TeV Cosmic-Ray Anisotropy from the Magnetic Field at the Heliospheric Boundary

Abstract

We performed numerical calculations to test the suggestion by Desiati and Lazarian that the anisotropies of TeV cosmic rays may arise from their interactions with the heliosphere. For this purpose, we used a magnetic field model of the heliosphere and performed direct numerical calculations of particle trajectories. Unlike earlier papers testing the idea, we did not employ time-reversible techniques that are based on Liouville's theorem. We showed numerically that for scattering by the heliosphere, the conditions of Liouville's theorem are not satisfied, and the adiabatic approximation and time-reversibility of the particle trajectories are not valid. Our results indicate sensitivity to the magnetic structure of the heliospheric magnetic field, and we expect that this will be useful for probing this structure in future research.

Test particle simulations of cosmic rays

“…It has been questioned whether backtracking can be used reliably to investigate the formation of (small-scale) anisotropies (López-Barquero et al 2017) and whether Liouville's theorem is valid in the presence of pitch-angle scattering. We therefore provide a few comments on its validity.…”

“…It has been claimed (López-Barquero et al 2017) that conservation of phase space density is equivalent to the conservation of the magnetic moment M = mv 2 ⊥ /(2B) of individual particles which can be checked by simulating test particles in random (electro)magnetic fields. We have elsewhere already argued against this view (Ahlers and Mertsch 2017): While conservation of phase space density requires only differentiability of forces, conservation of the magnetic moment requires the magnetic field to change only adiabatically, that is B/|∇B| r g and B/Ḃ −1 where r g and are the gyroradius and gyrofrequency.…”

Observation of Cosmic Ray Anisotropy with Nine Years of IceCube Data

“…The anisotropy is small (of order of 10 −3 in relative intensity) and it changes with energy as if a transition between two distinct causes occurs around 100 TeV. Observations also show that the anisotropy has a complex angular structure, spanning from the large-scale dipole and quadrupole (thought to be associated with scattering off magnetic turbulence leading to pitch angle diffusion [34]) down to smaller scales with relative amplitude smaller than 10 −4 (thought to be linked to non-diffusive processes within a scattering mean path [35,36]). While new, large, ground-based experiments under construction (LHAASO [37]) and under design (SWGO [38,39], IceCube-Gen2 [40]) will provide a leap in our anisotropy observations, existing experiments are still improving the quality of their data and analyses.…”

Experimental Biases on the Heliospheric Contribution to the Observed TeV Cosmic Ray Anisotropy

“…[30] for more details on the numerical calculations). The heliospheric magnetic field implemented in the numerical calculation is that used in López-Barquero et al [31]. It makes use of ideal Magneto-Hydrodynamic (MHD) treatment of ions and of a kinetic multi-fluid description of neutral interstellar atoms penetrating into the heliosphere [32].…”