The Big Bang Model is a broadly accepted theory for the origin and evolution of our universe. It postulates that 12 to 14 billion years ago, the portion of the universe we can see today was only a few millimeters across. It has since expanded from this hot dense state into the vast and much cooler cosmos we currently inhabit. We can see remnants of this hot dense matter as the now very cold cosmic microwave background radiation which still pervades the universe and is visible to microwave detectors as a uniform glow across the entire sky.
Foundations of the Big Bang Model
The Big Bang Model rests on two theoretical pillars:
General Relativity
The first key idea dates to 1916 when Einstein developed his General Theory of Relativity which he proposed as a new theory of gravity. His theory generalizes Isaac Newton's original theory of gravity, c. 1680, in that it is supposed to be valid for bodies in motion as well as bodies at rest. Newton's gravity is only valid for bodies at rest or moving very slowly compared to the speed of light (usually not too restrictive an assumption!). A key concept of General Relativity is that gravity is no longer described by a gravitational "field" but rather it is supposed to be a distortion of space and time itself. Physicist John Wheeler put it well when he said "Matter tells space how to curve, and space tells matter how to move." Originally, the theory was able to account for peculiarities in the orbit of Mercury and the bending of light by the Sun, both unexplained in Isaac Newton's theory of gravity. In recent years, the theory has passed a series of rigorous tests.
The Cosmological Principle
After the introduction of General Relativity a number of scientists, including Einstein, tried to apply the new gravitational dynamics to the universe as a whole. At the time this required an assumption about how the matter in the universe was distributed. The simplest assumption to make is that if you viewed the contents of the universe with sufficiently poor vision, it would appear roughly the same everywhere and in every direction. That is, the matter in the universe is homogeneous and isotropic when averaged over very large scales. This is called the Cosmological Principle. This assumption is being tested continuously as we actually observe the distribution of galaxies on ever larger scales. The accompanying picture shows how uniform the distribution of measured galaxies is over a 30° swath of the sky. In addition the cosmic microwave background radiation, the remnant heat from the Big Bang, has a temperature which is highly uniform over the entire sky. This fact strongly supports the notion that the gas which emitted this radiation long ago was very uniformly distributed.
These two ideas form the entire theoretical basis for Big Bang cosmology and lead to very specific predictions for observable properties of the universe. An overview of the Big Bang Model is presented in a set of companion pages.
Further Reading
• Peebles, P.J.E., Schramm, D.N., Turner, E.L. & R.G. Kron 1991, "The Case for the Relativistic Hot Big Bang Cosmology", Nature, 352, 769 - 776.
• Peebles, P.J.E., Schramm, D.N., Turner, E.L. & R.G. Kron 1994, "The Evolution of the Universe'', Scientific American, 271, 29 - 33.
• Will, Clifford, "Was Einstein Right?"
The Big Bang model of cosmology rests on two key ideas that date back to the early 20th century: General Relativity and the Cosmological Principle. By assuming that the matter in the universe is distributed uniformly on the largest scales, one can use General Relativity to compute the corresponding gravitational effects of that matter. Since gravity is a property of space-time in General Relativity, this is equivalent to computing the dynamics of space-time itself. The story unfolds as follows:
Given the assumption that the matter in the universe is homogeneous and isotropic (The Cosmological Principle) it can be shown that the corresponding distortion of space-time (due to the gravitational effects of this matter) can only have one of three forms, as shown schematically in the picture at left. It can be "positively" curved like the surface of a ball and finite in extent; it can be "negatively" curved like a saddle and infinite in extent; or it can be "flat" and infinite in extent - our "ordinary" conception of space. A key limitation of the picture shown here is that we can only portray the curvature of a 2-dimensional plane of an actual 3-dimensional space! Note that in a closed universe you could start a journey off in one direction and, if allowed enough time, ultimately return to your starting point; in an infinite universe, you would never return.
Before we discuss which of these three pictures describe our universe (if any) we must make a few disclaimers:
• Because the universe has a finite age (~13.7 billion years) we can only see a finite distance out into space: ~13.7 billion light years. This is our so-called horizon. The Big Bang Model does not attempt to describe that region of space significantly beyond our horizon - space-time could well be quite different out there.
• It is possible that the universe has a more complicated global topology than that which is portrayed here, while still having the same local curvature. For example it could have the shape of a torus (doughnut). There may be some ways to test this idea, but most of the following discussion is unaffected.
Matter plays a central role in cosmology. It turns out that the average density of matter uniquely determines the geometry of the universe (up to the limitations noted above). If the density of matter is less than the so-called critical density, the universe is open and infinite. If the density is greater than the critical density the universe is closed and finite. If the density just equals the critical density, the universe is flat, but still presumably infinite. The value of the critical density is very small: it corresponds to roughly 6 hydrogen atoms per cubic meter, an astonishingly good vacuum by terrestrial standards! One of the key scientific questions in cosmology today is: what is the average density of matter in our universe? While the answer is not yet known for certain, it appears to be tantalizingly close to the critical density.
Given a law of gravity and an assumption about how the matter is distributed, the next step is to work out the dynamics of the universe - how space and the matter in it evolves with time. The details depend on some further information about the matter in the universe, namely its density (mass per unit volume) and its pressure (force it exerts per unit area), but the generic picture that emerges is that the universe started from a very small volume, an event later dubbed the Big Bang, with an initial expansion rate. For the most part this rate of expansion has been slowing down (decelerating) ever since due to the gravitational pull of the matter on itself. A key question for the fate of the universe is whether or not the pull of gravity is strong enough to ultimately reverse the expansion and cause the universe to collapse back on itself. In fact, recent observations have raised the possibility that the expansion of the universe might in fact be speeding up (accelerating), raising the possibility that the evolution of the universe is now dominated by a bizarre form of matter which has a negative pressure.
The picture above shows a number of possible scenarios for the relative size of the universe vs. time: the bottom (green) curve represents a flat, critical density universe in which the expansion rate is continually slowing down (the curves becomes ever more horizontal). The middle (blue) curve shows an open, low density universe whose expansion is also slowing down, but not as much as the critical density universe because the pull of gravity is not as strong. The top (red) curve shows a universe in which a large fraction of the matter is in a form dubbed "dark energy" which is causing the expansion of the universe to speed up (accelerate). There is growing evidence that our universe is following the red curve.
Please avoid the following common misconceptions about the Big Bang and expansion:
• The Big Bang did not occur at a single point in space as an "explosion." It is better thought of as the simultaneous appearance of space everywhere in the universe. That region of space that is within our present horizon was indeed no bigger than a point in the past. Nevertheless, if all of space both inside and outside our horizon is infinite now, it was born infinite. If it is closed and finite, then it was born with zero volume and grew from that. In neither case is there a "center of expansion" - a point from which the universe is expanding away from. In the ball analogy, the radius of the ball grows as the universe expands, but all points on the surface of the ball (the universe) recede from each other in an identical fashion. The interior of the ball should not be regarded as part of the universe in this analogy.
• By definition, the universe encompasses all of space and time as we know it, so it is beyond the realm of the Big Bang model to postulate what the universe is expanding into. In either the open or closed universe, the only "edge" to space-time occurs at the Big Bang (and perhaps its counterpart the Big Crunch), so it is not logically necessary (or sensible) to consider this question.
• It is beyond the realm of the Big Bang Model to say what gave rise to the Big Bang. There are a number of speculative theories about this topic, but none of them make realistically testable predictions as of yet.
