COSMOLOGICAL DARK MATTER: An Overview

Historical aspects, Baryonic & Non-baryonic Candidates, Models of
Structure Formation incorporating cold and hot dark matter.

© 1996-7 by Alex Gary Markowitz. All rights reserved. This text may be
freely redistributed as long as it remains unedited and contains this notice.
Any republication requires the author's written permission.

CONTENTS:

Introduction

Historical
Aspects, M/L
Ratios in the universe, Kinematics of Dark
Matter

Baryonic DM
Candidates: Gravitational
Microlensing to search for MACHOs, White Dwarfs, Red Dwarfs, Brown Dwarfs &
Planetary Objects, LSB galaxies, Neutron Stars, Black Holes, Gas, Dust Clouds, Quark Nuggets

Non-Baryonic DM
Candidates: Neutrinos, SUSY particles, Axions

CDM &
HDM

Models of
Structure Formation, TDM, Biased Galaxy
Formation

Topological
Defects

WIMP
Detection, Non-Baryonic DM as a
Quantum Fluid & its role in Star Formation, Review & Bibliography

Links to
other DM sites

Note: Since it's impossible, as far as I know, to render most Greek symbols
in HTML, the following representations are used: rho (density) is
p; the density parameter Omega (univ.'s current density/univ.
critical dens.) is represented by a W; Pi (3.14159...) is pi; h-bar
(Planck's const./2pi) is h-; Lambda (repulsion term in Freidman Eqn.) is
L; nu, the symbol for neutrino, is n; alpha is a;
capital Delta is D; tau is t; Theta is q. Also, solar mass
is denoted by Mo. --AGM

Astronomers originally thought that all the luminous material in
the sky comprised all the mass in the universe. This line of thought is
virtually nonexistent nowadays, owing to the massive accumulation of evidence in
support of non-luminous matter known as cosmological dark matter. At both small
and large scale lengths, astronomers have found that there appears to be more
mass present than can be accounted for by known quantities of luminous matter.
It is estimated that at least 90% of all the matter in our universe is non-
luminous. Because dark matter has virtually no interaction with normal matter,
it emits blackbody radiation either very weakly or not at all, and so it can be
detected only by its gravitational influence. The presence of dark matter in
galaxies and clusters has an effect on the kinematics of these systems, and has
immense implications for structure formation.

HISTORICAL TIMELINE
The historical timeline of dark
matter consists of regular increases in pieces of evidence suggesting its
existence. Historically, even though most developments pertaining to dark matter
occurred during the twentieth century, there were dark matter-related
developments before 1900: the first suggestions of non-luminous objects. The
late 18th century saw predictions by Mitchell, Simon, and LaPlace of the
existence of black holes, objects with vesc > c. White dwarfs were
first detected as companions to Procyon and Sirius, and two new planets (Uranus
and Neptune) were discovered in our solar system during this time as well
(Planets are not completely non-luminous, but their mostly infrared
contributions to the universe's light can be ignored.). Jupiter- size planets,
white dwarfs, and black holes today remain three prime candidates for baryonic
dark matter, as we shall see later. {2G}

In the early twentieth century, both Johannes Kapetyn and Sir James Jeans
determined the approximate mass density in the solar neighborhood from the
distribution of stars above the galactic plane and their velocities. Both
concluded that non-luminous matter was present; Jeans stated "there must be
about three dark stars... to every bright star." {2G}

During the 1930s, Swiss astronomer Fritz Zwicky concluded that galaxies in
the Coma cluster, 300 million ly away, were moving too fast. Applying the Virial
Theorem (to be discussed later) to the cluster resulted in expected velocities
for the galaxies that were less than the observed velocities. Similarly,
Sinclair Smith, studying the Virgo cluster in 1936, observed galaxies moving
very swiftly, yet not escaping. Smith proposed that internebular material,
undetectable as of yet, provided the missing mass.

The first measurement of the rotational velocity curve for M31 was attempted
by Horace Babcock in 1939. Extragalactic determinations of properties such as
luminosity and mass depend on the distance to our galaxy, and this uncertainty
in the extragalactic distance scale often prevented astronomers from getting
accurate results. Though the extragalactic distance scale contains some
uncertainties today, there is a greater amount of accuracy. In the late 1930's,
the distance to M31 was estimated by Hubble to be 210 kpc instead of today's,
more accurate, value of 700 kpc. Using the 210 kpc value, Babcock found M31's
average M/L value to be 50. Today, we measure it as being about 14. Shirley
Patterson, in 1941, first determined the brightness distribution for M33, the
Triangulum Spiral. {2A}

During the 1940s and 1950s, Jan Oort studied the motions of stars normal to
the plane of the disk. Over millions of years, stars oscillate up and down as
they orbit the galactic center, and for nearby stars, Doppler shifts of the
spectrum yield this z-component of velocity. Oort found that the gravitational
field for the disk drops off linearly as one moves away from the plane of the
disk; it is given, for z < 50pc, by gz =
-go(z/zo).
For z > 50pc, the
field drops off much more strongly. Since
d(gz)/dz = -4piGp, the density in the
solar neighborhood is given by p=go/4piGzo. This
expression for p, which is the total density of all matter, is Oort's
Limit. {8} It was estimated by Oort to be
.15Mo/pc3. However, p from all known stars is
.038 Mo/pc3, and p from dust and gas in the solar
vicinity is around .08Mo/pc3, implying "hidden" matter.
Oort concluded that "light is not always a reliable trace of matter."
{1}

During the 1940s and 1950s, astronomers looked at motions of clusters in
Superclusters including Virgo, Hercules, and Canum Venaticorum, again finding
cluster velocities that were too high. M/L was found to be 100-1000.

By the early 1960s, opinions regarding the unusual observations seemed to
fall into two main categories: either there was dark matter (thought to be
associated with the clusters more than with individual galaxies), or the
clusters were somehow expanding outward, perhaps due to some explosive
mechanism.

Vera Rubin and W.K. Ford, of the Carnegie Institute in Washington, studied
the rotation curve of M31 using neutral hydrogen radio lines, over thirty years
after Babcock's first measurements of M31 in 1939. Their findings: The velocity
of the outer part of M31, which should drop off as r-1/2 as mandated
by Kepler's Laws and the Virial Theorem, leveled off at around 200 km/s. In the
early 1970s, radio astronomers concluded that hydrogen gas at the edge of
galaxies moved with roughly the same velocity as hydrogen gas towards the
center, an additional confirmation that the rotation curve flattened off with
increasing radius.

In 1973, J. Ostriker and P. James. E. Peebles of Princeton University
conducted a computer simulation of a luminous galaxy disk, without a spherical
halo of dark matter. The disk became unstable, star's orbits grew eccentric, and
some even flew off. The reason was that disruptive vibrations, resulting from
small concentrations of matter in the form of globular or galactic clusters,
amplified and shattered the disk. They concluded a spherical halo, at least as
massive as the luminous disk, was needed to dampen these vibrations and restore
stability to the disk. {3, 6}

In 1974, there were publications of data that proved that measurements of M/L
increase monotonically with the length scale over which it is measured. This
implies that mass is not directly proportional to luminosity. These publications
persuaded most in the astronomical community to favor dark matter as the source
of the "missing mass" (or "missing light," to be more exact) over other theories
such as the outwardly-expanding clusters.

There have been further observations since then that further support the
existence of dark matter. In 1987,
M. Aaronson, of the Univ. of Arizona,
studied the velocities of carbon stars in the Draco dwarf galaxy. The stars
moved more quickly than the Virial Theorem expected, again implying hidden
matter. In addition, without a dark matter halo, the Draco dwarf galaxy would be
tidally distorted. Furthermore, X-ray emissions from gas in M87, a big
elliptical galaxy at the center of the Virgo cluster are detectable. The gas
should have escaped, if not held in place by hidden matter. The stars form 5% of
the matter there, the gas, 5%, and hidden matter, 90%.

There is evidence for dark matter within our own Local Group. M31 and the
Milky Way are approaching each other at about 100km/s as they orbit around the
center of the cluster, a speed too high if mutual gravitational attraction
between the two giant spirals and the dwarf galaxies is considered. Astronomers
conclude that there should be about ten times as much dark matter as luminous
matter out there.

The Local Group is moving together with the Virgo Supercluster at about 600
kms, (It is this movement which gives us the dipole variation in the Cosmic
Microwave Background Radiation.) and the Hydra-Centaurus supercluster, too, is
falling towards what was dubbed "The Great Attractor," about 50Mpc beyond Virgo,
with a mass of 1015-16Mo. (See Figure 1, below)
Figure
1

In 1990, Faber and Dressler confirmed that galaxies on the other side of The
Great Attractor are being pulled towards it as well. There do exist rich
clusters in that direction, but they are about 160 Mpc away, too far away to
exert a substantial gravitational force. Until very recently, it was thought
that there was not enough luminous material in the area of The Great Attractor
to exert such a force; the conclusion was that is was form of dark matter,
perhaps even a cosmic string, a one-dimensional topological defect that will be
discussed later. {6} More recent observations have found that there
is indeed luminous material there- a massive supercluster. (As an aside, most
superclusters like it have massive clusters at their cores; the core of the
Great Attractor supercluster has recently been found to be the cluster Abell
3627. Though this cluster had been previously known, it was thought to be less
massive than it actually is because many of its galaxies were obscured by dust
in the Milky Way's disk) {12}

In 1986, Canadian astronomer Sidney Van den Bergh observed a faint (L =
10-5Lo) haze of dim filaments in the giant elliptical
galaxy M87. The haze could be normal stars mixed with brown dwarfs or other
baryonic candidates.

