Post on 03-Jan-2016
description
Hard X-ray Footpoint Source Sizes
Brian R. Dennis NASA GSFC
Eduard P. Kontar Department of Physics and Astronomy, University of Glasgow, United Kingdom
Anil A. Gopie Wyle Information Systems at NASA GSFC
A. Kim Tolbert Wyle Information Systems at NASA GSFC
Richard A. Schwartz
The Catholic University of America at NASA GSFC
AbstractRHESSI has detected compact hard (25 - 100 keV) X-ray sources that are
<4 arcseconds (FWHM) in extent for certain flares (Dennis and Pernak
(2009). These sources are believed to be at magnetic loop footpoints
that are known from observations at other wavelengths to be very small.
Flare ribbons seen in the UV with TRACE, for example, are ~1 arcsecond
in width, and white light flares show structure at a similar level. However,
Kontar and Jeffrey (2010) have shown that the measured extent should
be >7 arcseconds, even if the X-ray emitting thick-target source is point-
like. This is because of the strong albedo contribution in the measured
energy range for a source located at the expected altitude of 1 Mm near
the top of the chromosphere. This discrepancy between observations and
model predictions may indicate that the source altitude is significantly
lower than assumed or that the RHESSI image reconstruction procedures
are not sensitive to the more diffuse albedo patch in the presence of a
strong compact source. Results are presented here exploring the latter
possibility using the Pixon image reconstruction procedure.Dennis, B. R. and Pernak, R. L., Hard X-Ray Flare Source Sizes Measured with RHESSI, 2009, ApJ, 698, 2131-2143.
Kontar, E. P. and Jeffrey, N. L. S., Positions and sizes of X-ray solar flare sources, 2010, A&A, 513, L2.
Importance of Footpoint SizesThey enable electron energy flux density (erg s-1 cm-2)
to be determined from measured X-ray spectrum:HXR spectrum (photons cm−2 s−1 keV−1) electron spectrum (electrons s−1 keV−1) into thick target electron energy flux density (erg s-1 cm-2) for E > Ecutoff
Applications Chromospheric evaporation (Fisher et al. 1985)
Gradual vs. explosive for > 3 x 1010 erg s-1 cm-2 Return current saturation (Alexander and Daou 2007) Acceleration region properties (Xu et al. 2008) Vertical variation of magnetic flux tube dimension
(Kontar et al. 2010)
The Controversy
Dennis and Pernak (2009) reported 20 – 50 keV HXR source extents of <4” (FWHM)
Kontar and Jeffries (2010) say that albedo gives even point sources at altitude of >1 Mm (1.4”) apparent extents of ~7” (FWHM).
Possible Explanations
1. Dennis and Pernak are wrong, or2. Kontar and Jeffries are wrong, or3. Source altitude is <1 Mm, or4. Some combination of the above.
Dennis, B. R. and Pernak, R. L., 2009, ApJ, 698, 3131.Kontar, E. P. and Jeffries, N. L. S., 2010, A&A, 513, L2.
Dennis & Pernak (2009)
FWHM in arcseconds
Major Axis Frequency Distribution Minor Axis Frequency Distribution
Dennis & Pernak (2009)
RHESSI contours on a TRACE 171 Å image
Date: 2005 July 30Time: 06:31:58 UT.
Energy: 50–100 keV Contours: 5%, 10%, and
50%Black: Clean components
White: pixon
Yellow: VFF
Western source FWHM – pixonMajor axis 5.9”
Minor axis 2.8”
Albedo GeometryBrown, J. C. , Van Beek, H. F., and McClymont, A. N. Astron. & Astrophys. 41, 395 (1975)
Source SSource height hScattering point PSubsource point QDistance P to Q rQSP θSun center CSun’s radius RDirection to Earth
Albedo GeometrySource at solar disc center (L = 0)
dI(θ) (counts cm-2 arcsec-2) = f I0 F1 F2 F3 F4
dI Albedo flux from point P
θ Angle QSP in Figure 1
f Photospheric reflectance (~0.6 at 15 – 20 keV)
I0 Primary source flux (assumed isotropic)
F1 = (cos θ)-2 Inverse-square fall off from S
F2 = (cos θ)-1 Projection onto plane photosphere
F3 ~ 1 Compton scattering directivity
F4 ~ 1 Curvature correction
dI(θ) ~ f I0 / (2 cos3θ)
Albedo Patch (Kontar & Jeffries 2010) Lower flux density (photons s-1 cm-2 arcsec-2) compared to
primary source – down by factors of >10. Impossible to image using current version of CLEAN Should be possible to image albedo patch using pixon Evidence for extended source using Visibilities (VIS-FF)
Geometric foreshortening close to limb. Centroid shifted towards disc center compared to primary
source.
