[mesa-users] MESA profile binding_energy

[Josiah Schwab]

Hi All,

The following question was posed to me by Naveh Levanon:

> In the star profile there is an option to compute the binding
> energy. It is computed per cell as: binding_energy = v^2/2 - G*m/r + E
> + P/rho (energy per unit mass) Where E is the internal energy.  This
> is kinetic energy + gravitational energy + *enthalpy* rather than
> internal energy, and makes sense for the outermost cell, where the
> pressure from the star does work to unbind it.  However, this is
> computed for every cell - and the profile also provides an integral
> binding energy as simply the sum of binding_energy*dm per cell.  This
> would give a total binding energy that is larger than Ek + Egrav +
> Eint.  For example, if we take a relativistic white dwarf with gamma =
> 4/3, we get Egrav = -Eint so the star is marginally bound (no work is
> required to expand it). Including the additional P/rho term would
> result in a positive binding energy so the star is not bound at all!
> Why does the profile value integral_binding_energy take the P/rho term
> as well, for all cells down to center of the star, resulting in an
> enlarged total binding energy?

Perhaps it would be more clear to relabel what is now defined as
binding_energy as bernoulli_parameter and to define a column that is
kinetic energy + gravitational energy + internal energy as total_energy
and integral_total_energy.

Thoughts?

Best,
Josiah