Dark matter is needed to explain the structure of Polar Ring Galaxies, rare
structures that consist of a ring of stars around a sphere of stars. (see Figure
2) According to computer simulations, the rings would dissipate quickly without
dark matter's presence in a halo. {3}
Figure
2: A Polar Ring Galaxy

MASS/LUMINOSITY RATIOS; CONTRIBUTIONS TO DENSITY PARAMETER
OMEGA

We now discuss M/L (units are Mo/Lo) ratios for various
galaxy types and clusters.

In elliptical galaxies, Mdark/Mlum = 10. Tracers are
X-ray gas, globular clusters and planetary nebulae (Fabian, 1986; Lowenstein,
1992). In dwarf galaxies, Mdark/Mlum = 12-15, looking at
gas emission lines (Freeman, 1994). {5D} For large spirals,
Mdark/Mlum for the whole spiral = 3-5.

Figure 3:

M/L

Omega**

Solar neighborhood (Oort)

2±1

.0014/h (.002)

Luminous, inner parts of spirals, ellipticals

4-20/h (5-25)

.003-.014

Binary Galaxies, small groups

50-100/h (65-130)

.035 - .7

Clusters*

200-400/h (265-530)

.14 - .28

Spiral, at re***

2

Outer parts of Milky Way(<100kpc)

30.5

Irregular Gxy(at RHolmberg)

2 (starforming,lots of bright OB stars)

Sd gxy(at RHolmberg)

2-3

Sb gxy(at RHolmberg)

6

Sa gxy(at RHolmberg)

8-10

Ellipticals

20-40 (no starform., old red stars)
{5D}

* M for Coma cluster =
2.5*1015/h Mo = 3.3*1015Mo; L
=8*1012/h2 Lo =
1.4*1013Lo; M/L = 350h =260. (Using Ho = 75
kps/Mpc, h = Ho/(100 kps/Mpc))
**Using M/LB =
1900h*W*Mo/Lo (LB: for blue
light)
***re: defined as I(re)=½I(r=0)--radius of disk
where lumin. = ½ lumin. at center of disk

For M31, we can combine the brightness distribution (as first determined by
Redman and Shirley in 1937) and the the mass distribution (as first found by
Babcock in 1939 and Wyse & Mayall in 1942) to get M/L
(r). (see Figure 4). Average M/L for M31 as a whole, using today's values, is
about 14; we have L=2.1*109Lo, and
M=3.2*1010Mo.
Figure
4: M/L in M31
Babcock, who had used Hubble's estimated distance to M31
of 210 kpc instead of today's more accurately known value of 720kpc, obtained
M=1.02*1011Mo and M/L = 50. {2A}

For M33, M/L increases monotonically with distance (see Figures 5 and 6), as
first determined by Shirley Patterson in 1941.{2A}
Figure
5: M/L in M33

Figure 6: M/L in M33

Small groups of galaxies and binary galaxies yield W=.06 {5E}
Clusters' contribution to W=.1 - .3. Clusters made entirely of baryonic dark
matter contribute W = .1 - .3 {6}. The value of Wo,
judging from large-scale flows (LSF), flows relative to the Hubble
expansion-flow over length scales of megaparsecs, is WLSF =.3 - 1.
{5E} Clusters and LSF are strongest evidence that dark matter could
be non- baryonic, since the maximum contribution to Wo from baryonic
matter is 0.1 (to be discussed later).

Note that the mass contribution increases with larger scales, as
Wgxy < Wbinary galaxies < Wclusters <
WLSF.

It should also be mentioned that Wlum. = 0.05 - .01 {6}

KINEMATICS AND DARK MATTER

For large spirals, the luminous disk is described by I(r) =
Ioexp(-r/R), with R=4 kpc for the Milky Way.
The dark halo component, which could extend up to 100kpc from the center of
large spirals and ellipticals, does not follow the same distribution, but it can
be determined as follows: V(r) = constant, about 220km/s for the Milky Way,
towards the edges, from the rotation curves. For equilibrium, {5C} we
have mV2/r = GmM(<r)/r2, which
leads to M(<r) = rV2/G, or p(r) is proportional to
1/r2. p(r) could be described by p(r) =
po(Ro/r)2, except at the very center,
where this diverges. Another form for p(r) is po/(1
+ r2/a2), with a = 10kpc and
po = .01Mo/pc3 for our galaxy. {8}

If it is assumed that galaxies (disk + dark halo) are dynamically stable
systems and in steady-state equilibrium, we can apply the Virial Theorem, which
says 2K = -U, where K and U and kinetic and potential energies, respectively.
Since K=½m<V2>, and U = -aGMm/r (a depends on
the mass distribution, and is usually 0.5 - 2.), we have
M=<V2>r/aG. r and <V2> can be
determined from observations. Adding masses of all visible material together
yields an observed Mluminous less then the theoretical
Mvirial, implying hidden matter. {8}

Clusters are considered to be not as dynamically relaxed as galaxies. For
some clusters, the virial theorem can also be applied as above; the requirement
is that the mean crossing time for galaxies
(Tcr =
6*108yr*[(R/1Mpc)/(v/103kps)]; R= cluster radius; v=
average galaxy velocity) must be much less than the age of the universe. Once
the Virial Theorem is applied, it is found that for clusters, there is 10,
sometimes even 100, times as much dark matter as luminous matter. As an example,
for a typical cluster, there should be 1015Mo, but total
known galaxies and observed hot interstellar gas both account for
1014Mo. This would mean 80% of all matter in the cluster
is dark.

The distribution of hidden matter in clusters may not go as 1/r2
like in galaxies. If all or most of the dark matter is concentrated towards the
center of the cluster, and r decreases, then M (= <V2>r/aG)
also decreases. Here is a constraint, since if one reduces r too much,
Mhidden becomes negligible.{8}

Tyson used gravitational bending of light by the Abell 1689 cluster, finding
that the mass is mostly concentrated towards the cluster's center, becoming much
thinner towards and beyond the cluster's visible edges. The dark matter and
luminous matter again follow different mass distributions, (1/r2 for
DM) {1}

A discussion on how to physically make objects out of dark matter, using
phase space constraints, allows us to arrive at certain constraints. Assume that
the dark matter particles interact through gravity, but don't collide with each
other. If the phase space distribution function is
f(x,y,z,px,py,pz,t), then the number of
particles in volume DxDyDz with momentum
DpxDpyDpz at
time t will be
f*DxDyDzDpxDpyDpz.
If the available phase space is full up to some momentum po, then
f=Ns/h- (Ns:# of spin states; h-: h/2pi) for p
=
(px2+py2+pz2)½
<= po. f = 0 for p > po. The important point is that
f is constant, meaning that when gravity causes particles to move closer
together (Dvol (= DxDyDz)
decreases), there's a larger spread of momentum. However, the maximum momentum
must remain less than the escape momentum for structures to form. This
constraint on momentum restricts how the particles contract and grow closer
together. {8}

Dark matter is generally divided into two categories: Those composed of
baryonic material, and those composed of non-baryonic material. The baryonic
candidates emit only extremely weak blackbody radiation, and the best candidates
are generally massive aggregates of particles rather than individual particles.
The non-baryonic candidates are neutral; the lack of charge means there is no
electromagnetic interaction with other charged matter, and so there is no
radiation emitted from these particle. They are thought to be in the form of
separated, individual particles.

BARYONIC CANDIDATES

The suggestion that the dark matter has the same rotational velocity as the
visible matter suggests that both are composed of the same type of material --
baryonic. {2E} Baryonic dark matter candidates that comprise a dark
halo of a galaxy or cluster are often called Massive Astronomical Compact Halo
Objects, or MACHOs. (The name was suggested as a contrast to non-baryonic Weakly
Interacting Massive Particles, or WIMPS, which will be discussed later.)

The best candidate for baryonic dark matter is white dwarf stars (or black
dwarfs, equivalently); there is evidence that galaxy halos are composed of up to
50% white dwarfs. Another candidate is cold, fractal gas; there is evidence for
and against gas' being a major form of dark matter. Other candidates, including
brown dwarfs, jupiter-sized objects, dim/infrared stars, neutron stars, and
black holes, will be discussed, but they are probably not good choices for
baryonic dark matter.

