A microscopic model of cosmic ray small-scale anisotropies from magnetic turbulence

• Applicant: Professor Dr. Philipp Mertsch
• Subject Area: Astrophysics and Astronomy
• Term: from 2019 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 426614101

The Earth is constantly bombarded by a flux of charged particles from outer space, called cosmic rays. The standard picture for cosmic ray transport predicts very small fluctuations in their arrival directions at the largest angular scales (180 degrees), of about 1 part in 1000 for energies between 1 TeV and 1 PeV. Yet, observations have shown anisotropies on much smaller angular scales, down to a few degrees. These small-scale anisotropies are not predicted in the standard picture of cosmic ray transport and various ideas have been put forward to explain them. Arguably the most promising suggestion is that the small-scale anisotropies are a reflection of the turbulent structure of the magnetic field in our Galactic neighbourhood. In fact, the standard picture of cosmic ray transport is only considering the ensemble-averaged phase-space density, thus ignoring the correlations between pairs of cosmic rays, which leads to an underestimation of the level of anisotropies on small angular scales. In the revised picture, the spatial correlations of the turbulent magnetic field within a few mean-free paths of the observer are determining the angular correlations seen by the observer.This idea has so far only been tested by numerically tracking particles through turbulent magnetic fields, or in effective theories for the macroscopic behaviour, e.g. using heuristic parametrizations for the angular dependence of scattering rates. A rigorous theory for the mapping of spatial correlations of the turbulent magnetic field to angular correlations of cosmic ray arrival directions is thus urgently needed. An exciting application of such a theory would be the investigation of the turbulence structure of the interstellar medium (e.g. Kolmogorov or Kraichnan, outer scale of turbulence, ratio of turbulent to regular field) through the observation of cosmic ray anisotropies.We propose developing a detailed microscopical model that predicts the angular power spectrum of the small-scale anisotropies for a given model of the turbulent magnetic field. The goal is to describe the time-evolution of the correlations between pairs of cosmic rays, to investigate the formation of a quasi-steady state of anisotropies in the presence of cosmic ray streaming and to compute its angular power spectrum. At the heart of our approach is the computation of the two-particle propagator which can be expanded into a perturbative series in the strength of effective interactions of two particles. From this, we will compute the angular power spectrum and compare to available observations to test various turbulence models.This approach to cosmic ray transport, in particular the computation of the correlations of phase-space densities, is completely new and to the best of our knowledge has never been attempted before. While the project is certainly ambitious, we have laid out our project plan in some detail and are therefore confident that the chances of success are very high.

• DFG Programme: Research Grants
• International Connection: Denmark
• Cooperation Partner: Professor Dr. Markus Tobias Ahlers