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

Birationality of \'etale morphisms via surgery

We use a counting argument and surgery theory to show that if $D$ is a sufficiently general algebraic hypersurface in $\Bbb C^n$, then any local diffeomorphism $F:X \to \Bbb C^n$ of simply connected manifolds which is a $d$-sheeted cover away from $D$ has degree $d=1$ or $d=\infty$ (however all degrees $d > 1$ are possible if $F$ fails to be a local diffeomorphism at even a single point). In particular, any \'etale morphism $F:X \to \Bbb C^n$ of algebraic varieties which covers away from such a hypersurface $D$ must be birational.Comment: 17 pages. Replaced to add further references and make language more consistent with the literatur

Some notes about the density of states for a negative pressure matter

The main goal of this paper is deriving Density of states $g(\epsilon)$ (degeneracy function) per volume for an equation of state (EOS) $p=-\rho$ (we called it dark energy(DE)).We have concluded that thermodynamic quantities such as pressure and energy density are simple functions of temperature, fugacity, curvature and mass of Bosons. Our work has been expressed the origin of some claims about the negativity of the entropy for the scalar fields models of DE.Comment: 12 pages,Major revision,Typos fixed,References added,it has now been accepted for publication in International Journal of Modern Physics E. It was accepted on May 31, 201