A description of the big bang and cosmological principles.
The density of matter in the solar neighborhood is measured by sampling a uniform population of luminous stars that extends well above the disk of the galaxy. The average velocities of the stars and the vertical distances they traverse above the disk provide a measure of the gravitational restoring force that keeps these stars in the disk. From the strength of this force, one can deduce the total density of matter that exerts this gravitational pull. Comparing this density with actual counts of stars, one finds that the number of observed stars falls short, by perhaps as much as a factor of 2, of the number needed to account for this density. This is the first hint of any dark matter, and it is present in the vicinity of the sun. It should be noted that the amount of such a shortfall in the disk matter is controversial.
There is at most an amount of dark matter in the disk equal to the amount of luminous matter. A more conservative estimate might place the amount of dark matter at about 25 percent of the amount of luminous matter. In fact, this additional component of matter need be nothing very exotic.
What could the dark matter be? The dark matter in the disk most likely consists of very dim stars, such as white and even black dwarfs. White dwarfs are the destiny of stars like the sun, attained when the nuclear fuel supply is exhausted. A typical white dwarf has a mass of about 0.6 the mass of the sun but a size smaller than that of the earth. It formed as the hot core of a planetary nebula, the final luminous phase of stellar evolution when the envelope of a red giant is ejected as the core burns the last remnants of nuclear fuel. A white dwarf fades slowly to oblivion as it cools down to become a black dwarf.
A useful measure of mass is obtained by taking the ratio of the mass of all stars to the to the luminosity emitted by all stars, in a volume of a few hundred parsecs around the sun. If the typical star near the sun was equal in mass to the sun, the ratio of total mass to total light would be unity, larger than unity if the typical star was less massive, and smaller than unity for more massive stars. Since the resulting ratio is found to be 2 for nearby stars, in solar units of solar mass (M) to solar luminosity (L): M/L we conclude that the average star near the sun is slightly less massive than the sun. In the solar vicinity, there is little necessity for any dark matter other than the dark dwarfs. The first real surprise emerges in the outermost parts of galaxies, known as galaxy halos. Here, there is negligible luminosity, yet there are occasional orbiting gas clouds, both atomic and ionized, which allow one to measure rotation velocities and distances. The rotation velocity is found not to decrease with increasing distance from the galactic center. This constancy of velocity implies that the galaxy's cumulative mass must continue to increase with the radial distance from the center of the galaxy, even though the cumulative amount of light levels off.
Just how much additional mass is in the halo? This rise appears to stop at about 50 kiloparsecs, where the halo seems to be truncated. We infer that the mass--to--luminosity ratio of the galaxy, including its disk halo, is about five times larger than estimated for the luminous inner region, or equal to about 50. This is the first solid, incontrovertible evidence for dark matter. The rotation velocities throughout many spiral galaxies have been measured, and all reveal dominance by dark matter.
Moving further afield, the mass-to-light ratio can also be evaluated by studying galaxy pairs, groups, and clusters. In each case, one measures velocities and length scales, from which one determines of the total mass required to provide the necessary self-gravity to stop the system from flying apart. The inferred ratio of mass to luminosity is about 100M/L for galaxy pairs, which typically have separations of about 100 kiloparsecs. The mass-to-luminosity ratio increases to 300 for groups and clusters of galaxies over a length scale of about 1 megaparsec. Over this scale, 95 percent of the measured mass is dark.
The largest scale on which the mass density has been measured with any precision is that of superclusters. A supercluster is an aggregate of several clusters of galaxies, extending over about 10 megaparsecs. Our local supercluster is an extended distribution of galaxies centered on the Virgo cluster, some 10 to 20 megaparsecs distant. The mass between us and Virgo tends to decelerate the recession of our galaxy relative to Virgo, as expected according to Hubble's law, by about 10 percent. This deviation from the uniform Hubble expansion can be mapped out for the galaxies throughout this region, and provides a measure of the mean density within the Virgo supercluster. Over the extent of our local supercluster, about 20 megaparsecs, one again finds a ratio of mass to luminosity equal to approximately 300.
On the very largest scales, there are no longer any gravitationally bound objects. Yet the galaxies are not distributed perfectly uniformly: there remain small density fluctuations that have persisted since the very earliest epochs of the universe. The dark matter that accounts for the critical density should, at least in the case of some kinds of dark matter, participate in the density fluctuations on large scales. If one measures the `peculiar' velocities of galaxies relative to the Hubble flow, they will trace trace the fluctuating component of the dark matter. The resulting maps reveal large-scale bulk flows that amount to about 10 percent of the Hubble expansion and are coherent over 30 megaparsecs or more. The flows are induced by the gravitational attraction from all matter present, and therefore probe the total amount of clumped matter, dark as well as light. Preliminary indications are that an amount of dark matter about equal to the critical density must be present in order to account for the amplitude of the observed flows. One can even pinpoint the sources of the flows, since there are vast concentrations of matter that must be responsible. The nearest one has been dubbed the Great Attractor; it is located at a distance of 40 megaparsecs from us. If real, it must consist of more galaxies than would be found in a dozen rich galaxy clusters. Our galactic plane obscures a large part of the Great Attractor, so one cannot count the number of galaxies directly. There may well be other similar complexes of galaxies that help generate the bulk flows.
