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. The figure shows the radially-varying clumping factor for six different values of \(\bar{Q}\): 2000, 1700, 1300, 1000, 700, and 400 (todo: put legend on plot), as well as the velocity dispersion for each of these simulations (what do we make of the velocity dispersion?).

As in Sundqvist 2013, we find a rapid climb from low to peak clumping occuring at several stellar radii from the stellar surface, and then a relatively stable clumping factor in the outer wind. (some discussion of convergence at far radii?). (maybe some discussion of the effect logarithmic grid spacing?)

Following Puls 2006, we apply two radial ranges which are the primary regions of H-\(\alpha\) emission. We choose (FIRST RADIAL RANGE) and (SECOND ONE), and over these two we observe substantial variation of \(f_{cl}\) vs. the metal content, which we vary through \(\bar{Q}\).