Albedo and the modification of RHESSI results

From RHESSI Wiki

The albedo effect and our new simulations

Hard X-ray (HXR) photons produced by bremsstrahlung interactions in the solar chromosphere are not all going to be conveniently directed towards RHESSI. Some of the photons may first scatter in the denser photospheric layers before emerging. These are known as the albedo photons (Nugget #119,Nugget #42) and when viewed alongside directly emitted photons they can obscure the true properties of the HXR source in certain energy ranges, causing an increase in intensity and source size and producing a change in the position of the HXR source.

Albedo or the Compton scattering of X-rays is a well-studied phenomenon but the largest-to-date study was produced by Bai and Ramaty in 1978 [1]. Using Monte Carlo simulations, Bai and Ramaty re-created the process of hard X-rays scattering in the solar photosphere. Their simulations concluded that anisotropic HXR sources were generally dominated by their albedo photons, with the albedo component producing changes to the measured spectrum, intensity and polarisation but Bai and Ramaty did not actually measure HXR source position and size modifications due to the albedo effect.

RHESSI’s imaging capabilities and the use of visibility forward fitting [2] can reliably measure properties such as source position and size using moments of the X-ray distribution. The zeroth moment is just the total X-ray flux, while the first (mean) and second (variance) moments provide us with the source (x,y) centroid position and size (FWHM) respectively. Measurements such as these have fuelled renewed attention in the importance of the albedo component and our new simulations have focused on finding actual source size increases and shifts in position due to the albedo photons.

Results from the simulations

Our simulations [3] examined how the albedo photons altered the properties of the HXR source, most importantly its size (FWHM) and position (measured using the 1st and 2nd moments of the distribution – as with RHESSI visibility forward fitting). These changes were inspected for different positions (heliocentric angles) on the solar disk and for photons energies between 3 and 300 keV, typical observational HXR energy ranges for RHESSI. The results from all the simulations showed a general trend for both the measured source sizes and the shifts from the true source position. Generally the largest source increases due to albedo are observed nearer the solar centre (with limb sources least affected by the albedo photons) or at photon energies between 20-50 keV. The largest shifts in source position seem to occur again at energies between 20-50 keV and at mid-heliocentric angles with the measured position nearing its true position both at the solar centre and near the solar limb. For a modelled source of 5”, figure 1 depicts the increase in FWHM and the shift in position due to the albedo component. The red ellipse is the combined source that would be observed by an instrument such as RHESSI, while the black and blue ellipses represent the true HXR source and the scattered albedo component respectively. Shifts for an isotropic 5’’ source can be as large as 0.4’’ at peak heliocentric angles. Taking isotropic shifts as a lower limit, we would expect anisotropic sources to generally show an even greater shift from the true source position.

Figure 1: Click here to view the animation. The FWHM and (x,y) centroid of an observed source will change with position on the solar disk from the centre to the limb. Both the graphs and the red ellipse show the size and position of an observed source that is a combination of the true and albedo sources, both shown by the black and blue ellipses on the disk respectively

HXR sources with varying photon spectral indices, source sizes and anisotropies were also input into our simulations.

Source spectral index: The lower the spectral index of the photon distribution, the greater the source size increase and position shift over all disk positions and photon energies, compared with similar HXR sources with larger spectral indices. In figure 1, the original input photon distribution had a spectral index of 3.

Source size: We have observed that the smaller the true HXR source size, the greater the relative increase due to the albedo photons. An HXR point source may be observed as a source as large as FWHM=7’’ across when located near the solar centre or viewed at a peak energy range of 20-50 keV, whereas Figure 2 below shows that very large HXR sources show a much smaller relative increase due to the albedo photons, both in energy and location on the solar disk. The position shifts seem to be generally independent of source size if all other factors remain the same.

Figure 2:Observed FWHM for both the photon energy and location on the solar disk respectively. The true sources sizes are shown in the legend. Note the especially large increase for point-like HXR sources due to their albedo component.

Source anisotropy: The contribution from the albedo component depends greatly on the anisotropy of the HXR source. If the HXR source initially throws more photons into the photosphere than towards RHESSI then the albedo component can be very large compared to the true direct component. Large downward directivities from isotropic sources can produce shifts as large as 0.8.

Conclusions

Nearly all sources, including isotropic, are contaminated by albedo photons with even limb sources showing small changes in size and position. Our simulations are putting a strong case forward for the need for correction before size and position measurements are sought using RHESSI algorithms. Recent visibility forward fitting results have shown that RHESSI can produce (x,y) centroid positions with errors less than 0.5’’ but if the majority of the photons are narrowly directed towards the photosphere then we may see position shifts of 0.8’’ and some initial results using photon distributions simulated from a parent electron distribution have shown shifts may be greater than 1’’. Incorrect size and position measurements from RHESSI will ultimately lead to incorrect conclusions regarding the form and properties of the electron distribution. Separating, not removing the albedo component of the source is essential since it will also provide us with valuable information regarding the photons emitted towards the solar surface.

References

• [1] Backscatter, anisotropy and polarization of solar hard X-rays
• [2] The Sub-arcsecond Hard X-ray Structure of Loop Footpoints in a Solar Flare
• [3] Positions and sizes of X-ray solar flare sources