Cosmic ray physics in calculations of cosmological structure formation

Cosmic rays (CRs) play a decisive role within our own Galaxy. They provide partial pressure support against gravity, they trace past energetic events such as supernovae, and they reveal the underlying structure of the baryonic matter distribution through their interactions. To study the impact of CRs on galaxy and cosmic structure formation and evolution, we develop an approximative framework for treating dynamical and radiative effects of CRs in cosmological simulations. Our guiding principle is to try to find a balance between capturing as many physical properties of CR populations as possible while at the same time requiring as little extra computational resources as possible. We approximate the CR spectrum of each fluid element by a single power-law, with spatially and temporally varying normalisation, low-energy cut-off, and spectral index. Principles of conservation of particle number, energy, and pressure are then used to derive evolution equations for the basic variables describing the CR spectrum, both due to adiabatic and non-adiabatic processes. The processes considered include compression and rarefaction, CR injection via shocks in supernova remnants, injection in structure formation shock waves, in-situ re-acceleration of CRs, CR spatial diffusion, CR energy losses due to Coulomb interactions, ionisation losses, Bremsstrahlung losses, and, finally, hadronic interactions with the background gas, including the associated.-ray and radio emission due to subsequent pion decay. We show that the formalism reproduces CR energy densities, pressure, and cooling rates with an accuracy of similar to 10% in steady state conditions where CR injection balances cooling. It is therefore a promising formulation to allow simulations where CR physics is included. Finally, we briefly discuss how the formalism can be included in Lagrangian simulation methods such as the smoothed particle hydrodynamics technique. Our framework is therefore well suited to be included into numerical simulation schemes of galaxy and structure formation.