4.1.3. Cosmic-ray Method

A third method to determine the galactic magnetic field strength is through the gamma-ray emission (2.5 × 10^-5 Å) by collisions of cosmic-ray protons and cosmic-ray electrons with the interstellar matter, as well as collisions of cosmic-ray electrons with optical interstellar photons (inverse-Compton), or else through the x-ray emission (12 Å) by collisions of cosmic-ray electrons with infrared interstellar photons (inverse-Compton). The derivation of cosmic-ray particle densities K in starforming sites of size P is made first, and the diffusion assumption that these cosmic-ray particles can expand from size P to cover the whole galactic disk of size L is then made to explain the radio synchrotron emission I from relativistic electrons over the whole galactic size L, finally enabling the final derivation of the total galactic magnetic field strength, i.e.,: B_tot ~ I_v^s K^-s L^-s , where s = 2 / [ + 1] and is the cosmic ray electron energy index ( 2.5). Here we call B_cr the results obtained by this cosmic-ray particle method. Cosmic-ray electrons from a galactic nucleus (i.e., P) can find it difficult to diffuse quickly over a whole galactic disk (i.e., L). More details on the derivation of B_cr can be found in Chi & Wolfendale (1993), etc. The basic diffusion assumption of the cosmic ray method, i.e., that cosmic rays, gas, and magnetic fields are "well mixed" in the galaxy, has been questioned in the cases of the galaxies M82 and of the Large Magellanic Cloud (e.g., Table 2 in Vallée 1995a). In the Milky Way, most cosmic rays seem to come from SNR in the galactic disk (e.g., see Völk et al. 1984; Völk et al. 1989), and the basic diffusion assumption seems to work. Also, the wide use of a negligible cosmic-ray e/p flux ratio, in the cosmic-ray method, has been challenged recently (Pohl, 1993).