  The fine structure of solar prominences and filaments appears as thin and
long threads in high-resolution images. In H-alpha observations of filaments,
some threads can be observed for only 5 - 20 minutes before they seem to fade
and eventually disappear, suggesting that these threads may have very short
lifetimes. The presence of an instability might be the cause of this quick
disappearance. Here, we study the thermal instability of prominence threads as
an explanation of their sudden disappearance from H-alpha observations. We
model a prominence thread as a magnetic tube with prominence conditions
embedded in a coronal environment. We assume a variation of the physical
properties in the transverse direction, so that the temperature and density
continuously change from internal to external values in an inhomogeneous
transitional layer representing the particular prominence-corona transition
region (PCTR) of the thread. We use the nonadiabatic and resistive
magnetohydrodynamic equations, which include terms due to thermal conduction
parallel and perpendicular to the magnetic field, radiative losses, heating,
and magnetic diffusion. We combine both analytical and numerical methods to
study linear perturbations from the equilibrium state, focusing on unstable
thermal solutions. We find that thermal modes are unstable in the PCTR for
temperatures higher than 80,000 K, approximately. These modes are related to
temperature disturbances that can lead to changes in the equilibrium due to
rapid plasma heating or cooling. For typical prominence parameters, the
instability time scale is of the order of a few minutes and is independent of
the form of the temperature profile within the PCTR of the thread. This result
indicates that thermal instability may play an important role for the short
lifetimes of threads in the observations.
