Cosmic ray transport and acceleration in an evolving shock landscape

Abstract: The sources of cosmic rays between the knee and the ankle are still debated. The Galactic wind and its termination shock have been proposed to contribute to this transition between Galactic and extragalactic origin, but another possibility is large-scale shock structures from local sources in the Milky Way. In this paper, we investigate CR transport in a time-dependent landscape of shocks in the Galactic halo. These shocks could result from local outbursts, e.g. starforming regions and superbubbles. CRs re-accelerated at such shocks can reach energies above the knee. Since the shocks are closer to the Galaxy than a termination shock and CRs escape downstream, they can propagate back more easily. With such outbursts happening frequently, shocks will interact. This interaction could adjust the CR spectrum, particularly for the particles that are able to be accelerated at two shocks simultaneously. The transport and acceleration of CRs at the shock is modeled by Stochastic Differential Equations (SDEs) within the public CR propagation framework CRPropa. We developed extensions for time-dependent wind profiles and for the first time connected the code to hydrodynamic simulations, which were run with the public Athena++ code. We find that, depending on the concrete realization of the diffusion tensor, a significant fraction of CRs can make it back to the Galaxy. These could contribute to the observed spectrum around and above the CR knee ($E \gtrsim 10\,\mathrm{PeV}$). In contrast to simplified models, a simple power-law does not describe the energy spectra well. Instead, for single shocks, we find a flat spectrum ($E^{-2}$) at low energies, which steepens gradually until it reaches an exponential decline. When shocks collide, the energy spectra transiently become harder than $E^{-2}$ at high energies.