MICROLENSING, WHITE DWARFS

A prominent method to search for any MACHOs involves the MACHOs'
gravitationally microlensing light from distant stars. Just as the images of
quasars can be gravitationally lensed into arcs or rings by a massive galaxy
aligned between the quasar and Earth, light received by a distant star is
amplified by an intervening MACHO in the Milky Way's halo as the light rays are
gravitationally bent around the MACHO. The EROS project (Expérience de Recherche
d'Objets Sombres), conducted at ESO in Chile, looks at stars in the LMC to see
if their light is amplified. The amplification factor A, which typically results
in brightness by about 1 or 1.5 magnitude, is A =

( u2 + 2 )
-------
(u(u2+4)½)

where u=r/RE. r is the impact parameter, and RE is the
Einstein radius,
(2/c)(GMLx(1-x))½. M is
the mass of the MACHO, L is the distance to the LMC star, and xL is the distance
to the deflector (x = distance to deflector/ distance to star). (See Figures 7
and 8)
Figure 7

Figure 8

The mean timescale for the amplification of magnitude is given by <t> =
<RE>/VT, (where VT is the tangential
velocity of the MACHO). This equals (M/Mo)½*70 days for
stars in the LMC. For example, if the event lasts 30 minutes, the MACHO's mass
is 10-7Mo, typical for a planet. If <t> is 3 weeks,
the mass is 0.1Mo, typical of a red dwarf/IR star. A <t> of 5 -
8 weeks would indicate a MACHO mass in the white dwarf range. {5C}

Obviously, not all amplifications of LMC stars will go noticed, only those
with A > some Athreshold. This will happen when the bender is
inside the threshold area, when u < uthr = [2[ [Athr /
(Athr2 - 1)½] - 1] ] ]½

and so the number of expected events with A > Athr during some
observing time T will be
(1.7*10-6)(Mo/M)½(uthr)(T)(Nst).
Nst is the number of background stars. (It is necessary to continue
to observe the microlensed star after the event to make sure that the star's
fluctuating brightness is not due to its being a variable star.)

The EROS project observed two such microlensing events, in Dec.
1990-Jan. 1991, and Jan.-Feb. 1992. <t> was about 30 days for both,
implying a mass of .7Mo, in the range of white dwarf stars or black
dwarfs. White dwarfs (M < 1.4Mo) expire further to become black
dwarfs) {5C}

It was announced at the Jan. 1996 meeting of the AAS that a research team led
by Dr. D. Bennett of Lawrence Livermore National Laboratory had discovered, via
microlensing, a total of seven MACHOs, using telescopes in Australia to study
9*106 LMC stars. The average event time for all seven MACHOs was two
and a half months, and they all were in the white dwarf mass range. The team
assumed a value for the total mass of the dark halo, and estimated that as much
as 50% of the halo could be in the form of white dwarfs, judging from the number
of events. It is possible that these objects could be extremely small black
holes, but if the findings hold, then white dwarfs are a major component to the
dark halo.{9} The stars that turn into white dwarfs are very massive,
giving off a lot of their mass when they expire. A halo composed of white dwarfs
would require our galaxy to have a vast amount of interstellar material
throughout the halo, far more than we believe there to be, as well as a lot of
massive stars comprising the halo at some earlier time. This is very puzzling,
since the microlensing evidence is very strongly in support of white dwarfs (or
black dwarfs) as baryonic dark matter.

More microlensing events have also been recorded by the MACHO project; click
here to visit their list.

Microlensing of stars in M31 by MACHOs in M31's halo was originally proposed
by Arlin Crotts. While microlensing of M31 stars would be due to MACHOs in both
M31's halo and the Milky Way's halo, the majority of MACHOS detected should be
in M31 itself. {2B} A French group known as AGAPE (Andromeda Galaxy and
Amplified Pixels Experiment) is currently undertaking this task. Furthermore,
Crotts and Tomaney have reported possible two microlensing events in M31, again
caused by objects in the white dwarf range. They also reported not detecting any
microlensing caused by brown dwarf- or Jupiter-sized objects. {15}

DIM/IR STARS

The next baryonic dark matter candidate is dim infrared stars, which radiate
more in the infrared than in visible. IR stars have a mass of about
.1Mo. They are a candidate for dark matter because they are
intrinsically fainter than the low mass main sequence stars, and beyond the
solar vicinity, most are too faint to be detected. However, from direct star
counts in the solar vicinity, there are not enough to make a substantial
contribution to the dark matter mass. (Gilmore & Hewett, 1983; Richstone,
1992) {5D} Observers using the Hubble Space Telescope have arrived at
the same conclusion (see the press release at the HST web site, www.stsci.edu/pubinfo/press-releases/94-41.txt):
Dim stars account for at most 6% of the mass of our galaxy's
halo.{11}

BROWN DWARFS, JUPITERS

Another candidate for baryonic dark matter is brown dwarfs. These so- called
"aborted stars" have a mass around .08Mo, and can't convert hydrogen
into helium (Their cores never reach the threshold temperature for hydrogen
burning.). The only energy radiated is due to gravitational contraction
(Kelvin-Helmholtz contraction), which is why they are difficult to detect unless
they are located near us. To determine if brown dwarfs contribute substantially
to the dark matter mass, we need to estimate their number. We can use the
Stellar Mass Function, F(M) (proportional to M-2.33), to extrapolate
the number of brown dwarfs from the numbers of more massive stars. If F(M)dM =
the number of stars with mass between M and M+dM, then the total mass
contribution from brown dwarfs can be written as (M)(F(M))dM. The question is,
how does F(M) behave for very low M? F(M) is proportional to M-2.33
only for main sequence stars, not for brown dwarfs. In general, giant clouds of
gas and dust collapse, then fragment. The smaller fragments, which become K and
M stars, are more abundant then the larger fragments, which become O and B
stars. However, the amount of small fragments drops off right near the size
needed to make brown dwarfs, limiting the number of brown dwarfs that could
exist, and also providing a great uncertainty as to that number. It is generally
unknown whether the value where F(M) reaches its maximum is greater or less than
brown dwarf mass. It is also conceivable that F(M) is bimodal, (Figure 9),
allowing a large number of brown dwarfs to exist. {8}
Figure
9

If all the dark matter is composed of brown dwarfs, we would need one brown
dwarf every 30 ly3 of space, many trillions over the entire Milky Way
{1}. The number of known brown dwarfs and brown dwarf candidates in
our section of the galaxy are exceedingly slim, however, making it unlikely that
the density of the galaxy's brown dwarf population accounts for all the dark
matter.

Detection of brown dwarfs is difficult, since they are not only intrinsically
faint (LBr.Dw. = 10-4Lo), they could have a lot
of dust or other molecules in their atmospheres, to make them even fainter.
{1} Objects with even smaller masses, jupiter-sized or even smaller
planets, are even harder to detect. The only energy these objects radiate energy
is also from gravitational contraction. If a jupiter, brown dwarf, white dwarf
star or other massive object is orbiting another larger and brighter star, we
could potentially see the Doppler-shift "wobble" in the spectrum of the larger
star (the method by which the first planets outside our solar system were
discovered). However, as far as cosmological dark matter is concerned, these
objects are already counted as part of the mass of the larger star. A spherical
halo composed entirely of jupiters is possible, but because their mass is 10-100
times smaller than that of a brown dwarf, we would need a number density in our
galaxy even greater than that of the brown dwarfs, if jupiters were to comprise
all the baryonic dark matter. If present in the halo as MACHOs, jupiters
probably make only a minor contribution to the galaxy's mass density.

There could exist brown dwarfs or jupiters at the centers of rich clusters.
X-ray-emitting gas cools, and several hundred Mo/year falls towards
the cluster center, sometimes into massive (cD) galaxy at the center. Gas
becomes invisible at some point; it could form dozens of faint, low mass stars,
as well as brown dwarfs and jupiters. If the gas formed big stars, we would
observe them.

Another candidate for baryonic dark matter is comets ("dirty snowballs"), but
they would have to exist in extremely high quantities to have a
contribution to WDarkMtr. Perhaps comet or snowball clouds could
exist in the ISM of galaxies, or even have a spherical halo distribution just
like the other low- mass MACHOs, brown dwarfs and jupiters. {2A}

LOW SURFACE BRIGHTNESS GALAXIES

There aren't enough brown dwarfs or red dwarfs to constitute all of the
universe's hidden mass, but low surface brightness (LSB) galaxies (diffuse
galaxies with a surface brightness 5 - 20 times fainter than normal galaxies)
also make a contribution. Like other the previously mentioned forms of "dim
matter," LSB galaxies don't account for all the dark matter in the
universe. Their exact contribution is still undetermined since their exact
number is not yet well known. As telescopes improve, and more LSB galaxies are
discovered, astronomers will be able to get a better handle on their number.
{14}

LSB galaxies themselves contain large amounts of dark matter, as measured
from their rotation curves-- another contribution to the total amount of dark
matter in the universe.{14}

NEUTRON STARS

Neutron stars, with M (M > Chandrasekar limit) between 1.4 and 2
Mo, are probably not a major contributor to the dark matter mass. The
stars that form neutron stars are around 10Mo, so over 8Mo
of material is thrown off during the supernova, to be used as material to make
new stars, or remain as interstellar gas. If there is a significant number of
neutron stars, then a majority of all the galaxy's mass must have passed through
a large number of early supernovae. This would have lead to a larger abundance
of the heavier elements than what is currently observed, since so much material
was recycled. {5D}

BLACK HOLES

Massive black holes are generally frowned upon as a viable baryonic dark
matter candidate, since they would cause velocities of any other objects in
their vicinity, including disk stars if the black hole is near a spiral's disk,
to increase dramatically. Since the component of velocities normal to the disk
would also be amplified, spirals' disks would thicken; this is not
observed.{4, 5}

A halo composed of 106Mo black holes would result in a
black hole forming at the nucleus of the galaxy, since objects would fall into
and accumulate at the center. The black hole at the center would, under these
conditions, have a mass greater than the observed limit of
3*106Mo. A halo of 103Mo or greater
black holes would disrupt globular clusters in the halo.(Moore,1993) Black holes
of mass 102-3Mo, however, are a
possibility.{5D}

Primordial Black Holes, formed in the very early universe, are a candidate
for dark matter. Irregularities in the very early universe may have caused
spontaneous collapse of matter, leading to formation of very massive stars with
a very short lifetime, leading to black holes and neutron stars. At the time of
their deaths, they would have ejected little or no mass, or else we'd have seen
that evidence of their existence by now. Furthermore, primordial black holes
evaporate, according to Stephen Hawking. Due to the Heisenberg Uncertainty
Principle, the black hole's energy is not confined to RSchwartzchild
= MG2/c2. Unless they were above a
certain threshold mass (around 109-12 kg) when they formed, they
would have evaporated by the present day. {8}

GAS

At any temperature or density, gas will emit or absorb in some part of the
spectrum, making it very difficult to hide any gas in the solar neighborhood
{8}. (Cold gas emits radio frequencies; hot gas, UV and X-ray light)
Cold baryonic gas distributed uniformly around the Milky Way is therefore not
possible, since we'd have seen absorption lines in light from other galaxies. In
spiral galaxies, the gas that we know of tends to be more abundant in the the
outer regions than near the central bulge. Cold gas as clumps or clouds of
intergalactic material, as long as it's not in the line of sight of another
galaxy, would remain unnoticed. We do see frequent occurrences of Lyman-alpha
absorption lines in some quasars, and these clouds of intergalactic gas could be
as large as a normal galaxy.

