Center to Limb Variation of Hard X-Ray Spectra from RHESSI J. McTiernan SSL/UCB

ABSTRACT: We use the RHESSI flare database to measure the center to limb variation of the hard X-ray spectral index in the 50 to 100 keV energy range and the 100 to 300 keV energy range. If Coulomb collisions are the dominant scattering mechanism for accelerated electrons in solar flares, then there should be some variation in the steepness of the spectrum, the spectral index, from the center of the sun to the solar limb. The issue is complicated by the presence of backscatter of the radiation and the large spread in observed spectral index with respect to the expected center to limb variation. Previous work has shown that such a variation exists at high energies (300 to 1000 keV), but not necessarily at lower energies. It is also true that direct comparisons of energy spectra using multiple instruments have never found any noticeable anisotropy in solar flare X-rays. This research is supported by NASA contract NAS

Motivation: If Coulomb collisions are the dominant loss/scattering mechanism for HXR electrons, and if the magnetic field in the emission region is vertical with respect to the sun’s surface, then flare spectra should be flatter at the limb (E.g., McTiernan & Petrosian Apj 359, 541). CTL (Center to Limb) variation has been detected for SMM/GRS flares > 300 keV (Vestrand, et al, 1987, Apj 322, 1010). Never at lower energies (e.g., Kane, et al, 1988, Apj 326, 1017, Li, 1994, Apj 421, 381).

Complicating Factors: If Photon Flux = Constant x E -m, a power law The spread in observed spectral index, m, is larger than any expected variation in spectral index across the disk: m(center) – m(limb) = -0.5 for 50 to 100 keV = -0.9 for 100 to 300 keV But the spread in observed spectral indices is large, from 2.0 to 7.0. This makes variation hard to observe. Also backscatter of the radiation, or albedo, may have the opposite effect on the observed spectral index (Bai & Ramaty, 1988 Apj 219, 705). This effect is not included here, but will be in the future.

Spectra: Two sets of RHESSI spectra, in the energy ranges 50 to 100 keV and 100 to 300 keV were used. Time intervals of 40 seconds at flare peak – No attenuator state changes, no data gaps, no particles allowed – this condition may shorten the intervals. Every flare with > 50 (or 100) keV emission in the RHESSI flare list was used. Flares which were mis- identified and flares with obviously bad background subtraction were discarded. Limb flares which may have been partially occulted were left in the sample. For keV, this left 115 flares, for keV, 28 flares.

Summary for keV: Plot of spectral index versus view angle, angle=0 is disk center, angle=90 is limb. No evidence of any CTL variation: The slope of the (pink) regression line is , or a CTL variation in spectral index of This is consistent with no variation at all. In fact this small variation is opposite to what is should be. This is possibly due to albedo effect. This can be tested.

Summary for keV CTL variation is observed: The slope of the regression line is , or a CTL variation of -0.7 in spectral index. This is close to what you might expect from thick-target theory. This is not a statistically significant result. The probability of an observed variation this large resulting from random chance from a sample with no inherent variation is 23%. More flares please? Relaxing some of the selection criteria (in particular, relaxing the restriction on particle flux and using off-peak spectra) results in 41 flares, which does not help much. The solution is to add old data.

Summary for Multi-instruments: Black = RHESSI, 28 flares. Pink = ICE (originally ISEE-3), 171 flares, observed from , fit above 100 keV. Green = PVO data, originally used to compare with ICE data, 39 flares. (It is interesting to note that when the PVO spectra are compared to the ICE spectra for the same flares, only 18 of 39 spectra have flatter spectra for larger angle.) All 3 instruments have similar variation. With all of these flares (238), the probability of this variation arising from random chance is 0.1%.

Conclusions: We have pushed the lower limit for observed center to limb variation down to 100 keV, from the 300 keV observed by SMM/GRS. For lower energy spectra, no variation is apparent.