  The propagation of ion-acoustic waves (IAWs) in a collisionless unmagnetized
self-gravitating degenerate quantum plasma system (SG-DQPS) has been studied
theoretically for the first time. A nonlinear Schr\"{o}dinger equation is
derived by using the reductive perturbation method to study the nonlinear
dynamics of the IAWs in the SG-DQPS. It is found that for $k_c > k$ ($k_c < k$)
(where $k_c$ is critical value of the propagation constant $k$ which determines
the stable and unstable region of IAWs) the IAWs are modulationally unstable
(stable), and that $k_c$ depends only on the ratio of the electron number
density to light ion number density. It is also observed that the
self-gravitating bright envelope solitons are modulationally stable. The
results obtained from our present investigation are useful for understanding
the nonlinear propagation of the IAWs in astrophysical compact objects like
white dwarfs and neutron stars.
