1. Hard X-ray Albedo: A Spatial Perspective
Gordon Hurford
substituting for
Ed Schmahl
RHESSI Glasgow Workshop

2. Spatial Properties of Albedo Outline
Theory What do we expect
Interpretation - What can we learn
Observations - How can we measure it
Current status
Future work

6. Expected Spatial Properties (1)
Large size compared to primary source
Spatial profile:
Albedo size scales with primary source height
50% of flux is within ~3.5* h
90% of flux is within ~10 * h
Elongated parallel to limb
length / width = sec2()

7. Expected Spatial Properties (2)
Albedo patch is displaced away from limb
Low surface brightness
Albedo flux is independent of primary source height (except at limb)
Albedo flux ~1/4 to ~1/2 of primary source
Ratio depends on beaming parallel to LOS
Spectrally hard relative to primary source

8. What can we learn from albedo?
Is albedo more than just a nuisance ?
PRIMARY
Source height as a function of time and energy
Size of albedo patch is proportional to source height
3-D electron directivity as a function of time and energy
Albedo fraction directivity parallel to line of sight
Displacement of albedo location (relative to isotropic expectations)  directivity orthogonal to line of sight
SECONDARY
Isolation of albedo can (crudely) confirm calculation of albedo correction
Over-the-limb events provide cases where there is no albedo
Albedo fraction in over-the-limb events  source position along LOS

9. Measurement of Albedo Low surface brightness (<~1%)
Difficult / impossible to observe with focusing optics
Cannot be mapped by conventional RMC techniques
Cannot be seen in conventional displays
Albedo size scale >> primary source size scale
 Can be isolated using Fourier techniques (eg. RHESSSI)

11. How Are Amplitudes Measured?
Fit observed modulation profile directly
Assume circular sources
Statistical issues
Schmahl and Hurford 2002
Infer from single detector back projection maps
Requires circular sources
Schmahl and Hurford 2003
Calculate visibilities from stacked data
Handles elongated and multicomponent sources
Capability now available

14. Current Status
Profile Fitting and B.P. mapping techniques have been used to calculate amplitudes for circular sources
Dependence of amplitudes on spatial frequency has not been consistent with a compact source interpretation.
Results are consistent with an compact source + albedo interpretation
Initial indications are that the energy dependence of the extended component is consistent with an albedo interpretation.

15. Future Plans Calculate visibilities using new visibility software
Eases requirement of assuming circular symmetry
Determines visibility as a function of angle
For simple sources systematically evaluate
as a function of limb distance, time, energy:
Albedo fraction
Ellipticity and orientation of albedo component
Displacement of albedo component relative to compact source
Interpret in terms of electron source height and directivity
Make tools available
Extend analysis to multicomponent sources