Mg XII 8.421 Angstroms

Models with anisotropic porosity

Note: Both MEG and HEG are being fit simultaneously

Same continuum fit as we used for the non-porous and isoporous models: n=2, best-fit norm=1.65e-3.

We use the "numerical", "anisotropic", and "rosseland" switches in windprofile. Previously, we'd also fit anisotropic porosity models that used the standard, exponential opacity bridging law (as opposed to Rosseland).

Mg XII 8.421: anisoporous ross MEG
Mg XII 8.421: anisoporous ross HEG
powerlaw continuum, n=2; norm=1.65e-3
hinf=0.00 +/- (0.00:0.16) and for 90%
      confidence, (0.00:0.48)

taustar=1.14   +/- (0.77:1.76)
uo=0.729   +/- (0.659:0.864)
norm=2.94e-5 +/- (2.72e-5:3.18e-5)
rejection probability = 12% (C=186.53; N=188)

Note that there's evidence for some of the same fit-robustness problems we saw with the isotropic porosity models (and the aniso-exponential models), in that the confidence limits on the other wind parameters are tighter than we believe is realistic (in some cases, they're tighter than in the non-porous case, which doesn't make sense as that's a subset of this model family). In any case, we list the formal limits from the steppar command here, but they might be somewhat bigger. The confidence limit determination on the terminal porosity length, hinf, is robust, however.

Here are the 68%, 90%, and 95% joint confidence limits on hinf and taustar based on fitting the MEG and HEG data together. The asterisk represents the best-fit model, shown as the red histograms on the above two plots.

Mg XII 8.421: joint hinf taustar constraints using MEG+HEG data

The constraints are much tighter than in the isoporous case. Models with anisotropic porosity just don't give the right profile shapes. Also, smaller values of hinf have larger effects when clumps are flattened. Note that this grid doesn't have great resolution, it's only 20 by 20, because the run-time for numerically integrating the anisotropic model is quite long. But if need be, we can calculate a finer grid.

Forcing a fit with taustar=4:

Mg XII 8.421: anisoporous MEG with taustar=4
Mg XII 8.421: anisoporous HEG with taustar=4
powerlaw continuum, n=2; norm=1.65e-3
hinf=1.08 +/- (0.57:1.98) and for 90%
      confidence, (0.41:3.25)

uo=0.772   +/- (0.693:0.891)
norm=3.06e-5 +/- (2.76e-5:3.26e-5)
rejection probability = 24% (C=194.21; N=188)

As the confidence limit contour plot, above, shows, this higher optical depth model is outside the 95% confidence range. In fact, it has ΔC~8, which implies that the non-porous model is preferred at the 99.7% level. And even so, very large terminal porosity lengths are required in order to accommodate taustar=4 (which is our estimate of the optical depth value implied by the literature mass-loss rate). Finally, note that this model fit cannot be rejected outright; the statement we can make is that the model with lower wind opacity and negligible porosity is preferred.


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last modified: 7 May 2008