Intrinsic distribution of the line width, σ, in both observed and LSF-corrected forms. Blue diamonds and the blue line and shaded region replicate the distribution from Fig. 9, which is the intrinsic distribution of the observed line widths. This represents a convolution of the physical spread of the line emission with the wavelength-dependent LSF. The purple squares show the intrinsic distribution deconvolved from the LSF, as described in Sect. 4.5. While the observed σ distribution is well fit by a lognormal function, for the LSF-corrected distribution (shown with the solid purple line), this tends to produce a large tail at the high-σ end that is unrealistic for a procedure that reduces the values of σ. A smoothly broken power law function (dot-dash line), as used for the r_sH distribution, models the tail end of the distribution more successfully. The LSF deconvolution reduces the σ value of the peak of the distribution from 187 km/s to either 133 km/s (lognormal) or 157 km/s (power law).