VHE Neutrinos and Gamma-Rays as Probes for Anisotropy of Arrival Directions of EeV Cosmic Rays

We estimate the fluxes of very high energy (VHE) gamma-rays and neutrinos from the Galactic Center which are by-products of the hadronic interactions between primary protons which are accelerated up to $\sim 10^{19}$eV and ambient matter. We find that these signals depend strongly on the spectrum index of the primary protons. This means that detection of these signals from the Galactic Center will constrain the spectrum of the primary particles, which, in turn, should constrain the acceleration mechanism at the Galactic Center. We show that GeV-TeV gamma-rays will be detected by the ground-based Cherenkov telescopes such as CANGAROOIII and the next-generation satellites such as GLAST. Thus the acceleration region of the CRs below $\sim 10^{19}$eV will be determined accurately by gamma-ray telescopes, which should help our understanding on the particle acceleration. We estimate the event rate of VHE neutrinos for the planned 1 km$^{2}$ detectors such as IceCube, ANTARES and NESTOR. The event rate also depends on the spectrum index of the primary protons. In the optimistic case, the event rate amounts to $\sim 10^4$ events per year and the signals from the Galactic Center dominate the atmospheric neutrino background.