Molecular clouds: magnetohydrodynamics, gravitational collapse and turbulence

Molecular clouds are the sites of star formation. They are made by networks of filaments. They accumulate mass by accretion from the ambient medium until they become gravitationally unstable and fragment into cores, that eventually collapse into stars and stellar clusters. Fundamental open questions are what physical processes supports them against gravity and why star formation is an inefficient process. The candidates for supporting the clouds are large-scale magnetic fields and turbulence. It is then crucial to understand their role in the equilibrium and in the dynamical evolution of molecular clouds as well as how the gravitational collapse can affect them. During my Ph.D. I studied the stability and contraction of molecular clouds both in the hydrodynamical and magnetohydrodynamical case, in the quasi-static and dynamical phase of evolution. Under the hypothesis that the observed filaments and cores can be represented by a sequence of static models, I reproduced the observed radial density profiles of filamentary molecular clouds observed by the Herschel satellite with the help of a hydrostatic analytical model with a polytropic equation of state, underlying the need to non-thermal support due to magnetic fields or turbulence. I then introduced an helical magnetic field in the model, showing that the ratio between the poloidal and the toroidal components components (pitch angle) determines whether the filament is compressed (supported) by the toroidal (poloidal) field and confirming that magnetic field is an important ingredient in filamentary structures. However, molecular clouds must contract and fragment in order to form stars. After the stability analysis I tackled the problem of gravitational collapse in presence of turbulence. I studied the growth of small-scale density perturbation during the hydrodynamical collapse of a molecular core in two different frameworks: Hubble-like contraction and free-fall. I used the advanced ECHO code to perform 2D numerical simulations to compare with analytical results. I also analytically estimated the transition time to non-linear regime in analogy with the Burgers equation, pointing out that the formation of shocks and the subsequent dissipation prevents the onset of gravitationally unstable perturbations, thus other kind of mechanism are needed to explain the process of fragmentation in cores. In the last part of my Ph.D I took into account also the contribute of magnetic field. I studied the temporal evolution of a magnetised turbulent fluid element contracting along the mean magnetic field direction, in order to determine the condition for amplification and quenching of the turbulent fluctuations. I performed fully 3D MHD simulations with the ECHO code, studying the evolution of integrated quantities, like the density contrast. I showed that turbulence is sustained if the contraction time-scale and the dissipation time-scale are comparable.