[Mesa-users] A question about ionization energy

[Evan Bauer]

Hi Natsuko,

This is a good question, but I'm afraid there's not an easy answer that covers the general case for extracting ionization energy from the EOS under arbitrary conditions. The thermal energy being 3/2 P/rho is valid when the EOS is nearly ideal gas, but depending on your star, there may be regions (especially in the interior) where this is not a good approximation.

The example in section 8.4 of Paxton et al (2018) was specifically constructed using a stellar profile for which ideal gas is a good approximation to illustrate its point clearly, but it won't work out quite so nicely for all types of stars. Even there, in figure 55 you can see some deviation from the ideal gas solution after the model evolves for a while.

As far as I'm aware, the only way to extract the full information about ionization energy from the EOS is by running the code in $MESA_DIR/eos that was used to construct the EOS tables. Once the EOS is tabulated, the information about ionization energy is buried in the "internal energy" quantity reported by the EOS, and may not be possible to disentangle from other terms impacting the internal energy.

Cheers,
Evan


> On Sep 13, 2023, at 9:28 PM, Yamaguchi, Natsuko via Mesa-users <mesa-users at lists.mesastar.org> wrote:
> 
> Hello, 
> 
> I am using MESA to trace internal energy in stars, which by default is defined as the thermal energy + the ionization energy (Paxton et al. 2018). 
> 
> I would like to trace the two components separately - I understand the thermal energy density is simply 3/2 P/rho which can be integrated over mass to get thermal energy. The ionization energy is then simply this thermal energy subtracted from the total internal energy. 
> 
> But out of curiosity, how can I trace the ionization energy directly? I'm having a bit of trouble getting consistent values with the above. 
> 
> Thank you for the help,
> 
> Natsuko Yamaguchi
> 
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