Paper I. Below, we compare the $\sigma$ distribution for the LBGs against the predicted distribution of $V_{c7}$ for the massive–halo model to determine $\alpha(req)$. Secondly we reanalyse the seven measured rotation velocities and their associated values of $\sigma$, modelling the observational effects and selection cuts, as detailed below, to measure $\alpha(obs)$ – i.e. the value of $\alpha$ that gives the best fit to the distribution of $V_r/\sigma$ for the seven galaxies. We then compute the probability of observing the seven values of $V_r/\sigma$ assuming $\alpha$=$\alpha(req)$ – i.e. the probability that the massive–halo model fits the data.

At this point it is worth repeating, as emphasised in Paper I, that we make no assumption about the cause of the line broadening i.e. the relative contribution of pressure and rotational support to the velocity width. Our analysis is merely aimed at testing whether the observed seven values of the ratio $V_r/\sigma$ are large enough to reconcile the $\sigma$ distribution for LBGs with the massive–halo model.

Determining [$\alpha(req)$]{}
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![\[fig:lbg\_mmwdistribution\]The cumulative PDF of the line velocity widths (Paper I, table 1) for LBGs compared with the distribution of $V_{c \rm 7}$ predicted by the massive–halo model. A value $\alpha(req)=2.64$ is required to reconcile 