Lower-ionosphere electron density and effective recombination coefficients from multi-instrument space observations and ground VLF measurements during solar flares

A new model to predict the electron density and effective recombination coefficient of the lower ionosphere under solar flare conditions is presented. This model relies on space-borne solar irradiance measurements in coincidence with ground recorded active transmissions of Very Low Frequency (VLF), (<30 kHz) signals. Use is made of the irradiance measured by broad-band radiometers onboard the satellites: GOES, SDO, and PROBA2. Measurements are made over succeeding and partly overlapping wavelength intervals of the instrument band-pass ranges altogether covering the range 0.1-20 nm. The aim is to determine the effectiveness of the particular instrument bandpass in producing changes in the ionization of the lower ionosphere (D-region) during solar X-ray flares. Ionization efficiency is evaluated using modelled Solar Spectral Irradiance for each flare separately and for each instrument as a function of its bandpass.The new model is based on coupling of the continuity equation with the Appleton relation and uses the concept of time delay - the time lag of the extreme VLF amplitude and phase behind the flare irradiance maximum. The solution of the continuity equation predicts the electron density time -height profile for 55-100 km altitude.An analysis of M to X class flares shows the flare-enhanced electron densities due to a particular ionizing wavelength domain are in good agreement for the case where irradiance is taken over the bandpass of (1) either GOES (0.1-0.8 nm) or SDO/ESP (0.1-7 nm) for up to 90 km (2) either SDO/ESP or PROBA2/LYRA (1-2 +6-20 nm) at heights above 90 km. The results agree within 22% for heights up to 90 km, and differ by at most a factor of 2 for heights above 90 km. Remarkable agreement is shown between measured and evaluated time delay; discrepancies are generally less than 8%. The effective recombination coefficient is deduced from the model itself and is found to be consistent with other independent estimates.