  It is generally accepted that densities of quiet sun and active region plasma
are sufficiently low to justify the optically thin approximation, and it is
commonly used in the analysis of line emissions from plasma in the solar
corona. However, 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.
Further, 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 EVE on SDO that uses
6 lines, with peak formation temperatures between 8.9 and 15.8 MK, to show 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 x 1019 cm-2 for limb flares over the disk-center flare value.
It is shown that CTLV of hot coronal emissions reduces the amount of ionizing
radiation propagating into the solar system, and changes the relative
intensities of lines and bands commonly used for spectral analysis.
