Subject:
anisotropic porosity
From:
Maurice Leutenegger <maurice@astro.columbia.edu>
Date:
Mon, 28 Aug 2006 12:01:58 -0400
To:
David Cohen <cohen@hven.astro.swarthmore.edu>, Stan Owocki <owocki@bartol.udel.edu>

Hi David and Stan,

I've begun to consider adding anisotropic porosity to my XSPEC code.

I've attached two plots. They compare t(p,z) for p = 2, -10<z<10 for a variety of models. The black line is  the smooth wind value, while the colored lines are various porous models. The only difference between the plots is that tpzlarge is scaled to be able to see the smooth wind model, while tpzsmall is scaled to be able to see the porous wind models. Note that I am plotting t(p,z) and not tau(p,z). I am using the definition t(p,z) = tau(p,z) / tau_*.


There are four porous models. All have (tau_*) *  h = 30.
The magenta line is the isotropic stretch model , which has h = h_infty * w(r). It also uses
kappa_eff / kappa = 1 / (1 + tau_c).
The red line is the approximation to the anisotropic stretch porosity model, as derived by Stan. Note that this uses kappa_eff / kappa = (1 - e^-tau_c) / tau_c, but this is then approximated to be a step function around z_1.
The green line is a numerical integration of the same thing, using the exact expression for the effective opacity.
The blue line is a numerical integration of the anisotropic stretch porosity model, but now assuming the
1 / (1 + tau_c) form of the bridging law. This is the most directly comparable to the magenta line.

Conclusions:
At least for this one set of conditions I chose to test the models, the choice of bridging law is about as significant as the choice of isotropic vs anisotropic porosity, although anisotropic porosity does still have a significant mu dependence.

Maurice
tpzlarge.eps.gz
	
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tpzsmall.eps.gz
	
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