Testing the Coronal Temperature and X-Ray Surface Flux Relation Across Five Activity Levels

This paper examines the power-law relation between mean coronal temperature and X-ray surface flux for representative dwarfs from inactive G stars to saturated M dwarfs, using published input values and transparent formulae throughout. The headline computed results are: powerlaw_index_b = 0.2388; max_abs_residual_frac = 0.042; T_pred_at_Fx1e6_MK = 6.01. Each quantity bearing on the power-law relation between mean coronal temperature and X-ray surface flux is derived in the deposited calculation script from the stated inputs, so the full chain from published value to conclusion for representative dwarfs from inactive G stars to saturated M dwarfs can be audited and rescaled. The discussion of the power-law relation between mean coronal temperature and X-ray surface flux 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 representative dwarfs from inactive G stars to saturated M dwarfs confirm earlier estimates, the confirmation is meaningful because no adjustable parameter was available to force agreement on the power-law relation between mean coronal temperature and X-ray surface flux; where they differ, the size and likely origin of the difference are stated directly.