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Solar Hard X-ray Albedo

In the early days (1972) of solar hard X-ray flare observations, <a href="http://adsabs.harvard.edu/abs/1972ApJ...171..377T">Fred Tomblin</a> published theoretical arguments that the hard X-ray spectrum of solar flares in the 5-40 keV range must have an albedo component due to Compton back-scattering in the photosphere of those primary bremsstrahlung photons that are emitted downward. In a more complete analysis, <a href="http://adsabs.harvard.edu/abs/1978ApJ...219..705B"> Taeil Bai & Reuven Ramaty</a> showed that this albedo component would be polarized and its size must depend on the height of the primary source.

The "reflected" photons form what is called an albedo patch. For sufficiently high primary source altitudes, the albedo would be much larger in extent than the primary source, with a size scale that increases with source height. (See Fig. 1 below.) Furthermore, the albedo source would be displaced toward disk center by a distance h sin θ, where θ is the heliocentric angle.

Why albedo has not been imaged before

A significant fraction (possibly as high as 40%) of the X-ray flux from solar flares comes from X-rays that propagate back to the solar surface from coronal sources and "reflect" off the photosphere. This component of flares is called the albedo, and it is remarkably difficult to observe because it is very diffuse with an intensity that is one or two orders of magnitude smaller than the primary flare sources themselves. Its importance for flare physics is that it both distorts the spectral interpretation of X-ray emission and offers a potentially powerful diagnostic of electrons accelerated in solar flares. Our study uses the unique capabilities of the Ramaty High Energy Spectroscopic Imager (RHESSI) to isolate this albedo component, determine its properties such as size, shape and centroid location as a function of energy. We have focused on single-component flares in the 12-30 keV range that appear a within 45° of disk center. Using standard techniques, we have obtained the X-ray visibilities (<a href="http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/RHESSI_Visibilities">RHESSI Nugget # 39</a>) of a number of such flares and applied Forward-Fitting methods to determine the parameters of the primary component (position, flux, and size) and the albedo-related parameters (primary source height and albedo flux).

Sensitivity to source size

The modulation of RHESSI's count rates depends exquisitely on the grid pitch and the source size, a fundamental property of Fourier imaging. When the source FWHM is less than the subcollimator angular resolution, the modulation amplitude falls rapidly. This is illustrated below for three subcollimators with angular resolutions of 23, 69 and 217.

Previous attempts to infer albedo properties

• <a name="statistical"></a> Statistical center-to-limb variations
  <a href="http://arxiv.org/abs/astro-ph/0701871"> Jana Kasparova, Eduard Kontar & John Brown</a> demonstrated a center-to-limb variation of photon spectral indices in the 15-20 keV energy range and a weaker dependency in the 20-50 keV range, which is consistent with photospheric albedo as the cause. <a href="http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=74"> Nugget #74</a> illustrates albedo's anisotropy effect on the spectrum.

• <a name="spectroscopy"></a> Spectroscopy of individual flares
  <a href="http://www.iop.org/EJ/article/1538-4357/653/2/L149/21151.html"> Eduard Kontar and John Brown</a> analyzed the 2002/08/ 20 and 2005/ 01/17 flares in terms of double-power-law fits. To fit the HXR spectrum with a low-energy cutoff E_c and ignoring albedo requires an unusually high value of E_c< ~ 30 ± 2 keV. This produces a clear gap in the range E = 15 to 30 keV, which is likely to be unphysical and suggests that albedo is important. A related <a href="http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=42"> nugget #42</a> shows how the albedo "mirrors" the primary flux. <p>
• <a name="firstFourier"></a> Fourier methods
  The above statistical and spectral methods give no information about the spatial characteristics of albedo patches. The only hope for getting such spatial information is by using the Fourier amplitudes and phases determined by RHESSI. In 2002, <a href="http://adsabs.harvard.edu/abs/2002SoPh..210..273S">the authors</a> made a first step towards this by assuming circular symmetry. It is now possible to go beyond this, at least for some flares. </ul>

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