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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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slide1

Hard X-ray Footpoint

Fluxes & Areas

Ed Schmahl, R. Pernak, & G. Hurford

NASA/GSFC & Univ. MD

RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

slide2

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

slide3

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

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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

slide5

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

slide6

WHAT DOES VIS FWDFIT DO?

Visibility

amplitudes

(crosses)

are fit by a

model

black curve)

Residuals

(squares)

RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

slide7

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

slide8

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

slide9

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

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RESULTS (1): FLARE OF 2002/09/08

FWHM=

3.1,7.9

FLUX=

7.8, 13.

RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

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RESULTS (2): FLARE OF 2005/01/15

FWHM=

5.8, 15.

FLUX=

10.9, 43.

RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

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RESULTS (3): FLARE OF 2005/08/25

FWHM=

2.2, 9.7

FLUX=

55, 130

RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

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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

slide14

RESULTS (5): 2003/06/17 22:53:10

FWHM=

5.4, 4.0

FLUX=

46, 38

RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

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RESULTS (6): 2003/06/17 22:53:40

FWHM=

5.3, 3.6

FLUX=

49, 37

RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

slide16

RESULTS (7): 2003/06/17 22:54:10

FWHM=

5.8, 3.6

FLUX=

46, 34

RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

slide17

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

slide19

FWHM VS FLUX FOR SELECTED EVENTS

F

RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

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FWHM VS FLUX (WITH ERRORBARS)

F

RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

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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

slide22

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

slide23

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

slide24

FINI

RHESSI WORKSHOP, MEUDON, 2006 APRIL 5-8

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