Determination of electron density and filling factor for soft X-ray   flare kernels
  In a standard method of determining electron density for soft X-ray (SXR) flare kernels it is necessary to assume what is the extension of a kernel along the line of sight. This is a source of significant uncertainty of the obtained densities. In our previous paper (Bak-Steslicka and Jakimiec, 2005) we have worked out another method of deriving electron density, in which it is not necessary to assume what is the extension of a kernel along the line of sight. The point is that many flares, during their decay phase, evolve along the sequence of steady-state models [quasi-steady-state (QSS) evolution] and then the scaling law, derived for steady-state models, can be used to determine the electron density. The aim of the present paper is: (1) to improve the two methods of density determination, (2) to compare the densities obtained with the two methods. We have selected a number of flares which showed QSS evolution during the decay phase. For these flares the electron density, N, has been derived by means of standard method and with our QSS method. Comparison of the N values obtained with the two different methods allowed us: (1) to test the obtained densities, (2) to evaluate the volume filling factor of the SXR emitting plasma. Generally, we have found good agreement (no large systematic difference) between the values of electron density obtained with the two methods, but for some cases the values can differ by a factor up to 2. For most flare kernels estimated filling factor turned out to be about 1, near the flare maximum. 
Jerzy Jakimiec and Urszula Bak-Steslicka
astro-ph.SR