Spatial variation of the pickup-proton-injection rate into the ACR regime at the 3D-heliospheric termination shock

Abstract

Context. Anomalous cosmic rays are thought to be generated from pick-up ions that undergo Fermi-1 acceleration in the region close to the solar wind termination shock. This selective acceleration process depends on the efficiency at which upstream pick-up ions are injected into the first reflection mode, from where acceleration into higher energy anomalous cosmic rays starts. Aims. The injection efficiency is highly sensitive to the local inclination of the upstream magnetic field with respect to the shock normal. We determine the probability of pick-up ions being reflected at the shock depending on the magnetic inclination angle, which varies characteristically with latitude and longitude. This reflection is the relevant initial step in the acceleration of pickup ions to anomalous cosmic rays. Methods. We point out that the most dramatic change in the magnetic tilt angle occurs whenever two consecutive solar wind sector structures with different magnetic polarities, pass over the shock. We treat this effect by modeling the 3D- variation of the injection efficiency and start from calculations of the pick up ion reflection probability as function of the magnetic tilt angle. We first derive the magnetic tilt angle as function of latitude and longitude, representing the 3D-shape of the termination shock by a triaxial or prolate ellipsoid adaptable for conditions of different solar cycles, respectively. This allows us to semi-analytically express the 3D-variation of the injection efficiency and rate over a solar cycle. Results. We find a substantial variation in the injection efficiency by 5 orders of magnitude when passing from the upwind parts to the flanks of the termination shock or from low to high latitudes (except at the poles). Folding this with the normalized pickup ion density gives a normalized injection rate which increases from 0% to 30% from upwind to crosswind directions and analogously decreases from crosswind into downwind direction. The maximal value of the injection rate highly depends on the underlying sector structure of the heliospheric magnetic field. During solar minimum there is almost no injection in high latitudes, except at the pole itself, while the injection rate is everywhere fairly good during solar maximum. Conclusions. Our model indicates that the injection into the anomalous cosmic ray acceleration mainly takes place in crosswind directions e.g. in the flanks of the termination shock.