The Velocity Differential Emission Measure (VDEM) as Diagnostic of Solar Atmospheric Response to Flare Heating

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During solar flares, the Sun emits a great deal of soft X-rays, produced by plasma heated to temperatures >10(7) K by energetic flare processes. Motions of this heated plasma are reflected in the Doppler-shift and width of spectral lines. X-ray spectra therefore provide information about the solar atmosphere's response to a tremendous energy input at the initiation of the flare. In this dissertation, I extract the velocity information embedded in soft X-ray spectral lines to recover the velocity differential emission measure (VDEM), a new diagnostic concept which I define and develop in this text. VDEM serves as a direct measure of the amount of emission generated by a volume V of plasma moving with a specified line-of-sight velocity v: $VDEM = n_e(2) G(T) {dV/ dv}, where n_e is the electron number density and G(T) is the emissivity function for the ion responsible for the observed line emission. VDEM has units of power per unit velocity interval, or photons s^{-1} [cm s^{-1}]^{-1}$. This quantity can be deconvolved from observed soft X-ray spectra through the application of a linear regularization inversion technique. Spectra from a large sample of disk-center flares observed by the Yohkoh BCS were inverted and time histories developed to characterize the evolution of mass motions during flares. The plasma's line-of-sight velocity distribution represented by VDEM is used in conjunction with soft X-ray images and hard X-ray data observed by two other Yohkoh instruments to improve our understanding of plasma flows and the nature of heating in solar flares. Specifically, combining VDEM information with SXT images permits ambiguities between actual Doppler motion and apparent motion to be resolved. Furthermore, the correlation of hard X-ray flux with physical quantities computed from VDEM, such as total emitting mass and momentum, permits a test of impulsive heating mechanisms, such as the thick-target electron beam model.

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