To this point, the only assumption we have made about the universe is that its matter is distributed homogeneously and isotropically on large scales. There are a number of free parameters in this family of Big Bang models that must be fixed by observations of our universe. The most important ones are: the geometry of the universe (open, flat or closed); the present expansion rate (the Hubble constant); the overall course of expansion, past and future, which is determined by the fractional density of the different types of matter in the universe. Note that the present age of the universe follows from the expansion history and present expansion rate.
As noted above, the geometry and evolution of the universe are determined by the fractional contribution of various types of matter. Since both energy density and pressure contribute to the strength of gravity in General Relativity, cosmologists classify types of matter by its "equation of state" the relationship between its pressure and energy density. The basic classification scheme is:
• Radiation: composed of massless or nearly massless particles that move at the speed of light. Known examples include photons (light) and neutrinos. This form of matter is characterized by having a large positive pressure.
• Baryonic matter: this is "ordinary matter" composed primarily of protons, neutrons and electrons. This form of matter has essentially no pressure of cosmological importance.
• Dark matter: this generally refers to "exotic" non-baryonic matter that interacts only weakly with ordinary matter. While no such matter has ever been directly observed in the laboratory, its existence has long been suspected for reasons discussed in a subsequent page. This form of matter also has no cosmologically significant pressure.
• Dark energy: this is a truly bizarre form of matter, or perhaps a property of the vacuum itself, that is characterized by a large, negative pressure. This is the only form of matter that can cause the expansion of the universe to accelerate, or speed up.
One of the central challenges in cosmology today is to determine the relative and total densities (energy per unit volume) in each of these forms of matter, since this is essential to understanding the evolution and ultimate fate of our universe.
The Big Bang model was a natural outcome of Einstein's General Relativity as applied to a homogeneous universe. However, in 1917, the idea that the universe was expanding was thought to be absurd. So Einstein invented the cosmological constant as a term in his General Relativity theory that allowed for a static universe. In 1929, Edwin Hubble announced that his observations of galaxies outside our own Milky Way showed that they were systematically moving away from us with a speed that was proportional to their distance from us. The more distant the galaxy, the faster it was receding from us. The universe was expanding after all, just as General Relativity originally predicted! Hubble observed that the light from a given galaxy was shifted further toward the red end of the light spectrum the further that galaxy was from our galaxy.
The specific form of Hubble's expansion law is important: the speed of recession is proportional to distance. The expanding raisin bread model at left illustrates why this is important. If every portion of the bread expands by the same amount in a given interval of time, then the raisins would recede from each other with exactly a Hubble type expansion law. In a given time interval, a nearby raisin would move relatively little, but a distant raisin would move relatively farther - and the same behavior would be seen from any raisin in the loaf. In other words, the Hubble law is just what one would expect for a homogeneous expanding universe, as predicted by the Big Bang theory. Moreover no raisin, or galaxy, occupies a special place in this universe - unless you get too close to the edge of the loaf where the analogy breaks down.
Nucleosynthesis in the Early Universe
The term nucleosynthesis refers to the formation of heavier elements, atomic nuclei with many protons and neutrons, from the fusion of lighter elements. The Big Bang theory predicts that the early universe was a very hot place. One second after the Big Bang, the temperature of the universe was roughly 10 billion degrees and was filled with a sea of neutrons, protons, electrons, anti-electrons (positrons), photons and neutrinos. As the universe cooled, the neutrons either decayed into protons and electrons or combined with protons to make deuterium (an isotope of hydrogen). During the first three minutes of the universe, most of the deuterium combined to make helium. Trace amounts of lithium were also produced at this time. This process of light element formation in the early universe is called “Big Bang nucleosynthesis” (BBN).
The predicted abundance of deuterium, helium and lithium depends on the density of ordinary matter in the early universe, as shown in the figure at left. These results indicate that the yield of helium is relatively insensitive to the abundance of ordinary matter, above a certain threshold. We generically expect about 24% of the ordinary matter in the universe to be helium produced in the Big Bang. This is in very good agreement with observations and is another major triumph for the Big Bang theory.
However, the Big Bang model can be tested further. In order for the predicted yields of the other light elements to come out in agreement with observations, the overall density of the ordinary matter must be roughly 4% of the critical density. The WMAP satellite should be able to directly measure the ordinary matter density and compare the observed value to the predictions of Big Bang nucleosynthesis. This will be an important and stringent test of the model. If the results agree, it will be a further evidence in support of the Big Bang theory. If the results are in conflict, it will either point to 1) errors in the data, 2) an incomplete understanding of the process of Big Bang nucleosynthesis, 3) a misunderstanding of the mechanisms that produce fluctuations in the microwave background radiation, or 4) a more fundamental problem with the Big Bang theory.
Nucleosynthesis in Stars
Elements heavier than lithium are all synthesized in stars. During the late stages of stellar evolution, massive stars burn helium to carbon, oxygen, silicon, sulfur, and iron. Elements heavier than iron are produced in two ways: in the outer envelopes of super-giant stars and in the explosion of a supernovae. All carbon-based life on Earth is
The Big Bang theory predicts that the early universe was a very hot place and that as it expands, the gas within it cools. Thus the universe should be filled with radiation that is literally the remnant heat left over from the Big Bang, called the “cosmic microwave background radiation”, or CMB.1
Discovery of the Cosmic Microwave Background
The existence of the CMB radiation was first predicted by George Gamow in 1948, and by Ralph Alpher and Robert Herman in 1950. It was first observed inadvertently in 1965 by Arno Penzias and Robert Wilson at the Bell Telephone Laboratories in Murray Hill, New Jersey. The radiation was acting as a source of excess noise in a radio receiver they were building. Coincidentally, researchers at nearby Princeton University, led by Robert Dicke and including Dave Wilkinson of the WMAP science team, were devising an experiment to find the CMB. When they heard about the Bell Labs result they immediately realized that the CMB had been found. The result was a pair of papers in the Physical Review: one by Penzias and Wilson detailing the observations, and one by Dicke, Peebles, Roll, and Wilkinson giving the cosmological interpretation. Penzias and Wilson shared the 1978 Nobel prize in physics for their discovery.
Today, the CMB radiation is very cold, only 2.725° above absolute zero, thus this radiation shines primarily in the microwave portion of the electromagnetic spectrum, and is invisible to the naked eye. However, it fills the universe and can be detected everywhere we look. In fact, if we could see microwaves, the entire sky would glow with a brightness that was astonishingly uniform in every direction. The picture at left shows a false color depiction of the temperature (brightness) of the CMB over the full sky (projected onto an oval, similar to a map of the Earth). The temperature is uniform to better than one part in a thousand! This uniformity is one compelling reason to interpret the radiation as remnant heat from the Big Bang; it would be very difficult to imagine a local source of radiation that was this uniform. In fact, many scientists have tried to devise alternative explanations for the source of this radiation but none have succeeded.
Why study the Cosmic Microwave Background?
Since light travels at a finite speed, astronomers observing distant objects are looking into the past. Most of the stars that are visible to the naked eye in the night sky are 10 to 100 light years away. Thus, we see them as they were 10 to 100 years ago. We observe Andromeda, the nearest big galaxy, as it was about 2.5 million years ago. Astronomers observing distant galaxies with the Hubble Space Telescope can see them as they were only a few billion years after the Big Bang. (Most cosmologists believe that the universe is between 12 and 14 billion years old.)
