Thermal instability through the outer half of quasi-static spherically
  symmetric molecular clumps and cores
  Thermal instability (TI) is a trigger mechanism, which can explain formation
of condensations through some regions of the interstellar clouds. Our goal here
is to investigate some conditions for occurrence of TI and formation of
pre-condensations through the outer half a quasi-static spherical molecular
clump or core. The inner half is nearly singular and ambiguous so out of scope
of this research. We consider a spherically symmetric molecular cloud in
quasi-static and thermally equilibrium state, and we use the linear
perturbation method to investigate occurrence of TI through its outer half. The
origin of perturbations are assumed to be as Inside-Rush-Perturbation (IRP)
with outward perturbed velocity at inner region of the cloud, and
Outside-Rush-Perturbation (ORP) with inward perturbed velocity originated at
the outer parts of the cloud. The local thermal balance at the outer half of
the molecular cloud leads to a local loosely constrained power-law relation
between the pressure and density as $p \propto \rho^{1+\chi}$, where
$-0.4\lesssim \chi\lesssim 0.05$ depends on the functional form of the net
cooling function. Physically, the value of $\chi$ depends on the power of
dependence of magnetic field to the density, $\eta$, and also on the value of
magnetic field gradient, $\zeta$. For strong magnetic field (smaller $\eta$)
and/or large field gradient (greater $\zeta$), the value of $\chi$ decreases,
and vice versa. The results show that increasing of the value of $\chi$ leads
to form a flatter density profiles at the thermally equilibrium outer half of
the molecular clump or core, and to occur more thermally unstable IRP and ORP
with smaller growth time-scales, and vice versa.
