Maximum neutrino energy without (left column) and with (right column) secondary acceleration, as a function of the variability timescale t_var and the bolometric luminosity L_bol of a flaring source, with bulk Lorentz factor Γ = 1, 10, 100 (from top to bottom). Dashed and solid contours indicate the maximum energy of neutrinos produced respectively through charged pion and charged muon decay. Overlayed are examples of location of benchmark explosive transients in the t_var − L_bol parameter-space. The pale orange region indicates the domain where no source is expected to be found due to the excessive energy budget.