  Threads are the building blocks of solar prominences and very often show
longitudinal oscillatory motions that are strongly attenuated with time. The
damping mechanism responsible for the reported oscillations is not fully
understood yet. To understand the oscillations and damping of prominence
threads it is mandatory to investigate first the nature of the equilibrium
solutions that arise under static conditions and under the presence of
radiative losses, thermal conduction and background heating. This provides the
basis to calculate the eigenmodes of the thread models. The nonlinear ordinary
differential equations for hydrostatic and thermal equilibrium under the
presence of gravity are solved using standard numerical techniques and simple
analytical expressions are derived under certain approximations. The solutions
to the equations represent a prominence thread, i.e., a dense and cold plasma
region of a certain length that connects with the corona through a prominence
corona transition region (PCTR). The solutions can also match with a
chromospheric-like layer if a spatially dependent heating function localised
around the footpoints is considered. We have obtained static solutions
representing prominence threads and have investigated in detail the dependence
of these solutions on the different parameters of the model. Among other
results, we have shown that multiple condensations along a magnetic field line
are possible, and that the effect of partial ionisation in the model can
significantly modify the thermal balance in the thread and therefore their
length. This last parameter is also shown to be comparable to that reported in
the observations when the radiative losses are reduced for typical thread
temperatures.
