4. DISCUSSION

Detections of VHE -ray emission associated with ongoing star formation in M 82 and NGC 253 add significant new insight on the enhanced energetic electron and proton contents in SBGs, and on their propagation in disks of spiral galaxies. The common star-driven nature of NT phenomena in the wide class of non-AGN SFGs implies that energetic particle densities and radiation fields are self-similarly scaled with SF activity, from quiescent systems to intense SBGs, in spite of the wide range of intrinsic physical conditions in these systems.

We have briefly outlined our treatment of the steady state spectro-spatial distributions of energetic electrons and protons in SFGs, exemplified in the case of the two nearby SBGs M 82 and NGC 253. This approach is based on a numerical solution of the diffusion-convection equation for particle distribution functions, following the evolution from the acceleration sites throughout the disk as the particles lose energy and propagate outward. Key observational normalization is based on measurements of radio synchrotron emission which, through an initial (theoretically assumed) N_p / N_e ratio provides also the normalization of the proton component. Assuming equipartition then allows to relate the local value of the mean magnetic field to the particle energy densities. The numerical solution of the diffusion-convection equation is based on an iterative procedure to determine the particle densities and mean field strength in the galactic center, and evolve these quantities by accounting for all relevant energy losses, and normalizing central values of these quantities by fitting to the measured radio spectrum from the central galactic (or SB) region. The quantitative viability of this approach is confirmed by the good agreement between the predicted high energy emission from M 82 and NGC 253 and measuremnts with Fermi, H.E.S.S., and VERITAS.

Significant detections of the NT emission from above two SBGs at lower (below 100 keV) X-ray energies, as would be expected by the currently operational NuSTAR telescope, will provide additional spectral coverage that will allow separating out the spectral electron and proton components. NuSTAR is the first X-ray telescope with capability to resolve this emission; if this is indeed achieved, important new insight will be gained on the evolution of the electron spectro-spatial distribution across the disks of these nearby SBGs.

The three methods we have discussed to estimate energetic particle energy densities are clearly not independent. The -ray method and the radio method are coupled through the p/e ratio at injection, through the secondary-to-primary electron ratio, and through the imposed condition of particle-field equipartition. The SN method is not independent of the -ray method either, because both depend on the proton residence time, although - unlike the -ray and radio methods - it does not depend on the particle radiative yields but on the statistics of core-collapse SN. Also, the three methods do not stand on equal footing: with the -ray, radio, and SN methods we, respectively, either measure, infer, and or estimate the value of U_p. A substantial agreement among estimates based on the three methods is found for most of the galaxies in Table 1. The only exceptions are the SMC and NGC 1068. As for the former, the proton confinement volume could be small, so that most particles diffuse out to intergalactic space (Abdo et al. 2010d). If so, the -ray method yields the (lower) actual proton energy density, whereas the radio and SN methods estimate the (higher) produced amount. NGC 1068 hosts a prototypical Seyfert-2 nucleus (e.g., Wilson & Ulvestad 1982) surrounded by a spherical circumnuclear SB shell with external radius of 1.5 kpc and thickness 0.3 kpc, and mass 3.4 × 10⁹ M (Spinoglio et al. 2005); its implied energy density is U_p ≈ 65 eV cm^-3 from both the radio and SN methods. [We note that Lenain et al. (2010) suggested that the HE emissions of the above two SB and Sey II galaxies NGC 4945 and NGC 1068 are powered by, respectively, star formation and AGN activity.]

A debated aspect of proton energy loss and propagation times is whether the former is shorter than the latter; if so, the system is said to be a `proton calorimeter' (e.g., Lacki et al. 2010, 2011). No galaxy in the above sample is found to be in the calorimetric limit; the two SBGs M 82 and NGC 253 would seem to be only marginally close to this limit. The presence of fast, SB-driven galactic winds advecting energetic particles out of the disk seems to be a ubiquitous feature in SBGs, limiting the degree at which they can be calorimetric. More generally, it is known that energetic particles do diffuse out of non-AGN SFGs, as evidenced also by significant radio emission (Ferrari et al. 2008), and possibly also high energy NT X-ray emission (Rephaeli et al. 2008) from large central regions of galaxy clusters. The estimated intracluster particle (and indeed also the magnetic) energy densities are sufficiently high, suggesting origin in the cluster galaxies.

Based on the reasonable hypothesis that local SB galaxies resemble young galaxies which were particularly abundant in the early universe, their contributions to the X--ray backgrounds are of obvious interest (e.g., Rephaeli et al. 1991). Calculations of the superposed emission from SBGs (Pavlidou & Fields 2002, Persic & Rephaeli 2003, Thompson et al. 2007, Fields et al. 2010, Lacki et al. 2011, Steckers & Venters 2011) indicate that this emission constitutes at least a tenth of these backgrounds.