Luminous regions of galaxies
The luminous region of a galaxy extends over a radius of about 10 kpc. The sun
is on the outskirts of the Milky Way galaxy, and about this distance from the
center of the galaxy. One measures the total mass interior to the orbit of the
sun from the sun's rotation speed around the galaxy and its galactocentric
distance: this gives the centrifugal force, which must be balanced by the
gravitational force due to all the mass interior to the sun's orbit. One finds
that this mass is 10^11 M(Sun), while the cumulative luminosity of all the
stars in the Milky Way is about 10^10 L(Sun). The ratio of mass to luminosity
is therefore equal to 10, so that the average star is about half the mass of
the sun. This is not a great surprise: the solar neighborhood contains
younger, relatively more massive and luminous stars as do other spiral arm
regions as compared with the galaxy as a whole.
When we add up the luminosity from ale the stars in all the galaxies in the
universe we find that the mass is far less than that required to close the
universe. It is also significantly less than the mass density implied
by Big Bang Nucleosynthesis.
This deficit indicates that there may be "baryonic" dark matter (although
not enough to make the universe recollapse), as well as the more exotic
"particle" dark matter.