imaging spectroscopy in electron space marco prato pure and applied mathematics department...
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Imaging spectroscopyImaging spectroscopyin electron spacein electron space
Marco Prato
Pure and Applied Mathematics DepartmentUniversity of Modena and Reggio Emilia, Italy
CNR – INFM LAMIA, Genova, Italy
IX RHESSI WorkshopGenova, September 3rd 2009
www.dima.unige.it/~piana/mida/group.html
Previously…Previously…
Back to spectroscopy…Implementation of a software for the reconstruction of the mean electron flux spectrum in a flare given the X-ray spectrum observed by RHESSI and a cross section
dEEεQEFRπ
VnεI
q
),()(4
)(2
X-ray spectrum
Mean electron flux spectrum
Bremsstrahlung cross section
Massone A.M., Piana M. and Prato M. 2008, “Regularized solution of the solar bremsstrahlung inverse problem: model dependence and implementation issues”, Inverse Problems in Science and Engineering 16, 523-545
The ideaThe ideaRHESSI – NESSI IV, Paris, 3-4 April 2006
The spectroscopy software can be used here!
X-rays
Electrons
Reformulation of the methodReformulation of the methodTemporal modulation data
Count visibilities Count imagesFourier Transform
Electron imagesElectron visibilities
Regularized Inversion
Fourier Transform
x y
vyuxiπ dudveqvuVqyxJ )(2);,();,(
dEEqKEvuWR
qvuVq
),();,(4
1);,(
2
x y
vyuxi dudveEvuWEyxFyxN )(2);,();,( ),(
Piana M., Massone A.M., Hurford G.J., Prato M., Emslie A.G., Kontar E.P. and Schwartz R.A. 2007, “Electron flux spectral imaging of solar flares through regularized analysis of hard X-ray source visibilities”, The Astrophysical Journal 665, 846-855
N.B.: The electron visibilities extend over a greater energy range than the count visibilities!
New testNew testRHESSI – NESSI V, Berkeley, 6-8 November 2006
Ba
ck-p
roje
ctio
n
New test improvedNew test improved7th RHESSI Workshop, Santa Cruz, 25-29 June 2007
ME
M-N
JIT
Local fluxLocal flux7th RHESSI Workshop,
Santa Cruz, 25-29 June 20078th RHESSI Workshop,
Potsdam, 2-6 September 2008
Simulated dataSimulated data8th RHESSI Workshop, Potsdam, 2-6 September 2008
Prato M., Piana M., Emslie A.G., Hurford G.H., Kontar E.P. and Massone A.M., “A regularized visibility-based approach to astronomical imaging spectroscopy”, SIAM Journal on Imaging Sciences, in press
TodayToday
• New method to get electron images of a flare
• Software close to be ready
• Test on simulated data ok
• Test on (few) real data ok
• Need to understand why and how to use it
• Push people to use it
What we can do from electron mapsWhat we can do from electron maps get the variation of the electron spectrum in both space and time
at a more elementary level, "locate" (using centroids) where the electrons are (and the structure of the region in which they propagate), rather than where the X-rays are (which is of diagnostic, but not physical, interest)
locate the region of steepest spectrum, which is most likely the acceleration region itself
examine the variation of electron spectrum with position to understand the physical processes associated with electron propagation in the source (Emslie, Barrett & Brown 2001)
examine source asymmetries in order to better understand the flare geometry, and compare results with other observations (magnetograms, UV images, optical images)
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