Molecular shocks in the interstellar medium

Shocks in the interstellar medium occur as a result of a variety of phenomena, e.g. protostellar outflows, supernovae and cloud-cloud collisions. In these dense, molecular environments the ionisation fraction of the plasma is low and the magnetic fields threading the clouds can be significant. This results in the shocks from the bipolar outflows of young stellar objects being C-type, meaning there is a smoothing effect on the discontinuities in the fluid parameters through the shock. These shocks are important for the generation of molecules such as SiO which are otherwise heavily depleted from the gas phase as they are condensed into dust grains in these regions. Observations of SiO rotational lines in star-forming regions make SiO a reliable tracer for the shocks which propagate due to the outflows from young stellar objects. The presence of gas-phase SiO suggests that the dust grains undergo destructive processes. The destruction of dust grains in C-type shocks can occur due to both gas-grain sputtering and grain-grain collisions.

The aim of this thesis is to extend the treatment of dust grains in the model used by Van Loo et al. (2013) and Ashmore (2011) for simulations of oblique C-type shocks. The ability of numerical models such as these to accurately evolve dust grain-size distributions is important, as changes to the distribution have implications for the shock structure and dynamics which, in turn, impact the chemistry of the region.

A novel approach for evolving grain size-distributions is presented, which, when tested against piecewise-constant and -linear approaches which appear in the literature, is shown to be both accurate and computationally viable. This new method adopts a power-law discretisation and uses both the grain mass and number densities in each size bin to determine the power law parameters. In sputtering tests the relative error in the total grain mass remains below 0.01 per cent for greater than or equal to 8 bins, while other methods only achieve this for 50 bins or more. Likewise, shattering tests show that the method produces small relative errors in the total grain numbers while conserving mass. Not only does the power-law method conserve the global distribution properties, it also preserves the inter-bin characteristics so that the shape of the distribution is recovered to a high degree.

This new method has been implemented into the original time-dependent, multifluid MHD code and is used to evolve an initial MRN grain-size distribution in C-type shocks. Results are compared with those for multiple single-sized grain fluids and it is shown that 2 bins are sufficient to accurately model the shock structure and dynamics when destructive processes are neglected, in contrast to 16 single-sized grain fluids. When sputtering is applied, 8 bins are required to accurately describe the fraction of Si removed from the grains, and to reliably produce the shape of the downstream distribution function. This is due to the size dependency of the sputter rate, which is best captured when enough bins are used to correctly model the region in which the grains transition from moving with the charged particles to moving with the neutrals.

Grain-grain collisions have the potential to both alter the grain-size distribution, due to shattering, and contribute to the abundance of gas phase SiO, due to vaporisation. Expressions for the source terms for the number and mass densities of grains are formulated in a more accurate way than has been seen before in the literature. In particular, the fragments and remnants which result from grain-grain collisions are distributed into the appropriate size bins without the use of average values. The implementation of this routine is tested for a gas density of 10^{5} cm^{-3}, where it is shown that the fraction of Si removed from the grains by a combination of sputtering and grain-grain collisions is accurate for 8 bins. However, the grain-grain relative velocities are not sufficient for vaporisation to occur at this density. Simulations for higher density models (10^{6} cm^{-3}) prove to have a much greater impact on the downstream grain-size distribution, and vaporisation dominates over sputtering for the production of gas-phase SiO. Shattering increases the total number density of grains in the distribution by a factor of 3, due to the abundance of small fragments which are created. This causes the shocks to have a width approximately 30 per cent narrower than those which neglect grain-grain processing.

The development of the original multifluid MHD model through this thesis allows physical dust grain processes occurring in C-type shocks to be simulated in a more accurate way than has been seen previously in the literature. A new approach for modelling grain-size distributions, which works particularly well for power-law distributions, allows the evolution of grain sizes to be followed in a way that is both accurate and computationally viable. An improved routine for calculating changes to the numbers and mass of grains due to grain-grain collisions means that the grain-size distribution can be evolved using just a few necessary assumptions. Grain-grain collisions may be pertinent in explaining the enhanced abundances of SiO observed in shocked regions of molecular clouds, and our simulations have shown that for a pre-shock density of 10^{6} cm^{-3}, the amount of Si released from grains is increased by grain-grain processing.