[Mesa-users] Question about GR corrections for SMS

[Josiah Schwab]

Hi Bill,


> once you provide numbers indictating showing whether or not we need
> pressure dependence, i’ll take on the task adding the new hook to mesa/star
> so you can do your experiments without needing to change the private code.
>

 Just catching up with this thread.

For supermassive stars, you do need to solve the TOV equation, as these
objects are getting near GR instability.  That point goes back to at least
Iben (1963) and Chandrasekhar (1964) I think.
http://articles.adsabs.harvard.edu/pdf/1963ApJ...138.1090I
http://articles.adsabs.harvard.edu/pdf/1964ApJ...140..417C

An OOM way to see that the TOV P term is important is to estimate the
interior pressure from newtonian hydrostatic equilibrium

P ~ GM/(4 pi R^4)

and then ask about

4 pi P r^3 / (m_r c^2)

Taking P above and r ~ R and m_r ~ M, you get ~ GM / (Rc^2).  Note at this
level, the other TOV term (P/rho c^2) is also the same order (take rho ~
M/R^3).

That's all pretty crude of course --- Nicholas could make plots showing
these quantities in a real model --- but roughly in the interior, the
"small" quantity that you know and love in the usual MESA GR corrections is
of the same order as the other corrections in TOV.

The exact same argument would apply in neutron star interiors, but since we
just do the envelopes, that OOM estimate for P is not an appropriate
estimate near the surface (and Psurf << Pinteror) and so we can
ignore those other corrections.

Josiah
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.mesastar.org/pipermail/mesa-users/attachments/20200729/bffd73b5/attachment.htm>