  A detailed analysis of the dynamics of unstable modes present in the
linearized Navier-Stokes-Fourier system in the presence of a gravitational
field is carried out. The transition between the non-dissipative and
dissipative regimes is explored from the mathematical point of view by
considering the same equation of state in both cases, a procedure which sheds
light on the discontinuity present in the critical parameter. It is also shown
that two distinct behaviours for the propagation of unstable modes can be
identified below the critical value for a gravitational instability to occur,
depending on a parameter $r$ that quantifies the relevance of dissipation
relative to gravitational effects.