The CMB radiation was emitted only a few hundred thousand years after the Big Bang, long before stars or galaxies ever existed. Thus, by studying the detailed physical properties of the radiation, we can learn about conditions in the universe on very large scales, since the radiation we see today has traveled over such a large distance, and at very early times.
The Origin of the Cosmic Microwave Background
One of the profound observations of the 20th century is that the universe is expanding. This expansion implies the universe was smaller, denser and hotter in the distant past. When the visible universe was half its present size, the density of matter was eight times higher and the cosmic microwave background was twice as hot. When the visible universe was one hundredth of its present size, the cosmic microwave background was a hundred times hotter (273 degrees above absolute zero or 32 degrees Fahrenheit, the temperature at which water freezes to form ice on the Earth's surface). In addition to this cosmic microwave background radiation, the early universe was filled with hot hydrogen gas with a density of about 1000 atoms per cubic centimeter. When the visible universe was only one hundred millionth its present size, its temperature was 273 million degrees above absolute zero and the density of matter was comparable to the density of air at the Earth's surface. At these high temperatures, the hydrogen was completely ionized into free protons and electrons.
Since the universe was so very hot through most of its early history, there were no atoms in the early universe, only free electrons and nuclei. (Nuclei are made of neutrons and protons). The cosmic microwave background photons easily scatter off of electrons. Thus, photons wandered through the early universe, just as optical light wanders through a dense fog. This process of multiple scattering produces what is called a “thermal” or “blackbody” spectrum of photons. According to the Big Bang theory, the frequency spectrum of the CMB should have this blackbody form. This was indeed measured with tremendous accuracy by the FIRAS experiment on NASA's COBE satellite.
This figure shows the prediction of the Big Bang theory for the energy spectrum of the cosmic microwave background radiation compared to the observed energy spectrum. The FIRAS experiment measured the spectrum at 34 equally spaced points along the blackbody curve. The error bars on the data points are so small that they can not be seen under the predicted curve in the figure! There is no alternative theory yet proposed that predicts this energy spectrum. The accurate measurement of its shape was another important test of the Big Bang theory.
“Surface of Last Scattering”
Eventually, the universe cooled sufficiently that protons and electrons could combine to form neutral hydrogen. This was thought to occur roughly 400,000 years after the Big Bang when the universe was about one eleven hundredth its present size. Cosmic microwave background photons interact very weakly with neutral hydrogen.
The behavior of CMB photons moving through the early universe is analogous to the propagation of optical light through the Earth's atmosphere. Water droplets in a cloud are very effective at scattering light, while optical light moves freely through clear air. Thus, on a cloudy day, we can look through the air out towards the clouds, but can not see through the opaque clouds. Cosmologists studying the cosmic microwave background radiation can look through much of the universe back to when it was opaque: a view back to 400,000 years after the Big Bang. This “wall of light“ is called the surface of last scattering since it was the last time most of the CMB photons directly scattered off of matter. When we make maps of the temperature of the CMB, we are mapping this surface of last scattering.
As shown above, one of the most striking features about the cosmic microwave background is its uniformity. Only with very sensitive instruments, such as COBE and WMAP, can cosmologists detect fluctuations in the cosmic microwave background temperature. By studying these fluctuations, cosmologists can learn about the origin of galaxies and large scale structures of galaxies and they can measure the basic parameters of the Big Bang theory.
The Big Bang model was a natural outcome of Einstein's General Relativity as applied to a homogeneous universe. However, in 1917, the idea that the universe was expanding was thought to be absurd. So Einstein invented the cosmological constant as a term in his General Relativity theory that allowed for a static universe. In 1929, Edwin Hubble announced that his observations of galaxies outside our own Milky Way showed that they were systematically moving away from us with a speed that was proportional to their distance from us. The more distant the galaxy, the faster it was receding from us. The universe was expanding after all, just as General Relativity originally predicted! Hubble observed that the light from a given galaxy was shifted further toward the red end of the light spectrum the further that galaxy was from our galaxy.
The specific form of Hubble's expansion law is important: the speed of recession is proportional to distance. The expanding raisin bread model at left illustrates why this is important. If every portion of the bread expands by the same amount in a given interval of time, then the raisins would recede from each other with exactly a Hubble type expansion law. In a given time interval, a nearby raisin would move relatively little, but a distant raisin would move relatively farther - and the same behavior would be seen from any raisin in the loaf. In other words, the Hubble law is just what one would expect for a homogeneous expanding universe, as predicted by the Big Bang theory. Moreover no raisin, or galaxy, occupies a special place in this universe - unless you get too close to the edge of the loaf where the analogy breaks down.
The Life and Death of Stars
Where are Stars Born?
Astronomers believe that molecular clouds, dense clouds of gas located primarily in the spiral arms of galaxies are the birthplace of stars. Dense regions in the clouds collapse and form "protostars". Initially, the gravitational energy of the collapsing star is the source of its energy. Once the star contracts enough that its central core can burn hydrogen to helium, it becomes a "main sequence" star.
Image of "Star Birth" Clouds in M16:
PRC95-44b Hubble Wide Field Image
Text link to the HST press release describing this image
Main Sequence Stars
Main sequence stars are stars, like our Sun, that fuse hydrogen atoms together to make helium atoms in their cores. For a given chemical composition and stellar age, a stars' luminosity, the total energy radiated by the star per unit time, depends only on its mass. Stars that are ten times more massive than the Sun are over a thousand times more luminous than the Sun. However, we should not be too embarrassed by the Sun's low luminosity: it is ten times brighter than a star half its mass. The more massive a main sequence star, the brighter and bluer it is. For example, Sirius, the dog star, located to the lower left of the constellation Orion, is more massive than the Sun, and is noticeably bluer. On the other hand, Proxima Centauri, our nearest neighbor, is less massive than the Sun, and is thus redder and less luminous.
Since stars have a limited supply of hydrogen in their cores, they have a limited lifetime as main sequence stars. This lifetime is proportional to f M / L, where f is the fraction of the total mass of the star, M, available for nuclear burning in the core and L is the average luminosity of the star during its main sequence lifetime. Because of the strong dependence of luminosity on mass, stellar lifetimes depend sensitively on mass. Thus, it is fortunate that our Sun is not more massive than it is since high mass stars rapidly exhaust their core hydrogen supply. Once a star exhausts its core hydrogen supply, the star becomes redder, larger, and more luminous: it becomes a red giant star. This relationship between mass and lifetime enables astronomers to put a lower limit on the age of the universe.
Death of an "Ordinary" Star
After a low mass star like the Sun exhausts the supply of hydrogen in its core, there is no longer any source of heat to support the core against gravity. Hydrogen burning continues in a shell around the core and the star evolves into a red giant. When the Sun becomes a red giant, its atmosphere will envelope the Earth and our planet will be consumed in a fiery death.
Meanwhile, the core of the star collapses under gravity's pull until it reaches a high enough density to start burning helium to carbon. The helium burning phase will last about 100 million years, until the helium is exhausted in the core and the star becomes a red supergiant. At this stage, the Sun will have an outer envelope extending out towards Jupiter. During this brief phase of its existence, which lasts only a few tens of thousands of years, the Sun will lose mass in a powerful wind. Eventually, the Sun will lose all of the mass in its envelope and leave behind a hot core of carbon embedded in a nebula of expelled gas. Radiation from this hot core will ionize the nebula, producing a striking "planetary nebula", much like the nebulae seen around the remnants of other stars. The carbon core will eventually cool and become a white dwarf, the dense dim remnant of a once bright star.
