Non-thermal recombination – a neglected source of flare hard X-rays and fast electron diagnostic

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This article has an erratum: [erratum]

Issue		A&A Volume 481, Number 2, April II 2008


Page(s)		507 - 518
Section		The Sun
DOI		http://dx.doi.org/10.1051/0004-6361:20078103
Published online		04 February 2008

A&A 481, 507-518 (2008)
DOI: 10.1051/0004-6361:20078103

Non-thermal recombination - a neglected source of flare hard X-rays and fast electron diagnostic

J. C. Brown and P. C. V. Mallik

Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK
e-mail: john@astro.gla.ac.uk

(Received 17 June 2007 / Accepted 27 January 2008)

Abstract
Context. Flare Hard X-rays (HXRs) from non-thermal electrons are commonly treated as solely bremsstrahlung (free-free = f-f), recombination (free-bound = f-b) being neglected. This assumption is shown to be substantially in error, especially in hot sources, mainly due to recombination onto Fe ions.
Aims. We analyse the effects on HXR spectra $J(\epsilon)$ and electron diagnostics by including non-thermal recombination onto heavy elements in our model.
Methods. Using Kramers hydrogenic cross sections with effective $Z=Z_{\rm eff}$ , we calculate f-f and f-b spectra for power-law electron spectra within both thin and thick target limits and for Maxwellians with summation over all important ions.
Results. We find that non-thermal electron recombination, especially onto Fe, must, in general, be included with f-f for reliable spectral interpretation, when the HXR source is hot, such as occulted loops containing high ions of Fe (f-b cross-section $\propto$ Z⁴). The f-b contribution is greatest when the electron spectral index $\delta$ is large and any low energy cut-off $E_{\rm c}$ is small, because the electron flux spectrum F(E) emitting f-b photon energy $\epsilon$ is $\propto (E=\epsilon-V_Z)^{-\delta}$ (V_Z is the ionisation potential) and not $\propto (E=\epsilon)^{-\delta+1}$ as for f-f. The f-b spectra recombination edges mean a cut-off $E_{\rm c}$ in F(E) appears as an HXR feature at $\epsilon = E_{\rm c} + V_Z$ , offering an $E_{\rm c}$ diagnostic. For thick target sources, the presence of $E_{\rm c}$ appears as edges in $J'(\epsilon)$ , not in $J(\epsilon)$ , but it is still detectable. Including f-b lowers the F(E) needed for prescribed HXR fluxes greatly in some cases; and even when small, it seriously distorts F(E) as inferred by inversion or forward fitting of $J(\epsilon)$ based on f-f alone.
Conclusions. The f-b recombination from non-thermal electrons can be an important contributor to HXR spectra, so it should be included in spectral analyses, especially for hot sources. Accurate results will require use of better cross sections than ours and consideration of source ionisation structure.

Key words: atomic processes -- Sun: corona -- Sun: flares -- Sun: X-rays, gamma rays

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