Non-isobaric Thermal Instability
  Multiphase media have very complex structure and evolution. Accurate
numerical simulations are necessary to make advances in our understanding of
this rich physics. Because simulations can capture both the linear and
nonlinear evolution of perturbations with a relatively wide range of sizes, it
is important to thoroughly understand the stability of condensation and
acoustic modes between the two extreme wavelength limits of isobaric and
isochoric instability as identified by Field (1965). Partially motivated by a
recent suggestion that large non-isobaric clouds can `shatter' into tiny
cloudlets, we revisit the linear theory to survey all possible regimes of
thermal instability. We uncover seven regimes in total, one of which allows
three unstable condensation modes. Using the code Athena++, we determine the
numerical requirements to properly evolve small amplitude perturbations of the
entropy mode into the nonlinear regime. Our 1D numerical simulations
demonstrate that for a typical AGN cooling function, the nonlinear evolution of
a single eigenmode in an isobarically unstable plasma involves increasingly
larger amplitude oscillations in cloud size, temperature and density as the
wavelength increases. Such oscillations are the hallmark behavior of
non-isobaric multiphase gas dynamics and may be observable as correlations
between changes in brightness and the associated periodic redshifts and
blueshifts in systems that can be spatially resolved. Intriguingly, we discuss
regimes and derive characteristic cloud sizes for which the saturation process
giving rise to these oscillations can be so energetic that the cloud may indeed
break apart. However, we dub this process `splattering' instead of
`shattering', as it is a different fragmentation mechanism triggered when the
cloud suddenly `lands' on the stable cold branch of the equilibrium curve.
