Flare Frequency-Energy Power Laws and the Total Radiative Budget of an Active M Dwarf

This paper examines the integrated radiative budget implied by a flare frequency-energy power law for a very active M dwarf normalised to ten flares per year above 10^33 ergs, using published input values and transparent formulae throughout. The headline computed results are: N_gt_1e34_per_yr = 1.585; N_gt_1e35_per_yr = 0.2512; total_flare_power_erg_s-1 = 4.728e+27. Each quantity bearing on the integrated radiative budget implied by a flare frequency-energy power law is derived in the deposited calculation script from the stated inputs, so the full chain from published value to conclusion for a very active M dwarf normalised to ten flares per year above 10^33 ergs can be audited and rescaled. The discussion of the integrated radiative budget implied by a flare frequency-energy power law compares the outcomes with independent published estimates, identifies the input to which each result is most sensitive, and confines the conclusions to what the arithmetic supports. Where the computed values for a very active M dwarf normalised to ten flares per year above 10^33 ergs confirm earlier estimates, the confirmation is meaningful because no adjustable parameter was available to force agreement on the integrated radiative budget implied by a flare frequency-energy power law; where they differ, the size and likely origin of the difference are stated directly.