# Understanding breaks in solar flares x-ray spectra: Evaluation of a co-spatial return-current model

## TL;DR

This study evaluates a co-spatial return-current model to explain spectral breaks in solar flare hard x-ray spectra, using RHESSI observations to test the model's fit, plasma resistivity, and stability conditions.

## Contribution

It demonstrates that the return-current collisional thick-target model effectively explains strong spectral breaks and assesses plasma resistivity and stability in solar flare conditions.

## Key findings

- The RCCTTM fits spectra with strong breaks well.
- Resistivities are 2-3 orders higher than Spitzer values.
- Return current stability depends on electron and ion temperatures.

## Abstract

Hard x-ray spectral breaks are explained in terms of a 1D model with a co-spatial return current. We study 19 flares observed by RHESSI (Ramaty High Energy Solar Spectroscopic Imager) with strong spectral breaks at energies around a few deka-keV, that cannot be explained by isotropic albedo or non-uniform ionization alone. We identify these breaks at the HXR peak time, but we obtain 8 s-cadence spectra of the entire impulsive phase. Electrons with an initially power-law distribution and a sharp low-energy cutoff lose energy through return-current losses until they reach the thick target, where they lose their remaining energy through collisions. Our main results are: (1) The return-current collisional thick-target model (RCCTTM) provides acceptable fits for spectra with strong breaks. (2) Limits on the plasma resistivity are derived from the fitted potential drop and deduced electron-beam flux density, assuming the return-current is a drift current in the ambient plasma. These resistivities are typically 2-3 orders of magnitude higher than the Spitzer resistivity at the fitted temperature, and provide a test for the adequacy of classical resistivity and the stability of the return current. (3) Using the upper limit of the low-energy cutoff, the return current is always stable to the generation of ion acoustic and electrostatic ion cyclotron instabilities when the electron temperature is lower than 9 times the ion temperature. (4) In most cases the return current is most likely primarily carried by runaway electrons from the tail of the thermal distribution rather than the bulk drifting thermal electrons. For these cases, anomalous resistivity is not required.