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Of the stars that can be seen with the naked eye, what are the distributions of each type? For example, how many are main sequence? how many are Super Red giants/white dwarfs/neutron stars...etc. What's the distribution by mass and distance?

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For your first question - About 6000 stars on a really dark night. I don't have a citation for this number though. –  Kitchi Oct 12 '13 at 11:40
    
It should also be noted that several of the "stars" in the sky are actually galaxies –  Jerry Schirmer Oct 12 '13 at 17:36
    
The overall scaling @Kitchi refers to is discussed here, and in particular this answer cites a source for the 6000 (though that source could stand to be clearer on their methods). –  Chris White Oct 14 '13 at 7:01
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2 Answers

Most of the brightest stars are spectral types B,A,F main sequence stars (50%), but there are also a bunch of O-type main sequence and giant stars (5%) and another big clump of red giants (about 35%) and a few percent are supergiants. There are no white dwarfs, and definitely no neutron stars!

I have attached an image which I created by selecting 4992 bright (V<6, hence visible from a good site) stars from the Hipparcos catalogue with a parallax and plotted them on the absolute V vs B-V colour-magnitude diagram. Also shown is a zero age main sequence for stars <7Msun from Siess et al. 2000, A&A, 358, 593.

I also show a histogram of their log10(distance) in parsecs. It's basically lognormal with a peak at about 150pc. I'm afraid mass is not so straightforward - the Hipparcos catalogue can be found at http://cdsarc.u-strasbg.fr/viz-bin/Cat?I/239 if you fancy doing it yourself

Actually as a postscript, one thing we can say about the mass distribution is that if you look at the HR diagram you see that almost all the stars are either (a) evolved to become giants and therefore must have masses $>0.9M_{\odot}$ to have done so during the time the Galaxy has existed or (b) are main sequence stars more luminous than the Sun ($M_{V,\odot} = 4.75$) and so must be more massive. So almost all these stars are more massive than the Sun.

HR diagram of bright (V<6) stars in the Hipparcos catalogue Histogram of distance for the sample.

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I can have a stab at estimating the Neutron star population, and perhaps suggest how to do the others.

Now as far as I'm aware there aren't any Neutron stars you can actually see with the naked eye as there cold dead stars and we mostly observe them as pulsars in the radio band. But anyway, this article estimates we can observe objects up to "a little over 4000 light years away, " so lets use that.

Now the way to do this is to find a database, for pulsars there is the excellent ATNF Pulsar Catalouge. The joy of this site it it allows you to enter a condition.

So we ask it for names of pulsars with the condition dist < 1.266. Here we had to convert light years to kpc as that is the unit used by ATNF. The output gives us 146 objects.

You can repeat this exercise if you can find similar online catalouges for the other objects your interested in, I'm afraid I only know about Pulsars.

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I thought many neutron stars were still hot, due to the fact that, immediately prior to the collapse event, the neutron star was basically a stellar core. –  Jerry Schirmer Oct 12 '13 at 17:37
    
@JerrySchirmer. Having though about it and done some reading I think your correct. The closest NS to us is about 50000K so two orders of magnitude brighter than the sun. However, I still don't believe they are visible to the naked eye. –  Greg Oct 12 '13 at 17:52
    
Neutron stars may be very hot, relative to the sun, but they are also tiny, and quite a long way away. None are visible without a telescope. –  Dr Chuck Mar 28 at 19:22
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