Analytical solutions of continuity equation for joint collisional and Ohmic energy losses and their effects on hard X-ray emission.II. Mixed energy losses
Valentina Zharkova Submitted: 2016-03-08 04:49
In this paper we consider simultaneous analytical solutions of continuity equations for
electron beam precipitation a) in collisional losses and b) in Ohmic losses, or mixed
energy losses (MEL), by applying the iterative method to calculate the resulting differential densities at given precipitation depth. The differential densities of precipitating
electrons derived from the analytical solutions for mixed energy losses reveal increased flattening at energies below 10-30 keV compared to a pure collisional case. This flattening becomes stronger with an increasing precipitation depth turning into a positive
slope at greater precipitation depths in the chromosphere resulting in a differential
density distribution with maximum that shifts towards higher energies with increase
of a column depth. While the differential densities combining precipitating and returning electrons are higher at lower energies than those for a pure collisional case.
The resulting hard X-ray (HXR) emission produced by the beams with different initial
energy fluxes and spectral indices is calculated using the MEL approach for different
ratios between the differential densities of precipitating and returning electrons. The
number of returning electrons can be even further enhanced by a magnetic mirroring,
not considered in the present model, while dominating at lower atmospheric depths
where the magnetic convergence and magnitude are the highest. The proposed MEL
approach provides an opportunity to account simultaneously for both collisional and ohmic losses in flaring events, which can be used for a quick spectral fitting of HXR
spectra and evaluation of a fraction of returning electrons versus precipitating ones.
The semi-analytical MEL approach is used for spectral fitting to RHESSI observations of nine C, M and X class flares revealing a close fit to the observations and good resemblance to numerical FP solutions.
Authors: Zharkova V.V. and Dobranskis R.R.
Publication Status: MNRAS, in press
Last Modified: 2016-03-08 12:17