The structure and stability of molecular cloud cores in external radiation fields

We have considered the thermal equilibrium in pre-protostellar cores in the approximation where the dust temperature is independent of interactions with the gas and where the gas is heated both by collisions with dust grains and ionization by cosmic rays. We have then used these results to study the stability of cores in the limit where thermal pressure dominates over magnetic field and turbulence. We find that for cores with characteristics similar to those observed, the gas and dust temperatures are coupled in the core interior. As a consequence, the gas temperature like the dust temperature decreases towards the center of these objects. The density structure computed taking into account such deviations from isothermality are not greatly different from that expected for an isothermal Bonnor-Ebert sphere. It is impossible in the framework of these models to have a stable equilibrium core with mass above about 5 solar masses and column density compatible with observed values. We conclude from this that observed high mass cores are either supported by magnetic field or turbulence or are already in a state of collapse. Lower mass cores on the other hand have stable states and we conclude that the much studied object B68 may be in a state of stable equilibrium if the internal gas temperature is computed in self-consistent fashion. Finally we note that in molecular clouds such as Ophiuchus and Orion with high radiation fields and pressures, gas and dust temperatures are expected to be well coupled and hence one expects temperatures to be relatively high as compared to low pressure clouds like Taurus.Comment: 11 pages, 6 figures. Astronomy & Astrophysics, in pres

Nonlinear Boundary Value Problems via Minimization on Orlicz-Sobolev Spaces

We develop arguments on convexity and minimization of energy functionals on Orlicz-Sobolev spaces to investigate existence of solution to the equation \displaystyle -\mbox{div} (\phi(|\nabla u|) \nabla u) = f(x,u) + h \mbox{in} \Omega under Dirichlet boundary conditions, where $\Omega \subset {\bf R}^{N}$ is a bounded smooth domain, $\phi : (0,\infty)\longrightarrow (0,\infty)$ is a suitable continuous function and $f: \Omega \times {\bf R} \to {\bf R}$ satisfies the Carath\'eodory conditions, while $h$ is a measure.Comment: 14 page

Scalar perturbations and the possible self-destruction of the phantom menace

Some analysis of the supernovae type Ia observational data seems to indicate that the Universe today is dominated by a phantom field, for which all energy conditions are violated. Such phantom field may imply a singularity in a future finite time, called big rip. Studying the evolution of scalar perturbations for such a field, we show that if the pressure is negative enough, the Universe can become highly inhomogeneous and this phantom menace may be avoided.Comment: Latex file, 5 page