Required minimum cosmic-ray helium luminosity, L_CR, as a function of R and s_CR in the beta decay scenario for ﹩B={B}_{{\rm{\max }}}﹩ as defined in Equation (13). We find that L_CR exceeds L_bol ∼ L_Edd in the entire parameter space. Gamma-ray constraints from the Fermi-LAT data cannot be shown because the entire parameter space is excluded by the Fermi-LAT data (see Figure 5).