[Mesa-users] different 'MLT_option'

Tue Mar 23 09:48:20 UTC 2021

Hi Jared,

I compared the two MLT options for Cox and ML1 (MESA revision 10398 for the record) but could not find any difference, as expected from our maths.

Ok, then let's hope that Bill or another developer puts in an answer.

Again, thank you for your help.
Cheers,
Etienne

________________________________
From: Jared Goldberg <goldberg at physics.ucsb.edu>
Sent: 23 March 2021 01:08
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,

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<mailto: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<mailto:goldberg at physics.ucsb.edu>>
Sent: 19 March 2021 16:52
To: Etienne Kaiser <e.kaiser at keele.ac.uk<mailto:e.kaiser at keele.ac.uk>>
Cc: mesa-users at lists.mesastar.org<mailto:mesa-users at lists.mesastar.org> <mesa-users at lists.mesastar.org<mailto: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<mailto: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

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