Singular isothermal disks. II. Nonaxisymmetric bifurcations and equilibria

We review the difficulties of the classical fission and fragmentation hypot heses for the formation of binary and multiple stars. A crucial missing ing redient in previous theoretical studies is the inclusion of dynamically imp ortant levels of magnetic fields. As a minimal model for a candidate precur sor to the formation of binary and multiple stars, we therefore formulate a nd solve the problem of the equilibria of isopedically magnetized, singular isothermal disks, without the assumption of axial symmetry. Considerable a nalytical progress can be made if we restrict our attention to models that are scale-free, i.e., that have surface densities that vary inversely with distance <(<omega>)over bar> from the rotation axis of the system. In agree ment with earlier analysis by Syer & Tremaine, we find that lopsided (M = 1 ) configurations exist at any dimensionless rotation rate, including zero. Multiple-lobed (M = 2, 3, 4,...) configurations bifurcate from an underlyin g axisymmetric sequence at progressively higher dimensionless rates of rota tion, but such nonaxisymmetric sequences always terminate in shock waves be fore they have a chance to fission into M = 2, 3, 4,... separate bodies. On the basis of our experience in this paper and the preceding Paper I, we ad vance the hypothesis that binary and multiple star formation from smooth (i .e., not highly turbulent) starting states that are supercritical but in un stable mechanical balance requires the rapid (i.e., dynamical) loss of magn etic flux at some stage of the ensuing gravitational collapse.