The high rate of star formation and supernova explosions of starburst galaxies make them interesting sources of high energy radiation. Depending upon the level of turbulence present in their interstellar medium, the bulk of cosmic rays produced inside starburst galaxies may lose most of their energy before escaping, thereby making these sources behave as calorimeters, at least up to some maximum energy. Contrary to previous studies, here we investigate in detail the conditions under which cosmic ray confinement may be effective for electrons and nuclei and we study the implications of cosmic ray confinement in terms of multifrequency emission from starburst nuclei and production of high energy neutrinos. The general predictions are then specialized to three cases of active starbursts, namely M82, NGC253 and Arp220. Both primary and secondary electrons, as well as electron-positron pairs produced by gamma ray absorption inside starburst galaxies are taken into account. Electrons and positrons produced as secondary products of hadronic interactions are found to be responsible for most of the emission of leptonic origin. In particular, synchrotron emission of very high energy secondary electrons produces an extended emission of hard X-rays that represent a very interesting signature of hadronic process in starburst galaxies, potentially accessible to current and future observations in the X-ray band. A careful understanding of both the production and absorption of gamma rays in starburst galaxies is instrumental to the assessment of the role of these astrophysical sources as sources of high energy astrophysical neutrinos.

In nuclei of starburst galaxies, the combination of an enhanced rate of supernova explosions and a high gas density suggests that cosmic rays can be efficiently produced, and that most of them lose their energy before escaping these regions, resulting in a large flux of secondary products, including neutrinos. Although the flux inferred from an individual starburst region is expected to be well below the sensitivity of current neutrino telescopes, such sources may provide a substantial contribution to the diffuse neutrino flux measured by IceCube.Here we compute the gamma-ray and neutrino flux due to starburst galaxies based on a physical model of cosmic ray transport in a starburst nucleus, and accounting for the redshift evolution of the number density of starburst sources as inferred from recent measurements of the star formation rate. The model accounts for gammaray absorption both inside the sources and in the intergalactic medium. The latter process is responsible for electromagnetic cascades, which also contribute to the diffuse gamma-ray background at lower energies. The conditions for acceleration of cosmic ray protons up to energies exceeding ∼ 10 PeV in starburst regions, necessary for the production of PeV neutrinos, are investigated in a critical way. We show that starburst nuclei can account for the diffuse neutrino flux above ∼ 200 TeV, thereby producing 40% of the extragalactic diffuse gamma-ray background. Below ∼ 200 TeV, the flux from starburst appears to be somewhat lower than the observed one, where both the Galactic contribution and the flux of atmospheric neutrinos may account for the difference.

The origin of cosmic rays in our Galaxy remains a subject of active debate. While supernova remnant shocks are often invoked as the sites of acceleration, it is now widely accepted that the difficulties of such sources in reaching PeV energies are daunting and it seems likely that only a subclass of rare remnants can satisfy the necessary conditions. Moreover the spectra of cosmic rays escaping the remnants have a complex shape that is not obviously the same as the spectra observed at the Earth. Here we investigate the process of particle acceleration at the termination shock that develops in the bubble excavated by star clusters’ winds in the interstellar medium. While the main limitation to the maximum energy in supernova remnants comes from the need for effective wave excitation upstream so as to confine particles in the near-shock region and speed up the acceleration process, at the termination shock of star clusters the confinement of particles upstream in guaranteed by the geometry of the problem. We develop a theory of diffusive shock acceleration at such shock and we find that the maximum energy may reach the PeV region for powerful clusters in the high end of the luminosity tail for these sources. A crucial role in this problem is played by the dissipation of energy in the wind to magnetic perturbations. Under reasonable conditions the spectrum of the accelerated particles has a power law shape with a slope 4÷4.3, in agreement with what is required based upon standard models of cosmic ray transport in the Galaxy.

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