Disentangling the low-energy cutoff E0 from radio-inferred electron densities

Develop detailed modeling of gyrosynchrotron radio emission in AU Mic flares to determine the low-energy cutoff energy E0 of the nonthermal electron distribution and disentangle its effects on the inferred electron number density n_e, which cannot be achieved using the Dulk (1985) empirical equations that assume E0 = 10 keV.

Background

Estimating electron kinetic energies from optically thin radio flares requires assumptions about the electron energy distribution, including the low-energy cutoff E0. The commonly used Dulk (1985) formulae assume E0 = 10 keV, which couples inferred n_e to this assumption.

Because n_e and E0 are interdependent in these empirical relations, the authors state they cannot disentangle E0 without more detailed modeling. Resolving E0 is critical for accurate energy partitioning and consistency with modern radiative-hydrodynamic simulations of M-dwarf flares.

References

However, as $n_e$ is estimated from the empirical equations in \citet{Dulk1985} {which assume $E_0 = 10$ keV}, we are unable to disentangle the value without more detailed modeling\footnote{\citet{Fleishman2022} examined best-fit parameter correlations in EOVSA radio data of a solar flare. They note that while higher values of $E_0$ may indicate lower values of nonthermal $n_e$, their study found that high $n_e$ values in solar flares do not readily depend on $E_0$. This is because $\delta_r$ increases with $E_0$, diminishing its correlation with $n_e$.}.

— A 7-Day Multi-Wavelength Flare Campaign on AU Mic. II: Electron Densities and Kinetic Energies from High-Frequency Radio Flares (2503.14624 - Tristan et al., 18 Mar 2025) in Section 4.2 (Electron Kinetic Energies In Light of Multi-wavelength Observations)