While these facts suggest that gas cannot be dark matter because it cannot be
hidden, there is evidence to suggest there is both luminous and non- luminous
cold, baryonic gas in galaxies and clusters. The star formation properties of
galaxies supply evidence that dark matter is in the form of baryonic, cold,
fractal molecular gas. We know that the nearby interstellar medium is fractal
since we know of giant molecular clouds (100 pc) as well as tiny clumps (Bok
globules), .01 - .1 pc across. During tidal interaction between close galaxies,
the gas infalls, triggering a burst of star formation at the center for a
temporary period. Isolated galaxies do not display this phenomenon. In
interacting galaxies, we measure 4-5 times as much gas from CO emissions as the
isolated galaxies. {2E}

Furthermore, HI observations demonstrate that "early-type" spirals (Sa, Sb)
have a smaller dark mass/lum. mass ratio than "late-type" spirals (Sc, Sd). This
means that a large amount of baryonic dark matter is transformed into stars as
the system evolves, and in Sc and Sd galaxies, the dark matter must be in the
form of diluted H and He in order for star formation to occur. {2E}

There exists X-ray-emitting gas in rich clusters, and it can be studied by
various observatories including the Einstein and ASCA satellites. (Hot gas is a
good tracer for dark matter in clusters; it accumulates near over-densities of
non-luminous as well as luminous matter.) The gas, about 108°K, is
heated as it falls inward towards the cluster's center, and further by friction
between galaxies. Cold baryonic gas (about a third of it) therefore becomes
becomes visible to us, but only temporarily. The gas eventually cools, falls
towards the clusters center, and forms cold, tiny clumps of gas. Astronomers
estimate that the mass contribution of the gas is equal to the amount of mass
contributed by stars. or Wgas = Wlum = .05, approximately.
Wbaryon = .1, therefore. {2E}{13}

DUST CLOUDS

Clouds of dust, consisting of heavy (>He) elements, would redden and
absorb incoming light. The heavy elements, less than 2% by mass of all elements,
are produced in the interior of stars and injected into the ISM during
supernovae. If this dust were to be a major component of the dark halo, it would
necessitate a lot of other stars' being in the halo as well. Dust clouds are
therefore not a highly viable baryonic dark matter candidate. {8}

QUARK NUGGETS

Another baryonic candidate is quark nuggets, hypothetical clumps of many
quarks, up to 1mm- 1m in diameter, extremely heavy and slow-moving. A few
physicists have proposed that such an aggregate consisting of up, down, and even
a few strange quarks, could be stable. Quark nuggets could have been produced
during the early universe, and could make a non-negligible contribution to W if
they existed in sufficient numbers. {6}

NON-BARYONIC DARK MATTER

It is possible to determine the contribution of all baryonic matter in the
universe, luminous and non-luminous, to the density parameter W, by looking at
helium production from baryons during Big Bang Nucleosynthesis. When the
universe was one second old, the temperature was 1 MeV, and the ratio of the
number of neutrons to the number of protons is given by
Nn/Np = exp(-1.29MeV/1MeV) = 0.2
(The neutron is 1.29 MeV/c2 more massive than the
proton.). There was one neutron for every five protons. When the temperature of
the universe dropped to .1 MeV, deuterium production began (n + p -> D +
photon). A lone neutron has a half-life of only 11
seconds, so by the time deuterium production began, Nn/Np
was about 0.14. This was immediately followed by deuterium, protons, and
neutrons forming helium nuclei. Assuming all the neutrons ended up in helium
nuclei, we can find the primordial mass abundance of helium, Y, which equals
(2Nn/Np) / (1+ Nn/Np) = .25. The
experimentally determined primordial mass abundance of helium agrees with the
predicted value from Big Bang Nucleosynthesis: 23 to 25% of the universe's mass.
The amount of helium produced, as well as the abundances of more scarce elements
also produced at the Big bang such as deuterium and 7Li, help us to
fix limits for the value of Wbaryon. (Some primordial 3H
and 3He was also produced, as they are the products of intermediate
steps of helium production, but they are very unstable and haven't lasted until
today.) An increase in Wbaryon would mean an increase in helium
production and a decrease in deuterium abundance (The helium-producing reactions
are more efficient). A decrease in Wbaryon means a decrease in helium
production. Too high or too low a value of Wbaryon conflicts with
observed helium abundances. (See figure 10, below)

Figure
10

Wbaryon = np/h2, with np being
the number density of protons, and h = Ho/(100 kps/Mpc). Therefore

Wbaryon = (.02 ±.005)/h2. The most that
Wbaryon can be, using the upper limit above and
Ho =
50 kps/Mpc, is Wbaryon = 0.1. Since Wbaryon is so low, and
we believe that Wo is close to 1, as mandated by inflation, we arrive
at the conclusion that most matter in the universe is non-baryonic.
(W=1
means Wbaryon = .05 - .1 and Wnon-baryonic = .90 - .95)
Because all luminous matter is baryonic, the existence of non-baryonic matter
means the existence of non- luminous (dark) matter.

Non-baryonic dark matter is divided into two generic categories, cold dark
matter, CDM, and hot dark matter, HDM. Cold dark matter particles, which are
also called weakly interacting massive particles, or WIMPs, typically have
higher masses and move at slower speeds than HDM particles. Key differences,
which will be discussed later, are relevant to structure formation.

NEUTRINOS

The neutrino is an example of HDM, as it is almost massless, and it is an
excellent candidate for dark matter. There are, as of today, three families of
leptons, and therefore three families of neutrinos: the electron, with
ne- (associated with the up and down quarks and
anti-quarks), as well as their antiparticles, the positron and
anti-ne-; the muon, with nµ (and the strange
and charmed quarks) and their antiparticles; and the tau particle with its
associated neutrino nt, (and the top and bottom quarks) and all their
antiparticles. Their masses and lifetimes are given in Figure 11, below.

Particle

Mass (MeV/c2)

Lifetime

e-

.511

>2*1022 yr

ne-

<1.8*10-5

>300mnec2/eV

µ-

105.66

2.2*10-6 sec

nµ

<0.25

>1.1*105mnµc2/eV

t-

1784.2

3.04*10-13 sec

nt-

<35

?

(from source {8})

Figure 11: Lepton & Neutrino masses & lifetimes

It is difficult to determine the lifetimes, since interactions with normal
matter are so weak (virtually zero).

Initially, neutrinos were assumed to have a mass exactly equal to zero.
Today, it is generally assumed that neutrinos have a non-zero mass, but it is
difficult to pinpoint the exact value for the mass. Experiments can place an
upper limit on neutrino masses. The tau neutrino's mass, as determined by
experiments, is too high. Such a high mass, given the number density of
neutrinos, would cause W>>1, an over-closed universe. It is generally
assumed that the tau neutrino has a mass comparable with the other two, around
10-4me-. Currently, it is believed there are
108 ne-/m3. If neutrinos do have a
mass near its experimental upper limit, then it can have a major contribution to
the universe's mass. (Wntrno =
(mntrno/93eV/c2)/h2)

As stated before, there are, as of today, three known families of leptons,
and therefore three neutrinos (plus three antineutrinos). If there existed more
families of leptons and neutrinos that haven't been detected yet, these new
particles could comprise the non-baryonic dark matter. In 1989, physicists at
the Stanford Linear Accelerator Center and at the LEP particle collider at CERN
near Geneva examined the remains of the Z particle, which decays into neutrinos,
antineutrinos, and other particles as well. The Z can decay into any n's or
anti-n's that have less than half the Z's mass. The existence of extra neutrinos
would mean that there are additional ways for the Z particle to decay, which in
turn implies a shorter lifetime for the Z particle. Both groups concluded that
there were only three types of n's and anti-n's. {6}

Observations of SN 1987A suggest also suggest that there are only three
types. Neutrinos were detected on Earth hours before light from the SN reached
us. The calculated flux from the 3 known n's and 3 anti-n's yields the total
amount of energy carried by the 6 known particles. This energy is about equal to
the binding energy of a neutron star, which implies that all the energy released
that goes into neutrinos, goes into these three neutrinos, and no others.
Furthermore, there was a spread in arrival times of the SN 1987A neutrinos
(about 10 seconds), implying a spread in energies of the neutrinos. This implies
an upper limit of 25eV/c2 for the mass of the
ne- {6}. The uncertainties are great, however:
The star's central temperature could fluctuate as the neutrinos are emitted,
giving a larger spread of energies, and not all neutrinos were emitted at
precisely the same instant.

