A technique for interpretation of auroral bremsstrahlung X-ray spectra

The precipitating kiloelectronvolt electrons in the auroral zone that produce enhanced E-region ionization also produce bremsstrahlung X-rays. The spectral distribution of the emitted X-rays contains information from which the energy spectrum of the precipitating electrons may be inferred. Modeling of the interaction of auroral electrons with the atmosphere shows that the flux F of vertically-emitted X-rays as a function of energy K is given approximately by F(K) = g 1(K) ∫ K ∞ (E − K)J(E) dE where J( E) is the differential flux of electrons in the energy range E − E + dE and g 1( K) is a modified X-ray production function. With this functional form for the production function the quantity F(K) g 1(K) is an exponential if the electron distribution is exponential. Thus, by dividing the observed X-ray fluxes at energy K by g 1( K) and fitting the result to an exponential function, the average energy and energy flux of the electron distribution can be determined directly. The technique is especially useful for determining ionospheric properties that depend on the integral of the electron fluxes, for example, the total energy flux, the E-region peak density and the height-integrated electrical conductances. The best-fit exponential electron spectrum yields values for these parameters that are very nearly the same as the values computed from the actual spectrum, even though the actual spectrum may deviate substantially from an exponential. Accurate knowledge of the function g 1 ( K) is important in applying the technique to observations. For X-ray fluxes emitted at an escape angle of 180° from the nadir direction and assuming an isotroplc distribution of incident electrons g 1( K) is approximately equal to 1.96 × 10 −5 K −1.9 when energies are expressed in kiloelectronvolts. The values derived here for g 1( K) agree well with those derived from simultaneous measurements of electron fluxes and resulting X-ray bremsstrahlung emission.