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I have been trying to find an answer for this question for a while without a success, so I guess it might not have a specific answer. But to make things easier, let's take the Milky Way galaxy as an example.

The estimated mass of the Milky Way is $0.8×10^{12}$ $M_{\odot}$, and I have read from different sources that about 90% of this mass is dark matter. So the Milky Way has about $8×10^{10}$ $M_{\odot}$ of "visible matter". This visible matter should represent the mass of stars and the gas and dust between them. And here comes my problem. I don't actually know how much of this mass should be considered stars.

If we assume half of this mass is actually stars, then the mass of the stars of the Milky Way is about $4×10^{10}$ $M_{\odot}$. Assuming there are 200 billion stars in the MW, and by dividing by this number, we get the average mass per star as $0.2$ $M_{\odot}$.

So, how correct is this simple calculation I did above ? And is there a way to determine the total mass of the stars in galaxies other than the Milky Way ?

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  • $\begingroup$ And some fraction of the remaining mass will also be in black holes. $\endgroup$ – Jerry Schirmer Nov 28 '14 at 3:00
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    $\begingroup$ @KyleKanos certainly related, but hardly a duplicate - this seems to be asking more how to measure the stellar mass of a given galaxy than anything about the global baryon fraction, or stellar mass fraction. $\endgroup$ – Kyle Oman Nov 28 '14 at 4:50
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Ironically, it's actually harder to measure the mass of the Milky Way than that of other galaxies. You'd think that with it being RIGHT THERE it would be easy, but alas. Most of the difficulty comes from (1) the galaxy spans a huge part of the sky, so it takes an extremely long time to observe any particular feature in detail across the whole thing (say mapping the strength of an emission line, for instance), and (2) it's hard to get an overall picture of the galaxy because parts of it get in the way of seeing other parts - there's a lot of dust in the galactic disk that obscures our view of the more distant parts of the disk, and the disk is where most of the stars are.

Stellar mass is actually the easiest mass to measure in astronomy, because you can see it much more directly than other mass components. All that needs to be done is measure the intrinsic (rather than apparent) luminosity of a galaxy, assume a "mass-to-light ratio" and multiply to get the stellar mass. Mass to light ratios are on the order of $$\Upsilon\sim1{\rm M}_\odot/{\rm L}_\odot$$ So a galaxy with a luminosity a billion times solar has a stellar mass of about a billion solar masses. More accurate estimates get complicated quickly, as you need to account for the initial distribution of stars in the stellar population(s) involved (the initial mass function: IMF), the age of the populations, dust extinction, etc. etc.

Gas mass is not too bad either. Depending on the phase of the gas - whether it's ionized, molecular or atomic (neutral) hydrogen it may be possible to measure line emission. Neutral hydrogen shows up in the radio at 21cm from the hyperfine transition (spin flip). Most of the gas mass is in neutral hydrogen. Depending on conditions, the Lyman or Balmer series lines may be visible (the first Balmer line is called ${\rm H}\alpha$ in astronomy jargon, it's a common one to observe). Molecular hydrogen - the stuff that stars are made from directly, think Pillars of Creation, is tougher to measure as it has no strong emission lines. What's usually done is to measure emission from other molecular species - ${\rm CO}$ is a common one - and assume something about what fraction of the gas mass that species makes up.

Dark matter mass is inferred from things like galactic rotation curves or gravitational lensing, which both probe the total mass of the system. When we get a total mass from one of these tracers, we always seem to come up about an order of magnitude short (I'm using "always" very loosely here). This, coupled with cosmological observations that seem to imply there is a lot of matter ("dust" in cosmology jargon) that is not "baryonic", but is rather something else that outguns baryons a little less than 10:1 in mass.

As to the Milky Way, there are a number (about 10 that I know of) of ways you can try to measure the mass. I've co-authored a paper which uses several methods. One fairly well known measurement of the total (not just stellar) mass of the MW and M31 is this one, which is more than a factor of 2 bigger than the one you quote. Other sources are more in line with your number... the uncertainty is still rather large. Here's another paper that does the total mass with a different methodology (and get about $1.26\times10^{12}{\rm M}_\odot$), and also models the stellar mass, finding about $6.43\times10^{10}{\rm M}_\odot$, which is about the same ballpark as most estimates for the Milky Way.

If you're adventurous and want to get your hands dirty, stellar mass estimates for at least several hundred thousand galaxies from the SDSS are readily available. These are based on the luminosity of the galaxies, more or less as I've described above. Total mass estimates also exist, but I can't recall where they're easily obtained right now, and they're more uncertain.

