Electron Densities in Solar Flare Loops, Chromospheric Evaporation Upflows, and Acceleration Sites

We compare electron densities measured at three different locations in solar flares: (1) in soft X-ray (SXR) loops, determined from SXR emission measures and loop diameters from Yohkoh Soft X-Ray Telescope maps [n^{{\rm SXR}}_{e} <LATEX>$^{{&rm; SXR}}_e$</LATEX> =(0.2-2.5)x10 <IMG SRC="img2.gif" ALIGN="TOP" ALT="^{11}"/> 11 cm-3]; (2) in chromospheric evaporation upflows, inferred from plasma frequency cutoffs of decimetric radio bursts detected with the 0.1-3 GHz spectrometer Phoenix of ETH Zurich [n^{{\rm upflow}}_{e} <LATEX>$^{{&rm; upflow}}_e$</LATEX> =(0.3-11)x10 <IMG SRC="img4.gif" ALIGN="TOP" ALT="^{10}"/> 10 cm-3]; and (3) in acceleration sites, inferred from the plasma frequency at the separatrix between upward-accelerated (type III bursts) and downward-accelerated (reverse-drift bursts) electron beams [n^{{\rm acc}}_{e} <LATEX>$^{{&rm; acc}}_e$</LATEX> =(0.6-10)x10 <IMG SRC="img6.gif" ALIGN="TOP" ALT="^{9}"/> 9 cm-3]. The comparison of these density measurements, obtained from 44 flare episodes (during 14 different flares), demonstrates the compatibility of flare plasma density diagnostics with SXR and radio methods. The density in the upflowing plasma is found to be somewhat lower than in the filled loops, having ratios in a range n^{{\rm upflow}}_{e} <LATEX>$^{{&rm; upflow}}_e$</LATEX> /n^{{\rm SXR}}_{e} <LATEX>$^{{&rm; SXR}}_e$</LATEX> =0.02-1.3, and a factor of 3.6 higher behind the upflow front. The acceleration sites are found to have a much lower density than the SXR-bright flare loops, i.e., n^{{\rm acc}}_{e} <LATEX>$^{{&rm; acc}}_e$</LATEX> /n^{{\rm SXR}}_{e} <LATEX>$^{{&rm; SXR}}_e$</LATEX> = 0.005-0.13, and thus must be physically displaced from the SXR-bright flare loops. The scaling law between electron time-of-flight distances l' and loop half-lengths s, i.e., l'/s = 1.4 +- 0.3, recently established by Aschwanden et al. suggests that the centroid of the acceleration region is located above the SXR-bright flare loop, as envisioned in cusp geometries (e.g., in magnetic reconnection models).