Top left: line of sight ion velocity distribution f(v) plotted against the absolute value of velocity | v/v_th |, for a Maxwellian distribution and seven different kappa distributions using κ = 100,50,20,10,5,3,2, using Eq. (11). Top right: corresponding spectral lines produced from each of the ion velocity distributions in the left panel. We use the Fe XVI parameters of log ₁₀T = 6.4 ~ 2.5 MK, iron mass M = 56 × 1.673 × 10^-24 g, λ₀ = 262.9760 Å and set n = 1 cm^-3. The line profile curves all have the same value of σ_κ and v_th, but different values of κ. Bottom: (black) plotted against κ index. The width is displayed as a “Gaussian FWHM” for easy comparison with a Gaussian line profile. Each kappa line profile is fitted with a single Gaussian and the Gaussian widths are also plotted ( – red curve) for comparison. The actual line distribution variance σ² is also shown (displayed as ) and calculated using σ² = σ_κ/⁽1−3/2κ⁾ (light blue).