• turbulence
• ionization
• interstellar medium
• cosmic ray

This thesis presents an approach to modeling how low energy cosmic rays (CR) propagate by scattering and energy losses within diffuse interstellar clouds. The inter- stellar medium (ISM), containing a mixture of dust and gas that is not bound into stars, consists of an atomic and molecular state for the gas. It permeates the space between stars in all galaxies and is the birthplace of stars and the relic matter released during their lifetimes. The CRs have a variety of sources distributed throughout the Galaxy.
Their spatial diffusion is governed by a highly turbulent magnetic field coupled to the interstellar gas that forces a random walk of magnetic field lines and induces diusive particle propagation. In this study, I work in the strong turbulent regime, with no constant mean ambient and statistically isotropic fluctuations.
The diusion of charged particles depends on particle's energy. Given the Larmor radius RL of the charged particle and the outer lengthscale of the turbulence, lc, we can identify three diffusion regimes: the high energy limit R_L=l_c > 1, and intermediate region where R_L=l_c = 1, and the low energy range R_L=l_c < 1. In the high-energy limit, particles experience only small kicks from their initial trajectory due to small angle scattering on magnetic field irregularities. In the low energy limit, particles gyrate around the local field produced by large-scale fluctuations, while occasionally experiencing perturbations (mainly by scattering on magnetic perturbation at scales comparable to the gyroradius).
In this work I model the propagation of low energy CRs (less than a few hundreds MeV), given their fundamental role in the evolution of the ISM. For instance, they are able to significantly heat the medium, and drive its chemistry. I treat only the protons, which do not suffer synchrotron losses and are responsible for the bulk contribution to the ionization in optically thick media.
To our knowledge, the possible effects of reenergization of particles due to Fermi-like processes has not been explored in the context of cloud interiors. I examine whether particle reenergization can change the CR ionization rate, due to its strong dependence on the particle energy.
Magnetic turbulence in these environments is not well constrained, though turbulent motions can be described by a power-law energy distribution. Since it is beyond the scope of this thesis to develop a self-consistent theory of MHD interstellar turbulence, I base my model on an empirical description of the turbulent field observed in low density (translucent and diffuse) molecular clouds without internal star formation or driving.
Rare large fluctuations of the turbulent velocity and density distribution dominate the energy boosts. We follow the trajectory of each particle rather than the diffusion of the distribution function. To avoid a formal treatment of the turbulence that is not needed in this context, we take the novel approach of using an observationally determined set of probability distribution functions (PDFs) for the turbulence instead of imposing a particular power spectrum or statistical independence of the fluctuations.
The turbulence is driven by a large scale shearing ambient medium surrounding and incorporating the cloud. Since there are no internal drivers, the flow satisfies, at least schematically, the requirements for a classical cascade of the sort first described by Kolmogorov (1941). We use the derived velocity structure functions and probability distribution functions derived from spectral line (12C16O and 13C16O) observations taken from the translucent molecular clouds MBM 3 and MBM 40 to characterize the random walk of the magnetic field lines, assuming MHD turbulence.
This is the essential ingredient in simulating the CR propagation inside the clouds.
CR in the energy range relevant to our problem have a gyroradius of the order of 105 km in the typical magnetic field present in the diffuse ISM, a few microgauss. Turbulent motions do not fall below a lengthscale of about 0.1 pc, therefore protons cannot be scattered by magnetic fluctuations, and will simply stream across the local magnetic field lines of force.
I designed the requisite algorithms and Monte Carlo code for the proton random walk with energy losses from ionization of background atoms and molecules. In their travel, protons are continuously loosing energy to the medium via ionization losses, but also exchange energy with the turbulent field thorough Fermi-like processes. We find out that the reenegization does not significantly affect the propagation in an homogeneous medium. However reenergization is enhanced by some other effect, e.g. the presence of inhomogeneities in the medium. In denser regions, more typical of dark clouds or even cold cores (those in which star formation has not begun despite their densities being suffcient for gravitational instability) some particles will be trapped inside those regions, undergoing a large number of scattering events before escaping and I find indication of reenergization and modified spectral energy distributions. This effect appears to be too small to give an appreciable difference in the ionization rate of the diffuse medium.
Finally we discuss possible further implementation of the code, and what we expect to see from a more extended treatment of the problem.