RHESSITiming Studies: Multithermal Delays

Abstract

We investigate the energy-dependent timing of thermal emission in solar flares using high-resolution spectra and demodulated time profiles from the RHESSI instrument. We model for the first time the spectral-temporal hard X-ray flux f(,t) in terms of a multitemperature plasma governed by thermal conduction cooling. In this quantitative model we characterize the multitemperature differential emission measure distribution (DEM) and nonthermal spectra with power-law functions. We fit this model to the spectra and energy-dependent time delays of a representative data set of 89 solar flares observed with RHESSI during 2002-2005. Eliminating weak flares, we find 65 events suitable for fitting and obtain in 44 events (68%) a satisfactory fit that is consistent with the theoretical model. The best-fit results yield a thermal-nonthermal crossover energy of th = 18.0 ± 3.4 keV, nonthermal spectral indices of γnth = 3.5 ± 1.1 (at ≈30-50 keV), thermal multispectral indices of γth = 6.9 ± 0.9 (at ≈10-20 keV), and thermal conduction cooling times of τc0 = 101.6±0.6 s at th = 1 keV (or T0 = 11.6 MK), which scale with temperature as τc(T) ∝ T-β with β = 2.7 ± 1.2, consistent with the theoretically expected scaling of τc(T) ∝ T-5/2 for thermal conduction cooling. The (empirical) Neupert effect is consistent with this theoretical model in the asymptotic limit of long cooling times. This study provides clear evidence that all analyzed flares are consistent with the model of a multitemperature plasma distribution and with thermal conduction as dominant cooling mechanism (at flare temperatures of T 10 MK). Our modeling of energy-dependent time delays provides an alternative method for separating multithermal from nonthermal spectral components based on information in the time domain, in contrast to previous spectral fitting methods.