Dark baryonic matter

It is astonishing that it is possible to infer the total density of ordinary baryonic matter from the primordial synthesis of light nuclei $D,^3He,^4He$ and $^7Li$ because it is based on well known nuclear physics. The deuterium abundance is particularly relevant because it cannot be produced in stellar processes. The recent determination(4) of the ratio of abundances $D/H=\left( 3.4\pm 0.3\right) \times 10^{-5}$ in uncontaminated distant clouds through absorption of quasar radiation is explained by a ratio of baryon to photon number densities.

$$\eta =\frac{\eta _B}{\eta _\gamma }=(5-7)\times 10^{-10}.$$ (17)

Though this number of baryons seems very small, since its mass is around almost 13 orders of magnitude larger than the energy of photons, it leads to a mass density

$$\rho _B=(3.8\pm 0.4) \times 10^{-31}grcm^{-3},$$ (18)

and a fraction of critical density

$$\Omega _B=(0.02\pm 0.002)h^{-2}\sim 0.05,$$ (19)

ten times larger than the luminous matter.

This is the first evidence of dark matter, the baryonic one which could reside in the MACHO's detected by microlensing that might account for up to one third of the galactic halo, and probably more abundantly in diffuse gas very difficult to detect except in the $x-$ray emitting intracluster gas.

Why must there be a galactic halo? It happens that according to Kepler law, if the mass of the galaxy is $M$ the orbital velocity $v$ of an object at a distance from its centre is given by

$$\frac{v^2}r=G_N\frac M{r^2}$$ (20)

so that one would expect $v^2$ to decrease as $r^{-1}$ for large distances. But astronomers have observed that for increasing distances, through rare stars and atomic emission of 21 cm line, remains constant indicating that $M$ is not concentrated in the luminous part of the galaxy but increases as $r$ .

This proves the existence of a dark halo which on the whole gives to the galaxy a mass ten times larger than its luminous part. Note that if all the halo is baryonic this would explain the ratio between Eqs.(19) and (16), leaving no room for diffuse gas.

But a very important observation has been done for clusters of galaxies where most of baryons reside in the hot $x-$ray emitting intracluster gas. It has been determined (5) that the ratio of baryonic and total cluster mass, to explain its motion, is

$$f_{gas}=(0.07\pm 0.002)h^{-3/2},$$ (21)

so that assuming that clusters having a size of around $10\ Mpc$ are good samples for the composition of matter in universe, the total matter fraction of critical density is

$$\Omega _M=\frac{\Omega _B}{f_{gas}}\sim 0.4$$ (22)

This result, apart from giving evidence that most of baryonic dark matter must be in gaseous form, indicates that there is much more matter of non-baryonic type.