The number of classes of neutrinos is not only important for discussing the
contribution to W, but also Big Bang nucleosynthesis, since many parameters
influencing reaction rates depend on the total number of species present. If
there were four or five neutrinos, the helium abundance would be greater than
25% (See Figures 10 and 12: If there were four neutrinos, helium's mass
abundance would be around 27%; if there were only two types, it would be around
22-24%.) Our calculated abundances of primordial helium suggest that are only
three types of neutrinos, putting a restriction on the neutrino's contribution
to W.

Figure 12

SUSY PARTICLES

Other non-baryonic candidates for dark matter are the SUSY particles. During
the very early (before Planck time, 10-43 sec, or T >
1019GeV) universe's Super-Symmetry (SUSY), all four forces of nature
are united and indistinguishable. Fermions and bosons are indistinguishable in
this era, and can be transformed into one another. Every particle contains a
hypothetical SUSY partner particle with a spin differing by h-/2. The particles
associated with fermions are given names by adding "s" to the beginning of the
fermion name: The electron's SUSY partner is called the selectron, and there
also exists the sneutrino and the squark. For bosons, the associated SUSY
particle has "ino" attached to the end: gravitino, photino, gluino, higgsino,
etc. The W and Z particles have the Wino and Zino as their hypothetical SUSY
partners. SUSY is just a theory, and there isn't any experimental evidence or
detection of SUSY particle as of yet to directly confirm it. However, these
particles, if they have a non-zero mass (the fact that no SUSY particles have
been detected at particle colliders as of yet indicates that even the lightest
SUSY particle is at least 15GeV/c2), if they are stable enough to
last until today, and if they do exist, would contribute to the mass density of
the universe, and so they are candidates for dark matter. For example, the
hypothesized photino, the photon's antiparticle, has a mass 1-100
mproton and spin h-/2. {7} It is the lightest SUSY
particle, and can't decay into anything else, implying a nearly infinite
lifetime if left alone. Therefore, any photinos produced during the SUSY era
should exist today, and contribute to Wo; the photino is a non-
baryonic candidate for dark matter. {6}

AXIONS

Axions, extremely light hypothetical particles whose name was taken from an
old brand of laundry detergent{1}, are a prime candidate for non-
baryonic dark matter. They were proposed independently in 1978 by Steven
Weinberg of the Univ. of Texas (who proposed the name) and Frank Wilczek of
Princeton. Axions were produced in the early universe during a violation of CP
invariance. Three types of invariance apply to the laws of physics: Charge
invariance (C), the conservation of overall charge; Parity invariance (P), which
maintains that if the laws work for a certain system S, then they should hold
for a system S' spatially reflected through the origin; and Time invariance (T),
which maintains that the laws work when time is running either forwards or
backwards. The laws of physics are governed by CPT invariance (all three
operating simultaneously), but violations of P invariance and CP invariance
exist. In the very early universe, symmetries began to break down at some point,
leading to a violation of CP invariance. This CP invariance violation was
accompanied by large-scale production of axions; the number of axions produced
is probably even more than the number of neutrinos produced. {8}

Axion interaction is 1012 times lower than normal weak
interaction. If it were any stronger, then axions would be produced and emitted
from stars that make the stars' lifetimes much shorter than observed. Typical
mass: as low as 10-6 eV/c2 , and GUTs (Grand Unified
Theories - the stong, electromagentic, & weak forces were indistinguishable
in the very early universe) demand that their mass be
10-9me- {1}. If axions exist, there
would have to be 108/cm3 of space; they could account for
a substantial portion of the dark matter mass despite their extremely low
individual mass. {8} Their low velocities, despite their low mass,
and weak interaction with normal matter could potentially allow them to form
dark matter clumps very early on. {6}

Axions have not been detected yet, since their interactions with ordinary
matter are so weak. One theory on how to detect axions states that under an
external magnetic field, axions will transform into ordinary photons. However,
the axion's extremely low mass yields a correspondingly tiny photon energy. An
axion detector based on the axion's transformation into a photon would need to
store up the photons until they reach a detectable quantity. The detector would
also have to account for a wide range of frequencies since there are great
uncertainties in the axion's mass. (An axion with the typical mass, above,
yields microwave photons.) A few experiments to directly measure these photons
have been attempted, but they were not sensitive enough to detect anything.
Future prospects for axion detection must involve increased sensitivity. Another
experiment using the fact that axions turn into microwave photons in an external
magnetic field was proposed in 1983 by Pierre Sikivie of the Univ. of Florida.
The detector consists of an extremely strong magnetic field applied to a copper
cavity which is cooled near absolute zero (so that the thermal vibrations of the
copper itself do not interfere with the axions' microwave signals) and tuned to
a set microwave frequency. Axions inside the cavity would be converted into
microwave photons, which would show up as an excess amount of energy in the
oscillations of the cavity if the former axion's microwave frequency photon
matched the microwave- frequency oscillations of the copper cavity. Resonance
would occur, leading to the excess energy (see Figure 13).
Figure
13: Axion detector

In 1987, this detector was built and tested, but it was not sensitive enough
to detect any excess energy in the oscillations (and therefore not sensitive
enough to rule out the existence of axions altogether). {6} A larger,
more sensitive cavity has been built and is currently in use, but no axions have
been directly detected so far.

Axions decay into two equal photons, and the heavier the axion is, the more
quickly it will decay. Given these facts, if axions were to compose a galaxy's
halo, we would see soft glowing halos today if the axions had a mass greater
than 2 eV/c2 . Even thought the glow could potentially be so faint
that current technology isn't sensitive enough to detect it, its absence implies
the axion mass may be less than 2 eV/c2 , and, as seen before,
probably is. {6}

There are two possible mass ranges that make Wo = 1: Cold dark
matter, CDM, with individual particle masses around 1 GeV/c2 , and
hot dark matter, HDM, with individual particle masses of 10-100eV/c2.

CDM:
The exact mass of a cold dark matter particle depends on strength of
the particles' interaction with other matter, as well as the time and
temperature of the universe when the particles decoupled from other matter. CDM
particles interact with each other gravitationally and weakly with other
particles through the normal weak interaction. The mass range is around 1
GeV/c2. Early in the universe, the number density of CDM is about
equal to the number density of photons. After kBTuniv =
m(CDM)c2 , pair annihilation occurs, to produce more
photons, and lower the CDM particles' density until they decouple
(Tuniv =1010°K). What this means is a low number density,
but a high individual mass for each particle if Wo is to be 1. Masses
less than 1 MeV/c2 are ruled out, since they make
Wo<<1. {8}

HDM:
Much lighter in mass than cold dark matter particles,
hot dark matter particles travel at relativistic speeds. The known candidates
for HDM are the 3 known types of neutrinos and their corresponding
antineutrinos. ne- and nµ are known to be HDM,
but experimentally, nt's mass isn't low enough. If the
nt's mass is much greater than the mass of either of the other two,
then this would imply Wo>>1, which is incompatible with ages of
certain objects and the universe. It's assumed nt is comparable in
mass to ne- and nµ-, even though
that hasn't been experimentally confirmed yet. As stated earlier,
Wntrnoh2 = mntrno/93eV. The mass density
contribution of HDM can also be written as WHDM/Wo =
[(0.4)(Ns/6)(mprotc2/10eV)(Tradiationo/2.74°K)3(Ho/100kps/Mpc)-2]
Ns = number of spin states from all HDM particles. Ns = 6
if the known neutrinos are the only ones that exist; if other HDM particles
exist, that decoupled earlier than neutrinos, Ns will increase. This
implies an HDM mass of
10 - 100 eV/c2. Any relativistic particles
with mass above 100 eV/c2 would greatly overclose the universe, so
this value is assumed to be an upper limit. {8}

STRUCTURE FORMATION:

Visible (baryonic) structures form only after baryonic matter decouples from
radiation (around z = 1000). Before decoupling, the baryons can't
gravitationally contract through the radiation field. However, structure
formation is not determined by baryonic matter alone; non-baryonic dark matter
plays a critical role.

The key difference between CDM and HDM is their role in structure formation.
There are generally two opposing views on structure formation, both dependent on
which type of dark matter dominates. HDM domination is conducive to the method
of fragmentation, where structures the size of clusters form first, and galaxies
themselves appear later. CDM is conducive to the method of hierarchal
clustering, whereby galaxies form first, and then they aggregate to form groups
of galaxies, which in turn aggregate to form weak clusters, then rich clusters,
then superclusters. The main question is which came first, galaxies or clusters?
Dynamically speaking, clusters are much younger, more unstable, and
irregularly-shaped more often then galaxies are. There hasn't been enough time
for clusters to "relax" and become completely stable systems. Being able to
identify which objects were the first bound objects (galaxies or clusters) would
answer the question as well, and select one method of structure formation over
the other.