Image of a Planetary Nebula:
NGC 6543 Hubble Wide Field Image
Text Link to the HST press release describing this image
Death of a Massive Star
Massive stars burn brighter and perish more dramatically than most. When a star ten times more massive than Sun exhaust the helium in the core, the nuclear burning cycle continues. The carbon core contracts further and reaches high enough temperature to burn carbon to oxygen, neon, silicon, sulfur and finally to iron. Iron is the most stable form of nuclear matter and there is no energy to be gained by burning it to any heavier element. Without any source of heat to balance the gravity, the iron core collapses until it reaches nuclear densities. This high density core resists further collapse causing the infalling matter to "bounce" off the core. This sudden core bounce (which includes the release of energetic neutrinos from the core) produces a supernova explosion. For one brilliant month, a single star burns brighter than a whole galaxy of a billion stars. Supernova explosions inject carbon, oxygen, silicon and other heavy elements up to iron into interstellar space. They are also the site where most of the elements heavier than iron are produced. This heavy element enriched gas will be incorporated into future generations of stars and planets. Without supernova, the fiery death of massive stars, there would be no carbon, oxygen or other elements that make life possible.
Image of a Supernova Remnant:
Supernova 1987A Hubble Wide Field Image
Text Link to the HST press release describing this image
The fate of the hot neutron core depends upon the mass of the progenitor star. If the progenitor mass is around ten times the mass of the Sun, the neutron star core will cool to form a neutron star. Neutron stars are potentially detectable as "pulsars", powerful beacons of radio emission. If the progenitor mass is larger, then the resultant core is so heavy that not even nuclear forces can resist the pull of gravity and the core collapses to form a black hole.
White dwarfs are among the dimmest stars in the universe. Even so, they have commanded the attention of astronomers ever since the first white dwarf was observed bthe mass of many millions of stars are thought to lie at the center of most large galaxies. The evidence comes from optical and radio observations which show a sharp rise in the velocities of stars or gas clouds orbiting the centers of galaxies. High orbital velocities mean that something massive is creating a powerful gravitational field which is accelerating the stars. X-ray observations indicate that a large amount of energy is produced in the centers of many galaxies, presumably by the in-fall of matter into a black hole.
Schematic of
a Black Hole
How could a supermassive black hole form in the center of a galaxy? One idea is that an individual starlike black hole forms and swallows up enormous amounts of matter over the course of millions of years to produce a supermassive black hole. Another possibility is that a cluster of starlike black holes forms and eventually merges into a single, supermassive black hole. Or, a single large gas cloud could collapse to form a supermassive black hole.
Centaurus A
Recent research, including results from Chandra (see 3C294, Perseus Cluster, NGC 4636, Centaurus A) suggests that galaxies and their black holes do not grow steadily, but in fits and starts. In the beginning of a growth cycle, the galaxy and its central black hole are accumulating matter. The energy generated by the jets that accompany the growth of the supermassive black hole eventually brings the infall of matter and the growth of the galaxy to a halt. The activity around the central black hole then ceases because of the lack of a steady supply of matter, and the jets disappear. Millions of years later the hot gas around the galaxy cools and resumes falling into the galaxy, initiating a new season of growth. Stellar -Black holes with a mass of about 5 - 100 Suns formed at the end of very massive star's evolutionary cycle. Mid-mass -A newly discovered type of black hole that has a mass of 500 - 1,000's of Suns. Supermassive -Black holes with a mass of a million or more Sunsy optical telescopes in the middle of the 19th century. One reason for this interest is that white dwarfs represent an intriguing state of matter; another reason is that most stars, including our Sun, will become white dwarfs when they reach their final, burnt-out collapsed state.
A star experiences an energy crisis and its core collapses when the star's basic, non-renewable energy source - hydrogen - is used up. A shell of hydrogen on the edge of the collapsed core will be compressed and heated. The nuclear fusion of the hydrogen in the shell will produce a new surge of power that will cause the outer layers of the star to expand until it has a diameter a hundred times its present value. This is called the "red giant" phase of a star's existence.
dinary matter, or the stuff we and everything around us is made of, consists largely of empty space. Even a rock is mostly empty space. This is because matter is made of atoms. An atom is a cloud of electrons orbiting around a nucleus composed of protons and neutrons.
The nucleus contains more than 99.9 percent of the mass of an atom, yet it has a diameter of only 1/100,000 that of the electron cloud. The electrons themselves take up little space, but the pattern of their orbit defines the size of the atom, which is therefore 99.9999999999999% open space!
What we perceive as painfully solid when we bump against a rock is really a hurly-burly of electrons moving through empty space so fast that we can't see—or feel—the emptiness. What would matter look like if it weren't empty, if we could crush the electron cloud down to the size of the nucleus? Suppose we could generate a force strong enough to crush all the emptiness out of a rock roughly the size of a football stadium. The rock would be squeezed down to the size of a grain of sand and would still weigh 4 million tons!
Stellar -Black holes with a mass of about 5 - 100 Suns formed at the end of very massive star's evolutionary cycle. Mid-mass -A newly discovered type of black hole that has a mass of 500 - 1,000's of Suns. Supermassive -Black holes with a mass of a million or more Suns
ery 50 years or so, a massive star in our galaxy blows itself apart in a supernova explosion. Supernovas are one of the most violent events in the universe, and the force of the explosion generates a blinding flash of radiation, as well as shock waves analogous to sonic booms.
There are two types of supernovas: Type II, where a massive star explodes; and Type Ia, where a white dwarf collapses because it has pulled too much material from a nearby companion star onto itself.
The general picture for a Type II supernova goes something like this. When the nuclear power source at the center or core of a star is exhausted, the core collapses. In less than a second, a neutron star (or black hole, if the star is extremely massive) is formed. As in-falling matter crashes down on the neutron star, temperatures rise to billions of degrees Celsius. Within hours, a catastrophic explosion occurs, and all but the central neutron star is blown away at speeds in excess of 50 million kilometers per hour. A thermonuclear shock wave races through the now expanding stellar debris, fusing lighter elements into heavier ones and producing a brilliant visual outburst that can be as intense as the light of several billion Suns!
Astronomers observe considerable structure in the universe, from stars to galaxies to clusters and superclusters of galaxies. The famous "Deep Field Image" taken by the Hubble Space Telescope, shown below, provides a stunning view of such structure. How did these structures form? The Big Bang theory is widely considered to be a successful theory of cosmology, but the theory is incomplete. It does not account for the needed fluctuations to produce the structure we see. Most cosmologists believe that the galaxies that we observe today grew from the gravitational pull of small fluctuations in the nearly-uniform density of the early universe. These fluctuations leave an imprint in the cosmic microwave background radiation in the form of temperature fluctuations from point to point across the sky. The WMAP satellite measures these small fluctuations in the temperature of the cosmic microwave background radiation and in turn probe the early stages of structure formation. 2
Hubble Deep Field Image:
Text Link to the HST press release describing this image
In its simplest form, the Big Bang theory assumes that matter and radiation are uniformly distributed throughout the universe and that general relativity is universally valid. While this can account for the existence of the cosmic microwave background radiation and explain the origin of the light elements, it does not explain the existence of galaxies and large-scale structure. The solution of the structure problem must be built into the framework of the Big Bang theory.
