[mesa-users] Fwd: main sequence problem

[David A. <wda...@gm...>]

---------- Forwarded message ----------
From: David Arnett <wda...@gm...>
Date: Fri, Feb 15, 2013 at 9:16 AM
Subject: Re: [mesa-users] main sequence problem
To: Arlette Grotsch <Arl...@ul...>


Hi Arlette,
You are right as usual ;-)

On Fri, Feb 15, 2013 at 2:50 AM, Arlette Grotsch
<Arl...@ul...> wrote:
> Hi David,
>
> Thanks for your interesting comment. I agree with you that historically Schwarzschild was used in order to increase the mass of the convective core with no other physical reason behind. However the fact that Ledoux supposedly leads to a smaller convective core is highly questionable. In the earlier versions of stellar evolution codes, Henyey for instance, the implementation of the Ledoux criterion was correctly made and convective cores were about the same whatever criterion was used.

I had forgotten this Henyey work; thanks for the reminder!

By that I mean that the limit was diagnosed from the "inside" of the
convective region. If the layer just above the convective core is to
be engulfed in the convective core, its chemical composition becomes
the same as that of the convective core itself. On the contrary if the
layer adjacent to the convective core is treated as independent of a
possible extension of the core, Ledoux will prevent it from becoming
convective and convective cores are smaller. The easiest and more
coherent way to define the limit is to extrapolate the grad-rad from
the "inside" of the core and then to add a mesh point (double
preferentially if one wants to keep trace of the discontinuity in
chemical composition and density). This is true for H burning and for
He burning. Some He burning models have a discontinuity in grad-rad at
the convective boundary with a grad-rag higher than grad-ad. This is
of course not correct since this situation is unstable.

Even more, it is being buffeted by convective plumes; the boundary is dynamic.

>Now for a layer which is not adjacent to a convective region, it can only become convective if Ledoux criterion is violated since as you point out, Schwarzschild criterion has no chemical composition dependence.

Yes. That is similar to what I am trying to implement, based on the
simulations. This works for the radiation cooled regime, but needs
modification if the cooling is by neutrinos. In addition to using
directional derivatives as you suggest, there is work done by the
turbulent kinetic energy, eating away the stable boundary.

Actually we find an intermediate region (sort of like J. P. Zahn
said), which is mixed, subadiabatic, and decelerates and turns plumes
to keep them in the convective region. It is sometimes very narrow,
which may help in 1D codes.

Dave
>
> The simulations are a great challenge and we are all looking forward to seeing the progress made in this field!
>
> Cheers,
> Arlette
>
>> I wish to add a comment to the point made by Arlette.
>>
>> Actually, the convection region is not static, but fluctuates
>> vigorously (high Reynolds number).  Thus the boundary is determined by
>> the accumulated effect of these fluctuations (in velocity, pressure,
>> etc.). I think that, in addition to the suggestion of Arlette, there
>> will probably be important modifications due to this. We certainly see
>> such behavior in simulations.
>>
>> Note that many astro simulations are single fluid, so that the effect
>> of abundance is ignored (eg., the Stagger code and ASH, to name two
>> illustrious examples). Properly doing multi-fluid flow, to describe
>> composition differences, is still a challenge, but we seem to be
>> making progress.
>>
>> I think Schwarzschild was used historically because it gave more
>> mixing than Ledoux, and agreed with the larger cores needed for
>> fitting observational data on massive stars. Ledoux with entrainment
>> would also give larger cores than without entrainment. The
>> observations do not yet tell us which (if either) is what nature does.
>>
>> Experiment suggests Ledoux plus entrainment (basically a Richardson
>> criterion). Because Schwarzschild has no composition dependence, it
>> cannot be correct in general. Composition can affect stability, as
>> Arlette emphasizes.
>>
>> ------------------------------------------------------------------------------
>> Free Next-Gen Firewall Hardware Offer
>> Buy your Sophos next-gen firewall before the end March 2013
>> and get the hardware for free! Learn more.
>> http://p.sf.net/sfu/sophos-d2d-feb
>> _______________________________________________
>> mesa-users mailing list
>> mes...@li...
>> https://lists.sourceforge.net/lists/listinfo/mesa-users
>



--
David Arnett
Regents Professor
Steward Observatory
University of Arizona


-- 
David Arnett
Regents Professor
Steward Observatory
University of Arizona