[mesa-users] solar calibration with Asplund abundances

[David Arnett]

Hi Bill,
Beautiful work! I like the broader approach. Your results are interesting
and I think understandable:

 " 3. GS98 results when oscillation frequencies are included in the chi^2

now for giggles, let's see what happens if we rerun gs98 adding oscillation
frequencies to the chi^2. we'll keep the same 4 parameters;  the same 6
chi^2 terms from above will now be called the "spectral" chi^2;and we'll
add 74 frequencies as a "seismic" chi^2. the total chi^2 will be the
average of the spectral and seismic. as you might expect, the optimization
process gives up quality in the spectral chi^2 in order to improve the
seismic result. but in spite of that it isn't able to find a good overall
match. in fact, even though the spectral chi^2 has jumped from 0.8 above to
8.8 now, we still have a chi^2 seismic of 1863, so our total chi^2 is a
whopping 936 -- ugh.   one small bright spot is that the delta_nu value now
is within 1 sigma of the observed. but the frequencies are so well know
that they have very small sigmas and that gives us the big chi^2 seismic."

I think this is the difference between a scientific prediction and an
engineering fit. If the Sun has more than four degrees of freedom (it
must), we would then expect that adding data of a new and different kind
would give a different "spectral" solution because MESA (and we) do not yet
know all the physics involved. Adding the seismic data seems to indicate
that this is correct. As you point out, a total chi^2 of 936 is not pretty,
but it gives an important warning about our present understanding. To what
extent is it descriptive rather than predictive? Aldo should chime in here,
but I suspect this means that we do math (different codes give similar
results) better than we do physics (something, and maybe several things may
be missing in our conceptual picture).  This has the practical difficulty
for asteroseismology that we cannot be certain that solar calibrations are
reliable indicators for stars other than the Sun.

-- 
David Arnett
Regents Professor
Steward Observatory
University of Arizona

Facts are stubborn, but statistics are more pliable.  Mark Twain
Facts do not cease to exist because they are ignored.  Aldous Huxley
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