Jerry Schirmer mentioned black holes in the comments, so I may as well add a note. The MW black hole is thought to be about $10^{6}{\rm M}_\odot$, so less than one part in ten thousand of the stellar mass, and perhaps a millionth of the total mass. This is more or less typical, though some particularly large black holes get up to perhaps a hundredth of the mass of their galaxy, at most. SMBH's are not thought to be the dominant mass component in any known galaxy (though of course they do dominate in the very central regions).

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  • $\begingroup$ I don't know how you figured the mass to light ratio, but I don't think it's correct. I think so because: 1- Comparing the result for the MW with the link you provided, you easily find that your ratio is a factor of 6 smaller than the correct value. 2- According to the IMF, about half the stars in the MW galaxy should be less than 0.3 solar masses, assuming 200 billion stars, this would be 30 billion solar masses with luminosity of 0.3 billion solar luminosities. This basically means that you have 30 billion solar masses of stars that contribute almost nothing to the total luminosity of the MW $\endgroup$ – Abanob Ebrahim Nov 29 '14 at 13:09
  • $\begingroup$ @AbanobEbrahim note that what I stated was a rough STELLAR mass-to-light ratio, which is of course quite different from a TOTAL mass-to-light ratio. $\endgroup$ – Kyle Oman Nov 29 '14 at 16:55
  • $\begingroup$ See this paper for instance: adsabs.harvard.edu//abs/2001ApJ...550..212B The stellar M/L ratio has quite a bit of scatter, but it's more or less centered (on log scale) around $\log_{10}M_*/L\sim0.0$. So within an order of magnitude or so, $M_*/L=1$ is correct. $\endgroup$ – Kyle Oman Nov 29 '14 at 16:59
  • $\begingroup$ One last thing because actually I got confused. Does the "stellar mass" include the gas and dust between the stars ? or only the stars mass ? $\endgroup$ – Abanob Ebrahim Nov 29 '14 at 18:56
  • $\begingroup$ If the ratio you stated is correct, then with 10 billion solar luminosities, the Milky Way should have 10 billion solar masses of stars, which is not true. But still, I need to understand what "stellar mass" means here. $\endgroup$ – Abanob Ebrahim Nov 29 '14 at 19:04
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If you assume that there are 200 billion stars - that is objects with mass between say $0.075 M_{\odot}$ and $100 M_{\odot}$ you can use this to normalise a mass function - the number of stars per unit mass - and then integrate stellar mass, weighted by this mass function, to estimate the total mass in stars.

If you do that then what you find is (1) high mass objects contribute very little to the numbers of stars in the Galaxy and only a small fraction of the mass; (2) very low mass objects (i.e. anything of lower mass than assumed here - brown dwarfs) also contribute almost nothing to the mass (see Could the estimated stellar mass for the Milky Way galaxy include brown dwarfs?). (3) If you work out the mass of all the stars that have lived and died, that turns out to be a non-negligible number, dominated by white dwarfs - about $1.5\times 10^{10}$ with average mass $0.6M_{\odot}$). (4) The average mass of a non-degenerate star is about $0.25M_{\odot}$.

Thus from 200 billion stars you expect the stellar mass to be about $5\times10^{10}M_{\odot}$ with another $\sim 10^{10}M_{\odot}$ in the form of degenerate corpses and a further few percent in the form of black holes and brown dwarfs.

When dealing with stellar mass-to-light ratio, the games changes, because the luminosity of a (main sequence) star is proportional to $M^{3.5}$. As a result, the luminosity-weighted average mass of a living main sequence star is just below $1M_{\odot}$ - and therefore the stellar mass-to-light ratio is a little above 1. See the quite detailed calculation in What is the luminosity of the Milky Way galaxy? This will be pushed even higher by the presence of relatively dark white dwarfs.

Unfortunately, mass-to-light ratios are more complex than this because of the presence of relatively short-lived evolved stars with very high luminosities. In the Milky Way, red giants would dominate at visible and infrared wavelengths and the stellar mass-to-light ratio would be reduced to below one.

Note that all these numbers are very difficult to establish in our own galaxy; it is difficult to do accurate censuses of stellar populations because of dust obscuration and estimates of stellar numbers and masses in our Galaxy are extrapolations based on model density distributions. In other galaxies what we can see is the luminosity distribution but can't count individual stars. Here we must appeal to models of the rate at which stars are formed and with what mass distribution to estimate the correct mass-to-light ratio to use. However, this is not completely unconstrained in the sense that one can look at the spectral distribution of the light to see whether it also matches the stellar population model.

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