[Mesa-users] different 'MLT_option'

[Jared Goldberg]

Hi Etienne,

Ah, got it! I hadn't checked that algebra for those two cases, but doing so
I agree that these should yield the same results.
I just ran 2 models up the RGB with MESA defaults and Cox vs ML1 and am
finding no difference (as we'd expect), but I'll try to see if there is a
pathological case where the two disagree based on numerics.
Have you found any differences between models run with the two different
implementations?

My suspicion is that the different options were implemented at different
times and the availability of both is a relic of that (maybe in accordance
with the jumble of descriptions of the different prescriptions strewn
throughout the literature), but only Bill (or maybe another developer)
would be able to answer that question.

Also, for the users list, I was missing a factor of 1/9 in my formula for
convective_conductivity earlier in this thread, which makes the math work
out.

~Jared

On Mon, Mar 22, 2021 at 3:01 AM Etienne Kaiser <e.kaiser at keele.ac.uk> wrote:

> Hi Jared,
>
> thanks a lot for your fast and detailed answer.
>
> I arrived at the same conclusion as you wrote in your message. However, if
> I plug in
>
>    - the f_i constants for the 'ML1' case, i.e. f1=1/8, f2=1/2, f3=24 and
>    f4=0
>    - the way the optical depth is calculated in the code,
>    'omega=Lambda*Rho*opacity' (also Eq.(A4) in Ludwig et al. 1999)
>    - the pressure scale height, 'H_P = P/(Rho*g)'
>    - the mixing lenght, 'Lambda=alpha_mlt*H_P'
>
> and some rearrangements I arrive at the exact same formula for A as for
> Cox.
>
> So, I wonder what the actual difference between the 'Cox' and 'ML1'
> options is. I know that there are two different formulae in the code for A,
> as nicely outlined by you, but they are the same after rearrangement.
>
> What do I misunderstand?
>
> Cheers,
> Etienne
>
> ------------------------------
> *From:* Jared Goldberg <goldberg at physics.ucsb.edu>
> *Sent:* 19 March 2021 16:52
> *To:* Etienne Kaiser <e.kaiser at keele.ac.uk>
> *Cc:* mesa-users at lists.mesastar.org <mesa-users at lists.mesastar.org>
> *Subject:* Re: [Mesa-users] different 'MLT_option'
>
> 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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