The rise with energy of the neutrino-nucleon cross section implies that at energies above few TeV the Earth is becoming opaque to cosmic neutrinos. The neutrinos interact with the nucleons through the weak charged current, resulting into absorption, and the weak neutral current, which provides a redistribution of the neutrino energy. We Mellin transform the neutrino transport equation and find its exact solution in the moment space. A simple analytical formula is provided, which describes accurately the neutrino spectrum, after the neutrinos have traversed the Earth. The effect of the weak neutral current is most prominent for an initial flat neutrino spectrum and we find that at low energies (around 1 TeV) the neutrino intensity is even enhanced.

Abstract. NGC 2146 is a peculiar spiral galaxy which is currently undergoing a major burst of star formation and is immersed in a extended H I structure that has morphological and kinematical resemblence to a strong tidal interaction. This paper reports aperture synthesis observations carried out in the 21 cm line with the Very Large Array (VLA ) of two fields positioned to optimally cover the H I streams to the north and south of the galaxy, along with a 300 ft total power spectral mapping program to recover the low surface brightness extended emission. The observations reveal elongated streams of neutral hydrogen towards both the north and the south of the optical galaxy extending out up to 6 Holmberg radii. The streams are not in the principle plane of rotation of the galaxy, but instead are suggestive of a tidal interaction between NGC 2146 and a LSB companion that was destroyed by the encounter and remains undetected at optical wavelengths. Part of the southern stream is turning back to fall into the main galaxy, where it will create a long-lived warp in the H I disk of NGC 2146. Analysis of the trajectory of the outlying gas suggests that the closest encounter took place about 0.8 billion years ago and that infall of debris will continue for a similar time span.

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