See also: The standard model -- Supersymmetry -- CP symmetry violation -- Dark energy -- Magnetic monopoles
There are more things in heaven and earth, Horatio,|
Than are dreamt of in your philosophy.
William Shakespeare - Hamlet, I.v.166
Baryonic dark matter
"Hot" dark matter: neutrinos
Magnetic monopoles, cosmic strings, membranes
Dark energy and quintessence
Kaluza-Klein dark matter
But of course, the distinction isn't quite as clearcut as it may seem. According to the special theory of relativity, matter and energy are in some sense equivalent: E = mc2. Matter and energy can transform into each other. So what is special about "stuff" when it has the form of matter as opposed to energy? The answer, as far as we will be concerned, is that matter has a nonzero amount of "mass" -- the "m" in the equation above -- while energy does not. (Even this definition could be debated. Fundamental particles called "neutrinos" were considered to be matter long before it was established that neutrinos have nonzero mass. Fortunately, this is no longer an issue.)
Nevertheless, we've only shifted the question. Now the problem is to define what "mass" is. Before the general theory of relativity came along, physics recognized two manifestations of mass. First, there was mass as related to the force of gravity. Between any two material objects there is a gravitational force determined by the equation
F = Gm1m2 / r2where G is a constant of proportionality (Newton's gravitational constant), m1 and m2 are the masses of the objects, and r is the distance between the centers of mass of the objects. From this equation it follows that if any object had zero mass, it would not experience a gravitational force with other objects. This is the main reason we count something as matter only if it has nonzero mass.
But there is another property an object can have, which is also called mass, and it enters into a different law. This is Newton's second law of motion, which states that the velocity of an object can change (in magnitude or direction) only if a force is applied. Acceleration is another name for change of velocity, and it is related to force by the equation F = ma, where F is the force, a is the acceleration, and m is the mass of the object.
Now, a priori, there is no reason to suppose that the property of an object called mass in this sense, more precisely inertial mass, because it measures inertia, i. e. resistance to change of velocity, is the same as mass in the previous sense, gravitational mass. However, no one ever observed a situation in which the two sorts of mass were different for the same object, so it was routinely assumed that they were the same, without enquiring too deeply about why this was.
In formulating the general theory of relativity, Einstein didn't explain this either, but he did make it a fundamental postulate, known as the equivalence principle, which says there is no way to distinguish the two sorts of mass. Stated differently, there is no way to distinguish the force on an object due to acceleration from the force due to gravitation, as long as all you can measure is the force itself, and not the motion of the object or the presence of a gravitational field. From this, it was possible to relate both types of mass to local curvature of space itself. Simply put, there is no mass anywhere space is locally flat, and nonzero mass only if space is curved to some degree at the location of the mass. Matter having mass "causes" space to curve, and the curvature produces the force known as gravity.
That's it. We really know nothing more about the nature of mass than that. If this is all we know, why bother even with this discussion? The answer is that it suggests two ways that astronomers can detect the presence of objects having mass -- matter, in other words -- and yet remain confident they are talking about the same thing. The first way is by looking at the motion of large visible objects like stars and galaxies. It must be possible to account for any observable motion in terms of the presence of matter, whether or not all the matter itself is visible. The existence of matter can be deduced from the motion of visible objects, even if the matter is not visible.
This was one of the great successes of Newton's theory of gravity and his laws of motion. It could predict very precisely how the planets of the solar system move, and could even account for changes in the orbits of asteroids and comets when they happened to come close to large planets like Jupiter. The theory predicted the existence of Pluto long before it was observed, because of peculiarities in the orbit of Neptune. One consequence of these laws of motion is that the planets do not revolve around the Sun as if they were attached to a rigid wheel. That is, each planet revolves around the Sun at a different rate, and the farther a planet is from the Sun, the longer it takes. In other words, the length of a year is different for each planet. It varies from about 88 days for Mercury to 248 years for Pluto.
Although the structure of a galaxy is rather different from that of a solar system, the same laws of orbital motion apply. A solar system with a single star is usually dominated by the mass of the star. In our solar system, the mass of the Sun is about 1000 times that of all the planets combined. In a galaxy there is usually no central object that is so dominant. Nevertheless, all the stars in the galaxy should revolve around the center of mass (also called the "center of gravity") of the galaxy more or less as if all of the mass were concentrated at the center. In particular, the farther away from the center of mass a star is, the longer it should take for the star to revolve around the center.
