In Figure XX, we compare the measured clumping factor in the two extreme models (\(\bar{Q} = 400\), 2000). The low clumping at the base, followed by a peaking and then slow decrease in structure is apparent, as seen in previous work (Owocki, Runacres, etc). Due to the large radial variations in clumping factor, we make conclusions about the mass-loss rate using two radial ranges which are thought to correspond to the major formation zones of \(H_{\alpha}\), Range A (1.05 – 1.5) and Range B (1.5 – 2 \(R_*\)), both of which fall into Puls 2006’s “Region 2”. (NOTE: How much \(H_{\alpha}\) emission do we expect outside of this range? personal communication Jon Sundqvist – not so much in the inner wind) Zack: Jon sent some plots a few weeks ago, showing how little is produced outside the range.

Weighting by \(\rho^2\) according to the steady state Sobolev solution, we compute the \(H_{\alpha}\) emission-weighted clumping factor in these two radial ranges. We plot the expected clumping factor in each range in Figure XX, with power law fits for each radial range. Table XX contains the power law parameters for each fit. For each different \(\bar{Q}\) value, we measure the clumping factor \[f_{cl} = \langle \rho^2 \rangle / \langle \rho \rangle^2.\] in each grid cell, over a time period of \(10^6\) seconds. In addition, we apply a \(3 \times 10^5\) second “settling time” before calculating statistics, to evolve away transients arising from the initial conditions.