Viscous overstability and eccentricity evolution in three-dimensional gaseous discs

We investigate the growth or decay rate of the fundamental mode of even symmetry in a viscous accretion disc. This mode occurs in eccentric discs and is known to be potentially overstable. We determine the vertical structure of the disc and its modes, treating radiative energy transport in the diffusion approximation. In the limit of very long radial wavelength, an analytical criterion for viscous overstability is obtained, which involves the effective shear and bulk viscosity, the adiabatic exponent and the opacity law of the disc. This differs from the prediction of a two-dimensional model. On shorter wavelengths (a few times the disc thickness), the criterion for overstability is more difficult to satisfy because of the different vertical structure of the mode. In a low-viscosity disc a third regime of intermediate wavelengths appears, in which the overstability is suppressed as the horizontal velocity perturbations develop significant vertical shear. We suggest that this effect determines the damping rate of eccentricity in protoplanetary discs, for which the long-wavelength analysis is inapplicable and overstability is unlikely to occur on any scale. In thinner accretion discs and in decretion discs around Be stars overstability may occur only on the longest wavelengths, leading to the preferential excitation of global eccentric modes.Comment: 11 pages, 8 figure

The Near-Infrared Structure and Spectra of the Bipolar Nebulae M 2--9 and Afgl 2688: The Role of UV-Pumping and Shocks in Molecular Hydrogen Excitation

High-resolution near-infrared images and moderate resolution spectra were obtained of the bipolar nebulae M~2--9 and AFGL 2688. The ability to spatially and spectrally resolve the various components of the nebulae has proved to be important in determining their physical structure and characteristics. In M~2--9, the lobes are found to have a double-shell structure. Analysis of \h2\ line ratios indicates that the \h2\ emission is radiatively excited. A well-resolved photodissociation region is observed in the lobes. The spectrum of the central source is dominated by H recombination lines and a strong continuum rising towards longer wavelengths consistent with a $T = 795$ K blackbody. In AFGL 2688, the emission from the bright lobes is mainly continuum reflected from the central star. Several molecular features from C$_2$ and CN are present. In the extreme end of the N lobe and in the E equatorial region, the emission is dominated by lines of \h2 in the 2--2.5 \microns region. The observed \h2 line ratios indicate that the emission is collisionally excited, with an excitation temperature $T_{ex} \approx 1600\pm 100$ K.Comment: 28 pages, 13 figures,uuencoded compressed postscript, printed version available by request from [email protected], IfA-94/3