Size and Flux Asymmetry of Footpoint Sources

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Size and Flux Asymmetry of Footpoint Sources
Schmahl1, Pernak2, and Hurford3 1NASA/GSFC
and Univ of MD 2NASA/GSFC and CUA 3SSL, UC
Berkeley
RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8
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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
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MOTIVATION

• HXR footpoint fluxes are often asymmetric
• They are also often asymmetric in size 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 photospheric field should be stronger where
  flux is lower
• The size of the footpoint should be smaller where
  flux is lower
• Side-benefit Knowledge of source sizes can also
  yield
• Electron and energy densities,
• Information about loss-cone physics in flares

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

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WHAT DOES VIS FWDFIT DO?
Visibility amplitudes (crosses) are fit by a
model black curve) Residuals (squares)
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HOW DOES VIS_FWDFIT FIND WIDTHS? a) Simplest
case single Gaussian source (simulated
profiles)
FWHM3''
FWHM7''
The amplitudes roll off as a function of SC FWHM
T
Subcollimator
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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
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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...
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RESULTS (1)
FWHM 4.1,3.6 FLUX 21.4, 20.9
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RESULTS (2)
FWHM 5.4, 4.0 FLUX 46, 38
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RESULTS (3)
FWHM 5.3, 3.6 FLUX 49, 37
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RESULTS (4)
FWHM 5.8, 3.6 FLUX 46, 34
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TESTS of an 8-parameter fit Slices through ?2
space
Source 1
Source 2
Plots like this demonstrate how well the extremum
is defined in 8-parameter space.
FWHM FLUX X-POS Y-POS
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Examples of fits for 4 flares
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FWHM VS FLUX FOR SEVERAL EVENTS
F
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FWHM VS FLUX (WITH ERRORBARS)
F
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HOW ARE VIS_FWDFIT ERROR BARS COMPUTED?

• See Gordon Hurford for the details

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PRELIMINARY CONCLUSIONSs
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WHAT NEXT?
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RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8