Superflare Energy Budgets and the Starspot Areas They Require on G and M Dwarfs

This paper examines the starspot areas that superflare energies require under a magnetic energy budget for Kepler superflare stars and active M dwarfs, using published input values and transparent formulae throughout. The headline computed results are: spot_fraction_1e34_G_1kG = 0.00304; spot_fraction_1e35_G_1kG = 0.01411; spot_fraction_1e36_G_3kG = 0.01513. Each quantity bearing on the starspot areas that superflare energies require under a magnetic energy budget is derived in the deposited calculation script from the stated inputs, so the full chain from published value to conclusion for Kepler superflare stars and active M dwarfs can be audited and rescaled. The discussion of the starspot areas that superflare energies require under a magnetic energy budget 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 Kepler superflare stars and active M dwarfs confirm earlier estimates, the confirmation is meaningful because no adjustable parameter was available to force agreement on the starspot areas that superflare energies require under a magnetic energy budget; where they differ, the size and likely origin of the difference are stated directly.