RHESSI Microflare Statistics

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

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Spectrum Characterisation
Background Corrected Count Rate

• Microflare photon spectrum
• Thermal Bremsstrahlung
• Temperature T
• Emission Measure EMn2V
• Non-Thermal
• Power-law index ?

Non-Thermal ?
Thermal T, EM
Photon Spectrum -Thermal Model (ph) Line Fit
Remainsgt ?
Counts (4.67-5.67) keV Thermal Model (ph-gtc) _at_
(T, 1049) gt EM
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June Peak
ratio
ospex
KeyDataTherm modelNon-therm modelTotal Model
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May Peak
ratio
ospex
KeyDataTherm modelNon-therm modelTotal Model
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May Decay
ratio
ospex
KeyDataTherm modelNon-therm modelTotal Model
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Thermal Time Profiles
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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
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OSPEX Comparison
Ratio Ospex
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Non-Thermal Time Profiles
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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 lt 100.
So smaller events have underestimated energies.
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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..)