# Mass-to-light-ratio and dark matter in galaxy

Suppose one measures the total mass of a galaxy somehow and its total luminosity. What mass to light ratio (in solar units) is considered a signal for dark matter and why?

For example if M(galaxy)/L(galaxy) = 10 M(sun)/L(sun), is that considered 'too high' and a signal of dark matter?

My question is related to the fact that there are many stars that have higher mass-to-light ratio than the sun. Why would we expect the total galactic mass-to-light ratio be of the order of the sun's if there is no dark matter present?

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malawi_glenn
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The stars having M to L ratio greater than the sun are very very few, i.e not "many stars that have higher mass-to-light ratio than the sun". That is at least what I remember from my astrophysics class, do you have any sources on that statement of yours? I can try fining some for mine after the 17th Dec when my exams are over:)

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That's what some pages of wikipedia say:

http://en.wikipedia.org/wiki/Sun
The Sun is brighter than 85% of the stars in the galaxy, most of which are red dwarfs.
http://en.wikipedia.org/wiki/Red_dwarf
Red dwarfs are very low mass stars with no more than 40% of the mass of the Sun.[1] Consequently they have relatively low temperatures in their cores and energy is generated at a slow rate through nuclear fusion of hydrogen into helium via the proton-proton (PP) chain mechanism. Thus these stars emit little light, sometimes as little as 1/10,000th that of the Sun. But even the largest red dwarf has only about 10% of the Sun's luminosity.[2]
Another potential problem is that red dwarfs emit most of their radiation as infrared light
The above shows that red dwarf are the major star type in Milky way and have mass to light ratio of 4 for the biggest ones and possibly more for the others. Also, if they emit mostly in infrared, their mass to light ratio in any visible band would be even higher.

I also imagine, the allowed M/L ratio without dark matter should depend on the morphology class and age of the galaxy under consideration. Galaxies at high redshifts are early in their development and must have more brighter stars so M/L should be lower for them.

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malawi_glenn
Homework Helper
Now I have checked in my astrophysics books: there is a good picture of mass-luminosity in Annu. Rev. Astron. Astrophys.,18,115,1980 by Popper.

And one has of course ruled out the possibility that the dark matter is dark baryonic matter, i.e very very faint stars and also brown drawfs. But even with the highest theoretical account for that, there is still much matter missing. Also how gruop of galaxies are clustered points to dark non-baryonic matter.

The mean mass of a star in the milky way is 0.7M_sun according to my books. And even tough there are many more low mass stars, their weight is much lower. Combine IMF + L/M and you can get an estimation on the M/L for the milky way.

Using H I lines (21cm) are very useful, they can penetrate the most.

L/L_sun = (M/M_sun)^alpha
Where alpha is a paramter about 4-2.3. 4 is for masses belox 0.5M_sun. 2.3 is for higher mass stars.

Just to let you know, there is not a relation between age and morpholgy class. At least my books tells that it is wrong, that Hubble was wrong on that.

And you also use the virial theorem, to calculate the mass of an ensamble of objects, by measuring velocity dispersions. So in this way you calculate the mass of something.

Gravity lenses + flattening velocity curves for galaxies should give firm indications for dark matter also :)

I am not a fan of dark matter myself until it is detected. In this thread though I am more concerned with measuring M(stars)/L with a minimal set of assumptions.

L/L_sun = (M/M_sun)^alpha
Where alpha is a paramter about 4-2.3. 4 is for masses belox 0.5M_sun. 2.3 is for higher mass stars.
Has anyone used that mass-luminosity relation for stars to actually infer the M(stars)/L of MilkyWay or at least in the solar neighborhood? I suppose such a study is possible only for MilkyWay cause other galaxies are too far to have their stars resolved?

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malawi_glenn
Homework Helper
That depends on how you define resolved..

Dark matter can also be very very faint stars etc.. But no theoretical models can explan their existens either, and we know very very much more about star formation, life and properties of stars and well baryonic matter. So either make a new theory about stars and gas and galaxies just using baryonic matter, or search for new super symmetric particles. (or both).

The L to M ratio and the "missing" mass in galaxies and galaxy CLUSTERS is known scince very long time and there is a lot of research of this. If you are not a reasearching astrophysicis yourself, then I think you should first try to study more formal astrophysics and ask what real reseachers tell you. Myself is just an undergraduate in Sub-atomic physics, doing a lots of astrophyiscs cuorses as well.

I think one has done it, in my astro-book "Instroduction to Modern Astrophysics" , by Caroll. in the chapter about milky way, there is a lot of derivations of using that L to M relation to get certain properties of the milky way.

And to notknowing: Arxiv is preprint, not published and approved articles. Of course there are alternative theories, but the current "paradigm" is the thing we write most about in these forums.