The Inversion of Electron Time-of-Flight Distances from Hard X-Ray Time Delay Measurements

Details The Inversion of Electron Time-of-Flight Distances from Hard X-Ray Time Delay Measurements The Inversion of Electron Time-of-Flight Distances from Hard X-Ray Time Delay Measurements

Jun 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996apj...464..974a&link_type=abstract

Astrophysical Journal v.464, p.974

Astronomy and Astrophysics

Astronomy

21

Radiation Mechanisms: Nonthermal, Radiative Transfer, Sun: Flares, Sun: X-Rays, Gamma Rays

Scientific paper

The electron time-of-flight distance 1 between the acceleration site and the chromosphere can be measured during solar flares from energy-dependent hard X-ray (HXR) time delays τ(ɛ), based on the applicability of the thick-target model. The determination of the path length l represents an inversion problem because the time-dependent electron injection spectrum at the acceleration site, N(E, t, x = 0), is retarded by the propagation time tprop(E)=l/v(E) at the thick-target site, i.e., N(E, t, x = l) = N[E, t - tprop(E), x - 0], and has to be convolved with the bremsstrahlung cross section σ(ɛ, E) and the instrumental detector response function Ri(ɛ) to reproduce the observed HXR time profiles I(Ei, t) (in different detector channels i), from which the time delay differences τ(ɛi) - τ(ɛi) can be measured.
In this study, we solve this inversion problem by numerical forward integration of time-dependent electron injection spectra N(E, t) with Gaussian pulse shapes to obtain the convolved time-dependent HXR spectra I(ɛ, t), using specific detector response functions from the Burst and Transient Source Experiment/Compton Gamma Ray Observatory and the Hard X-Ray Burst Spectrometer/Solar Maximum Mission. We find that the timing of HXR pulses can be accurately represented with the (monoenergetic) photon energy ɛi that corresponds to the median of the channel count spectra Ci(ɛ) = I(ɛ)Ri(ɛ). We compute numerical conversion factors qE(ɛ, y, E0) that permit the conversion of the timing of photon energies ɛi(t) (for a power-law spectrum with slope γ and upper cutoff energy E0) into electron energies Ei(t) = qEɛi(t), from which kinematic parameters can be fitted to determine the electron time-of-flight path length l. We test the inversion procedure with numeric simulations and demonstrate that the inversion is accurate within σl/l ≤ 1% for noise-free data. This inversion procedure is applied to the Masuda flare (in this volume) to localize the electron acceleration region.

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