  Growth rates for gravitational instabilities in a thick disk of gas and stars
are determined for a turbulent gas that dissipates on the local crossing time.
The scale heights are derived from vertical equilibrium. The accuracy of the
usual thickness correction, 1/(1+kH), is better than 6% in the growth rate when
compared to exact integrations for the gravitational acceleration in the disk.
Gas dissipation extends the instability to small scales, removing the minimum
Jeans length. This makes infinitesimally thin disks unstable for all Toomre-Q
values, and reasonably thick disks stable at high Q primarily because of
thickness effects. The conventional gas+star threshold, Qtot increases from ~1
without dissipation to 2 or 3 when dissipation has a rate equal to the crossing
rate over a perturbation scale. Observations of Qtot~2-3 and the presence of
supersonic turbulence suggest that disks are unstable over a wide range of
scales. Such instabilities drive spiral structure if there is shear and clumpy
structure if shear is weak; they may dominate the generation of turbulence.
Feedback regulation of Qtot is complex because the stellar component does not
cool; the range of spiral strengths from multiple arm to flocculent galaxies
suggests that feedback is weak. Gravitational instabilities may have a
connection to star formation even when the star formation rate scales directly
with the molecular mass because the instabilities return dispersed gas to
molecular clouds and complete the cycle of cloud formation and destruction. The
mass flow to dense clouds by instabilities can be 10 times larger than the star
formation rate.
