Hard X-ray Footpoint Source Sizes

1. Hard X-ray Footpoint Source Sizes

2. Abstract RHESSI 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.

3. Importance of Footpoint Sizes They 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 1010erg 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)

4. 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 • Dennis and Pernak are wrong, or • Kontar and Jeffries are wrong, or • Source altitude is <1 Mm, or • 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.

5. Dennis & Pernak (2009) Major Axis Frequency Distribution Minor Axis Frequency Distribution FWHM in arcseconds

6. Dennis & Pernak (2009) RHESSI contours on a TRACE 171 Å image Date: 2005 July 30 Time: 06:31:58 UT. Energy: 50–100 keV Contours: 5%, 10%, and 50% Black: Clean components White: pixon Yellow: VFF Western source FWHM – pixon Major axis 5.9” Minor axis 2.8”

7. Albedo GeometryBrown, J. C. , Van Beek, H. F., and McClymont, A. N. Astron. & Astrophys. 41, 395 (1975) Source S Source height h Scattering point P Subsource point Q Distance P to Q r QSP θ Sun center C Sun’s radius R Direction to Earth 

8. 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 = (cosθ)-2 Inverse-square fall off from S F2 = (cosθ)-1 Projection onto plane photosphere F3 ~ 1 Compton scattering directivity F4 ~ 1 Curvature correction  dI(θ) ~ f I0 / (2 cos3θ)

9. 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.

10. Albedo Fraction vs. X-ray Energy • Albedo flux assuming isotropic emission • Peaks between 30 and 50 keV • Greater for flatter spectra

11. Simulated DataCLEAN Image Source Alone Cross-section through single source Count-rate vs. roll angle for all 9 detectors Red: simulated data Black: predicted from CLEAN image

12. 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

13. Simulated DataPixon Image Source Alone Cross section through source Count-rate vs. roll angle for detectors 1 - 7 Red: simulated data Black: predicted from pixon image

14. Simulated DataPixon – Circular Source + Albedo Pixon does see the albedo wings

15. Disc Flare6 Nov. 2004 Possible compact source + albedo patch Altitude = 2 – 3 Mm

16. Limb Flare20 Feb. 2002 Possible compact source + albedo patch Evidence for foreshortening???

17. Disc Flare – Early Impulsive Emission2 June 2002 Note double HXR footpoint sources. Possible symmetric wings around each source.

18. Limb Flare21 April 2002 Note two footpoint HXR sources along TRACE 195Å ribbons and extended coronal HXR source(s) above the limb.

19. Limb Flare21 April 2002 Note more intense wings closer to the limb.

20. 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

21. Change in C-statistic vs.Clean Beam Width Factor (CBWF) Nominal CBW sigma = 2.4 arcsec

22. CLEAN Beam WidthNatural Weighting(clean_sigma.pro)

23. Albedo Detection? • Schmahl and Hurford (2002, 2009) report detection of extended HXR sources. Possible Explanations • Albedo patch • Extended coronal source(s) • Extended footpoint(s) along ribbons • 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,

24. 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.

25. 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.