[mesa-users] Thermal timescale

[Bill Paxton]

Try these in your profile_columns.list

thermal_time_to_surface
log_thermal_time_to_surface

It is given by this expression (in star/private/profile_getval.f90)

sum(s% dm(1:k)*s% cp(1:k)*s% T(1:k))/s% L(1)

i.e., the sum of dm*cp*T from surface inward divided by the surface luminosity.

-Bill



On Jul 26, 2015, at 12:44 PM, Rene Breton wrote:

> Hi,
> 
> I'm looking into calculating the thermal timescale in the envelope of a star and I was wondering how to go about it. The goal is basically to investigate possible thermal instabilities. As far as I know, MESA does not store any variable directly related to timescales pertaining to various shells of the star, either in the history file or in the profile.
> 
> I know that for the star as a whole, the Kelvin-Holmholtz timescale would be:
> t_{KH} = \Omega / (2L) \approx GM^2 / (2RL)
> 
> with \Omega the gravitational binding energy.
> 
> It is less clear to me how I would calculate it for, say, the envelope of a star (or a certain layer within it) in terms of whatever variables are available from MESA. Presumably the timescale would go like:
> t_{KH,s} = \Omega / (2L) = - \int_{R_in}^{R_out} G m(r) dm(r) / r / (2L)
> 
> i.e. the integral of the binding energy from R_in to R_out divided by 2L.
> 
> This integral could always be recast in terms of pressure I suppose but perhaps I'm just overcomplicating it.
> 
> Would anyone have a clue?
> 
> Thanks,
> 
> Rene
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