Title: RHESSI Microflare Statistics
1RHESSIMicroflare Statistics
Iain Hannah, S. Christe, H. Hudson, S. Krucker,
L. Fletcher M. A. Hendry
2Motivation
- 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
3Spectrum 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
4June Peak
ratio
ospex
KeyDataTherm modelNon-therm modelTotal Model
5May Peak
ratio
ospex
KeyDataTherm modelNon-therm modelTotal Model
6May Decay
ratio
ospex
KeyDataTherm modelNon-therm modelTotal Model
7Thermal Time Profiles
8T 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
9OSPEX Comparison
Ratio Ospex
10Non-Thermal Time Profiles
11Non-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.
12Validity 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..)