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.