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RHESSI Microflare Statistics

RHESSI Microflare Statistics. Iain Hannah, S. Christe, H. Hudson, S. Krucker, L. Fletcher & M. A. Hendry. Motivation:. Automated Spectrum Characterisation OSPEX Sophisticated fitting Channel Ratios + Line Fitting Simple Easy to determine errors and bias Complementary results

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RHESSI Microflare Statistics

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

  2. 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. Spectrum Characterisation Counts Ratio => T Background Corrected Count Rate Microflare photon spectrum • Thermal Bremsstrahlung • Temperature T • Emission Measure EM=n2V • Non-Thermal • Power-law index γ Non-Thermal γ Thermal T, EM Photon Spectrum -Thermal Model (ph) Line Fit Remains=> γ Counts (4.67-5.67) keV ÷Thermal Model (ph->c) @ (T, 1049) => EM

  4. June Peak ospex ratio Key:DataTherm modelNon-therm modelTotal Model

  5. May Peak ospex ratio Key:DataTherm modelNon-therm modelTotal Model

  6. May Decay ospex ratio Key:DataTherm modelNon-therm modelTotal Model

  7. Thermal Time Profiles

  8. 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. OSPEX Comparison RatioOspex

  10. Non-Thermal Time Profiles

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

  12. 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…..)

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