# Presentation: 371591

##   Evidence for albedo sources--

-   inferences on source height, and
-   possible X-ray directivity

- http://hesperia.gsfc.nasa.gov/~schmahl/albedo

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

- Determining albedo properties from RHESSI data
-   Large extent  over resolution
-   Use relative amplitudes
-   Select flares for study
-   Find relative amplitudes

- What do we expect for albedo relative amplitudes?
-   Geometry of albedo & primary source
-   Predicted relative amplitudes
-   Basis functions
-   Fitting observed profiles

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- Other effects
-  Energy dependence?
-  Azimuthal signatures?
-  Phase shifts?

- Steps towards full characterization of albedo

## Effect of source size on RHESSI 

-             relative amplitudes

- http://hesperia.gsfc.nasa.gov/~schmahl/albedo

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

## Getting the relative amplitudes

-  Back-projection + transmission probability                               (Schmahl & Hurford 2003)

- Results: relative amplitude vs wavenumber
-   (Fourier amplitude normalized to unit flux)

- http://hesperia.gsfc.nasa.gov/~schmahl/albedo

**RHESSI-NESSI WORKSHOP, JUNE 2003**

## Selected Flares

- Back-projection maps of selected flares that are
- compact and round.  (12-25 keV, 1 pixels)

- http://hesperia.gsfc.nasa.gov/~schmahl/albedo

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

## Observed relative amplitudes

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

## Albedo theory's prediction of spatial profiles

-  Rapid falloff of (k) => large-scale components
-  Albedo theory predicts a Moffat function profile

- I(r)= A cos()/d2  = A h/(h2 +r)3/2

- Adapted from Brown et al., 1974

- http://hesperia.gsfc.nasa.gov/~schmahl/albedo

**d**

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

## Predicted relative amplitudes for Albedo

- http://hesperia.gsfc.nasa.gov/~schmahl/albedo

- (Squares show the RHESSI response for 9 detectors).

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

## Size scale profiles  Relative amplitudes 

-  Exponential profile  Moffat function
-  Gaussian profile  Gaussian relative amplitude

- Size scale profiles  Relative amplitudes

- http://hesperia.gsfc.nasa.gov/~schmahl/albedo

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

## Fits to observed relative amplitudes

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

## IMPORTANT EFFECTS     Identifier  Characterize

-  Energy dependence			X				X
-  Ellipticity of albedo				X
-  Tilt of albedo patch			X
-  Phase shift of albedo			X				X
-  Anisotropic Compton scattering?			X
-  Extended primary source?					X

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

## Exponential + Gaussian Fits vs. Energy

- Note the increasing exponential component with increasing energy.

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

## RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

## Albedo patch for primary source height h=16 

- at 6 different longitudes. The outermost contour
- is the albedo "horizon".

- The inner elliptical contours show the extent of the albedo
- flux at 25, 50, 75, and 90% of the total.  Here, the 90%
- contour is 120 wide in the y direction.

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

## Albedo patch for h=16, 8successively zoomed-in by factors 

- Albedo patch for h=16, 8successively zoomed-in by factors
- of 2.  Note that the flux contours scale the same way, The horizon does
- not scale linearly (width h1/2), so it appears progressively larger.

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

##  The half-flux contour scales with the primary source height

-   We find that the the widths of the 50 and 90% flux      contours are, respectively, ~3.5 and  ~9.9  times h.
-  The ellipticity  (height/width) goes as sec.
-  The x and y cross-sections of the albedo patch are of the form      X:     c/([h cos2+r2)3/2  ,        Y:     c/(h2+r2)3/2
-   The albedo ellipse tilts with the limb for non-equatorial flares.

**Properties of the Albedo Patch**

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

## Fourier transforms of the albedo patch, and

- determination of visibility and modulation profile.

- The 2-D Fourier amplitude for the off-center albedo patch
- has cross sections that are straight lines in log-linear plots.

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

## Variation of relative amplitude with azimuth

-   of albedo patch modulation profiles

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

##         PHASE SHIFTS OF ALBEDO PATCH?

-         PHASE SHIFTS OF ALBEDO PATCH?
-     Single-SC back-projection maps vs energy band
-                             2002 July 03

- Note that the SC-9 maps shift with energy. Is this
- a signature of albedo?

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

- LIMB

## Realistic modulation profile + flare data

- Realistic modulation profile + flare data

- Need 6-parameter fit: albedo amplitude, primary
- height, x-y position, amplitude and width.

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

- STEPS TOWARD A FULL CHARACTERIZATION

## Tasks for full characterization:

- Tasks for full characterization:
-   Constrain the albedo, including Longitude, Latitude
-   Constrain the primary source using Clean, Pixons,...
-   Fit the 6-parameter model to modulation profiles.
-   Obtain energy spectrum, primary source height.
-   Test against theoretical models.
-   Test against pixelized map data (phase shifts, flux,...)
-   Determine corrections to primary spectrum.
-   Assess X-ray/beam  directivity using inferred albedo    characteristics.

## THE END

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

## Tentative Conclusions

**RHESSI-NESSI WORKSHOP, JUNE 2003**

- http://hesperia.gsfc.nasa.gov/~schmahl/albedo

- Can beam anisotropies explain the diversity of the    of the albedo/primary flux ratios?

- Brown, 1972b

## Slide 23

## On-going and Future Work

- http://hesperia.gsfc.nasa.gov/~schmahl/albedo

- On-going and Future Work

-  **Energy dependence**
- Where is the spectral peak of the albedo patch?
-  **Center****-****to****-****limb effects**
- Shift of albedo patch centroid?
- Elliptical shape from profile?
- Do heights agree with other imaging methods?
-  **Beam vs thermal differences**
- impulsive *vs* main-phase?
- anisotropic bremmstrahlung effect on flux ratioof albedo patch and primary source?

## Collimated Beaming and/or Directivity?

**RHESSI-NESSI WORKSHOP, JUNE 2003**

- Either one of the two possibilities suggested
- by Smith et al. can account for the large albedo/primary
- flux ratio implied by some relative amplitude profiles.

## AZIMUTHAL MODULATION OF IDEAL PROFILES

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003

## IDEAL PROFILES FOR ALBEDO + 3” SOURCE

- RHESSI-NESSI WORKSHOP JUNE 4-6, 2003