Introduction
173
Further, this bound effectively applies to all neutrino species, since the SuperK
[2] and SNO [3] data show that the mass differences for atmospheric and solar
neutrinos are tiny:
l\m~.atmos :::::: 3 x 10- 3 eV 2
(6.6)
l\m~.solar:::::: 7 x 10- 5 eV 2 .
(6.7)
Thus the sum of the neutrino masses is at most, 6.6 eV and likely to be much
smaller. (When mv « To, the relativistic fennion density gives Qv = 0.230 y .)
In addition, simulations of structure fonnation in a neutrino-dominated universe
are unable to reproduce the observed structure. The best fit to all of the
cosmological data [4] gives
Ov < 0.015
(6.8)
which for three degenerate species implies
mVe < 0.23 eV
at 95% CL.
(6.9)
It is, therefore, clear that relic neutrinos too constitute only a small fraction of the
total energy density. We might have anticipated that the dominant contribution to
the present energy density would come from the matter comprising the galaxies
and the contribution of the baryons is the largest. However, it is nowhere near
large enough to account for the total energy density. Thus, we may be confident
that the major contributions to 00 are not from known sources. In any case, as we
shall shortly see, there is strong evidence that there is a large amount of invisible
'dark matter' in the universe [5].
The possibility of dark matter was first suggested by Kapteyn [6) in 1922,
who noted that its mass could be estimated from the velocity distribution of stars
in our galaxy. The strongest evidence for its existence comes from measurements
of rotation speeds of spiral galaxies. If we consider a star moving with speed v(r)
in a circular orbit of radius r outside of a spherically symmetric mass distribution
with a total mass M (r) interior to r, then
GNM(r) = rv(r)2.
(6.10)
The speed v(r) can be detennined for luminous objects such as stars or gas clouds
by measuring the Doppler shifts in emission or absorption lines and the mass
distribution M (r) is then inferred from (6.10). The mass of a spiral galaxy can be
detennined by taking r to be the radius within which most of the light is emitted.
In this way, the average galactic mass (mgaJ) can be calculated. Combining this
with the measured number density ngaJ detennines the average energy density
(Plum) = ngaJ(mgaJ).
(6.1 I)
These measurements show that the contribution of luminous matter is
Olum ~ 0.01.
(6.12)
173
Further, this bound effectively applies to all neutrino species, since the SuperK
[2] and SNO [3] data show that the mass differences for atmospheric and solar
neutrinos are tiny:
l\m~.atmos :::::: 3 x 10- 3 eV 2
(6.6)
l\m~.solar:::::: 7 x 10- 5 eV 2 .
(6.7)
Thus the sum of the neutrino masses is at most, 6.6 eV and likely to be much
smaller. (When mv « To, the relativistic fennion density gives Qv = 0.230 y .)
In addition, simulations of structure fonnation in a neutrino-dominated universe
are unable to reproduce the observed structure. The best fit to all of the
cosmological data [4] gives
Ov < 0.015
(6.8)
which for three degenerate species implies
mVe < 0.23 eV
at 95% CL.
(6.9)
It is, therefore, clear that relic neutrinos too constitute only a small fraction of the
total energy density. We might have anticipated that the dominant contribution to
the present energy density would come from the matter comprising the galaxies
and the contribution of the baryons is the largest. However, it is nowhere near
large enough to account for the total energy density. Thus, we may be confident
that the major contributions to 00 are not from known sources. In any case, as we
shall shortly see, there is strong evidence that there is a large amount of invisible
'dark matter' in the universe [5].
The possibility of dark matter was first suggested by Kapteyn [6) in 1922,
who noted that its mass could be estimated from the velocity distribution of stars
in our galaxy. The strongest evidence for its existence comes from measurements
of rotation speeds of spiral galaxies. If we consider a star moving with speed v(r)
in a circular orbit of radius r outside of a spherically symmetric mass distribution
with a total mass M (r) interior to r, then
GNM(r) = rv(r)2.
(6.10)
The speed v(r) can be detennined for luminous objects such as stars or gas clouds
by measuring the Doppler shifts in emission or absorption lines and the mass
distribution M (r) is then inferred from (6.10). The mass of a spiral galaxy can be
detennined by taking r to be the radius within which most of the light is emitted.
In this way, the average galactic mass (mgaJ) can be calculated. Combining this
with the measured number density ngaJ detennines the average energy density
(Plum) = ngaJ(mgaJ).
(6.1 I)
These measurements show that the contribution of luminous matter is
Olum ~ 0.01.
(6.12)