Cosmic rays in clouds:
The cosmic ray ionization rate is one of the most important and most uncertain inputs into models of the dynamics and chemistry of molecular clouds and prestellar cores. For that reason, I am working on understanding the physics governing the propagation of cosmic rays into molecular clouds. Below I describe two projects related to the interaction of cosmic rays with the magnetic fields that permeate these regions.
Magnetic mirroring and focusing of cosmic rays:
In the simplest picture of cosmic ray penetration into molecular clouds, developed in this 2009 paper by Marco Padovani and collaborators, cosmic rays move freely along field lines passing through molecular clouds, but lose energy via interaction with the matter in the cloud. As the cosmic rays penetrate deeper into the cloud, the ionization rate decreases, as progressively higher energy particles are attenuated, leaving only the rarer high-energy cosmic rays to generate ionization in the center of the cloud. When field lines enter a dense region with an increased magnetic field such as the core of a molecular cloud, they come together. This focusses the cosmic rays, thus enhancing their density. On the other hand, cosmic rays with high initial pitch angles are excluded from the region of higher magnetic field. We showed that these two effects generally cancel to within a factor of two (and that they cancel exactly if energy losses are ignored). One exception to this cancellation is in the case of what we term "magnetic pockets". These are shown in the diagram below, which depicts a sketch of the magnetic field strength as a function of position along a particular field line. In the regions denoted "pockets", cosmic rays with low initial pitch angles are blocked by the mountains of high field strength on either side, but the magnetic field is not high enough to provide the counterbalancing focusing factor. We are now exploring the prevalence and depth of these pockets in numerical simulations.
Diffusive vs. free-streaming cosmic ray propagation
Another question we consider is the propagation mode for cosmic rays. If, as above, they are assumed to stream along the magnetic field lines, then the column density passed through by the particle (and therefore the degree of attenuation suffered) is proportional to the column density of the cloud integrated along magnetic field lines. MHD waves, excited by turbulence in the medium can change the cosmic rays' pitch angles. If the pitch angles change so much that the memory of the initial direction of travel is lost, then the motion of the cosmic rays is best described by spatial diffusion in one dimension along the field line. In this case the column traversed by the particle scales roughly with the square of the column density integrated along the magnetic field line (only roughly, since the diffusion coefficient is energy-dependent). Whether the turbulence is able to cascade to small enough scales to interact resonantly with the cosmic rays which dominate the ionization in these clouds is an open question.
We calculated the ionization rate as a function of column density in a molecular cloud, assuming both a free-streaming cosmic ray propagation model, and a diffusive model, and a hybrid model in which cosmic rays propagate diffusively in the outer part of the cloud where the ionization fraction is higher (and therefore one would expect more energy in magnetic field fluctuations at the scale of the cosmic ray gyroradius. The figure on the left shows the ionization rate as a function of column density in these three models.
The data points are taken from Neufeld & Wolfire (2017). Black points are those for which the molecular hydrogen column density was measured directly with UV spectroscopy, and grey points is where it was estimated from indirect measures. The initial spectrum is a model spectrum taken in Padovani et al., (2018), which was constructed to match the data assuming a free-streaming model. Neufeld & Wolfire analysis hints that the power law exponent of the curve of ionization vs. column depth is much steeper than that which is found with this free-streaming model, and diffusive propagation is one way such a steep slope could come about.