The theory of inflation predicts that we live in a flat universe, where the density parameter Omega is equal to unity. That is, the density of matter in the universe should just equal the critical density at which the universe is closed. Can we tell from the amount of dark matter observed whether the universe is indeed at critical density, as the theory of inflation predicts? One can translate the Omega parameter, which measures mass density in terms of the critical value into a ratio of mass to light. One does this by taking the ratio of the critical density to the observed luminosity density of an average, and large, volume of the universe. The result is that the mass-to-light ratio equals 1500 Omega. In other words, if Omega is 1, one needs a mass-to-light ratio of 1500 to close the universe. This amount of mass is far greater than is observed directly. Alternatively, if we adopt the mass-to-light ratio of 300 measured on large scales as being a universal value, we would conclude that Omega is 0.2, far less than the value predicted by inflation. One can reconcile inflation theory with observation only if the bulk of the dark matter is uniformly distributed over scales up to 10 megaparsecs. In this case, the dark matter would not have shown up, since on these scales only the clumped component of the matter has been measured. Indeed, a critical density would be compatible with the density measured by the bulk flows, which only sample scales larger than 10 megaparsecs or so.
The nature of the dark matter predicted by inflation is a profound and unresolved puzzle. We have two choices. Either the dark matter consists of ordinary, baryonic matter, or else it consists of some more exotic form of matter. The history of the universe during the first few minutes provides an interesting measure of the total amount of baryonic matter in the universe that may help resolve the puzzle.
For a significant clue to the composition of the dark matter, we look to the abundance of the heavier isotope of hydrogen, weighing twice the mass, called deuterium, created during the big bang. There is no alternative source for the extra deuterium other than the big bang, since stars destroy deuterium rather than produce it. By now, a considerable fraction of any primordial deuterium present at the birth of the galaxy would have been destroyed inside stars. This is confirmed by observation: interstellar clouds contain deuterium, as do gravitationally-powered stars that have not yet developed nuclear burning cores; on the other hand, evolved stars have no deuterium.
To estimate how much deuterium was created in the big bang, one has to factor in all the deuterium that has since been destroyed. The percentage of the isotope destroyed since the big bang can be calculated if one knows the its rate of destruction, which can be found by comparing the abundance of deuterated molecules in the atmosphere of Jupiter with the abundance of deuterium in interstellar clouds. One has to choose a value for the density of baryons that cannot exceed about a tenth of the critical density for closure of the universe, or too little primordial deuterium would have been synthesized. Conversely, the density of baryons cannot be too low, below 2 or 3 percent of the critical density, or else one would overproduce deuterium, compared to what is observed in the solar system. If the universe is at critical density, 90 percent of the matter in the universe must be nonbaryonic.
If, in a universe at critical density, most dark matter could not be baryonic, what other forms could it take? Likely relics of the early universe are species of stable, weakly interacting particles. One example is the neutrino, if it possesses a small mass. Normally, the neutrino is assumed to be practically massless, but a finite mass is not implausible. There are so many neutrinos left over from the big bang that a neutrino mass of even 50 eV, or one ten-thousandth the mass of an electron, would suffice to close the universe. Laboratory experiments are underway in several countries to determine a definitive mass for the neutrino, but at present these experiments are inconclusive. The current upper limit on the electron neutrino mass, which is obtained from tritium decay experiments, is about 10 eV. Other species of neutrinos could have higher masses.
If the particles are very massive, possessing more mass than, say, a proton, a special name has been coined: the WIMP, for weakly interacting, massive particle. Exotic WIMPs such as the photino have been postulated to exist in sufficient quantity to close the universe. The problem is that there is no guarantee that these particles do exist. Disregarding this uncertainty, the big bang theory predicts their density today, if they do exist and are stable over the age of the universe.
The existence of the photino is predicted in a theory called supersymmetry. This theory doubles the number of known particles by postulating the existence of partner `-ino' particles. These particles are almost all short-lived, and exist in large numbers only in the very early universe, when the temperature was high enough to exceed the energy scale characteristic of supersymmetry, affectionately abbreviated to SUSY. As the universe cools, supersymmetry is broken. The relevant energy scale is not known from theory, but it must exceed 100 GeV to avoid conflict with particle experiments. In our low-energy universe today, the lightest supersymmetric particle should still survive. It is expected to be the partner, in the sense of having a complementary spin, of the photon, and is therefore known as a photino. Its mass is expected to be 10 to 100 times that of the proton. The photino is uncharged and interacts very weakly with matter.
There is strong evidence for SUSY from experiments at CERN that measure the strength of the nuclear interactions, which increase with increasing energy. There is no guarantee, however, that the weak and strong nuclear force strengths will all converge to the same energy. That they do converge at very high energy is the thesis of grand unification of the fundamental forces, whose breakdown in the very early universe gave rise to inflation. While this energy, some 10 to the 15 GeV, is very much higher than is directly accessible by experiment, the trend towards convergence of the disparate forces is already apparent. Only if SUSY describes the high energy world do these three fundamental forces become indistinguishable at a unique energy. Only therefore with SUSY could one construct a strong case for the inevitability of grand unification.
