A theoretical review of solar albedo and how

A theoretical review of solar albedo and how particle directivity influences the albedo Eduard Kontar Natasha Jeffrey and Marina Battaglia Department of Physics and Astronomy University of Glasgow, UK RHESSI workshop , August, 2010

Primary and Compton scattered flux Id Flaring region Iu Downward emitted Xray photons can be either a) Compton scattered X -rays into observer direction b) or c) Photoelectrically absorbed Observer Observed Flux = Direct + Scattered

Primary and Compton scattered flux For photons with energies below 10 ke. V, absorption of photons is the dominant process over scattering. Absorption is modelled using up-to-date solar photospheric abundances (Asplund et al. 2009) and absorption codes for H, He, C, N, O, Ne, Na, Mg, Al, Si, S, Cl, Ar, Ca, Cr, Fe and Ni (Balucinska. Church & Mc. Cammon, 1992). Above 10 ke. V, scattering of photons becomes the dominant interaction process and the absorption cross-section can be modelled using:

Albedo: basic physics Fe edge 7. 1 ke. V Mg Si S Ar Ca Cr Ni edge 8. 3 ke. V

Albedo: basic properties Albedo has two major effects: HXR spectrum The spatially integrated reflected flux (HXR spectrum) depends: -Spectrum of primary source -Anisotropy of primary source -Does not depend on the source height (h<<R_sun) -Does not depend on the source geometry HXR spatial distribution HXR brightness distribution depends: -Spectrum of primary source -Anisotropy of primary source -The primary source height - The source geometry (e. g. size)

Albedo: spectroscopy Observed flux Primary Reflected flux can be ~40 -45 % of the total flux even for an isotropic source!

Source sizes X-ray source size Primary source: h, source height a) Source (r) ~ exp(-r 2/(2 Size 2)) b) Photon spectrum is power-law Radial distance from the source centre How does X-ray albedo affect the source sizes?

Source sizes

Isotropic source of photons Isotropic distribution Total observed flux Primary Gaussian source Reflected flux

Source sizes “Pan-cake” distribution “Beamed” distribution Note that total Flux downwards = total Flux upwards!

Spatial properties Changes in source size and position due to the scattered albedo photons The positions and sizes of the combined (primary and the albedo) source in the x and y directions are found using the first and second moments of the intensity distribution, given respectively by: Mean Variance Where I(x, y) is the combined brightness distribution. The size of the source can then be measured using the Full Width Half Maximum (FWHM) given by:

changes with heliocentric angle Photon energy range = 20 -50 ke. V. POSITION SHIFT SIZE INCREASE So the albedo effect will cause even a primary point source to appear as an extended source with a maximum FWHM of ~ 7”.

Position and size changes with energy For a heliocentric angle of POSITION SHIFT . SIZE INCREASE Both the shift and the size increase over energy follow the general trend of the reflectivity and peak at 30 -40 ke. V.

Source sizes and Compton back-scattering

Source sizes and Compton back-scattering X-ray back-scattering need to be taken into account when X-ray source sizes are discussed X-ray back-scattering component is probably better seen for sources height > source size X-ray source sizes are sensitive to angular distribution of electrons (additional method to detect angular distribution of electrons? )