Solar flares are known to be prolific electron accelerators, yet identifying the mechanism(s) for such efficient electron acceleration in magnetic reconnection events at the Sun (and similar astrophysical settings) presents a major challenge in Astrophysics (e.g. Holman et al 2011). Accelerated Electrons with energies above $\sim 20$ keV are revealed by hard X-ray (HXR) bremsstrahlung emission, while accelerated electrons with even higher energies usually manifest themselves through radio gyrosynchrotron emission. Of considerable interest is the nature of the process that accelerates particles to high energies are the ratios of the number densities (cm$^{-3}$) of nonthermal and thermal electrons ($n_{nth}$ and $n_{th}$, respectively) to the total number density of background electrons in acceleration region.
Recently Kontar et al, 2023 have combined RHESSI HXR observations of a well-observed solar flare with contemporaneous EUV observations from the Solar Dynamics Observatory Atmospheric Imaging Assembly in order to better constrain both the total number of accelerated electrons and the all-important ratio $n_{nth}/n_p$ in 2017 September 10 solar flare (Figure 1) that revealed clear evidence for a reconnection current sheet located above the flare loop-top. The results indicates that the ratio of nonthermal electrons to ambient electrons in ROI-1 at a time near the peak of the X-ray emission is $n_{nth}/\, n_p \simeq 0.01 – 0.02$.
Figure 1: Left: Clean RHESSI X-ray images using Detectors \#3 and \#6 for the 20 second interval centered on 15:58~UT, with three regions of interest identified. The color-scale image represents thermal (10-12 keV) emission. The blue dashed lines are the contours at 20, 70, and 90% of the peak 50-100 keV non-thermal emission. The region of interest labeled ROI-0 is defined by the solid blue contour at the 50% level of the 50-100 keV image. Regions of interest ROI-1 and ROI-2 are depicted by solid black and magenta boundary lines, respectively. Right: Thermal plasma density map, also showing ROI-1 and ROI-2. This was constructed by applying a regularized differential emission measure algorithm (Hannah & Kontar, 2012) to SDO/AIA data for the event in question, assuming the same line-of-sight distance of $8^{\prime \prime}$ used by Fleishman et al, 2022.
Conclusions
HXR observations provide important constraints on the fraction of electron acceleration above 20 keV. RHESSI observations suggest that this fraction of accelerated electrons remains less than a few present. Such numbers are consistent with the classical flare accelerating electrons ($>20$ keV) at the rate of $\dot{N}=10^{36}$ electrons per second, so the number density of electrons leaving acceleration box through the area of $A=10^{18}$ cm$^2$ with speed $v(>20\mbox{keV})\simeq 10^{10}$ cm/sec.
$$
N_{nth}(>20 \mbox{keV})=\frac{\dot{N}}{A v(>20\mbox{keV})}\simeq 10^8\;\;\mbox{cm}^{-3}
$$
It is interesting to note that the microwave spectrum analysis by Fleishman et al. (2022) using 2” pixels, which are smaller than EOVSA beam resolution of $(45-5)”$ for the $(2-18)$ GHz range, gives approximately hundred times larger fraction of accelerated electrons in the same region of flare.
Based on a recent paper by Kontar, E. P., Emslie, A. G., Motorina, G. G., and Dennis, B.R., The Efficiency of Electron Acceleration during the Impulsive Phase of a Solar Flare, The Astrophysical Journal Letters, 947 L13, (2023), DOI:10.3847/2041-8213/acc9b7
References:
Holman, G. D., Aschwanden, M. J., Aurass, H., et al. 2011, SSRv, 159
Fleishman, G. D., Nita, G. M., Chen, B., Yu, S., & Gary, D. E., 2022, Nature, 606, 674
Hannah, I. G., & Kontar, E. P. 2012, A&A, 539, A14
