No Title

What we see from the sky is light - light from stars and hot gas. It is more-or-less straightforward to count how much mass is there in the form of stars and hot gas.

In order to do that we need to translate light into mass. This is done by measuring the so called mass-to-light ratio,

M/L.

It is measured in solar units.

$\framebox{\Huge\bf ?}$ The mass-to-light ratio for the Sun is

A.: 0
B.: 1
C.: 10

$\framebox{\Huge\bf ?}$ The mass-to-light ratio for the photon is ...

We can measure the mass-to-light ratios of galaxies by using the Kepler's third law: we can see how fast stars are moving in a galaxy, and we can also see how large a galaxy is. Then we can compute the total mass inside some radius in a galaxy, and we can also count all the light from all the stars.

A few results:

For stars around the Sun, the average M/L = 3.
For our Milky Way and other similar spiral galaxies, $M/L\approx 20$ (more like between 10 and 30).
$\Omega_0=1$ implies that on average in the universe $M/L\approx 500$ .

The mass-to-light ratios of galaxies is much larger than that of stars $\rightarrow$ galaxies contain more mass than is just present in shining stars.

Thus, galaxies contain the dark matter.

Galactic dark matter

Possible sources of galactic dark matter:

cold gas.
stellar cinders: white dwarfs, neutron stars, black holes.
brown dwarfs.
jupiters.
non-baryonic dark matter.

The mass-to-light ratios of spiral galaxies can be explained by the baryonic dark matter. It is only when we move to the galactic halos, we discover evidence for the non-baryonic dark matter.

Galactic halos

The mass in shining stars in the universe can be expressed as an omega-parameters of stars,

$\begin{displaymath}\Omega_* = 0.007. \end{displaymath}$

The mass in spiral galaxies corresponds to

$\begin{displaymath}\Omega_{\rm SG} \approx 0.05, \end{displaymath}$

very close to the nucleosynthesis value, $\Omega_B=0.04$ . So, all the matter in galaxies could be baryonic.

However, the observations of rotation curves of galaxies indicate that there is matter around galaxies well beyond the edge of a galaxy. This matter is called the galactic halo.

Observations show that

$\begin{displaymath}\Omega_{\rm HALO} \approx 0.1, \end{displaymath}$

about twice as large as that of galaxies themselves.

If we believe in Big Bang nucleosynthesis, there is no way the galactic halos can be baryonic.

MACHOs

In about 1992 a MACHO (MAssive Compact Halo Object) collaboration formed which used gravitational microlensing to detect compact massive objects in the halo of our Galaxy.

After seven years of observations, they concluded that about 20-100% of the halo is made out of MACHOs with an average mass of about one half solar. This is suspiciously close to the average mass of a white dwarf.

The precise fraction of halo mass in form of MACHOs is very difficult to measure. If it is as high as 100%, the Big Bang nucleosynthesis is in big trouble. If it is as low as 20%, everything is ok.

Several other similar projects are under way, so this question should soon be resolved. Stay tuned!

Clusters of galaxies

The same way as we measure masses of galactic halos, we can measure masses of clusters of galaxies. The value of omega that we get from clusters is

$\begin{displaymath}\Omega_{\rm CL} \approx 0.2, \end{displaymath}$

and it can be even higher, as we mentioned above.

If we trust the Big Bang nucleosynthesis, there is no way this matter can be baryonic $\rightarrow$ this is one of the strongest proofs of the existence of the non-baryonic dark matter within the standard Big Bang theory.

Another clue: if there is so much baryons in the universe as to make $\Omega_B=0.2$ , why is there so little mass in stars: $\Omega_*=0.007$ ?

Nature of the dark matter

There are two main candidates for the non-baryonic dark matter:

massive neutrinos, or
WIMPs (Weakly Interacting Massive Particles).

Neutrino mass

In standard particle physics neutrino has no mass. However, this has not been verified experimentally until last summer.

In summer 1998 in a neutrino detector called SuperKamiokande in Japan scientists detected a difference between the flux of atmospheric muon neutrinos ( $\nu_\mu$ ) coming from above and from below. This is interpreted as transformation of muon neutrinos into tau neutrinos ( $\nu_\tau$ ). This kind of transformation is only possible if neutrinos have mass.

SuperKamiokande experiment cannot measure the mass per se, but only the difference between the muon and tau neutrino masses. This difference was found to be very small, corresponding to

$\begin{displaymath}\Omega_\tau - \Omega_\mu = 0.01. \end{displaymath}$

Interpretation

In standard particle physics theory all three neutrino species have very different masses. The SuperKamiokande result then implies that in terms of cosmological contributions,

$\begin{displaymath}\Omega_\tau = 10^{-2} = 0.01, \end{displaymath}$

$\begin{displaymath}\Omega_\mu \approx 10^{-5}, \end{displaymath}$

$\begin{displaymath}\Omega_e \approx 10^{-8}. \end{displaymath}$

However, this is not tested experimentally yet, So, it is still possible that

$\begin{displaymath}\Omega_\tau = 0.101, \end{displaymath}$

$\begin{displaymath}\Omega_\mu = 0.1, \end{displaymath}$

$\begin{displaymath}\Omega_e = 0.099, \end{displaymath}$

and then neutrinos can be the dark matter.