Help:For Authors

From RHESSI Wiki

Revision as of 22:21, 12 January 2010

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

• 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.
• 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.

• 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>

  Full Exploitation of Fourier methods

  We have found 9 flares with reliable enough amplitudes and phases to compare models of simple sources with albedo patches. The flares all lie within 45° of sun center, where albedo is expected to be strong. These flares form a small subset of RHESSI events for which MEM maps show only single, compact primary components in the range 12 to 30 keV.

  Forward Fitting

  Given the RHESSI amplitudes and phases for a flare, one may compare the observed values with those computed from a model. This process is called "Forward Fitting". At the present time, this method is reliable for computing albedo patch parameters only for single elliptical primary sources because the number of parameters (8 in this case) must be much smaller than the number of amplitudes. (For a discussion of Forward Fitting of amplitudes and phases, see <a href="http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=35">RHESSI Nugget #35</a>.)

  Amplitude model of a primary source both with and without albedo</h2> Modeling the albedo patch in addition to the primary source makes it possible to infer the height of the primary source, and the fraction of the total flux emitted by the reflected photons. Here we show an example of a flare where the primary source amplitudes (blue crosses) are fit by a 6-parameter model (flux, position, ellipse FWHMs and orientation) with an albedo patch fit by 2 parameters (primary height and albedo fraction). For comparison we show a fit made for a primary source without albedo. <h3> Model Albedo Visibility Back-Projection

  In those cases where the primary source and albedo patch are both well represented by a model, it is possible to display both sources using back projection. We have done this for a number of flares, with one example "bpmap" here (for the flare and band of Fig. 3.)

  We have visualized the albedo patch by back-projecting our Forward-Fit model of the best-fit albedo parameters. If the back-scattering process is isotropic (as we assume in the Forward-fit model), the albedo patch is displaced toward sun center from the projected location of the primary source, such that it is vertically below the primary source.

  Amplitude Fits

  Top row: Amplitudes vs subcollimator (SC) and grid position angle (PA) for flare models including back-scattered emission (solid) and without (dashed). The axes in these figures are the same as for Fig. 3. The black dashed curve is the difference between the models with and without albedo. Much of the errors in fitting are due to inter-detector calibration errors. Although these can be compensated for, they introduce uncertainties in the inferred albedo fraction and the source height.

  Bottom row: Back-projection maps for 15-20 and 20-30 keV for the flare above. As in Fig. 4, the arrows point from map center to Sun center. In each case, the model albedo patch was back-projected from a Fourier plane with uniformly spaced roll bins.

  Conclusions

  Using Fourier amplitudes and phases for nine simple (single primary, slowly varying) flares we have found evidence for X-rays back- scattered from the photosphere (the albedo patch). Note that these results are only for the so-called "thermal phase" when a single component dominates the emission.

  We have visualized the albedo patch by back-projecting our Forward-Fit model of the best-fit albedo parameters. If the back-scattering process is isotropic (as we assume in the Forward-fit model), the albedo patch is displaced toward sun center from the projected location of the primary source, such that it is vertically below the primary source.

  We make several inferences from our results for 9 flares:

  • The model fits of the amplitudes and phases to the observations are significantly better when back-scattered (albedo) emission is included than if it is not. (Compare the dashed and solid red curves in Figurs 3 & 5.)
  • The albedo fraction increases with energy in the range 12-30 keV, in qualitative agreement with theory (Bai and Ramaty 1978).
  • We have inferred primary heights ranging from about 10 to 30 Mm, in agreement with the range seen in limb flare observations.
  • In any given flare, the heights of the primary source determined by Forward Fitting do not significantly change with energy, consistent with a thermal interpretation, and also consistent with the single-component nature of our flares.
  • Relative detector-to-detector responses affect these results, and improved calibration would improve our albedo measurements significantly.
  • Extension of these results to some 2-component ("footpoint") flares may be possible, and this would have great significance for spectral work.

  Acknowledgements

  The RHESSI software team has given invaluable help in making visibility software available to the community. Without their continued support, this research would have been impossible.

  Biographical notes: Ed Schmahl is a retired University of Maryland and GSFC scientist, currently employed at NWRA/CoRA and Gordon Hurford is a senior RHESSI team member based at UC Berkeley.

  Adding Figures

  In order to add a figure it is first necessary to upload the image to the wiki. This can be done by using the link on the left titled "Upload File". Please use a descriptive name for the file and add a description of its contents. Once uploaded the file can be added to articles using the following command

  [[Image:POF.jpg|200px|thumb|right|'''Figure 1''': This is the figure caption.]]
  

  whose results can be seen to the right. Most of these parameters should be self explanatory. The "thumb" parameters tells the wiki that this is a figure and therefore displays the figure caption. The float parameters (in this case set to "right") tells the wiki where to float the image. Possibilities include "left", "center", or "right".

  

  

  Figure 1: This is the figure caption. Note that the figure has properlyy appeared on the right, but that you can't really control how the text will wrap around it - that depends on the browser.

  If you'd like to experiment with more advanced methods read this article on Wikipedia's website.

  Style and content

  We try to write the Nuggets so that a technically literate reader won't be baffled. That means that the text should appear in plain English, and that jargon is a no-no. Many scientists don't realize they are writing gibberish so please be careful about this. On the plus side, you can freely use cgs units if you wish. Also please be aware that many of the audience are not native English speakers, so phrases like "X must have been a gutsy operator to have diagonalized those macrospicules" would not do so well. Writing as though for a newspaper, rather than as for a boring archival journal, would be best - there is no need really to have complete literature

  citation, since those really knowledgeable about the field will certainly know where to go (ADS).