Towards First-principle Characterization of Cosmic-ray Transport Coefficients from Multi-scale Kinetic Simulations

Abstract

A major uncertainty in understanding the transport and feedback of cosmic-rays (CRs) within and beyond our Galaxy lies in the unknown CR scattering rates, which are primarily determined by waveparticle interaction at microscopic gyro-resonant scales. The source of the waves for the bulk CR population is believed to be self-driven by the CR streaming instability (CRSI), resulting from the streaming of CRs downward a CR pressure gradient. While a balance between driving by the CRSI and wave damping is expected to determine wave amplitudes and hence the CR scattering rates, the problem involves significant scale separation with substantial ambiguities based on quasi-linear theory (QLT). Here we propose a novel "streaming box" framework to study the CRSI with an imposed CR pressure gradient, enabling first-principle measurement of the CR scattering rates as a function of environmental parameters. By employing the magnetohydrodynamic-particle-in-cell (MHD-PIC) method with ion-neutral damping, we conduct a series of simulations with different resolutions and CR pressure gradients and precisely measure the resulting CR scattering rates in steady state. The measured rates show scalings consistent with QLT, but with a normalization smaller by a factor of several than typical estimates based on single-fluid treatment of CRs. A momentum-by-momentum treatment provides better estimates when integrated over momentum, but is also subject substantial deviations especially at small momentum. Our framework thus opens up the path towards providing comprehensive subgrid physics for macroscopic studies of CR transport and feedback in broad astrophysical contexts.

Deciphering the physical basis of the intermediate-scale instability

“…Second, there are resonant instabilities, which occur when the CR current is low but the CR mean drift is faster compared with the local ion Alfvén speed. Within galactic and stellar environments, CR transport (with energies below 100 GeV) is believed to be primarily regulated by two dominant resonant instabilities: the gyro-resonant instability (Kulsrud & Pearce 1969;Lebiga, Santos-Lima & Yan 2018;Bai et al 2019;Holcomb & Spitkovsky 2019;Bai 2021;Bambic, Bai & Ostriker 2021;Plotnikov, Ostriker & Bai 2021) and the recently discussed intermediate-scale instability (Shalaby, Thomas & Pfrommer 2021;Lemmerz et al 2023). Provided CRs propagate with a finite pitch angle relative to the large-scale magnetic field, they induce an instability in electromagnetic waves (propagating along the background magnetic field) on scales intermediate between the gyroradii of ions and electrons.…”