Because HDM particles' speed is close to c, gravity won't easily confine them
until their speeds drop to non-relativistic speeds. Any small fluctuations in
density tend to be erased by neutrino free-streaming (particles' speed is so
great that any small scale density pattern is lost immediately). The result, if
HDM dominates, is that short-length perturbations are erased, and the long-
length perturbations remain. The length scale is given by L =
(13/Wh2)Mpc = 41 (mntrno/ 30eV/c2)Mpc.
(Fluctuations less than this critical wavelength become damped out by the
free-streaming.) The critical mass equals galaxy cluster mass, and the first
bound objects are associated with large scale structure. Cluster-sized objects
form first, and these structures collapse into pancake- shaped structures, which
later fragment into galaxies. This gives us galaxies that are concentrated into
walls of bubbles and voids, giving us the large-scale (length scale of hundreds
of megaparsecs) structure we see today.

One suggestion of structure formation related to fragmentation involves
gigantic explosions, megaparsecs across, sweeping up interstellar gas to form
shells during initial structure formation. These spherical shells fragment and
form the galaxies we see today concentrated into walls of bubbles. Inside the
shells, there were no seeds for formation, and hence virtually no galaxies exist
inside those voids today. {7}

In contrast to the HDM, CDM particles are heavier, and slower-moving, so
gravity can confine them in the small density perturbations. In the CDM-
dominated scenario, after decoupling of CDM with radiation and other particles,
objects the size of globular clusters form. Critical mass is about
105-6Mo. Larger objects subsequently form by aggregation,
as hierarchal clustering occurs.

Because HDM particles can't form self-contained structures until their speed
drops to non-relativistic speeds, they form structures much later than the CDM
particles will. Because of this, galaxies appear earlier on in the CDM-
dominated model than in the HDM model.

Models of structure formation, from decoupling until the present era, are
subject to several constraints. These models are best calculated as N-body
simulations on a computer, which is given some initial density and velocity
distribution, in some expanding spatial region. Other initial conditions are the
number and size of density fluctuations, which can't conflict with the observed
Cosmic Microwave Background Radiation, or CMBR. Typically, N= 1-2 million, mass
of each test particle is 1011Mo (one galaxy), in a volume
(80 Mpc/h). (h = Ho/100) All interactions between dark matter
particles must be gravitational only. Furthermore, clustering properties of the
model or simulation must reflect clustering as observed. A good way to compare
the amount of clustering between the model and reality is to discuss the galaxy
correlation function. Given one randomly chosen galaxy, the probability of
finding a neighboring galaxy a distance r away from the first is p =
(n)(Vol)(1+x(r)), where n is number density, x(r) is the spatial correlation
function, and Vol is a given volume of space. If the points are correlated
(clustered), then x(r)>0. If x(r)=0, there is no clustering, and the formula
reduces to p=(n)(Vol), which is what we expect for a completely random
distribution of points. One can also define the angular correlation function,
w(q) (theta is represented by the letter q), by
p=(n)(DW)(1+w(q)), for some solid angle DW. For the observed universe,
x(r)=(r/ro)-g, with g =1.8 and ro=6.7Mpc/h.
Also, w(q) =(q/qo)-g+1. x(r) is large for small r, meaning
there's a high probability of finding galaxies right next to each other. This
comes as no surprise: galaxies tend to cluster right next to each other. For
very large r, x(r) approaches 0, and the formula reduces to p=(n)(Vol), meaning
there's a more random chance of finding a galaxy at a large r. This is
consistent with the universe's property of tending to bubbles, walls and voids
at large (hundreds of megaparsecs) scales. The main point is that the spatial
and angular galaxy correlation functions for the computer model must match w(q)
and x(r) for the observed universe. If the computer simulation yields x(r) with
an ro not 6.7 Mpc/h or g not 1.8, then it needs to be corrected or
revised. One can simlarly define spatial and angular correlation functions for
clusters and use them in the same way.

In comparing the results of N-body simulations to with what's observed, one
must keep in mind that large-scale observations of the universe and distances to
clusters are not without uncertainties, mainly because the extragalactic
distance scale is not known precisely. Furthermore, the random velocities of
galaxies with respect to their cluster's center of mass are not well known; what
we observe is the random component plus the radial velocity of the whole
cluster. Applying Hubble's law, vrad=Hod, and directly
plotting what is observed yields the "Fingers of God" effect-- an apparent
elongation in the values for vrad. (see Figure 14) {7, 8}

Figure 14

A model that favors CDM over HDM, or vice versa, and that agrees with the
observed universe also implies the method by which structures formed
(aggregation or fragmentation). It appears that galaxies first formed very
roughly around z=3, and some quasars have z well above 4. A major problem with
an HDM-dominated model is that since larger structures form first, smaller
structures like galaxies don't appear on the scene until very late-- redshift of
2 or even 1. However, we do observe very large scale structure (about 100 Mpc)
in the universe, a length more natural for HDM than CDM.

In all the models, Wtotal is set to 1, as mandated by inflation.
Models that are purely baryonic (no dark matter at all, Wbaryon = 1)
are not plausible, not only because they don't directly agree with what is
observed, but because the observed light element abundances would be different
from what is observed. (From Big Bang nucleosynthesis, Wbaryon is
generally equal to .05, approximately.)

Models of pure HDM (Wn =1) are implausible. They do not resemble
what is observed, since the observed universe tends to have more clustering of
matter than the HDM models do. (and there is an excess number of great galaxy
clusters) (Figures 15 and 16) In addition, as stated earlier, galaxy formation
in the HDM model doesn't occur until as late as z=1, and we observe galaxies
with z=3 and quasars with z>4. {7}

Figure 15:
Galaxy Formation Scenarios. Aggregation/CDM (top) and Fragmentation/HDM
(bottom)

Figure 16: CDM
& HDM (simulated) Galaxy Distribution vs. Observed Distribution

Models of pure CDM (WCDM =1) are an improvement over the HDM
models; the CDM models have a greater amount of clustering. Models of CDM plus
baryons (WCDM = .95, Wbaryon = .05) produce similar
results (Figures 15, 16 and 17).
Figure
17

However, these models, along with the purely baryonic model, the pure HDM
model, and HDM + baryonic model are all inconsistent with the observed CMBR,
DT/T = 10-5. {7}

Certain combinations of CDM, HDM, and baryonic matter tend to solve most
problems. (WCDM + Wneutrino/HDM + Wbaryon = 1,
as mandated by inflation, and Wbaryon=0.05, from Big Bang
Nucleosynthesis). Chung-Pei Ma discusses two models employing combinations of
both. One model is Wntrno=.2, Wbaryon=.05,
WCDM= .75, which uses mntrno=4.7 eV/c2. The
second model consists of Wn=.3, Wbary=.05,
WCDM=.65,
with mn = 7 eV/c2. In both
models, 1283 CDM particles, each of mass
2.5*1010Mo, and 10*(1283) HDM particles, each
of mass 6.6*108Mo, were used. Snapshots (Figure 18) of the
CDM and HDM components of both simulations at z=1.5 reveal that the neutrinos
become trapped in the gravitational potential wells provided by the CDM, but the
neutrino distribution is smoother, due to the free-streaming.

Figure 18:
Comparison slices of two CDM & HDM models

To determine which is more correct, we can compare the model's quantity of
massive dark halos, which can host quasars or luminous galaxies, with observed
quasar or galaxy counts. The Wn=.3 model tends to have not enough
structure at z >= 4. There are too few massive dark halos formed, and this
model cannot host enough quasars to be consistent with observed quasar counts
for z up to 4.5. If one concludes that the Wn=.2 model is more
correct, then an upper limit of 4.7eV/c2 (the value used in this
model) is placed on the neutrino's mass. {2D}

One can also discuss how CDM, HDM, and combinations of both differ in forming
structures by looking at their linear power spectra-- how well fluctuations of a
certain length scale influence Dp/p over that length scale, as
in Figure 19.
Figure 19

Note that as more HDM is added, the shortwave fluctuations display a decrease
in the amount of the density fluctuations Dp/p, leading to a
reduction in the formation of small-scale structures (This is just another way
of saying how the small-scale density fluctuations are suppressed.) The presence
of CDM causes the shortwave fluctuations to be more overdense than without CDM,
and too much CDM (as in the pure CDM model) causes too much small scale
structure. {2D}

(Recent observations with the Japanese satellite ASCA suggests that CDM is at
least partially correct. ASCA studied hot X-ray gas in the Fornax cluster. (Hot
gas is a tracer of dark matter because it collects at over-dense regions of both
dark matter and luminous matter. An accumulation of gas where there is no
luminous material is indictive of dark matter.) The observations suggest that
dark matter tends to exist in clumps- both on the scale of the whole cluster and
around NGC 1399, the massive elliptical galaxy at the center of the Fornax
cluster. The fact that the dark matter clumps and aggregates in this manner
indicates hierarchal clustering (CDM) is preferred. However, the fact that it
clumps on two separate scales (cluster-scale and galaxy-scale) suggests that
both HDM and CDM are involved in structure formation. Either way, CDM is
present.){13}

The suggestion of tilted cold dark matter, or TDM, is an attempt
to reconcile the discrepancies of CDM and HDM by using a power spectra obtained
as follows: Take the power spectrum line of pure CDM in Figure 19, and rotate it
clockwise about the point marked "X". TDM (Figure 20), therefore, continues to
agree with the models at large scale lengths, and at short scale lengths, the
TDM power spectrum has an effect in between that of the cold and hot components.