Gravitational Formation of Structure
Most cosmologists believe that the galaxies that we observe today grew gravitationally out of small fluctuations in the density of the universe through the following sequence of events:
• When the universe was one thousandth its present size (roughly 500,000 years after the Big Bang), the density of matter in the region of space that now contains the Milky Way, our home galaxy, was perhaps 0.5% higher than in adjacent regions. Because its density was higher, this region of space expanded more slowly than surrounding regions.
• As a result of this slower expansion, its relative over-density grew. When the universe was one hundredth its present size (roughly 15 million years after the Big Bang), our region of space was probably 5% denser than the surrounding regions.
• This gradual growth continued as the universe expanded. When the universe was one fifth its present size (roughly 1.2 billion years after the Big Bang), our region of space was probably twice as dense as neighboring regions. Cosmologists speculate that the inner portions of our Galaxy (and similar galaxies) were assembled at this time. The stars in the outer regions of our Galaxy were probably assembled in the more recent past. Some cosmologists suspect that some of the objects recently detected by the Hubble Space Telescope may be galaxies in formation.
HST Images of Galaxies in Formation?
Observing These Small Fluctuations
Tiny variations in the density of matter in the early universe leave an imprint in the cosmic microwave background radiation in the form of temperature fluctuations from point to point across the sky. These temperature fluctuations are minute: one part of the sky might have a temperature of 2.7251 Kelvin (degrees above absolute zero), while another part might have a temperature of 2.7249 Kelvin. NASA's Cosmic Background Explorer (COBE) satellite, has detected these tiny fluctuations on large angular scales. WMAP re-measures the fluctuations with both higher angular resolution and sensitivity. The mission summary page offers a quick introduction to how WMAP achieves this sensitivity - more details are available on the technical information page.
What Made These Small Fluctuations?
While gravity can enhance the tiny fluctuations seen in the early universe, it can not produce these fluctuations. Cosmologists speculate about the new physics needed to produce the primordial fluctuations that formed galaxies. Two popular ideas are:
• Inflation
• Topological Defects
These different theories make very different predictions about the properties of the cosmic microwave background fluctuations. For example, the inflationary theory predicts that the largest temperature fluctuations should have an angular scale of one degree, while the defect models predict a smaller characteristic scale. WMAP, with its superb sensitivity, indicates that the inflationary model is more likely.
Learn More About Structure Formation at These Sites:
The Sloan Digital Sky Survey (SDSS)
This group plans to map the positions of over 100 million galaxies and determine the distances to over a million galaxies and quasars. The effort will produce the largest (known) survey to date of cosmic structure in the universe. You can learn more about the details of the SDSS by visiting their home page at Fermilab.
The Virgo Consortium
The Virgo Consortium is an international grouping of scientists carrying out super computer simulations of the formation of galaxies, galaxy clusters, large-scale structure, and of the evolution of the intergalactic medium. Although most of the consortium members are British, there are important nodes in Canada, the United States, and Germany.
The University of Washington N-Body Shop
This group creates software simulations for studying large-scale structure formation and planet formation, and host an interesting image gallery.
The Hubble Space Telescope
HST has been able to observe distant galaxies and study the formation and evolution of galaxies. The lead figure on this page is a Hubble Deep Field image. You can learn more about this image by clicking here.
n the 1920s, Edwin Hubble, using the newly constructed 100" telescope at Mount Wilson Observatory, detected variable stars in several nebulae. Nebulae are diffuse objects whose nature was a topic of heated debate in the astronomical community: were they interstellar clouds in our own Milky Way galaxy, or whole galaxies outside our galaxy? This was a difficult question to answer because it is notoriously difficult to measure the distance to most astronomical bodies since there is no point of reference for comparison. Hubble's discovery was revolutionary because these variable stars had a characteristic pattern resembling a class of stars called Cepheid variables. Earlier, Henrietta Levitt, part of a group of female astronomers working at Harvard College Observatory, had shown there was a tight correlation between the period of a Cepheid variable star and its luminosity (intrinsic brightness). By knowing the luminosity of a source it is possible to measure the distance to that source by measuring how bright it appears to us: the dimmer it appears the farther away it is. Thus, by measuring the period of these stars (and hence their luminosity) and their apparent brightness, Hubble was able to show that these nebula were not clouds within our own Galaxy, but were external galaxies far beyond the edge of our own Galaxy.
Hubble's second revolutionary discovery was based on comparing his measurements of the Cepheid-based galaxy distance determinations with measurements of the relative velocities of these galaxies. He showed that more distant galaxies were moving away from us more rapidly:
v = Hod
where v is the speed at which a galaxy moves away from us, and d is its distance. The constant of proportionality Ho is now called the Hubble constant. The common unit of velocity used to measure the speed of a galaxy is km/sec, while the most common unit of for measuring the distance to nearby galaxies is called the Megaparsec (Mpc) which is equal to 3.26 million light years or 30,800,000,000,000,000,000 km! Thus the units of the Hubble constant are (km/sec)/Mpc.
The universe was not static, but rather was expanding! This discovery marked the beginning of the modern age of cosmology. Today, Cepheid variables remain one of the best methods for measuring distances to galaxies and are vital to determining the expansion rate (the Hubble constant) and age of the universe.
What are Cepheid Variables?
The structure of all stars, including the Sun and Cepheid variable stars, is determined by the opacity of matter in the star. If the matter is very opaque, then it takes a long time for photons to diffuse out from the hot core of the star, and strong temperature and pressure gradients can develop in the star. If the matter is nearly transparent, then photons move easily through the star and erase any temperature gradient. Cepheid stars oscillate between two states: when the star is in its compact state, the helium in a layer of its atmosphere is singly ionized. Photons scatter off of the bound electron in the singly ionized helium atoms, thus, the layer is very opaque and large temperature and pressure gradients build up across the layer. These large pressures cause the layer (and the whole star) to expand. When the star is in its expanded state, the helium in the layer is doubly ionized, so that the layer is more transparent to radiation and there is much weaker pressure gradient across the layer. Without the pressure gradient to support the star against gravity, the layer (and the whole star) contracts and the star returns to its compressed state.
Cepheid variable stars have masses between five and twenty solar masses. The more massive stars are more luminous and have more extended envelopes. Because their envelopes are more extended and the density in their envelopes is lower, their variability period, which is proportional to the inverse square root of the density in the layer, is longer.
Text Link to the HST press release describing this image.
Difficulties in Using Cepheids
There have been a number of difficulties associated with using Cepheids as distance indicators. Until recently, astronomers used photographic plates to measure the fluxes from stars. The plates were highly non-linear and often produced faulty flux measurements. Since massive stars are short lived, they are always located near their dusty birthplaces. Dust absorbs light, particularly at blue wavelengths where most photographic images were taken, and if not properly corrected for, this dust absorption can lead to erroneous luminosity determinations. Finally, it has been very difficult to detect Cepheids in distant galaxies from the ground: Earth's fluctuating atmosphere makes it impossible to separate these stars from the diffuse light of their host galaxies.
Another historic difficulty with using Cepheids as distance indicators has been the problem of determining the distance to a sample of nearby Cepheids. In recent years, astronomers have developed several very reliable and independent methods of determining the distances to the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC), two of the nearby satellite galaxies of our own Milky Way Galaxy. Since the LMC and SMC contain large number of Cepheids, they can be used to calibrate the distance scale.
Recent Progress
Recent technological advances have enabled astronomers to overcome a number of the other past difficulties. New detectors called CCDs (charge coupled devices) made possible accurate flux measurements. These detectors are also sensitive in the infrared wavelengths. Dust is much more transparent at these wavelengths. By measuring fluxes at multiple wavelengths, astronomers were able to correct for the effects of dust and make much more accurate distance determinations.
