Equilibrium Initialization and Stability of Three-Dimensional Gas Disks
  We present a new systematic way of setting up galactic gas disks based on the
assumption of detailed hydrodynamic equilibrium. To do this, we need to specify
the density distribution and the velocity field which supports the disk. We
first show that the required circular velocity has no dependence on the height
above or below the midplane so long as the gas pressure is a function of
density only. The assumption of disks being very thin enables us to decouple
the vertical structure from the radial direction. Based on that, the equation
of hydrostatic equilibrium together with the reduced Poisson equation leads to
two sets of second-order non-linear differential equation, which are easily
integrated to set-up a stable disk. We call one approach `density method' and
the other one `potential method'. Gas disks in detailed balance are especially
suitable for investigating the onset of the gravitational instability. We
revisit the question of global, axisymmetric instability using fully
three-dimensional disk simulations. The impact of disk thickness on the disk
instability and the formation of spontaneously induced spirals is studied
systematically with or without the presence of the stellar potential. In our
models, the numerical results show that the threshold value for disk
instability is shifted from unity to 0.69 for self-gravitating thick disks and
to 0.75 for combined stellar and gas thick disks. The simulations also show
that self-induced spirals occur in the correct regions and with the right
numbers as predicted by the analytic theory.
