Accuracy, Uncertainties, and Delay Distribution of Electron Time-of-Flight Measurements in Solar Flares

Details Accuracy, Uncertainties, and Delay Distribution of Electron Time-of-Flight Measurements in Solar Flares Accuracy, Uncertainties, and Delay Distribution of Electron Time-of-Flight Measurements in Solar Flares

Dec 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995apj...455..699a&link_type=abstract

Astrophysical Journal v.455, p.699

Astronomy and Astrophysics

Astronomy

20

Radiation Mechanisms: Nonthermal, Sun: Corona, Sun: Flares, Sun: Particle Emission, Sun: X-Rays, Gamma Rays, Particle Acceleration

Scientific paper

A systematic time lag of ≍20 ms between the 25-50 keV and 50-100 keV hard X-ray (HXR) emission has been recently discovered in solar flares. This was interpreted in terms of electron time-of-flight differences (Aschwanden, Schwartz, & Alt 1995c). Here we attempt to determine the accuracy and uncertainties of such energy-dependent time delay measurements using burst-trigger data from DISCSC/BATSE on the CGRO spacecraft, recorded with a time resolution of 64 ms. We evaluate the time delays by cross-correlating entire flare time profiles at different energies and evaluate the statistical uncertainty of a delay measurement with a Monte Carlo method, in which random noise is added to the raw data. We examine also uncertainties resulting from aliasing, incomplete sampling, and pulse pileup.
We measure the time delays τ = t25keV - t50keV in 622 flares, with a statistical uncertainty of u ≤ 32 ms in 29% of the events, or u < 64 ms in 65% of the events. The distribution f(τ) of the time delays from all flares can be characterized with three components: (1) a Gaussian peak at τ = 23.2 + 1.2 ms with a standard deviation of στ = 25.5 ms, (2) a power-law tail with a slope of - 2.0 for large positive delays (τ = 0.1-4 s), and (3) a power-law tail with a slope of - 1.3 for large negative delays ( |-τ| = 0.1-7.7 s). The percentages of flares in these three regimes are 15%, 69%, and 16%. Flares with short delays (|τ| ≤ 0.1 s) exhibit rapid fluctuations with subsecond pulses. Such rapid fluctuations are almost absent in flares with longer delays. We find also a systematic trend of softer spectra in flares with large positive delays.
We develop a simple physical model that combines electron time-of-flight differences in the thin-target and thick-target model. We are able to reproduce the observed time delay distribution in the range of |τ| ≲ 0.1 s, requiring a distribution of electron densities in the range of ne ≤ 3.0 × 1012 cm-3 and flare loop heights in the range of h ≤ 35,000 km. Large negative delays (τ ≲ -0.1 s) can be produced in low-density loops with efficient magnetic trapping. Large positive delays (τ ≳ 0.1 s) occur in flares with a strong thermal component due to the convolution of the injection profile with the heating and cooling function. This study demonstrates that energy-dependent HXR time delays can be used as a diagnostic and discriminator of flare models.

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