  Acceleration can change the ionization of X-ray irradiated gas to the point
that the gas becomes thermally unstable. Cloud formation, the expected outcome
of thermal instability (TI), will be suppressed in a dynamic flow, however, due
to the stretching of fluid elements that accompanies acceleration. It is
therefore unlikely that cloud formation occurs during the launching phase of a
supersonic outflow. In this paper, we show that the most favorable conditions
for dynamical TI in highly supersonic outflows are found at radii beyond the
acceleration zone, where the growth rate of entropy modes is set by the linear
theory rate for a static plasma. This finding implies that even mildly
relativistic outflows can become clumpy, and we explicitly demonstrate this
using hydrodynamical simulations of ultrafast outflows. We describe how the
continuity and heat equations can be used to appreciate another impediment
(beside mode disruption due to the stretching) to making an outflow clumpy:
background flow conditions may not allow the plasma to enter a TI zone in the
first place. The continuity equation reveals that both impediments are in fact
tightly coupled, yet one is easy to overcome. Namely, time variability in the
radiation field is found to be a robust means of placing gas in a TI zone. We
further show how the ratio of the dynamical and thermal timescales enters
linear theory; the heat equation reveals how this ratio depends on the two
processes that tend to remove gas from a TI zone -- adiabatic cooling and heat
advection.
