Gradients and anisotropies of high energy cosmic rays in the outer heliosphere

Two cosmic rays which pass through the same point going in opposite directions will, in the absence of scattering and inhomogeneities in the magnetic field, trace helices about adjacent flux tubes, whose centerlines are separated by one gyrodiameter. A directional anisotropy at the point suggests a difference in the number of cosmic rays loading the two flux tubes; that is, a density gradient over the baseline of a gyrodiameter. Previous studies at lower energies have shown that the cosmic ray density gradients vary in time and space. It is suggested that the radial gradient associated with solar cycle modulation is supported largely by narrow barriers which encircle the sun and propagate outward with the solar wind. If so, the anisotropy is a desirable way to detect spatial gradients, because it can be associated with the local solar wind and magnetic field conditions. Anisotropic measurements made by Cerenkov detectors on Pioneers 10 and 11 were studied. It was found that local anisotropy varies greatly, but that the long term average is consistent with the global radial gradient measured between two spacecraft over a baseline of many AU