1. RHESSI Microflare Statistics Iain Hannah, S. Christe, H. Hudson, S. Krucker, L. Fletcher & M. A. Hendry

2. RHESSI/Meudon July 20042 Motivation: Automated Spectrum Characterisation –OSPEX Sophisticated fitting –Channel Ratios + Line Fitting Simple Easy to determine errors and bias Complementary results Microflare Statistics –Maximum Likelihood vs. Histogram Fitting –Selection Effect Bias & Correction Techniques

3. RHESSI/Meudon July 20043 Spectrum Characterisation Microflare photon spectrum Thermal Bremsstrahlung –Temperature T –Emission Measure EM=n 2 V Non-Thermal –Power-law index γ Non-Thermal γ Thermal T, EM Photon Spectrum -Thermal Model (ph) Line Fit Remains=> γ Background Corrected Count Rate Counts Ratio => T Counts (4.67-5.67) keV ÷ Thermal Model (ph->c) @ (T, 10 49 ) => EM

4. RHESSI/Meudon July 20044 June Peak ratio ospex Key: Data Therm model Non-therm model Total Model

5. RHESSI/Meudon July 20045 May Peak ratio ospex Key: Data Therm model Non-therm model Total Model

6. RHESSI/Meudon July 20046 May Decay ratio ospex Key: Data Therm model Non-therm model Total Model

7. RHESSI/Meudon July 20047 Thermal Time Profiles

8. RHESSI/Meudon July 20048 T vs EM at Peak Time Background Subtracted GOES class Dotted Line: Feldman et al [1996] Average of BCS T against EM from BCS, GOES (1-8)Å and (0.5-4)Å

9. RHESSI/Meudon July 20049 OSPEX Comparison Ratio Ospex

10. RHESSI/Meudon July 200410 Non-Thermal Time Profiles

11. RHESSI/Meudon July 200411 Non-Thermal Energy Distribution For Total Energy only used P with error < 100%. So smaller events have underestimated energies. Parnell & Jupp [2000] method is independent of bin size. So objectively fits Skew-Laplace Distribution to log(E) using approximate Maximum Likelihood method.

12. RHESSI/Meudon July 200412 Validity of Energy Distribution ? Physical and Instrumental Bias –Malmquist like Selection effect bias Aschwanden & Charbonneau [2002] /Parnell [2002] –Monte Carlo method of bias removal on TRACE events We have semi-analytical way of correcting for this bias [Hendry 1990, Willick 1994]: –Valid as long as parameter scaling laws and assumption of Multivariate Normal Distribution correct: –So can numerically iterate from biased observations to intrinsic distribution (work in progress…..)