Figure
20: TDM

TDM may be mathematically feasible, but models employing TDM prove to be
incompatible with CMBR observations, mostly on large scales-- large DT/T
fluctuations form. {2F}

In another model, 80% of the universe's energy density is in the cosmological
constant L, the repulsion term in the Freidman Equation. WL = .8,
WCDM = .15, and Wbaryon = .05. Note that in this model,
WCDM/Wbaryon = 3, meaning that CDM, not MACHOs, are more
prominent in halos. {5E} Other models include topological defects
such as cosmic strings (to be discussed later), which act as seeds for formation
of structures. The HDM plus baryonic model can be remedied somewhat if loops of
cosmic string are present; galaxies are allowed to seed earlier than without the
seeds. {5E}

The concept of Biased Galaxy Formation answers the question of
whether or not the baryonic, luminous matter is distributed the same way as the
dark matter. A model that insists on having baryon density exactly proportional
to the quantity of dark matter at a given location is not consistent with what
is observed. Biased Galaxy Formation assumes that baryonic matter is
concentrated only at the highest peaks of dark matter concentration, and models
employing Biased Galaxy Formation (with baryonic matter concentrated at only the
top 10% of peaks) are more consistent with what is observed. (see Figure 21,
below)

Figure 21:
Biased Galaxy Formation

One possible physical explanation for Biased Galaxy Formation is that a
minimum or threshold baryon density is required for star formation, but this
baryon density is dependent on the dark matter density, achieving the threshold
density only where the dark matter density is sufficiently high enough. (Below a
certain dark matter density, no baryons will collect to form stars.)
{8}

A possible explanation for why galaxies consist of dark halos surrounding
luminous matter relates directly to their formation: Matter (baryonic, but not
yet luminous, and non-baryonic) collapses at an overdensity, until it reaches a
size where its radius is equal to half its initial radius. (This can be proved
from the Virial Theorem.) This is the radius of the dark halo, and it remains
fixed. If the dark halo is massive enough, then it can host material that will
eventually form a luminous component. This is related to Biased Galaxy
Formation-- some, not all, halos will be allowed to host, say, a collapsing
luminous disk.

TOPOLOGICAL DEFECTS

A discussion of structure formation in the universe is not complete without
mention of topological defects. Supersymmetry (SUSY) was present only in the
early, hot universe. The symmetry broke at some point, as the universe cooled.
The loss of symmetry didn't occur everywhere at once, giving us topological
defects such as the magnetic monopole, the one-dimensional cosmic string (The
Great Attractor was considered to be a cosmic string.), and the two- dimensional
cosmic wall (or domain wall). Magnetic monopoles must have been produced in
large amounts at the start of the universe (during the era of the GUTs), but
have not been observed yet. The theory of inflation of the early universe gets
rid of most or all of them, leaving only one per particle horizon, and
accounting for this discrepancy. Cosmic strings and domain walls, could serve as
seeds for galaxy formation in the hierarchal clustering (CDM- dominating) model,
since they can attract baryonic matter (see Figure 22). Neil Turok has shown
that if galaxies are allowed to condense upon loops of cosmic strings,
megaparsecs in diameter, the result is a model of the universe with the correct
cluster correlation function. Loops of cosmic strings tend to work better than
randomized overdensities as initial conditions. Cosmic strings and domain walls
can radiate their energy away, in the form of gravitational waves, and so they
may or may not exist today. {6}

Figure 22: Cosmic Strings

DETECTION OF WIMPS

There have been attempts to experimentally detect CDM particles, also called
weakly interacting massive particles, or WIMPs. If WIMPS are present in stars,
they will leave the Main Sequence and become a red giant sooner than if no WIMPS
were present. Globular clusters would therefore appear younger than without
WIMPS. Wimps could form a halo around the galaxy, around globular clusters,
smaller collections of stars, or both. If Wimps are to fill a spherical halo
larger than the visible disk of a galaxy the speed of the particles must be less
than the galaxy's escape speed. The Milky Way's fastest star (assuming it is a
permanent member) moves at about 430 km/s, and so Vesc must be at
least 430, maybe as high as 600, km/s. For a globular cluster, WIMP velocity
must be less than Vesc for the cluster as well. Assuming the halo of
Wimps for a galaxy or globular cluster is proportional to 1/r2
(p = po(ro/r)2, except right
at r=0, where this diverges; or p =
po/(1+r2/a2)), stars near the edges
collect less WIMPS than those towards the center. High mass stars (O,B,A) live
for only 107 years, too short a lifetime to collect many Wimps. Lower
mass stars (K,M) live longer, but collect less Wimps because of their smaller
size. F and G-type stars are best at capturing Wimps.

It has been suggested that WIMPs' presence in our sun can account for the
results of the current experiment to detect neutrinos emitted by the sun, which
is as follows: A tank of C2Cl4, located underground in the
Homestake Gold Mine in South Dakota to screen out cosmic rays, intercepts and
detects electron neutrinos emitted from the sun, in accordance with the equation

37Cl + ne- -> 37Ar +
e-. The 37Ar decays into 37Cl; this decay is
detected and recorded. However, the experiment detects less solar neutrino flux
than is calculated and expected.

Existence of WIMPs in stars, including our sun, can possibly account for the
discrepancy. WIMPS in stellar interiors can travel long distances between
collisions, longer than photons. They conduct energy away from the center,
lowering the central temperature, which in turn causes less 8B to be
produced. (Neutrinos are produced from reactions involving the decay of
7Be and 8B, but the 7Be neutrinos are generally
not energetic enough to stimulate the chlorine.) If WIMPS are to have a mass of
5GeV/c2 (about 5 protons), the predicted neutrino flux is about equal
to the observed value at Homestake. {8}

There are other proposals to explain the low flux observation. It is possible
that some of the electron neutrinos can transform into t- and
µ- neutrinos before reaching Earth. The Homestake experiment measures
only electron neutrino flux, not total neutrino flux. Also, Ralph McNutt of
Johns Hopkins University has recently noticed that neutrino counts depend on the
solar wind intensity, which depends on the sun's magnetic field. Assuming
neutrinos have magnetism (which hasn't yet been observed), the solar magnetic
field could flip the magnetic polarity of some of the neutrinos as they zip
through the sun's convection layers, making them undetectable by the Homestake
experiment. {10}

There are proposals for experiments on Earth to directly measure WIMPs.
However, if all the dark matter in the universe is baryonic, and none of it is
non-baryonic, then there will be nothing for these experiments to detect. In the
solar neighborhood, the average density of hidden matter, according to Oort's
limit, is not more than
.04 Mo/pc3, or
3.4*10-18kg/m3. WIMPS, if they form a spherical halo, will
yield a local WIMP density of around 6*10-22 kg/m3, maybe
as high as 4*10-21kg/m3 {8}.

Some WIMP detectors are based on the idea of a WIMP's colliding with or
interacting with the nucleus of an atom, causing the nucleus to recoil and hence
be detected. If WIMPS exist, and have masses around 1 GeV/c2,
collision with a nucleus could result in transferring up to 1 keV of energy.
Other experiments around the world (in progress or in the construction phase) to
detect WIMPS or SUSY particles include the Boutry, UK, detector, which relies on
GaAs; and detectors at Gran Sasso, Italy, which rely on liquid Xe.
{5A}

Another detector for WIMPS uses semiconductors, materials that, below a
certain critical temperature, display virtually no resistance and through which
current can flow for long periods of time. The detector maintains the
temperature of the substance very slightly below Tcritical. WIMPs'
interaction with the substance causes the temperature to increase by some amount
dT, raising the temperature above Tcrit. The current will then stop
flowing. The detector needs a large number of superconducting elements to ensure
that enough events occur and are detected. The fractional temperature change in
the semiconductor, held at temperature T, due to a WIMP's transferring energy
dE, is given by dT/T = A[(dE/keV)/(T/°K)4] , with A =
3*10-10 for silicon superconductor, volume 1 cm3.
Typically, dE would be around 10 keV, and for this dE and T = 0.1°K, dT/T =
3*10-5. Detectors are potentially capable of determining changes in
temperature dT/T = 1 * 10-5. These detectors are generally suited for
heavy, non-baryonic (CDM) particles, with mass > 2 GeV/c2. In
1990, physicist David Caldwell, who was working with crystals of germanium to
study forms of nuclear decay, realized his detector was sensitive enough to act
as a WIMP detector: It was sensitive enough to record the effects of electrons
shifted around by protons moving about after WIMPS with mass greater than
15GeV/c2 collided with the protons. There were no such effects
recorded, implying an upper limit of 15GeV/c2 on the mass of WIMPs.
{8}

As for neutrinos, the study of solar neutrinos will be improved in the future
by the completion of new detectors or upgrading of old ones around the world.
These include the Sudbury Neutrino Observatory in Ontario, Canada, which uses
D2O; the Borexino experiment in Gran Sasso, Italy; and the Super
Kamiokande Experiment in Japan (an upgrade of the original Kamioka detector).
There is also the ICARUS detector in Gran Sasso, Italy, which uses liquid argon
to search for low energy neutrinos
resulting from protons' decaying into
kaons. (p -> K+ + anti-nµ){5A}

NON-BARYONIC MATTER AS A QUANTUM FLUID; THE STAR FORMATION RATE
OF GALAXIES
Non-baryonic matter plays a critical role in individual galaxy
formation, not just general large scale structure, according to one proposal.
Korean physicists Chul H. Lee and Sang J. Sin have proposed a mechanism that
explains star formation in elliptical galaxies and that involves nonbaryonic
dark matter acting as a quantum fluid. A system of bosons becomes a quantum
fluid (the wavefunctions overlap) through bose condensation at low temperatures.
For a given mass density, the
wavefunctions will overlap if h/mc >=
(po/m)1/3. For the mass density of dark matter in

a galaxy, po = 10-25g/cm3 =
10-7eV4, and m <= 5*10-2eV/c2. In
any quantum fluid, rotation (angular momentum) is not allowed; pre-galaxies,
however, must have picked up some angular momentum through tidal interactions.
All the angular momentum in pregalaxies could be in the form of a finite number
of quantum vortices-- circulation about singular points, with circulation
strength, energy, and angular momentum all quantized.