Despite the weakness of the photino's interactions, several experiments are being designed to search for this particle. These experiments are of four types. One uses particle accelerators, atom-smashing machines, to verify the particle's existence. The high-energy collisions in these machines normally produce jets of energetic hadrons, including particles and antiparticles that are ejected during the collision. So that momentum is conserved, the hadronic jets go off in two opposite directions, transverse to the collision direction. Although the weakly interacting photino would be invisible, it carries off momentum that must be balanced on the other side by a detectable jet. A one-sided jet would be evidence for a supersymmetric particle.
Sensitive laboratory detectors search directly for photinos in the galaxy's halo that have been intercepted by the earth and by the sun as the sun orbits the galaxy. Photinos that are trapped by the sun actually annihilate in its core. The heat they produce can slightly, but perhaps significantly, affect the sun's evolution. A byproduct of the annihilations is the generation of some energetic neutrinos that are quite distinct from those produced by the thermonuclear fusion reactions in the solar core. These high-energy neutrinos, as well as neutrinos produced by photino interactions in the earth, may be detectable in some of the underground detectors that are searching for solar and supernova neutrinos.
Radically different methods are used to search for the debris of photino interactions in the halo. Space or balloon-borne telescopes hunt above the earth's absorbing atmosphere for particles such as cosmic ray antiprotons and positrons produced in the halo by photino annihilations. However, cosmic ray protons interacting with heavy interstellar atoms also generate relatively low energy antiprotons and positrons. A way is needed to disentangle the two signals. Of course, the detection of a single heavier antinucleus, even antihelium, would be a phenomenal discovery and would require the existence of antistars and even antigalaxies. No such particles have been detected, needless to say. A similar strategy is to search for another relic of photino interactions; these are photons, specifically gamma rays, also produced when photinos annihilate in the halo.
The most natural form for dark matter is matter that we know exists, namely baryons. The big bang explanation of the light element abundances requires the existence of baryonic dark matter. Although these same abundances imply that most dark matter is nonbaryonic, the amount of dark baryonic matter is still most likely several times that in luminous baryonic matter, or about 3 percent of the critical density for closing the universe. But where do we look for the baryonic dark matter? One's first expectation might be that baryonic dark matter consists of burnt-out stars in the galactic halo, yet other forms, such as planets and black holes, are also possible. Baryonic dark matter does exist: it is far more uncertain whether there exists enough to solve any of the dark matter problems, that is to say, dark matter in galaxy halos, dark matter in galaxy clusters and superclusters, or dark matter in an amount suficient to close the universe. It is most unlikely that baryonic dark matter can account for the closure density, as we will now see: for this, one must appeal to WIMPs, or some other weakly interacting particle. However, baryonic dark matter is a serious candidate for dark matter at least in galaxy halos, if not on larger scales. In acknowledgment of the rivalry between these two forms of dark matter, the favored baryonic dark matter candidates have been dubbed MACHOs, for massive compact halo objects.
Among the possible astrophysical objects contained in the halo are the relics of stars, dim stars such as white dwarfs, neutron stars, or even black holes, as well as objects that have never quite fulfilled themselves as stars because of their low mass. Because these objects are invisible, or almost so, they are excellent candidates for dark matter. Moreover, MACHOs are more natural candidates for the halo dark matter than WIMPs, because they are already known to exist.
Two experiments reported in 1993 have found strong evidence for the existence of MACHOs. The technique used is gravitational microlensing. If a MACHO in our galaxy's halo passes very close to the line of sight from earth to a distant star, the gravity of the otherwise invisible MACHO acts as a lens that bends the starlight. The star splits into multiple images that are separated by a milliarc-second, far too small to observe from the ground. However, the background star temporarily brightens as the MACHO moves across the line of sight in the course of its orbit around the Milky Way halo. To overcome the low probability of observing a microlensing event, the experiments were designed to monitor several million stars in the Large Magellanic Cloud. Each star was observed hundreds of times over the course of a year. A preliminary analysis of the data, taken with both red and blue filters, revealed several events that displayed the characteristic microlensing signatures. The event durations were between 30 and 50 days.
The duration of the microlensing event directly measures the mass of the MACHO, although there is some uncertainty because of the unknown transverse velocity of the MACHO across the line of sight. The event duration is simply the time for the MACHO to cross the effective size of the gravitational lens, known as the Einstein ring radius. The radius of the Einstein ring is approximately equal to the geometric mean of the Schwarzschild radius of the MACHO and the distance to the MACHO. For a MACHO half-way to the Large Magellanic Cloud, that distance is 55 kiloparsecs. The Einstein ring radius is about equal to 1 astronomical unit, or the earth-sun distance. In order to be lensed, the MACHOs must be objects that are smaller than the lens, so they must be smaller than an astronomical unit, roughly the radius of a red giant star. The events detected are, to within a factor of a few, as the MACHO model of dark halo matter predicts, and the event durations suggest a typical mass of around 0.1 solar masses; however, there is at least a factor of 3 uncertainty in either direction.