These advances enabled more accurate study of the nearby galaxies that comprise the "Local Group" of galaxies. Astronomers observed Cepheids in both the metal rich inner region of the Andromeda galaxy and its metal poor outer region. (To an astronomer, a "metal" is any element heavier than helium - the second lightest element in the periodic table. Such elements are produced in stars and are ultimately released into the interstellar medium as the stars evolve.) This work showed that the properties of Cepheids did not depend sensitively on chemical abundances. Despite these advances, astronomers, limited by the Earth's atmosphere, could only measure the distances to the nearest galaxies. In addition to the motion due to the expansion of the universe, galaxies have "relative motions" due to the gravitational pull of their neighbors. Because of these "peculiar motions", astronomers need to measure the distances to distant galaxies so that they can determine the Hubble constant.
Trying to push deeper into the universe, astronomers have developed a number of new techniques for determining relative distances to galaxies: these independent relative distance scales now agree to better than 10%. For example, there is a very tight relation, called the Tully-Fisher relation, between the rotational velocity of a spiral galaxy and its luminosity. Astronomers also found that Type Ia supernova, which are thought to be due to the explosive burning of a white dwarf star, all had nearly the same peak luminosity. However, without accurate measurements of distance to large numbers of prototype galaxies, astronomers could not calibrate these relative distance measurements. Thus, they were unable to make accurate determinations of the Hubble constant.
Over the past few decades, leading astronomers, using different data, reported values for the Hubble constant that varied between 50 (km/sec)/Mpc and 100 (km/sec)/Mpc. Resolving this discrepancy, which corresponds to a factor 2 uncertainty, was one of the most important outstanding problems in observational cosmology.
Hubble Key Project
One of the "key projects" of the Hubble Space Telescope is to complete Edwin Hubble's program of measuring distances to nearby galaxies. While the Hubble Space Telescope (HST) is comparable in diameter to Hubble's telescope on Mount Wilson, it has the advantage of being above the Earth's atmosphere, rather then being located on the outskirts of Los Angeles. NASA's repair of the Hubble Space Telescope restored its vision and enabled the key project program. The photos below show before and after images of M100, one of the nearby galaxies observed by the key project program. Note that with the refurbished HST, it is much easier to detect individual bright stars in M100, a necessary step in studying Cepheid variables. The project also checks to see if the properties of Cepheid variables are sensitive to stellar composition.
HST image of M100 before and after repair
Text Link to the HST press release describing this image.
Overall, the key project aims to get distances to 20 nearby galaxies. With this large sample, the project can calibrate and cross check a number of the secondary distance indicators. Because M100 is close enough to us that its peculiar motion is a significant fraction of its Hubble expansion velocity, the key project team used relative distance indicators to extrapolate from the Virgo cluster, a nearby cluster of galaxies containing M100, to the more distant Coma cluster and to obtain a measurement of the Hubble constant of 70 (km/sec)/Mpc, with an uncertainty of 10%.
The key project determination of the Hubble constant is consistent with a number of independent efforts to estimate the Hubble constant: a recent statistical synthesis by G.F.R. Ellis and his collaborators of the published literature yields a value between 66 and 82 (km/sec)/Mpc. However, there is still not complete consensus on the value of the Hubble constant: a recent analysis by Allan Sandage using Type Ia supernovae yields a value for the Hubble constant that is formally inconsistent with many of measurements: 47 (km/sec)/Mpc.
WMAP and the Hubble Constant
By characterizing the detailed structure of the cosmic microwave background fluctuations, WMAP has accurately determined the basic cosmological parameters, including the Hubble constant, to better than 5%. This measurement is completely independent of traditional measurements using Cepheid variables and other techniques. The current results show the Hubble Constant to be 73.5 +/-3.2 (km/sec)/Mpc. If the WMAP data is combined with other cosmological data, the best estimate is 70.8 +/- 1.6 (km/sec)/Mpc. These results assume that the universe is spatially flat, which is consistent with all available data. However, if we relax this assumption, the uncertainty in the Hubble constant increases to +/-4 (km/sec)/Mpc, or slightly over 5%.
This page was adapted from the article "The age of the universe", D.N. Spergel, M. Bolte (UC, Santa Cruz) and W. Freedman (Carnegie Observatories). Proc. Natl. Acad. Sci. USA, Vol. 94, pp. 6579-6584, June 1997.
Further Reading:
• More on the Hubble Constant from Space Telescope Science Institute including movies.
• Freedman, Wendy L., "The Expansion Rate and Science of the Universe", Scientific American, Nov. 1992.
• Osterbrock, D.E., Gwinn, J.A. & Brashear, R.S., "Hubble and the Expanding Universe", Scientific American, July 1993.
Until recently, astronomers estimated that the Big Bang occurred between 12 and 14 billion years ago. To put this in perspective, the Solar System is thought to be 4.5 billion years old and humans have existed as a species for a few million years. Astronomers estimate the age of the universe in two ways: 1) by looking for the oldest stars; and 2) by measuring the rate of expansion of the universe and extrapolating back to the Big Bang; just as crime detectives can trace the origin of a bullet from the holes in a wall.
Older Than the Oldest Stars?
Astronomers can place a lower limit to the age of the universe by studying globular clusters. Globular clusters are a dense collection of roughly a million stars. Stellar densities near the center of the globular cluster are enormous. If we lived near the center of one, there would be several hundred thousand stars closer to us than Proxima Centauri, the star nearest to the Sun.
Text Link to the HST press release describing this image
The life cycle of a star depends upon its mass. High mass stars are much brighter than low mass stars, thus they rapidly burn through their supply of hydrogen fuel. A star like the Sun has enough fuel in its core to burn at its current brightness for approximately 9 billion years. A star that is twice as massive as the Sun will burn through its fuel supply in only 800 million years. A 10 solar mass star, a star that is 10 times more massive than the Sun, burns nearly a thousand times brighter and has only a 20 million year fuel supply. Conversely, a star that is half as massive as the Sun burns slowly enough for its fuel to last more than 20 billion years.
All of the stars in a globular cluster formed at roughly the same time, thus they can serve as cosmic clocks. If a globular cluster is more than 20 million years old, then all of its hydrogen burning stars will be less massive than 10 solar masses. This implies that no individual hydrogen burning star will be more than 1000 times brighter than the Sun. If a globular cluster is more than 2 billion years old, then there will be no hydrogen-burning star more massive than 2 solar masses.
The oldest globular clusters contain only stars less massive than 0.7 solar masses. These low mass stars are much dimmer than the Sun. This observation suggests that the oldest globular clusters are between 11 and 18 billion years old. The uncertainty in this estimate is due to the difficulty in determining the exact distance to a globular cluster (hence, an uncertainty in the brightness (and mass) of the stars in the cluster). Another source of uncertainty in this estimate lies in our ignorance of some of the finer details of stellar evolution. Presumably, the universe itself is at least as old as the oldest globular clusters that reside in it.
Extrapolating Back to the Big Bang 3
An alternative approach to estimating is the age of the universe is to measure the “Hubble constant”. The Hubble constant is a measure of the current expansion rate of the universe. Cosmologists use this measurement to extrapolate back to the Big Bang. This extrapolation depends on the history of the expansion rate which in turn depends on the current density of the universe and on the composition of the universe.