Albedo Fraction vs. X-ray Energy
Albedo flux assuming isotropic emission• Peaks between 30 and 50 keV• Greater for flatter spectra
Simulated DataCLEAN Image
Source Alone
Cross-section through single source Count-rate vs. roll angle for all 9
detectorsRed: simulated data
Black: predicted from CLEAN image
Simulated DataCLEAN Image
Source + Albedo
Cross-section through source
Clean doesn’t see the albedo wings Count-rate vs. roll angle for all 9 detectors
Red: simulated data
Black: predicted from CLEAN image
Source Alone
Simulated DataPixon Image
Count-rate vs. roll angle for detectors 1 - 7
Red: simulated data
Black: predicted from pixon image
Cross section through source
Pixon does see the albedo wings
Simulated DataPixon – Circular Source + Albedo
Simulated FlareLongitude = 80
Color: simulated flare + albedoContours: Pixon Image
Simulated Flare - Longitude = 80
Color: simulated flare + albedoContours: MEM_NJIT Image
Flux contour of sourceGreen: original sourceRed: MEM_NJIT image
Disc Flare6 Nov. 2004
Possible compact source + albedo patchAltitude = 2 – 3 Mm
Limb Flare20 Feb. 2002
Possible compact source + albedo patchEvidence for foreshortening???
Disc Flare – Early Impulsive Emission2 June 2002
Note double HXR footpoint sources. Possible symmetric wings around each source.
Limb Flare21 April 2002
Note two footpoint HXR sources along TRACE 195Å ribbons and extended coronal HXR source(s) above the limb.
RHESSI – 25 to 50 keV
TRACE - 195Å
Limb Flare21 April 2002
Note more intense wings closer to the limb.
21 April 2002
Visibility Correction Factors21 April 200212 to 25 keV
Visibility Correction Factors21 April 200215 to 25 keV
Source Feature Significance Determine change in C-statistic
Probability of getting measured number of counts compared to expected number of counts
Based on probabilities from Poisson statistics Use when number of counts per bin is <~10
Reduced C-statistic (C-stat/no. of degrees of freedom) Unlike 2, expectation value ≠ 1 Probability distribution depends on
Mean number of counts per bin Distribution of counts per bin Must be determined by Monte Carlo simulations for each
case
Change in C-statistic vs.Clean Beam Width Factor (CBWF)
C-statistic vs. 1/CBWF2 Sept. 2002
1.05
1.10
1.15
1.20
1.25
1.30
1.35
0 0.5 1 1.5 2
Clean Beam Width x nominal
C-st
atisti
c
Det.1
2
3
4
5
6
7
8
9
Sum
Nominal CBW sigma = 2.4 arcsec
CLEAN Beam WidthNatural Weighting(clean_sigma.pro)
Albedo DetectionImaging?
Schmahl, E. J. and Hurford, G. J. (2002, 2009)
Report detection of extended HXR sources.
RHESSI Observations of the Size Scales of Solar Hard X-ray Sources
Sol. Phys., 210, 273 (2002)
Solar Hard X-ray AlbedoRHESSI Science Nugget #119 (2009)
Schmahl and Hurford (2002)
Schmahl and Hurford (2002)
Cumulative flux vs. radius (r)
Schmahl, and Hurford, 2009, RHESSI Science Nugget #119
Flare on 10 April 2002Schmahl and Hurford, 2009, RHESSI Science Nugget #119
Schmahland Hurford 2009 RHESSI Science Nugget #119
Detector # + position angle/180
Schmahl and Hurford (2009) RHESSI Science Nugget #119
But, reduced chi-squared = 7.And, 15 – 20 keV and 12 – 15 keV are low energy ranges to see albedo.
Clean Images10 April 2002 12:30 UT
Detector #6 Effect
Detectors 4, 5, 7, 8, 9Detectors 4, 5, 6, 8, 9
Visibility Correction Factors10 April 2002
Albedo Detection? Schmahl and Hurford (2002, 2009) report detection
of extended HXR sources.
Possible Explanations1. Albedo patch2. Extended coronal source(s)3. Extended footpoint(s) along ribbons4. Instrumental Effects
Pulse pile-up Image reconstruction technique (Visibility
Forward Fit) Detector mismatch
Schmahl, E. J. and Hurford, G., J., 2002, Sol. Phys., 210, 273.Schmahl, E. J. and Hurford, G., J.,, 2009, RHESSI Science Nugget,
Conclusion Controversy unresolved. Dennis & Pernak source dimensions
OK for near-limb flares? OK if albedo component is too weak to be included in analysis.
Simulations show that pixon image reconstruction is capable of showing albedo wings.
Wings detected in pixon images for most flare sources. Origin of wings uncertain.
No evidence of foreshortening effect as function of heliocentric longitude in wings.
Not certain that albedo has ever been conclusively detected with RHESSI.
Future Work Examine images and spectra for more flares.
Spectral analysis for consistency with imaging. Further simulations with more realistic multiple
source geometries and background rates. Variations with longitude to reveal
foreshortening and altitude effects. Visibility Forward Fit with assumed albedo
patches. Schmahl and Hurford
Pixon reconstructions to image albedo patches. Correct annular sector to XY coordinates problem
with compact sources.