Center-to-Limb Variability of Hot Coronal EUV Emissions During Solar Flares

It is generally accepted that densities of quiet-Sun and active region plasma are sufficiently low to justify the optically thin approximation, and this is commonly used in the analysis of line emissions from plasma in the solar corona. However, the densities of solar flare loops are substantially higher, compromising the optically thin approximation. This study begins with a radiative transfer model that uses typical solar flare densities and geometries to show that hot coronal emission lines are not generally optically thin. Furthermore, the model demonstrates that the observed line intensity should exhibit center-to-limb variability (CTLV), with flares observed near the limb being dimmer than those occurring near disk center. The model predictions are validated with an analysis of over 200 flares observed by the EUV Variability Experiment (EVE) on the Solar Dynamics Observatory (SDO), which uses six lines, with peak formation temperatures between 8.9 and 15.8 MK, to show that limb flares are systematically dimmer than disk-center flares. The data are then used to show that the electron column density along the line of sight typically increases by \(1.76 \times 10^{19}~\mbox{cm}^{-2}\) for limb flares over the disk-center flare value. It is shown that the CTLV of hot coronal emissions reduces the amount of ionizing radiation propagating into the solar system, and it changes the relative intensities of lines and bands commonly used for spectral analysis.