# Exploring the effects of varying *beta*

For the purposes of this exercise, we will fit the Fe XVII line at 15.014 over the wavelength range [14.87:15.13] and assume a terminal velocity of 2250 km/s - the *baseline* model. We will use only the MEG data and will *not* subtract any background (which makes this model fit very slightly different from the pure *baseline* case shown at the top of the main page (and many other places).

Here is the baseline model fit, shown on the background subtraction effects page.

We can use non-integer values of *beta* if we perform the optical depth integration numerically. So, parameter number 8 has to be set to 1, and then we can also set *beta*=0.8, for example. Below, we show this model, with a new normalization fit, but without any of the other parameters (taustar, *u*_{o}) adjusted to improve the fit. Note that C has increased by about 7; this is pretty significant. The profile looks different. But it's hardly surprising. The value of *beta* affects the optical depth through the density (via mass continuity), and it also affects the Doppler shift of the emission at each location in the wind.

[14.87:15.13]
v _{inf}=2250
β=0.8
powerlaw continuum, n=2; norm=1.91e-3
q=0
h_{inf}=0
taustar=1.98
u_{o}=0.657norm=5.33e-4
rejection probability = 41% (C=103.34; N=102) |

Now we find the best-fit model with *beta*=0.8, allowing taustar and *u*_{o} to be free parameters.

The differences in best-fit values and parameter ranges isn't all that small. Here's the reference fit (shown at the top of this page) with *beta*=1 again:

Here's how the confidence regions in taustar-*u*_{o} space compare:

So, the value of *beta* does make a difference, both on the derived value and confidence range of taustar and of *u*_{o}. Again, this isn't surprising. The Doppler shift of any volume element will depend on the velocity law. If we change this mapping by changing *beta* then there will be compensating changes in *u*_{o} and if we change the run of density with radius by changing *beta* then there will be compensating changes in taustar. And not only will the best-fit models change with *beta*, but as the plots immediately above show, the shapes and position of the confidence regions in parameter space will also change.

For ζ Pup, there are a range of *beta* values in the literature, from *beta*=0.8 to *beta*=1.15 (even just looking at papers by the Munich group). The more recent determinations (e.g. Repolust et al.) have *beta*=0.9, but still... there's some uncertainty. Using *beta*=1 for our fitting seems reasonable, but we should keep the sensitivity to the value used in mind.

Back to main page.

*last modified*: 25 April 2008