[Mesa-users] different 'MLT_option'

[Jared Goldberg]

Hi Etienne,

I was just looking into this recently, too... A is different for Cox
compared to the other prescriptions.
Looking at the mlt_get_results.f90 here's my best summary of what's going
on.

Looks like Cox prescription does have an expression for Gamma = Grad -
Grad_e/(Grad_e - Grad_ad).
However, this expression does not depend on optical depth at all for Cox, but
it does for other prescriptions (ML1, ML2, Henyey, etc.).

Gamma = convective_velocity*A/(sqrt_x*alpha)
where I think x = 1/2 Q rho/P
This quantity A is where the prescriptions differ

*Cox: *
x = Q*Rho / (2*P). <<<< Note that this cancels out when going from A to
Gamma...
convective_conductivity = Cp*grav*Lambda*Lambda*Rho*(sqrt(x))
radiative_conductivity = 4*arad*c*T*T*T/3
A = convective_conductivity / radiative_conductivity !  unitless.

*Other MLT: *
A0 = sqrt(f1*P*Q*Rho)
A1 = 4*A0*Cp
A2 = alpha*omega*(1 + f4/(omega^2))
A_numerator = A1*A2
A_denominator = f3*ar*c*T^3
A = A_numerator/a_denominator. So this, plugged into Gamma, recovers the
expression in Ludwig/Kippenhahn.

Hope this helps!

~Jared


On Fri, Mar 19, 2021 at 4:02 AM Etienne Kaiser via Mesa-users <
mesa-users at lists.mesastar.org> wrote:

> Dear MESA-user
>
> I am interested in the implementation of the different 'MLT_option' in
> MESA. In particular, I am interested in the difference between the options
> 'Cox' and 'ML1'
>
> I did a 'grep' search and found that the mlt module solves the mlt
> equations and defines a_0 and A following Cox & Giuli (1968), Eqs.
> (14.71)-(14.73). The two variables a_0 and A differ, depending on the
> mixing-length version chosen in 'MLT_option'. While for 'MLT_option =
> 'Cox'' the code calculates A according to Eq.(14.70), it follows Ludwig et
> al. (1999) for the other 'MLT_options', for example the 'ML1' option, by
> setting ff_i parameters. After putting the ff_i parameter into the
> equation for A and some rearrangement, I arrive at the conclusion that the
> A and a_0 are identical for 'MLT_options = 'Cox'' and 'ML1'
>
> I now wonder, if I overlooked something else in the code or, if not, why
> there are two different implemented options in the code that compute the
> same A.
>
> Thanks for your help.
> Cheers,
> Etienne
>
> _______________________________________________
> mesa-users at lists.mesastar.org
> https://lists.mesastar.org/mailman/listinfo/mesa-users
>
>
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