[mesa-users] Yet about Brunt calculation ...

Ehsan Moravveji moravveji at iasbs.ac.ir
Sat Jul 9 14:35:50 EDT 2011

Dear Bill and mesa friends,
I'm totally aware that
implimentation of Brunt-Vaisala is challenging for you, and you made a lot
of efforts to implement Brassard et al. receipe into MESA. Great ...

I read the first 4 pages of the paper. They clearly
state in a paragraph above Eq. 14 that "We thus may use Y ... as a
unique indicator of composition change" and indeed they are true for
a model of white dwarf, which is quite simple star. One can even model a
white dwarf with a composite polytrope of varying n and still succeed to
explain many phenomena. But, in my opinion this cannot be the case for
evolved stars off the main sequence.

Here, I have attached a
plot of the abundance profile variations within a model of Rigel. We are
all familiar with similar plots.

1- The H profile variation
could be quite profound outside the core.
2- For other heavier
species, their abundances are small, but the differential of their
logarithm may still contribute appreciably to the last term in Eq. 13 of
Brassard et al. at least for the first few abundant species in normal
3- caling multiple times to EOS could be demanding and CPU
expensive, but in my opinion, a better evaluation of N2 is by considering
Eq. 13 and letting the sum over just few species, say those that are
followed by the rates.
4- I admit that I might be totally wrong, but
need to be justified.
5- I have no idea how difficult it might be to
implement numerically the more "standard" (in the sense of
literature) N^2 using \nabla_\mu rather than B term in Brassard et al. 
Physically, \nabla_\mu is very meaningful; it carries the weighted
presence of all species in each layer, plus electrons! Not only He.
6- Unfortunately, I'm not familiar with the Lars formula called
"simple". But, what I intend to do is to scape from free
parameters once a quantity is free from this, and N^2 is. I'm really
annoyed when I have to decide upon brunt_H_frac and test the effects of
this keeping all parameters fixed, and repeating and repeating. And even
after that, being yet worried of it's potential effects with the changes
in the model. Of course, this is my problem and comes from my lack of

N^2 has a very critical role in asteroseismology,
and that's indeed why it is worth to discuss. Specially, it is an input to
pulsation codes, and when N^2 profile has some spikes, it makes the
solution of pulsation equations tough.

With kind regards.

Moravveji, Ehsan.
Ph.D student of Astrophysics.
Department of Physics, Institute for Advanced Studies in Basic Sciences
(IASBS), GavaZang Road, 
Zanjan 45137-66731, Iran.

(+98)241-415 2118
Fax:    (+98)241-415 2104

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