Gravitational instabilities in protostellar disks

The nonaxisymmetric stability of self-gravitating, geometrically thick accretion disks has been studied for protostellar systems having a wide range of disk-to-central object mass ratios. Global eigenmodes with four distinctly different characters were identified using numerical, nonlinear hydrodynamic techniques. The mode that appears most likely to arise in normal star formation settings, however, resembles the 'eccentric instability' that was identified earlier in thin, nearly Keplerian disks: It presents an open, one-armed spiral pattern that sweeps continuously in a trailing direction through more than 2-pi radians, smoothly connecting the inner and outer edges of the disk, and requires cooperative motion of the point mass for effective amplification. This particular instability promotes the development of a single, self-gravitating clump of material in orbit about the point mass, so its routine appearance in our simulations supports the conjecture that the eccentric instability provides a primary route to the formation of short-period binaries in protostellar systems

Phase-Transition Theory of Instabilities. II. Fourth-Harmonic Bifurcations and Lambda-Transitions

We use a free-energy minimization approach to describe the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Our approach is fully nonlinear and stems from the Ginzburg-Landau theory of phase transitions. In this paper, we examine fourth-harmonic axisymmetric disturbances in Maclaurin spheroids and fourth-harmonic nonaxisymmetric disturbances in Jacobi ellipsoids. These two cases are very similar in the framework of phase transitions. Irrespective of whether a nonlinear first-order phase transition occurs between the critical point and the higher turning point or an apparent second-order phase transition occurs beyond the higher turning point, the result is fission (i.e. ``spontaneous breaking'' of the topology) of the original object on a secular time scale: the Maclaurin spheroid becomes a uniformly rotating axisymmetric torus and the Jacobi ellipsoid becomes a binary. The presence of viscosity is crucial since angular momentum needs to be redistributed for uniform rotation to be maintained. The phase transitions of the dynamical systems are briefly discussed in relation to previous numerical simulations of the formation and evolution of protostellar systems.Comment: 34 pages, postscript, compressed,uuencoded. 7 figures available in postscript, compressed form by anonymous ftp from asta.pa.uky.edu (cd /shlosman/paper2 mget *.ps.Z). To appear in Ap

A new criterion for Bar-Forming Instability in Rapidly Rotating Gaseous and Stellar Systems. II. Nonaxisymmetric Form

We have previously introduced the parameter `alpha' as an indicator of stability to m=2 nonaxisymmetric modes in rotating, self-gravitating, axisymmetric, gaseous and stellar systems. This parameter can be written as a function of the total rotational kinetic energy, the total gravitational potential energy, and as a function of the topology/connectedness and the geometric shape of a system. Here we extend the stability criterion to nonaxisymmetric equilibrium systems, such as ellipsoids and elliptical disks and cylinders. We test the validity of this extension by considering predictions for previously published, gaseous and stellar, nonaxisymmetric models. The above formulation and critical values account accurately for the stability properties of m=2 modes in gaseous Riemann S-type ellipsoids (including the Jacobi and Dedekind ellipsoids) and elliptical Riemann disks as well as in stellar elliptical Freeman disks and cylinders: all these systems are dynamically stable except for the stellar elliptical Freeman disks that exhibit a relatively small region of m=2 dynamical instability.Comment: 17 pages, postscript, compressed, uuencoded. 10 figures available by anonymous ftp from ftp://asta.pa.uky.edu/shlosman/bar2/ (mget *.ps.Z). To appear in Ap.J

Collapse of a Molecular Cloud Core to Stellar Densities: The First Three-Dimensional Calculations

We present results from the first three-dimensional calculations ever to follow the collapse of a molecular cloud core (~ 10^{-18} g cm^{-3}) to stellar densities (> 0.01 g cm^{-3}). The calculations resolve structures over 7 orders of magnitude in spatial extent (~ 5000 AU - 0.1 R_\odot), and over 17 orders of magnitude in density contrast. With these calculations, we consider whether fragmentation to form a close binary stellar system can occur during the second collapse phase. We find that, if the quasistatic core that forms before the second collapse phase is dynamically unstable to the growth of non-axisymmetric perturbations, the angular momentum extracted from the central regions of the core, via gravitational torques, is sufficient to prevent fragmentation and the formation of a close binary during the subsequent second collapse.Comment: ApJ Letters, in press (will appear in Nov 20 issue; available from the ApJ Rapid Release web page). 7 pages, incl. 5 figures. Also available at http://www.mpia-hd.mpg.de/theory/bat