achieve an appropriate strength and inclination then a rapid burst of ejection may occur. For weaker fields it may be possible to study the launching process in parallel with the magnetorotational instability, but this will require three-dimensional simulations.Comment: 8 pages, 4 figures, to be published in MNRA