Images of very high energy cosmic ray sources in the Galaxy: I. A source towards the galactic centre

Recent analyses of the anisotropy of cosmic rays at $10^{18}$ eV (the AGASA and SUGAR data) show significant excesses from regions close to the Galactic Centre and Cygnus. Our aim is to check whether such anisotropies can be caused by single sources of charged particles. We investigate propagation of protons in two models of the Galactic regular magnetic field (with the irregular component included) assuming that the particles are injected by a short lived discrete source lying in the direction of the Galactic Centre. We show that apart from a prompt image of the source, the regular magnetic field may cause delayed images at quite large angular distances from the actual source direction. The image is strongly dependent on the time elapsed after ejection of particles and it is also very sensitive to their energy. For the most favourable conditions for particle acceleration by a young pulsar the predicted fluxes are two to four order of magnitudes higher than that observed. The particular numbers depend strongly on the Galactic magnetic field model adopted but it looks that a single pulsar in the Galactic Centre could be responsible for the observed excess.