Cosmic Ray Interstellar Propagation Tool using Itô Calculus (criptic): software for simultaneous calculation of cosmic ray transport and observational signatures

Abstract

We present, the Cosmic Ray Interstellar Propagation Tool using Itô Calculus, a new open-source software package to simulate the propagation of cosmic rays through the interstellar medium and to calculate the resulting observable non-thermal emission. C solves the Fokker-Planck equation describing transport of cosmic rays on scales larger than that on which their pitch angles become approximately isotropic, and couples this to a rich and accurate treatment of the microphysical processes by which cosmic rays in the energy range ∼MeV to ∼PeV lose energy and produce emission. C is deliberately agnostic as to both the cosmic ray transport model and the state of the background plasma through which cosmic rays travel. It can solve problems where cosmic rays stream, diffuse, or perform arbitrary combinations of both, and the coefficients describing these transport processes can be arbitrary functions of the background plasma state, the properties of the cosmic rays themselves, and local integrals of the cosmic ray field itself (e.g., the local cosmic ray pressure or pressure gradient). The code is parallelised using a hybrid OpenMP-MPI paradigm, allowing rapid calculations exploiting multiple cores and nodes on modern supercomputers. Here we describe the numerical methods used in the code, our treatment of the microphysical processes, and the set of code tests and validations we have performed.

The cosmic ray ionisation and $γ$-ray budgets of star-forming galaxies

“…We show both the full numerical results obtained using and the CSDA approximation; for the latter, we use the cross sections computed exactly as in the full numerical results. We refer readers Krumholz et al (2022) for full details, but to summarise here: we use the semi-analytic model of Rudd et al (1992) to compute the total and differential proton ionisation cross sections, while our nuclear inelastic scattering cross section and corresponding differential photon production cross section come from Kafexhiu et al (2014), who provide analytic fits to the results of a large suite of particle Monte Carlo simulation results.…”

“…In the simulations, we use a packet injection rate of 2×10 −7 s −1 , a secondary production factor 𝑓 sec = 0.2, and a step size control parameter 𝑐 step = 0.05 -see Krumholz et al (2022) for precise definitions of these parameters. We follow CRs until their energies drop below 1 keV; below this energy, loss processes that are not included in such as charge exchange cannot be neglected.…”

“…Our goal in this section is to determine how efficiently cosmic rays that are injected into the interstellar gas in a galaxy can be converted into ionisations and observable 𝛾-ray emission. We will ultimately derive our final results for these quantities from numerical Monte Carlo calculations of CR evolution using the CR propagation code (Krumholz et al 2022). However, before beginning the numerical calculations, it is of benefit to develop a simple analytic model using the continuous slowing-down approximation (Fano 1953; Section 2.1), whereby we approximate loss of energy by CRs as a continuous process.…”

“…The primary conclusion to be drawn from the figure is 7 The only other difference is that for electron energies above 10 5 GeV in the 𝑓 sync = 𝑓 IC = 10 −7.5 case we reduce the secondary sampling factor 𝑓 sec from 0.2 to 0.1. This change does not impact the physics being simulated, and is made solely for computational convenience, to avoid having to follow a very large number of secondary sample packets in a case where the catastrophic loss mechanism of bremsstrahlung is dominant compared to the mostly continuous inverse Compton and synchrotron mechanisms; see Krumholz et al (2022) for details in the meaning of 𝑓 sec in simulations. that changing 𝑓 sync and 𝑓 IC by half of dex on either side of our fiducial value induces completely negligible changes in the ionisation efficiency for either protons or electrons.…”