From: Frederick.A.Ringwald@dartmouth.edu (Frederick A. Ringwald)
Newsgroups: sci.astro
Subject: Re: Spectral Abundances? and why OBAFGKM?
Date: 28 Jul 92 05:04:32 GMT
Organization: Dartmouth College, Hanover, NH

In article <1992Jul27.102023.3108@desire.wright.edu>
jbatka@desire.wright.edu writes:

> Could someone post or Email to me the approximate relative
> abundance of stars both on and off of the main sequence?

What exactly do you mean? Zero-Age or TAMS? Subgiants, giants, or
supergiants? Versus what types? Cluster stars or field stars? The
particulars matter. Stars are complex beasts, and asking this about
them is like asking "what are the relative abundances of young and
adult animals?"

But all right: a decent rule of thumb, and no more than a rule of
thumb, is that number density (number of stars per unit volume) ought
to be proportional to the relative lifetime. Therefore, about 90% of
the G stars should be on the main sequence, since they live for about
10^10 years, and spend about 10^9 years evolving onto and off of the
main sequence. But this is oversimplified: in this example, they will
be cooler off the main sequence, and so will not be G stars then. But,
to give you a succinct and shamefully oversimplified answer,
a-few-to-about-10%.

This is for the middle of the MS. In a volume-limited,
high-Galactic-latitude sample, this ratio is much less for cool stars,
since M dwarfs have evolutionary timescales longer than the age of the
Universe, and so, practically, do not evolve at all. But, evolved stars
are bright, and so can be seen a long way, and so will be more numerous
than they ought to be in bright star catalogs (i.e., magnitude-limited
samples). The evolved ones will not have evolved from M dwarfs, of
course, but earlier types, which evolve faster. The ratio should be
roughly the same for hot stars, which form, live, and burn out quickly;
also, for full-tilt, million-Solar-luminosity O types, it's not as
clear what main sequence and evolved mean, since they evolve rapidly
back and forth over the top of the H-R diagram. This is why, in perfect
hindsight, it should not have surprising that SN 1987A came from a
luminous blue star, and not a red giant.

Tell you what: two good sources of this type of material are:

C. W. Allen, Astrophysical Quantities, 3rd ed. (1973),

which any decent university library ought to have, and a much newer
one,

K. R. Lang, Astrophysical Data: Planets and Stars (1992).
 
Both have extensive tables of what's what, which you can peruse
yourself. 

> I would also like the approximate abundances of Binary and
> Trinary star systems.

So would we. This is a controversial matter: numerous attempts to
determine this in the past can only agree in that binaries are in the
majority (most likely 60 - 80%, although some studies have gotten close
to 100%), and that triples are less common (maybe 5-10%). Here, too,
the results vary with spectral type and luminosity class. The best
reference on this is probably still the review article by Helmut Abt,
in the 1983 Annual Review of Astronomy and Astrophysics (vol. 21, p.
343).

> I do not care what group the sample is taken from just please
> include what it is (e.g. local neighborhood, galaxy, etc.).

But the particulars of the sample matter, a LOT. Population I stars, in
the plane of the Milky Way, have a lot more O and B stars; Population
II, as in the halo and Globular Clusters, show a lot more evolved red
stars, and practically no O and B stars, since there has much less
recent star formation.

[...]

> I do not need great accuracy (definitely no more then 2 significant
> figures), I am just trying to get a feel for relative star abundances.

You will not get great accuracy: this is astrophysics, remember? If one
can get any result to within 10%, one is a happy person. Then again,
considering the subject matter, if one *can* get any result, RELIABLY,
to within 10%, one *ought* to be a happy person. Besides, many of the
quantities you want are controversial in the first digit, or even order
of magnitude (for brown dwarfs or black holes, for instance).

> Now a serious question.  How was this lettering scheme picked to 
> define stellar spectral class?  Why wasn't something like A,B,C,D,E,F,etc
> picked instead?

This part is much easier. When Annie Jump Cannon was classifying the
objective prism spectra of 225,300 stars brighter than 11th magnitude
for the Henry Draper Catalogue, at Harvard College Observatory,
starting in 1896, her first cut at classification was to judge by the
strength of the hydrogen lines. Therefore, A, B, C, etc. This was
strictly empirical: it was not understood how stellar spectra form,
only that they display certain characteristics. It wasn't until 1925
that Cecilia Payne-Gaposchkin, in her Ph.D. thesis, the first in
astronomy at Harvard, showed that spectral types are a temperature
sequence. The hydrogen lines increase in strength with temperature up
to the A stars, but they decrease in strength for hotter stars, since
the hydrogen ionizes. This was what unalphabetized everything, with the
O and B types before A, after which come F, G, K, and M.

By then, too, some types were deemed superfluous and removed. For
example, type H was found to be identical to type K, observed under
favorable conditions. Net result: the alphabet soup of the Harvard
classification, now deeply entrenched, so there is no chance of
changing it.

Fred Ringwald
Department of Physics & Astronomy
Dartmouth College
Hanover, NH 03755-3528
Newsgroups: sci.astro