Quantitative analysis of lower ionospheric response time delay associated to the solar flares

Abstract

The D-layer of the ionosphere doesn’t respond instantaneously to the incoming solar irradiation, rather, there’s a measurable amount of time delay (\(\Delta t\)) between the incoming solar X-ray flux (\(\phi (t)\)) during a solar flare and the respective change in the electron density profile (\(N_e(t)\)). The \(\Delta t\) depends on the peak of the incoming X-ray flux (\(\phi _{max}\)) during the flare. We solve the ‘electron continuity equation’ for the D-layer by numerical method for a selected set of 455 solar flares to obtain \(\Delta t\) over six suitably chosen latitudes of the mid-latitude regions of both hemispheres and analyse the \(\Delta t\)–\(\phi _{max}\) profile. To analyse the latitude dependence of the dispersed nature of \(\Delta t\)–\(\phi _{max}\) profile, we define and compute two parameters, namely, (i) the RMS value of the D-layer response time delay (\(\Delta t_{rms}\)) and (ii) the gradient of the slope (m) of the linear fitting on \(\Delta t\)–\(log_{10}(\phi _{max})\) profile over each of those chosen latitudes. Further, we compute the latitudinal variation of D-layer response time delay (\(\Delta _{lat}(\Delta t)\)) for selected pairs of chosen latitudes. To analyse the \(\Delta _{lat}(\Delta t)\)–\(\phi _{max}\) profile, we compute a third parameter, namely, the RMS value of latitudinal variation of D-layer response time delay (\(\Delta _{lat}(\Delta t)_{rms}\)). We do a comparative analysis of these parameters across the chosen set of latitudes. Finally, we conclude quantitatively with possible explanations about the systematic latitude dependence and variation of the dispersed nature of \(\Delta t\)–\(\phi _{max}\) profile.