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I am tring to simulate the evolution of a star. As we know, opacity plays an important role and has many forms like: free-free, bound-free, bound-bound, electron scatter. But I am confused about their approximated formula and the temperature range which they can be applied to. If I can't limit the temperature they applied to and if I don't use the accurate approximated formula of them, the simulation will be inaccurate.

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    $\begingroup$ What you need to do depends on what you want to do. What range of temperatures and metallicities do you want to consider? That will tell you what you need to do. $\endgroup$ Dec 12, 2021 at 11:54
  • $\begingroup$ I use the metallicities of Sun. And the initial(center) temperature is about 1e7~1e8. $\endgroup$ Dec 12, 2021 at 12:33
  • $\begingroup$ What units is the temperature in? Surely that cannot be Kelvin... $\endgroup$ Dec 12, 2021 at 12:41
  • $\begingroup$ Why ont Kelvin? $\endgroup$ Dec 12, 2021 at 13:05
  • $\begingroup$ Oh sorry, you said that's the temperature at the center of the core. What have you tried so far? What mass range are you considering? What formulae are you looking at? PLease include as many details as possible in your question. AS it currently is, your question is kinda vague. $\endgroup$ Dec 12, 2021 at 13:56

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There is no "formula" for opacity if you are constructing a numerical model of a star. The opacity is wavelength-dependent and also depends on composition, temperature and density - each of which are a function of radial distance from the centre of the star.

What stellar modellers do is use "opacity tables" which give numerical values for weighted mean opacities as a function of composition, temperature and density.

For analytic calculations, the approximation is often made that the mean opacity can be roughly represented by the sum of: Kramer's opacity $$ \bar{\kappa} = A_0 \rho T^{-7/2}\ ,$$ where $\rho$ is density, $T$ is temperture and $A_0$ is a composition-dependent constant; and Thomson scattering from free electrons, which just depends on the number of free electrons per nucleus in the gas and therefore on the mass-fraction of hydrogen.

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