Required minimum cosmic-ray proton luminosity, L_CR, as a function of the emission radius R and the power-law index s_CR for ﹩{\varepsilon }_{p}^{{\rm{\min }}}=1﹩ GeV and ﹩{\varepsilon }_{p}^{{\rm{\max }}}=30﹩ TeV in the hadronic scenario. The blue contour corresponds to L_corona, which is the total coronal X-ray luminosity. The red and orange lines correspond to the upper limits from gamma-ray observations for ξ_B = 1 and ξ_B = 0.01, respectively.