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RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

Hard X-ray Footpoint Fluxes & Areas Ed Schmahl, R. Pernak, & G. Hurford NASA/GSFC & Univ. MD. RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8. INTRODUCTION AND SUMMARY. Motivation: Why are HXR source sizes important? Method: VIS_FWDFIT How it Works Preliminary Results Tests of validity

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RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

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  1. Hard X-ray Footpoint Fluxes & Areas Ed Schmahl, R. Pernak, & G. Hurford NASA/GSFC & Univ. MD RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  2. INTRODUCTION AND SUMMARY Motivation: Why are HXR source sizes important? Method: VIS_FWDFIT How it Works Preliminary Results Tests of validity What next? RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  3. MOTIVATION • Double footpoints are often asymmetric in flux • They are also often asymmetric in radio and magnetic field • The usual explanation is in terms of trapping in an asymmetric magnetic field (Melrose & White, 1979) • If this model is correct, The size of the footpoint should be smaller where flux is lower • Knowledge of source sizes can also yield • Electron and energy densities, • Information about loss-cone physics • Magnetic loop geometry RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  4. In asymmetric loops, the footpoint is larger where the mirror point is lower, hence flux correlates with width. A CARTOON: SYMMETRIC & ASYMMETRIC FLARE LOOPS RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  5. METHOD FOR DETERMINING SIZES, POSITIONS & FLUXES Don't use CLEAN OR MEM or PIXON Use FORWARD FIT with VISIBILITIES REASONS: Old algorithms don't weight size sensitivity properly Better to find the closest fit to the calibrated visibilities of a specific model (e.g. Gaussians + albedo) Select energy and time range with good S/N Compute visibility using SSW tools Run vis_fwdfit with 8-10 parameters RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  6. WHAT DOES VIS FWDFIT DO? Visibility amplitudes (crosses) are fit by a model black curve) Residuals (squares) RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  7. HOW DOES VIS_FWDFIT FIND WIDTHS? a) Simplest case: single Gaussian source (simulated profiles) FWHM=3'' FWHM=7'' The amplitudes roll off as a function of SC FWHM T Subcollimator RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  8. HOW DOES VIS_FWDFIT FIND WIDTHS? Harder example: double identical sources The two sources beat against each other, cancelling at some points, reinforcing at others. In regions of reinforement, rolloff is the same as for a single source. T RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  9. HOW DOES VIS FWDFIT WORK? -- More complex examples c) Double sources, equal sizes, different flux Reinforcement region shows the sum Cancellation region shows the difference d) Double sources, different sizes, equal flux Reinforcement regions have different SC rolloffs e) Different sizes & different flux... f) And so on... RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  10. RESULTS (1): FLARE OF 2002/09/08 FWHM= 3.1,7.9 FLUX= 7.8, 13. RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  11. RESULTS (2): FLARE OF 2005/01/15 FWHM= 5.8, 15. FLUX= 10.9, 43. RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  12. RESULTS (3): FLARE OF 2005/08/25 FWHM= 2.2, 9.7 FLUX= 55, 130 RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  13. RESULTS (4): 2003/06/17 22:52:40 FWHM= 4.1, 3.6 FLUX= 21.4, 20.9 RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  14. RESULTS (5): 2003/06/17 22:53:10 FWHM= 5.4, 4.0 FLUX= 46, 38 RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  15. RESULTS (6): 2003/06/17 22:53:40 FWHM= 5.3, 3.6 FLUX= 49, 37 RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  16. RESULTS (7): 2003/06/17 22:54:10 FWHM= 5.8, 3.6 FLUX= 46, 34 RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  17. RELIABILITY of the 8-parameter fit: Slices through 2 space Source 2 Source 1 Plots like this demonstrate how well the extremum is defined in 8-parameter space. FWHM FLUX X-POS Y-POS RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  18. Examples of fits for 4 flares

  19. FWHM VS FLUX FOR SELECTED EVENTS F RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  20. FWHM VS FLUX (WITH ERRORBARS) F RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  21. Visibilities come with their own sigmas • After vis_fwdfit gets a solution • The fit parameters are varied randomly over the space of the visibility sigmas • Vis_fwdfit finds a new solution • This is repeated 10 or 12 times • The SD of these new fits is the new sigma HOW ARE VIS_FWDFIT ERROR BARS COMPUTED? See Gordon Hurford for the details RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  22. Reasonable FWHMs can be determined • Error bars are relatively small • In the selected flares and energy ranges... • Width ratios range from 1.2 to 5 • Width values range from ~2'' to ~15'' • Flux ratios range from 1.1 to 3 • The brighter component is larger PRELIMINARY CONCLUSIONS RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  23. Get a larger sample of flares Any counterexamples to width-flux correlation? Examine regimes of poor fits Need elliptical sources, albedo? Look at time evolution What does increasing/decreasing size imply? Look at energy dependence Can one see effects of reduced scattering? Compare with radio, magnetograms Are they compatible with simple model? Trap-precipitation models Quantitative interpretation Loss-cone angles WHAT NEXT? RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

  24. FINI RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

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