If the universe is flat and composed mostly of matter, then the age of the universe is
2/(3 Ho)
where Ho is the value of the Hubble constant.
If the universe has a very low density of matter, then its extrapolated age is larger:
1/Ho
If the universe contains a form of matter similar to the cosmological constant, then the inferred age can be even larger.
Many astronomers are working hard to measure the Hubble constant using a variety of different techniques. Until recently, the best estimates ranged from 65 km/sec/Megaparsec to 80 km/sec/Megaparsec, with the best value being about 72 km/sec/Megaparsec. In more familiar units, astronomers believe that 1/Ho is between 12 and 14 billion years.
An Age Crisis?
If we compare the two age determinations, there is a potential crisis. If the universe is flat, and dominated by ordinary or dark matter, the age of the universe as inferred from the Hubble constant would be about 9 billion years. The age of the universe would be shorter than the age of oldest stars. This contradiction implies that either 1) our measurement of the Hubble constant is incorrect, 2) the Big Bang theory is incorrect or 3) that we need a form of matter like a cosmological constant that implies an older age for a given observed expansion rate.
Some astronomers believe that this crisis will pass as soon as measurements improve. If the astronomers who have measured the smaller values of the Hubble constant are correct, and if the smaller estimates of globular cluster ages are also correct, then all is well for the Big Bang theory, even without a cosmological constant.
WMAP Can Measure the Age of the Universe
Measurements by the WMAP satellite can help resolve this crisis. If current ideas about the origin of large-scale structure are correct, then the detailed structure of the cosmic microwave background fluctuations will depend on the current density of the universe, the composition of the universe and its expansion rate. WMAP has been able to determine these parameters with an accuracy of better than 5%. Thus, we can estimate the expansion age of the universe to better than 5%. When we combine the WMAP data with complimentary observations from other CMB experiments (ACBAR and CBI), we are able to determine an age for the universe closer to an accuracy of 1%.
The expansion age measured by WMAP is larger than the oldest globular clusters, so the Big Bang theory has passed an important test. If the expansion age measured by WMAP had been smaller than the oldest globular clusters, then there would have been something fundamentally wrong about either the Big Bang theory or the theory of stellar evolution. Either way, astronomers would have needed to rethink many of their cherished ideas. But our current estimate of age fits well with what we know from other kinds of measurements: the Universe is about 13.7 billion years old!
The shape of the universe is determined by a struggle between the momentum of expansion and the pull of gravity. The rate of expansion is expressed by the Hubble Constant, Ho, while the strength of gravity depends on the density and pressure of the matter in the universe. If the pressure of the matter is low, as is the case with most forms of matter we know of, then the fate of the universe is governed by the density. If the density of the universe is less than the "critical density" which is proportional to the square of the Hubble constant, then the universe will expand forever. If the density of the universe is greater than the "critical density", then gravity will eventually win and the universe will collapse back on itself, the so called "Big Crunch". However, the results of the WMAP mission and observations of distant supernova have suggested that the expansion of the universe is actually accelerating which implies the existence of a form of matter with a strong negative pressure, such as the cosmological constant. This strange form of matter is also sometimes referred to as the "dark energy". If dark energy in fact plays a significant role in the evolution of the universe, then in all likelihood the universe will continue to expand forever.
Geometry of the Universe
The density of the universe also determines its geometry. If the density of the universe exceeds the critical density, then the geometry of space is closed and positively curved like the surface of a sphere. This implies that initially parallel photon paths converge slowly, eventually cross, and return back to their starting point (if the universe lasts long enough). If the density of the universe is less than the critical density, then the geometry of space is open, negatively curved like the surface of a saddle. If the density of the universe exactly equals the critical density, then the geometry of the universe is flat like a sheet of paper. Thus, there is a direct link between the geometry of the universe and its fate.
The simplest version of the inflationary theory, an extension of the Big Bang theory, predicts that the density of the universe is very close to the critical density, and that the geometry of the universe is flat, like a sheet of paper. That is the result confirmed by the WMAP science.
Measurements from WMAP
The WMAP spacecraft can measure the basic parameters of the Big Bang theory including the geometry of the universe. If the universe were open, the brightest microwave background fluctuations (or "spots") would be about half a degree across. If the universe were flat, the spots would be about 1 degree across. While if the universe were closed, the brightest spots would be about 1.5 degrees across.
Recent measurements (c. 2001) by a number of ground-based and balloon-based experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know that the universe is flat with only a 2% margin of error.
Einstein first proposed the cosmological constant (not to be confused with the Hubble Constant) usually symbolized by the greek letter "lambda" (), as a mathematical fix to the theory of general relativity. In its simplest form, general relativity predicted that the universe must either expand or contract. Einstein thought the universe was static, so he added this new term to stop the expansion. Friedmann, a Russian mathematician, realized that this was an unstable fix, like balancing a pencil on its point, and proposed an expanding universe model, now called the Big Bang theory. When Hubble's study of nearby galaxies showed that the universe was in fact expanding, Einstein regretted modifying his elegant theory and viewed the cosmological constant term as his "greatest mistake".
Many cosmologists advocate reviving the cosmological constant term on theoretical grounds. Modern field theory associates this term with the energy density of the vacuum. For this energy density to be comparable to other forms of matter in the universe, it would require new physics: the addition of a cosmological constant term has profound implications for particle physics and our understanding of the fundamental forces of nature.
The main attraction of the cosmological constant term is that it significantly improves the agreement between theory and observation. The most spectacular example of this is the recent effort to measure how much the expansion of the universe has changed in the last few billion years. Generically, the gravitational pull exerted by the matter in the universe slows the expansion imparted by the Big Bang. Very recently it has become practical for astronomers to observe very bright rare stars called supernova in an effort to measure how much the universal expansion has slowed over the last few billion years. Surprisingly, the results of these observations indicate that the universal expansion is speeding up, or accelerating! While these results should be considered preliminary, they raise the possibility that the universe contains a bizarre form of matter or energy that is, in effect, gravitationally repulsive. The cosmological constant is an example of this type of energy. Much work remains to elucidate this mystery!
There are a number of other observations that are suggestive of the need for a cosmological constant. For example, if the cosmological constant today comprises most of the energy density of the universe, then the extrapolated age of the universe is much larger than it would be without such a term, which helps avoid the dilemma that the extrapolated age of the universe is younger than some of the oldest stars we observe! A cosmological constant term added to the inflationary model, an extension of the Big Bang theory, leads to a model that appears to be consistent with the observed large-scale distribution of galaxies and clusters, with COBE's measurements of cosmic microwave background fluctuations, and with the observed properties of X-ray clusters.
WMAP and the Cosmological Constant
By characterizing the detailed structure of the cosmic microwave background fluctuations, WMAP should be able to accurately determine the basic cosmological parameters, including the cosmological constant, to better than 5%.
Further Reading:
• Donald Goldsmith, "Einstein's Greatest Blunder? The Cosmological Constant and Other Fudge Factors in the Physics of the Universe", (Harvard University Press: Cambridge, Mass.) A well written, popular account of the cosmological constant and the current state of cosmology.
How did the universe start and evolve?
WMAP found that the universe is 13.7 billion years old. The universe began with an unimaginably enormous density and temperature. This immense primordial energy was the cauldron from whence all life arose. Elementary particles were created and destroyed by the ultimate particle accelerator in the first moments of the universe.
