A. K. Tolbert

A TEST OF THICK-TARGET NONUNIFORM IONIZATION AS AN EXPLANATION FOR BREAKS IN SOLAR FLARE HARD X-RAY SPECTRA

Solar nonthermal hard X-ray (HXR) flare spectra often cannot be fitted by a single power law, but rather require a downward break in the photon spectrum. A possible explanation for this spectral break is nonuniform ionization in the emission region. We have developed a computer code to calculate the photon spectrum from electrons with a power-law distribution injected into a thick target in which the ionization decreases linearly from 100% to zero. We use the bremsstrahlung cross section from Haug, which closely approximates the full relativistic Bethe-Heitler cross section, and compare photon spectra computed from this model with those obtained by Kontar et al., who used a step-function ionization model and the Kramers approximation to the cross section. We find that for HXR spectra from a target with nonuniform ionization, the difference (Δγ) between the power-law indexes above and below the break has an upper limit between ~0.2 and 0.7 that depends on the power-law index δ of the injected electron distribution. A broken power-law spectrum with a higher value of Δγ cannot result from nonuniform ionization alone. The model is applied to spectra obtained around the peak times of 20 flares observed by the Ramaty High-Energy Solar Spectroscopic Imager from 2002 to 2004 to determine whether thick-target nonuniform ionization can explain the measured spectral breaks. A Monte Carlo method is used to determine the uncertainties of the best-fit parameters, especially on Δγ. We find that 15 of the 20 flare spectra require a downward spectral break and that at least six of these could not be explained by nonuniform ionization alone because they had values of Δγ with less than a 2.5% probability of being consistent with the computed upper limits from the model. The remaining nine flare spectra, based on this criterion, are consistent with the nonuniform ionization model.

Estimating the Properties of Hard X-Ray Solar Flares by Constraining Model Parameters

We wish to better constrain the properties of solar flares by exploring how parameterized models of solar flares interact with uncertainty estimation methods. We compare four different methods of calculating uncertainty estimates in fitting parameterized models to Ramaty High Energy Solar Spectroscopic Imager X-ray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scale-size of the minimum in a hypersurface formed by the weighted sum of the squares of the differences between the model fit and the data as a function of the fit parameters, and are implemented as commonly practiced. The fourth method is also based on the difference between the data and the model, but instead uses Bayesian data analysis and Markov chain Monte Carlo (MCMC) techniques to calculate an uncertainty estimate. Two flare spectra are modeled: one from the Geostationary Operational Environmental Satellite X1.3 class flare of 2005 January 19, and the other from the X4.8 flare of 2002 July 23. We find that the four methods give approximately the same uncertainty estimates for the 2005 January 19 spectral fit parameters, but lead to very different uncertainty estimates for the 2002 July 23 spectral fit. This is because each method implements different analyses of the hypersurface, yielding method-dependent results that can differ greatly depending on the shape of the hypersurface. The hypersurface arising from the 2005 January 19 analysis is consistent with a normal distribution; therefore, the assumptions behind the three non-Bayesian uncertainty estimation methods are satisfied and similar estimates are found. The 2002 July 23 analysis shows that the hypersurface is not consistent with a normal distribution, indicating that the assumptions behind the three non-Bayesian uncertainty estimation methods are not satisfied, leading to differing estimates of the uncertainty. We find that the shape of the hypersurface is crucial in understanding the output from each uncertainty estimation technique, and that a crucial factor determining the shape of hypersurface is the location of the low-energy cutoff relative to energies where the thermal emission dominates. The Bayesian/MCMC approach also allows us to provide detailed information on probable values of the low-energy cutoff, Ec , a crucial parameter in defining the energy content of the flare-accelerated electrons. We show that for the 2002 July 23 flare data, there is a 95% probability that Ec lies below approximately 40?keV, and a 68% probability that it lies in the range 7-36?keV. Further, the low-energy cutoff is more likely to be in the range 25-35?keV than in any other 10?keV wide energy range. The low-energy cutoff for the 2005 January 19 flare is more tightly constrained to 107 ? 4?keV with 68% probability. Using the Bayesian/MCMC approach, we also estimate for the first time probability density functions for the total number of flare-accelerated electrons and the energy they carry for each flare studied. For the 2002 July 23 event, these probability density functions are asymmetric with long tails orders of magnitude higher than the most probable value, caused by the poorly constrained value of the low-energy cutoff. The most probable electron power is estimated at 1028.1 erg s?1, with a 68% credible interval estimated at 1028.1-1029.0 erg s?1, and a 95% credible interval estimated at 1028.0-1030.2 erg s?1. For the 2005 January 19 flare spectrum, the probability density functions for the total number of flare-accelerated electrons and their energy are much more symmetric and narrow: the most probable electron power is estimated at 1027.66 ? 0.01 erg s?1 (68% credible intervals). However, in this case the uncertainty due to systematic sources of error is estimated to dominate the uncertainty due to statistical sources of error.

Instrumental oscillations in RHESSI count rates during solar flares

Aims. We seek to illustrate the analysis problems posed by RHESSI spacecraft motion by studying persistent instrumental oscillations found in the lightcurves measured by RHESSIs X-ray detectors in the 6-12 keV and 12-25 keV energy range during the decay phase of the flares of 2004 November 4 and 6. Methods. The various motions of the RHESSI spacecraft which may contribute to the manifestation of oscillations are studied. The response of each detector in turn is also investigated. Results. We find that on 2004 November 6 the observed oscillations correspond to the nutation period of the RHESSI instrument. These oscillations are of greatest amplitude for detector 5, while in the lightcurves of many other detectors the oscillations are small or undetectable. We also find that the variation in detector pointing is much larger during this flare than the counterexample of 2004 November 4. Conclusions. Sufficiently large nutation motions of the RHESSI spacecraft lead to clearly observable oscillations in count rates, posing a significant hazard for data analysis. This issue is particularly problematic for detector 5 due to its design characteristics. Dynamic correction of the RHESSI counts, accounting for the livetime, data gaps, and the transmission of the bi-grid collimator of each detector, is required to overcome this issue. These corrections should be applied to all future oscillation studies.