| Abstract * |
: |
In many statistical solar flare studies, power laws are claimed and exponents derived by fitting a line to a log-log histogram. It is well-known that this approach is statistically unstable, and very large statistics are needed to produce reliable exponent estimates. This may explain part of the observed divergence in power law exponents in various studies. Moreover, the question is seldom addressed to which extent the data really do support power law behavior. We perform a comprehensive study of 6,924 flares detected in SDO/AIA 9.4 nm images by the Solar Demon flare detection software between 2010 May 13 and 2018 March 16, and 9,601 flares detected during the same period in GOES/XRS data by the LYRAFF flare detection software.
We apply robust statistics to the SDO/AIA 9.4 nm peak intensity and the GOES/XRS raw peak flux, background-subtracted peak flux, and background-subtracted fluence, and find clear indications that all background-corrected data are better described by a lognormal distribution than by a power law, while the raw GOES/XRS peak flux is best described by a power law. This may explain the success of power law fits in flare studies using uncorrected data.
The behavior of flare parameter distributions has important implications for large-scale science questions such as coronal heating and the nature of solar flares. The apparent lognormal character of flare parameter distributions in our data sets suggests that the assumed power law nature of flares and its consequences need to be re-examined with great care. |
