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It is often said that the Sun is a medium size, or even dim star, but is that true?

According to this list of stars within 21 light years, only six stars are brighter than the Sun out of the closest 121 stars. That indicates that the Sun is in the top 6%. If you also count brown dwarfs, the Sun is even closer to the top. Does not this indicate that the Sun is really one of the big stars?

7/121

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I think your comment is fundamentally correct. It used to be said that the sun was a medium sized/small star based on preliminary observations. Better telescopes reversed that observation as many many many more smaller stars became observable. It's worth pointing out that very few of the stars we can actually see in the sky are smaller than the sun. None of the visible stars are red dwarfs or smaller. A similar correction was made on binary stars being the majority. – userLTK Jan 10 at 3:44
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Define your terms. By "medium" do you mean mean or median? By "size" do you mean mass or radius? – Mike Scott Jan 10 at 6:41
    
@MikeScott Just give me any size metric that actually makes the Sun a medium sized star. As for "medium", I meant median. – Hohmannfan Jan 10 at 13:25
    
@Hohmannfan If you're using the median as your "medium", then the Sun is bigger than that. But if you're using the more normal mean as your medium, I think the Sun is probably smaller than the mean mass of all stars, and it's certainly smaller than the mean mass of all known stars. – Mike Scott Jan 10 at 15:15
    
The Sun s about 3 times more massive than a median field star and is more luminous than about 90% of stars. It is only typical in the sense of being on the main sequence, where most stars are. – Rob Jeffries Jun 2 at 11:31
up vote 12 down vote accepted

It is true that a surprisingly large number of stars are smaller (and thus less massive) than the Sun. However, the stars that are bigger than the Sun are often much bigger.

Look at this chart:


Image courtesy of Wikipedia user Jcpag2012 under the Creative Commons Attribution-Share Alike 3.0 Unported license.

Notice how small the Sun is compared to some of the other stars. It's tiny! It is indeed a small star - in technical terms a main sequence dwarf.

However, despite its size, it is clear that there are many more stars less massive than the Sun that there are stars more massive than the Sun. Why? There are two reasons:

  1. Lower-mass stars live longer.
  2. More low-mass stars can form in a given region than high-mass stars.

Encyclopedia of Astronomy and Astrophysics

The distribution of masses can be quantified in an initial mass function, typically given in the form $$\xi(m)=km^{-\alpha}$$

When you integrate this over a range of masses, you can find how many stars are within that range. Not surprisingly, this number gets lower and lower as you slide the endpoints to more massive stars. You can see this decrease from the fact that $\xi'(m)<0$, so long as $k>0$ and $\alpha>0$ - which is assumed by the model, according to empirical data.

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See also what-if.xkcd.com/83 : "Our Sun isn't a grain of sand on a soft galactic beach; instead, the Milky Way is a field of boulders with some sand in between." – j-g-faustus Jan 9 at 23:00

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