The model for forming galaxies with the dark matter being a non- baryonic,
light boson that has no interaction with visible matter, is as follows: First, a
mixture of baryons and dark matter collapses at an over-dense region. Then, the
dark matter condenses into a quantum fluid. The tidal interaction between
pre-galaxies causes the vortices to form. The vortex cores are under- dense
regions and the inter-vortex regions (outside core) are over-dense regions. The
vortices, since they don't interact with the baryonic matter, do not rotate
about the center of the galaxy. Baryonic matter falls into the potential wells
provided by the vortices, losing their angular momentum about the galaxy center.
At the vortices, rapid star formation occurs.

The amount of total angular momentum determines how efficient star formation
will be. Lee and Sin state that the overdense inter-vortex (outside the core)
regions of their quantum vortices will increase in size as one goes from the
galactic center towards the edge. Towards the edges, these regions will not be
small enough and strong enough to efficiently capture baryonic matter.
Therefore, if the galaxy has a small amount of total angular momentum, rapid
star formation will occur only near the galaxy's center (leading to a spiral
galaxy). If large tidal interactions between pre-galaxies existed, they will
have large amounts of total angular momentum. The quantum vortices throughout
most of the galaxy will be intense enough to capture the baryonic matter, and
there will be rapid star formation all throughout the galaxy, leading to an
elliptical galaxy.

Young elliptical galaxies have much higher star formation rates than do
spirals of the same age. Today, ellipticals appear more red, with mainly old K
and M stars; all the star forming activity occurred earlier in the elliptical's
lifetime (first one billion years). Spirals, in contrast, do exhibit star
formation today. They are bluer, with more younger O and B stars, the star
formation occurring over 10 billion years. The conclusion is that the visible
component of young ellipticals has less angular momentum than spirals do, since
more angular momentum was transferred to the dark matter vortices, leading to
the higher star formation rate. {2C}

REVIEW
This paper has listed the historical developments
pertaining to dark matter, which include the flattened rotation curves for
galaxies, and the fact that stars velocities in galaxies and galaxies'
velocities around clusters faster than implied by application of the virial
theorem. The existence of dark matter is not in as much doubt as the exact
nature of it. Baryonic candidates were discussed, as was microlensing, a
prominent technique to search for MACHOs in the Milky Way's halo. There is
compelling evidence that white dwarfs comprise much of the halo. The other
candidates, for which there isn't as much evidence, include gas and dust clouds,
low mass objects such as brown dwarfs, and high-mass objects such as black
holes, primordial black holes, and neutron stars. W is probably very close to 1
(as mandated by inflation), but from Big Bang nucleosynthesis, baryonic matter
can contribute at most 0.1 to W. Non-baryonic matter should be out there, too,
and non-baryonic candidates for dark matter include neutrinos, axions, and SUSY
particles. The differences between CDM and HDM were discussed, as were their
roles in structure formation: If CDM, which is slower and more massive,
dominates, then small lengthscale perturbations prevail, and structure formation
proceeds via hierarchal clustering: Galaxies appear first, followed by galaxy
groups, clusters, and then superclusters. If HDM, which includes neutrinos,
dominates, then the prevailing density perturbations are on the length scale of
hundreds of megaparsecs.are on the length scale of hundreds of megaparsecs, and
structure formation proceeds via a top-down method: Clusters appear first and
then fragment into small galaxies. Models employing various combinations of
baryonic matter, CDM and HDM work better than pure models when comparing them
with the observable universe. Topological defects were briefly discussed. Future
prospects include more sensitive axion and WIMP detectors. Furthermore, particle
colliders around the world are being upgraded to higher energies to assist with
the search for massive CDM particles. This paper has ended with an application
of dark matter-- if dark matter is considered to be a quantum liquid, then
quantum vortices form in pre-galaxies. These vortices can explain why young
elliptical galaxies have a higher star formation rate than young spirals do.

BIBLIOGRAPHY

{1} Bartusiak, Marcia. _Through a Universe Darkly_. New York: Harper-
Collins, 1993.

{2} Cline, _David B. Proceedings of the First International Symposium on
Sources of Dark Matter in the Universe, 16 - 18 February 1994, Bel Air,
California_. Singapore: World Scientific Publishing, 1995.

{2A} Aller, Lawrence H. "Early Clues to Abnormal Mass/Light Ratios in
Galaxies M31 and M33." p. 3-8

{2B} Gould, Andrew. "MACHOs: Unraveling the Mystery."p. 148

{2C} Lee, Chul H, and Sang J. Sin. "Star Formation in Elliptical
Galaxies and Quantum Aspects of Dark Matter." p. 109-115

{2D} Ma, Chung-Pei. "Dark Halos in Two Cold and Hot Dark Matter Models,
p. 88-95.

{2E} Pfenniger, D. and F. Combes."Cold Fractal Gas as Galactic Dark
Matter." p. 156-161

{2F} Silk, Joseph. "Cosmological Constraints on Dark Matter." p. 23-32

{2G} Tremble, Virginia. "The World Line of Dark Matter: Its Existence
and Nature Through Time." p. 9-19

{3} Cohen, Nathan. _Gravity's Lens: Views of the New Cosmology_. New York:
Harper-Collins, 1993.

{4} Luminet, Jean-Pierre. _Black Holes_. Great Britain: Cambridge
University Press, 1987.

{5} Perez, J. W. F., and A. Valle. _Proceedings of the International
School on Cosmological Dark Matter, Valencia, Spain, 4-8 October 1993_.
Singapore: World Scientific Publishing, 1994.

{5A} Cline, David. "Present and Future Underground Experiments." p.
159-184

{5B} Frenk, Carlos S. "The Large Scale Structure of the Universe."p.
65-80

{5C} Moscoso, L. "Possible Observation of Gravitational Microlensing of
Stars in the Large Magellanic Cloud." p. 19-28

{5D} Rowan-Robinson, Michael. "Evidence For Dark Matter." p. 7-18

{5E} Steigman, Gary. "An Introduction to Cosmological Dark Matter." p.
1-6

{6} Riordan, Michael and David Schramm. _The Shadows of Creation: Dark
Matter and the Structure of the Universe_. New York: W. H. Freeman and Co.,
1991.

{7} Silk, Joseph. _The Big Bang, updated and revised edition_. USA: W. H.
Freeman & Co., 1989.

{8} Tayler, Roger John. _The Hidden Universe_. Great Britain: Ellis
Horwood Publishing, 1991.

{9} "Found: Most of Missing Matter Lost Around Edges of Universe." The New
York Times, 17 January 1996.

{10} "Breakthroughs: Flipping Neutrinos" in "Discover", April 1996. p. 12.

{11} NASA Hubble Space Telescope Web site, <www.stsci.edu>

{12}"Astro News: Core of Great Attractor Found" in "Astronomy", June 1996,
p. 20

{13}"Astro News: Dark Matter Hierarchy" in "Astronomy", June 1996, p. 24

{14}"Ghost Galaxies of the Cosmos" in "Astronomy", June 1996, p. 40-45

{15}"Astro News: No M31 MACHOS?" in "Astronomy", October 1996, p. 30

*****

Sources for Figures/Illustrations:
#1 (Great Attractor): Riordan, p.
152
#2 (Polar Ring Gxy): Cohen, p. 189
#4 (Table of M/L for M31):
Cline\Aller, p.4
#5 (Table of M/L for M33): Cline\Aller, p. 6
#6 (Graph of
M/L for M33) Cline\Aller, p. 7
#8 (Microlensing Amplification) Perez\Moscoso,
p. 21
#9 (Bimodal F(M)): Tayler, p. 120
#10 & #12 (Wbaryon, He
abundance): From Astronomy 169 lecture notes.
#13 (Axion Det.): Riordan, p.
246
#14 (Fingers of God effect): Tayler, p. 148
#15, #16 (CDM, HDM) Silk,
p. 195-6
#17 (CDM) Silk, p. 315
#18, #19 & #20 (Wn = .2,.3; power
spectrum): Cline\Chung-Pei Ma, p. 91
#21 (Biased Gxy Formation): Tayler, p.
149
#22 (Cosmic Strings): Riordan, p. 213 (also: Silk, p. 125)

LINKS to other Dark Matter sites:

EROS - Expérience de
Recherche d'Objects Sombres

MOA-
Microlensing Observations in Astrophysics

AGAPE

MACHO home page

Optical
Gravitational Lensing Experiment (OGLE). Includes microlensing in the
direction of the galactic bulge

Center for Particle
Astrophysics, Direct Detection Group

U.K. Dark Matter Collaboration

Back to Home Page