The shocking thing is, when this idea was actually put to the test, it was found to be false. Testing the idea wasn't all that easy. The problem is, with stars in our own galaxy, the Milky Way, it's not that easy to tell how far away most of them are, so we can't tell how far they are from the galactic center either. It's much easier to calculate distances of stars from the center in galaxies outside our own, simply because we can see the relative positions of the stars and the center, and so we know the distance of the star from the center as soon as we know the distance of the galaxy itself. Determining the velocity of stars is a little harder. It can be done by measuring the Doppler shift of a star's spectrum provided we are not viewing the galaxy from exactly above (or "below") the center. The only problem is that most stars outside our galaxy are so far away that recording their spectra was difficult with available telescopes until a few decades ago. In 1970 Vera Rubin finally made suitable measurements of the velocity of stars around the center of the Andromeda galaxy, our closest large neighbor galaxy, which is about 2 million light years away. She found that all stars had about the same velocity (around 150 miles per second).
It was as if the stars in Andromeda were attached to a rigid wheel. The most likely actual explanation is that there is far more matter associated with Andromeda than is visible as stars, and most of it is located outside the visible part of the galaxy. This was the first solid evidence for the existence of "dark" matter. Since 1970, a great deal of additional evidence has accumulated, as we will describe.
The notion that mass is associated with curvature of space also provides a second way it is possible to detect large amounts of matter even if the matter is dark and does not glow. Namely, it is possible to look for evidence of actual curvature in space. How is that done? Fairly simple, actually. One relies on the idea that light always travels in a "straight" line. However, in space which may be curved, "straight" has to be defined carefully. The actual definition of a straight line in curved space is a line which is the shortest distance between any two points that lie on the line. Distance, in turn, is measured in terms of a function called a metric, which defines the actual geometry of space. Mathematical properties of this metric make it possible to determine how much space is curved at any point, without having to go "outside" space to measure it. Einstein's equations of general relativity relate properties of this metric to the presence of mass.
But the immediately relevant point is that under exactly the right circumstances, we can detect curvature in space, and relate it to the presence of mass (and matter), by observing the path of light. This was how the general theory of relativity was first tested. In 1919 Arthur Eddington led an expedition to observe stars during an eclipse of the Sun. During the eclipse, stars could be seen very close to the edge of the Sun... and they were slightly displaced from where they "should" have been, because of the curvature of space caused by the Sun.
Using the same principle, we can now look for very distant objects such as quasars, and detect a large quantity of mass which lies in the immediate line of sight to these objects -- if there is any. Such an object may be a large galaxy or a galaxy cluster. If such an object is in the exact line of sight (which is a fairly rare occurrence), a phenomenon called gravitational lensing is observed, as the light from the distant object is magnified or distorted much as if it had passed through an optical lens. The amount by which the light appears to be bent is a measure of how much mass is in the intermediate object. In the case of a galaxy, for instance, there can appear to be 10 or 20 times as much matter present as can be accounted for by visible stars. This "invisible" matter is, again, called "dark" matter.
The question, of course, is: What does this dark matter consist of? We need to examine, systematically, the possibilities.
All visible matter in the universe is composed of ordinary matter, as far as we can tell. Stars and the galaxies they make up account for the most obvious examples of visible matter, because they are luminous. Other objects such as planets, dust, and interstellar gas are also ordinary matter, but such matter may or may not be readily visible, since it in general is not self-luminous.
Planets in our own solar system are visible, of course, by reflected light, but planets in other solar systems, though known to exist, are not visible, since the light they reflect is too dim to be visible with current technology. This may change before too long, but only for relatively nearby solar systems. Additionally, in 2004 the first claim was made of the detection of an extrasolar planet by emitted infrared light. Dust around other stars can be detected, sometimes by the way it obscures the light from stars, sometimes by emitted infrared light.
Interstellar gas can be detected by light whose emission is stimulated by nearby hot stars, sort of like the glow of a neon light. Some interstellar gas is so hot that the light it emits is in the form of X-rays. Gas can also be observed by absorption lines caused in the spectra of stars that lie inside or behind the gas.
In addition, ordinary matter can occur in isolated clumps that are larger than planets but still unable to glow as a result of internally sustained thermonuclear reactions as occur in "real" stars. Some of these may be "failed" stars which are too small and cold to be capable of thermonuclear reactions and are known as brown dwarfs. Real stars that have simply burned up all their nuclear fuel and are now dark would also be in this category.
All particles of matter, such as protons and neutrons, which are composed of quarks are called baryons, from Greek barys, meaning "heavy". Electrons are not baryons. They belong to a category called leptons, from Greek leptos, meaning "small" or "light". An electron has only about 1/2000 of the mass of either a proton or a neutron (which have about the same mass). Neutrons have no electric charge, protons have an electric charge of +1, and electrons have a charge of -1. There seem to be a roughly equal number of protons and electrons in the universe, since there is no evidence for large objects with net electric charge or for a large number of free protons or electrons. Hence most of the mass accounted for by ordinary matter must be in the form of baryons. So this type of matter is also called baryonic.
