A regularization approach for the analysis of RHESSI X-ray spectra^*

¹ INFM, Unità di Ricerca di Genova, via Dodecaneso 33, 16146 Genova, Italy e-mail: massone@ge.infm.it
² INFM and Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italy e-mail: piana@dima.unige.it
³ Department of Physics, Open University, Milton Keynes MK7 6AA, UK e-mail: a.j.conway@open.ac.uk
⁴ Department of Physics and Astronomy, The University, Glasgow G12 8QQ, UK e-mail: andrew@astro.gla.ac.uk
⁵ Department of Physics, Open University, Milton Keynes MK7 6AA, UK e-mail: b.a.c.eves@open.ac.uk

Corresponding author: M. Piana, piana@dima.unige.it

Received: 9 January 2003
Accepted: 1 April 2003

Abstract

The Ramaty High Energy Solar Spectroscopic Imager (RHESSI) mission provides high resolution X-ray spectra emitted by collisional bremsstrahlung of electrons with the ions of the plasma. One of the aims of the mission is to infer information about the acceleration and transport mechanisms of electrons and ions in solar flares. Within the framework of an optically thin model and under the assumption of isotropic conditions in the solar plasma, the emitted photon spectrum is related to the electron flux density spectrum by an integral equation of the first kind. This problem is characterized by a notable numerical instability as a consequence of the experimental errors in the measured photon data. We address the solution of this problem by using the Tikhonov regularization algorithm. The method is applied to the case of three photon spectra registered by RHESSI detectors in the first months of the observational activity of the satellite. Furthermore a comparison of the reconstructions provided by the algorithm is performed in the case of the Kramers, Bethe-Heitler and Bethe-Heitler with the Elwert correction models for the bremsstrahlung cross-section.