Solar Physics

, 294:105 | Cite as

Statistical Study of Hard X-Ray Spectral Breaks in Solar Flares

  • Meriem AlaouiEmail author
  • Säm Krucker
  • Pascal Saint-Hilaire


The Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) provides hard X-ray spectral observations with \({\approx}\,1~\mbox{keV}\) resolution to study flare-accelerated (\({>}\,10~\mbox{keV}\)) electrons through their bremsstrahlung emission. Here we report on a statistical study of RHESSI flares with emission above 150 keV, focusing on the spectral shape at the hard X-ray peak. Spectral parameters are derived by fitting the photon spectrum with a broken power law and by the standard thick-target fit. Consistent with previous studies, the most common spectral shape of the photon spectrum (52 out of 65 events) is a double power law with a downward break (“knee”), with ten events showing a single power law and three events having an upward break (“ankle”). The spectral breaks occur typically around 55 keV and the difference of the spectral index above and below the break, \(\gamma _{2}\) and \(\gamma _{1}\), is typically between 0.3 and 1. We show correlations between the downward break parameters. The most prominent correlation, with a rank order coefficient of \(\rho =0.92\), is between the power-law indices above and below the break: \(\gamma _{1} = (0.74\pm 0.04)\gamma _{2} + (0.34 \pm 0.14)\). Applying a thick target fit to the photon spectrum, a similar correlation is also found for the flare-accelerated electron spectra with \(\delta _{1} =(0.85\pm 0.08)\delta _{2} - (0.3\pm 0.3)\) (\(\rho =0.67\)). Spectral breaks could be a property of the acceleration mechanism itself or they could be a secondary effect produced by particle transport or wave-particle interactions. Any theoretical models should be consistent with these correlations. In addition, we find that one upward and 23 (49%) downward breaks are consistent with nonuniform ionization within the thick target.


Sun: flares Sun: X-rays, gamma rays 



We would like to thank Robert Lin for major contributions to the spectral analysis and interpretation in this paper. We also acknowledge Brian Dennis, Gordon Holman, Richard Schwartz, and Kim Tolbert for critical comments. The work was supported through NASA contract NAS 5-98033 for RHESSI.

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Meriem Alaoui
    • 1
    • 2
    Email author
  • Säm Krucker
    • 3
    • 4
  • Pascal Saint-Hilaire
    • 3
  1. 1.NASA Goddard Space Flight CenterGreenbeltUSA
  2. 2.Physics DepartmentCatholic University of AmericaWashington D.C.USA
  3. 3.Space Sciences LaboratoryUniversity of CaliforniaBerkeleyUSA
  4. 4.Institute for Data ScienceUniversity of Applied Sciences and Arts Northwestern SwitzerlandWindischSwitzerland

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