by the fraction of observations with each slit. We now explain the modelling in detail.

![\[fig:lbg\_cumf\] Cumulative PDF of the ratio $V_r/\sigma$ for the seven galaxies of Pettini et al. and Erb et al. (table 2 in Paper I) shown as the solid stepped line. The dotted line shows the ratio of $V_r/V_{c\rm 7}$ for our model galaxies, including errors and selection criteria. The solid smooth line shows the same curve, stretched by the best fit value of $\alpha=\alpha(obs)$, to match our model to the data.](./images/PLOT_cumf){width="0.85\columnwidth"}

The galaxy rotation curves are assumed to reflect the halo mass profile; therefore the galaxies are modelled as massless stellar discs of exponential luminosity profile – the choice of scale radius, $R_0$, is discussed below. The distribution of galaxy circular velocity profiles is defined by the MMW halo circular velocity distribution, and the NFW mass profile, with concentration $c=4$. No information on the inclination angles and position angles of the major axes were available at the time the spectra were acquired; therefore, we assume random inclination angles (over $\cos(i)$), and random orientations relative to the slit. The 2D luminosity–tagged velocity maps are convolved with the seeing, and the resulting luminosity–weighted velocity maps are averaged 