Simulating COsmic Rays

During my time as a Blue Waters Graduate Fellow, I worked on adding cosmic rays to the astrophysical simulation code Enzo.  Cosmic ray pressure affects galactic evolution (suppressing star formation, driving galactic outflows, and altering the ionization state of the circumgalactic medium), so it is important for state-of-the-art simulation codes to implement realistic cosmic ray physics.

Below is a summary of the different approximations to cosmic ray transport. For a more detailed description of the implementation, check out this work on the arXiv (coming soon).

 
 

Advection: Treating Cosmic Rays like a fluid

The general approach of grid-based simulation codes is to simulate the motion of a fluid through the boundaries of different cells. These cells may employ adaptive mesh refinement (AMR) techniques to resolve areas of interest, but they are nevertheless treated as though they're fixed in space and the simulated fluid moves through them. A common approach is to model cosmic rays a second fluid that advects (moves with the bulk motion) with the thermal gas. This cosmic ray fluid also exerts pressure on the thermal gas.  There are two main approximations for cosmic ray transport relative to thermal gas: diffusion and streaming, both of which are described below. There is no current consensus on which approach yields the most realistic results. 

  Figure 1:  We test the advection properties of our cosmic ray fluid with the modified Brio-Wu shock-tube 

Figure 1: We test the advection properties of our cosmic ray fluid with the modified Brio-Wu shock-tube 


Diffusion

One way to approximate cosmic ray transport along magnetic field lines is to assume that the scattering of cosmic rays results in a net motion down the gradient of cosmic ray energy and along magnetic field lines. Because magnetic fields are computationally expensive, many studies have used isotropic diffusion as an approximation. In this case, cosmic rays propagate by moving down their energy gradient, with a velocity that is modulated by a constant diffusion coefficient. See the figure below for a visual representation of anisotropic diffusion around magnetic field lines. 

  Figure 2:  An initial wedge of cosmic ray energy density diffuses around circular magnetic field lines over time. 

Figure 2: An initial wedge of cosmic ray energy density diffuses around circular magnetic field lines over time. 


  Figure 3:  Although no analytic solution exists for cosmic ray streaming, we compare the evolution of an initial Gaussian overdensity of cosmic ray energy under diffusion and streaming. 

Figure 3: Although no analytic solution exists for cosmic ray streaming, we compare the evolution of an initial Gaussian overdensity of cosmic ray energy under diffusion and streaming. 

Streaming 

In the streaming approximation, cosmic rays move down their energy gradient, around magnetic field lines, with a velocity that is proportional to the strength of the magnetic field (the Alfven velocity). This approximation also has a heating term through which cosmic rays transfer their momentum to the thermal gas.