# How many sun-like stars are there in the universe?

After yesterday's announcement of the Kepler telescope finding a huge amount of newly observed exoplanets, i saw a headline claiming that as much as 22% of sun like stars in the universe have planets in their habitable zone. There are loads of stars in the universe, so the number of planets in the habitable zone has to be enourmous. But how many of the stars in the universe are about the same size as our sun?

This is a question that concerns the initial mass function (IMF) - an empirical (that is, defined by observations rather than theory) function that describes the statistical distribution of stellar masses.

Edwin Salpeter (1955) was the first to describe the IMF, though if you read Chabrier (2003) there are some reasonably comprehensive explanations of the theory and history. However, these lecture notes are a fair bit more accessible.

From the approximations in the UCSC lecture notes I linked above, I get that around 4% of stars are between 0.7 and 1.3 solar masses (92% are between 0.1 and 0.7 solar masses!).

There are perhaps 100 billion stars in a galaxy and 100 billion galaxies in the observable universe, giving something on the order of $4\times 10^{20}$ (400 billion billion) stars that are about ($\pm 30\%$) one solar mass.

• Great response. I haven't followed your link(s) yet, but I seem to recall there being quite a lot of assumptions made about actually getting the IMF. I don't personally know how sensitive it is to different assumptions. – astromax Nov 8 '13 at 17:56
• @astromax Oh yes, assumptions and approximations galore! My 4% should be accurate to within a few per cent, anyway. Star formation isn't my area of research, so it would take me a while to understand all the deficiencies in that simple model. Perhaps there's some easily accessible survey data of our own galaxy that will have better accuracy (at least in our own neighbourhood). If I have time to learn some new things I might post an answer to your new IMF question. – Moriarty Nov 8 '13 at 23:26
• Good answer. I presume the 4% is 4% of all objects with $M>0.075M_{\odot}$? I guess the only thing I'd say is that it's a huge extrapolation to go from the IMF in our solar neighbourhood to assume that it is the same everywhere in the Universe (but unavoidable). – ProfRob Mar 12 '15 at 21:10
• @Moriarty: lecture notes link is dead. – ThePopMachine Mar 13 '15 at 16:40
• @WilliamHirtz Saying 100 billion of each is a useful order-of-magnitude guesstimate, that in reality fudges the numbers a bit in order to compensate for those complexities which may confuse the layman. There are likely many more than 100 billion galaxies (and the Milky Way may have 200 to 400 billion stars). The mass of the observable universe is about 1.7 x 10^24 solar masses. Is it really that unbelievable that there exist 10^22 stars? – Moriarty Feb 16 '16 at 10:40