Diffusion and the AGASA Anisotropy

The AGASA anisotropy suggests that, at about 10¹⁸eV, cosmic rays are diffusing past us from the direction of the central galactic regions. That diffusion produces a flux component which has, in its simplest case, a cosinusoidal distribution with angle from the source direction. We expect this to be modified somewhat by any systematic galactic magnetic fields. Clay (2000) has shown that the modelled magnitude of the anticipated flux at these energies is dependent on detail in the magnetic field model and that, at energies approaching 10¹⁹eV, the diffusion model is likely to break down.

The excess in the galactic centre direction may have a point source component due to neutral particles. We therefore take the magnitude of the deficit in the anticentre direction as a better measure of the magnitude of the unidirectional anisotropy. At the peak of the deficit that is of the order of 5-10% of the total flux. In terms of a total outflowing flux averaged over all directions, this reduces to 1-2%. As we saw, the total flux includes a significant extragalactic component at these energies, which means that the amplitude of the anisotropy in terms of the galactic component alone is several times this value. Assuming that the resulting galactic anisotropy has a value of the order of 10%, we can attempt to estimate the scattering mean free path in the plane of the galaxy. If we consider simple diffusion, with scattering which typically occurs at a distance of about one mean free path, this implies a mean free path of the order of kiloparsecs to fit the anisotropy as observed at the Earth. This is comparable with results of our modelling (see below) for propagation in the turbulent galactic plane magnetic fields which have strengths of a few microgauss. There are sufficiently large dimensions in the galactic plane to allow such a process to occur. Thus, our interpretation of the AGASA deficit appears plausible.

The AGASA anisotropy (apart from the spiral arm excess) shows no other discernible features. There are, for instance, no other deficit directions. It may thus appear that the data support a simple unidirectional anisotropy model with simple diffusion as a first approximation. However, it is not clear how this might be so. At energies of about 10¹⁸eV, we expect our galaxy to become a poor cosmic ray container (Lee and Clay 1995, Clay and Smith 1996b). This is because of the flat and thin structure of the galaxy. Cosmic rays are expected to readily leak away above and below the galactic plane magnetic fields. This leakage would be expected to result in cosmic ray deficits from directions out of the galactic plane. Such deficits are not observed, even though the minimum in the anticentre direction is clearly seen. We therefore wish to examine the scattering properties of turbulent galactic magnetic fields at these energies. We will then be in a better position to understand the data and their implications for the galactic magnetic field.

© Copyright Astronomical Society of Australia 1997