On Symplectic Coverings of the Projective Plane

We prove that a resolution of singularities of any finite covering of the projective plane branched along a Hurwitz curve $\bar H$ and, maybe, along a line "at infinity" can be embedded as a symplectic submanifold into some projective algebraic manifold equipped with an integer K\"{a}hler symplectic form (assuming that if $\bar H$ has negative nodes, then the covering is non-singular over them). For cyclic coverings we can realize this embeddings into a rational algebraic 3--fold. Properties of the Alexander polynomial of $\bar{H}$ are investigated and applied to the calculation of the first Betti number $b_1(\bar X_n)$ of a resolution $\bar X_n$ of singularities of $n$-sheeted cyclic coverings of $\mathbb C\mathbb P^2$ branched along $\bar H$ and, maybe, along a line "at infinity". We prove that $b_1(\bar X_n)$ is even if $\bar H$ is an irreducible Hurwitz curve but, in contrast to the algebraic case, that it can take any non-negative value in the case when $\bar H$ consists of several irreducible components.Comment: 42 page

Cosmic Rays from Gamma Ray Bursts in the Galaxy

The rate of terrestrial irradiation events by galactic gamma-ray bursts (GRBs) is estimated using recent standard-energy results. We assume that GRBs accelerate high-energy cosmic rays, and present results of three-dimensional simulations of cosmic rays moving in the Galactic magnetic field and diffusing through pitch-angle scattering. An on-axis GRB extinction event begins with a powerful prompt gamma-ray and neutron pulse, followed by a longer-lived phase from cosmic-ray protons and neutron-decay protons that diffuse towards Earth. Our results force a reinterpretation of reported ~ 10^{18} eV cosmic-ray anisotropies and offer a rigorous test of the model where high-energy cosmic rays originate from GRBs, which will soon be tested with the Auger Observatory.Comment: 9 pages, 4 figures, ApJ Letters, in press. Clarified limit of test-particle approximation, prediction that Auger will not confirm SUGAR source. (Data may not appear onscreen at low magnification.) Simulations at http://heseweb.nrl.navy.mil/gamma/~dermer/invest/sim/index.ht

High energy cosmic-ray interactions with particles from the Sun

Cosmic-ray protons with energies above $10^{16}$ eV passing near the Sun may interact with photons emitted by the Sun and be excited to a $\Delta^+$ resonance. When the $\Delta^+$ decays, it produces pions which further decay to muons and photons which may be detected with terrestrial detectors. A flux of muons, photon pairs (from $\pi^0$ decay), or individual high-energy photons coming from near the Sun would be a rather striking signature, and the flux of these particles is a fairly direct measure of the flux of cosmic-ray nucleons, independent of the cosmic-ray composition. In a solid angle within $15^\circ$ around the Sun the flux of photon pairs is about \SI{1.3e-3}{} particles/(km$^2\cdot$yr), while the flux of muons is about \SI{0.33e-3}{} particles/(km$^2\cdot$yr). This is beyond the reach of current detectors like the Telescope Array, Auger, KASCADE-Grande or IceCube. However, the muon flux might be detectable by next-generation air shower arrays or neutrino detectors such as ARIANNA or ARA. We discuss the experimental prospects in some detail. Other cosmic-ray interactions occuring close to the Sun are also briefly discussed.Comment: 8 pages, 11 figure