How Does Flare EUV Emission Scale with Magnetic Flux in Flare Ribbons?

It was noted over a decade ago that spatially integrated, steady (non-flare) intensities of active regions (ARs) in both soft X-ray (SXR) and EUV wavelength ranges scale as power laws with the total unsigned photospheric magnetic flux in each AR. A key finding was that the details of AR magnetic structure (field strengths and their spatial gradients, including measured electric currents) appear not to affect spatially integrated emission. More recently, GOES SXR peak intensities in flares were found by Kazachenko et al. (2017) to scale as a power of the ribbon magnetic flux (i.e., the total unsigned photospheric magnetic flux swept across by emission in flare ribbons). Given the power-law scaling of steady EUV emission with magnetic flux, it is plausible that flaring EUV emission, like flaring SXR emission, also scales as a power law with ribbon magnetic flux. If both GOES and EUV flare emission scale, separately, as power laws with ribbon flux, then log-log scatter plots of flare EUV vs. GOES intensities would follow approximately straight-line trends — a finding recently reported by Reep et al. (2022). Here, for a sample of a few hundred flares, all C-class or greater, we characterize the relationships (or lack thereof) between SDO/EVE flare intensities and flare ribbon fluxes. Departures from power-law scalings in EVE lines have the potential to reveal important aspects of the heating mechanisms that drive flare emission, and merit investigation. Differences in power-law exponents between the steady and flaring cases would suggest that the underlying mechanisms of the two processes differ. One consequence would be that nanoflares, if they are responsible for steady coronal emission, must differ in key ways from processes involved in flare emission.