The class of leptons includes several other types of particles. Two of these, the muon and the tau have properties very like those of electrons, except for a larger mass. A muon is about 207 times as heavy as an electron, and a tau is 3477 times as heavy as an electron. However, muons and taus are unstable, and they decay very rapidly, so they contribute essentially nothing to mass in the universe.
Aside from electrons, muons, and taus, there is just one other kind of lepton -- neutrinos. There are three types of neutrino, associated with electrons, muons, and taus. Only since 1998 has it been determined that neutrinos have nonzero mass. The mass of each type of neutrino has not yet been well measured, but it must be very small. There are other observational reasons for believing that the amount or mass in the universe due to neutrinos is fairly small, and this will be explained a little later. Although neutrinos are not baryons, and hence not part of baryonic matter, at least they are a kind of particle that has been observed and measured. It is estimated that matter in the form of neutrinos might has a mass that is about 10% that of baryonic matter.
High-energy particle physics today has a reasonably coherent theory that covers all types of particles which have been observed in matter to date. This theory is called the standard model of particle physics. It recognizes no other type of matter particles apart from baryons and leptons. (More accurately, there are also "force" particles such as photons and gluons. Photons are massless. Gluons are probably massless, but never observed in isolation. There are other force particles known as W and Z which have mass, but they are also not observed in isolation as they decay very quickly.) Therefore, if there is dark matter other than baryonic matter, it must be in some "exotic" form based on particles not described by the standard model.
In fact, there are two sorts of reasons for believing the universe must contain more matter in an exotic, non-baryonic form than there is ordinary matter -- quite a bit more. One sort of reason is theoretical, having to do with the way atomic nuclei were originally created very early in the Big Bang. This process is called nucleosynthesis, and it places a limit on how much baryonic matter can exist, given the relative proportions of several atomic nuclei observed to exist in the unverse at present. The other sort of reason is based on other kinds of observations. Some of these observations also limit the amount of baryonic matter that can exist, while others imply the total amount of dark matter is much above the limit of what can be baryonic, and hence there must be a great deal of matter which is not baryonic.
The nature of this non-baryonic dark matter is mostly not known at all, but we will talk about some of the possibilities. First, though, we'll look at nucleosynthesis and then the observational evidence for dark matter.
The density of baryons (protons and neutrons) is the key parameter of interest, because it is the number which tells us how much matter was in the form of baryons. The density at that time was vastly greater than it is now, because the universe has expanded so hugely since then. However, the number of baryons now is exactly the same as it was then. There are two reasons for this: (1) There were no anti-protons or anti-neutrons left, so they could no longer annihilate with protons and neutrons. (2) A neutron could change into a proton by emission of an electron (or vice versa if a proton captured an electron), but protons have a half-life of at least 1032 years and may in fact be completely stable.
The important thing is that we can estimate the density of baryons at that time from observations we can make today and the facts we know about the process of nucleosynthesis. The observation we can make today is that most of the matter that exists today in stars is in the form of just two nuclei: hydrogen (H) and helium-4 (He4). The proportions are about 75% H, 24% He4, and only 1% everything else. We know this from studying the spectra of stars, where the presence and amount of any chemical element can be determined from characteristic spectral emission lines. While there may be quite a lot of matter around that isn't part of stars, the proportion of different elements in that matter should not be much different from what is in stars, simply because all but the oldest stars have condensed out of the available supply of baryonic matter.
During the process of nucleosynthesis, two things are going on. First, the temperature is decreasing and, second, the density of baryons is decreasing. These are both consequences of the fact that the universe is rapidly expanding. Now, temperature is essentially the same thing as the average energy possessed by all particles. If the temperature and density are too high, nuclei consisting of more than a single particle cannot form, because if any did, they would be blasted apart by another collision. When the temperature and density are "just right" a proton and a neutron can collide and stick together to form a nucleus of deuterium (H2). Another collision with a neutron will produce helium-3 (He3). And finally, a collision with a proton will form He4.
Heavier elements can form, namely lithium and beryllium, but that is relatively improbable. H2 and He3 are energetically less stable than He4, so they tend to either build up to that nucleus or else decompose back into neutrons and protons. Further, when the temperature and density fall far enough, the probability of a collision to occur with enough energy to form a new nucleus becomes so small that the whole process essentially stops, and the proportions of the different nuclei do not change thereafter. The proportions established then are pretty close to what we still see today.
What we can compute is that in order to have the proportion measured today, the density of baryons at the time of nucleosynthesis must have had a certain value. There is a convenient way to express that density. The symbol Ω is used to stand for matter density. By convention, Ω=1 is the density of matter required for the universe to be perfectly flat in a global sense. Let Ωb be the actual density of baryonic matter. Then it can be computed from what is known about nucleosynthesis and the H:He4 ratio that the value of Ωb has to be about .05, or in other words, about 5% of the density required for the universe to be flat.
Copyright © 2002 by Charles Daney, All Rights Reserved