Fragmentation of a dynamically condensing radiative layer
  In this paper, the stability of a dynamically condensing radiative gas layer
is investigated by linear analysis. Our own time-dependent, self-similar
solutions describing a dynamical condensing radiative gas layer are used as an
unperturbed state. We consider perturbations that are both perpendicular and
parallel to the direction of condensation. The transverse wave number of the
perturbation is defined by $k$. For $k=0$, it is found that the condensing gas
layer is unstable. However, the growth rate is too low to become nonlinear
during dynamical condensation. For $k\ne0$, in general, perturbation equations
for constant wave number cannot be reduced to an eigenvalue problem due to the
unsteady unperturbed state. Therefore, direct numerical integration of the
perturbation equations is performed. For comparison, an eigenvalue problem
neglecting the time evolution of the unperturbed state is also solved and both
results agree well. The gas layer is unstable for all wave numbers, and the
growth rate depends a little on wave number. The behaviour of the perturbation
is specified by $kL_\mathrm{cool}$ at the centre, where the cooling length,
$L_\mathrm{cool}$, represents the length that a sound wave can travel during
the cooling time. For $kL_\mathrm{cool}\gg1$, the perturbation grows
isobarically.
  For $kL_\mathrm{cool}\ll1$, the perturbation grows because each part has a
different collapse time without interaction. Since the growth rate is
sufficiently high, it is not long before the perturbations become nonlinear
during the dynamical condensation. Therefore, according to the linear analysis,
the cooling layer is expected to split into fragments with various scales.
