Longitudinal variation of the pickup-proton-injection efficiency and rate at the heliospheric termination shock

Abstract

Context. Pickup ions are considered to be the seed population of the anomalous cosmic rays. The acceleration of the pickup ions at the solar wind termination shock depends on the efficiency with which they are injected into the first reflection mode, from where acceleration into high energy anomalous cosmic rays begins. In this letter, we study the longitudinal variation of this efficiency.

Aims. We consider the specific MHD conditions at the longitudinal position of the termination shock, which are highly sensitive to the local inclination angle between the magnetic field and the shock normal. We determine the probability for pickup-ions to become reflected which depends on how the inclination angle varies with longitude. This is the first and relevant step in the acceleration of pickup ions to anomalous cosmic rays. Methods. The most dramatic change in the magnetic tilt angle occurs in the current sheet between two consecutive solar wind sector structures of different polarity, when they pass over the shock. We consider this effect by modeling the longitudinal variation in the injection efficiency. Starting from calculations of the pickup-ion reflectance probability as a function of the magnetic tilt angle with respect to the normal, we find an analytic expression for the injection efficiency: to do this we need the magnetic tilt angle as a function of longitude, which we obtain from an analytic representation of the termination shock shape. This enables us to determine the longitudinal dependence of the injection efficiency. Results. We find that a substantial variation in the injection efficiency of a factor of 3 occurs when passing from the upwind part to the flanks of the termination shock. Folding this with the longitudinal dependence of the pickup ion density gives an analytic expression the injection rate which varieis by a factor of 2 between up- and ecliptical crosswind direction and a factor of 5 between cross- and downwind direction. Conclusions. Our model indicates that injection into the anomalous cosmic ray acceleration predominantly occurs in the ecliptical crosswind direction e.g. in the flanks of the termination shock