There was matter and there was antimatter. When they met, they annihilated each other and created light. Somehow, it seems that there was a tiny fraction more matter than antimatter, so when nature took its course, the universe was left with some matter, no antimatter, and a tremendous amount of light. Today, WMAP measures that there is more than a billion times more light than matter.
We aren't made of hydrogen!
WMAP determined that about 4.4% of the mass and energy of the universe is contained in atoms (protons and neutrons). All of life is made from a portion of this 4.4%.
The only chemical elements created at the beginning of our universe were hydrogen, helium and lithium, the three lightest atoms in the periodic table. These elements were formed throughout the universe as a hot gas. It's possible to imagine a universe where elements heavier than lithium would never formed and life never developed. But that is not what happened in our universe.
We are carbon-based life forms. We are made of and drink water (H2O). We breathe oxygen.
Carbon and oxygen were not created in the Big Bang, but rather much later in stars. All of the carbon and oxygen in all living things are made in the nuclear fusion reactors that we call stars. The early stars are massive and short-lived. They consume their hydrogen, helium and lithium and produce heavier elements. When these stars die with a bang they spread the elements of life, carbon and oxygen, throughout the universe. New stars condense and new planets form from these heavier elements. The stage is set for life to begin. Understanding when and how these events occur offer another window on the evolution of life in our universe.
WMAP determined that the first stars in the universe arose only about 200 million years after the Big Bang. But what made the stars?
Things that go bump in the night.
The motor for making stars (and galaxies) came early and was very subtle. Before the completion of the first fraction of a second of the universe, sub-atomic scale activity, tiny "quantum fluctuations", drove the universe towards stars and life. With the sudden expansion of a pinhead size portion of the universe in a fraction of a second, random quantum fluctuations inflated rapidly from the tiny quantum world to a macroscopic landscape of astronomical proportions. Why do we believe this? Because the microwave afterglow light from the Big Bang has an extraordinarily uniform temperature across the sky. There has not been time for the different parts of the universe to come into an equilibrium with each other *unless* the regions had exponentially inflated from a tiny patch. The only way the isotropy (uniformity) could have arisen is if the different regions were in thermal equilibrium with each other early in the history of the universe, and then rapidly inflated apart. WMAP has verified that other predictions from the inflation theory also appear to be true..
Quantum Fluctuations are the random nature of matter's state of existence or nonexistence. At these incredibly small sub-atomic scales, the state of reality is fleeting, changing from nanosecond to nanosecond.
As the universe inflated, the tiny quantum fluctuations grew to become tiny variations in the amount of matter from one place to another. A tiny amount is all it takes for gravity to do its thing. Gravity is one of the basic forces of nature and controls the evolution of the large scale structure of the universe. Without gravity there would be no stars or planets, only a cold thin mist of particles. Without the variations in the particle soup initiated by the quantum fluctuations, gravity could not begin to concentrate tiny amounts of matter into even larger amounts of matter. The end result of the pull of gravity: galaxies, stars and planets. The fluctuations, mapped in detail by the WMAP mission, are the factories and cradles of life.
The recipe for life requires a delicate balance of cosmic ingredients.
The differences in the early soup of universe particles were very small, so large scale changes take time to manifest themselves. What if our universe had only lasted for a second, or a year, or one million years? The age of the universe is controlled by the basic rules that govern matter, energy, and time. We needed almost 13.7 billion years to evolve and come to recognize this fact.
How long the universe lasts and how it evolves depends on its total energy and matter content. A universe with enormously more matter than ours would rapidly collapse back under its own gravity well before life could form. A very long lived universe might not have enough mass for stars to ever form. In addition, WMAP has confirmed the existence of a dark energy that acts like an anti-gravity, driving the universe to accelerate its expansion. Had the dark energy dominated earlier, the universe would have expanded too rapidly to support the development of life. Our universe seems to have Goldilocks properties: not too much and not too little -- just enough mass and energy to support the development of life.
Is there other intelligent life in the universe?
We don't know whether or not there is other intelligent life in the universe. There is no reason there shouldn't be. We know by our own existence that the universe is conducive to life. But there are many hurdles to overcome for intelligent life to form, and many threats to its continued existence once it does form. Life constantly faces the prospect of extinction. Life requires energy, water, and carbon; an environmental disaster that removes water, dooms life. Other environment disasters threaten. On Earth we have had huge meteor impacts that are believed to have caused mass extinctions. The harsh radiation of space is blocked only by Earth's atmosphere and magnetic field. Environmental instabilities cause ice ages. One day, billion of years from now, our Sun will burn out. Other, heavier stars end their lives in explosions called supernovae; the blast and radiation from a nearby supernova could destroy all life on Earth.
The dark energy will inexorably stretch the universe into an icy cold end. Since we don't know what the dark energy is, this might be wrong, but no less deadly depending on how the nature of the dark energy changes.
Many people are engaged in efforts to detect life in the universe. There are two strategies: we look for it, or it finds us. Perhaps a middle ground would be if we detected signals coming from life elsewhere in the universe. The Search for Extraterrestrial Intelligence (SETI) program pioneered searches for life. WMAP itself is, in a small way, a mini-SETI experiment, since it constantly scans the skies over a wide range of microwave frequencies. WMAP was not optimized to search for life. Other efforts are (have been). Some day, we may know for sure whether we are alone in the universe. In the meantime the search goes on, as we also try to understand the universe and how it may be conducive to life.
By detecting and measuring the density fluctuations in the cosmic microwave background using the WMAP space mission we are learning about the early universe; and we begin to understand the basic ingredients that make life possible. In the future, we would like to enhance these efforts with other missions, such as NASA's Einstein Inflation Probe, which would strive to detect the gravity disturbances from the era when the universe originally inflated. This passionate search for knowledge is characteristic of
"Some Say the World Will End in Fire, Others Say in Ice"4
Just as Robert Frost imagined two possible fates for the Earth in his poem, cosmologists envision two possible fates for the universe:
• Endless expansion
• The “Big Crunch”
The evolution of the universe is determined by a struggle between the momentum of expansion and the pull (or push!) of gravity. The current rate of expansion is measured by the Hubble Constant, while the strength of gravity depends on the density and pressure of the matter in the universe. If the pressure of the matter is low, as is the case with most forms of matter we know of, then the fate of the universe is governed by the density. If the density of the universe is less than the critical density which is proportional to the square of the Hubble constant, then the universe will expand forever, like the green or blue curves in the figure above. If the density of the universe is greater than the critical density, then gravity will eventually win and the universe will collapse back on itself, the so called “Big Crunch”, like the orange curve. However, recent observations of distant supernova have suggested that the expansion of the universe is actually accelerating or speeding up, like the red curve, which implies the existence of a form of matter with a strong negative pressure, such as the cosmological constant. This strange form of matter is also sometimes referred to as the “dark energy”. If dark energy in fact plays a significant role in the evolution of the universe, then in all likelihood the universe will continue to expand forever.
There is a growing consensus among cosmologists that the total density of matter is equal to the critical density, so that the universe is spatially flat. Approximately 3/10 of this is in the form of a low pressure matter, most of which is thought to be “non-baryonic” dark matter, while the remaining 7/10 is thought to be in the form of a negative pressure “dark energy”, like the cosmological constant. If this is true, then the universe will continue in a runaway expansion, as depicted in the red curve above.
Measurements from WMAP
The WMAP satellite measures the basic parameters of the Big Bang theory including the fate of the universe. The results suggest the geometry of the universe is flat
What is the Universe Made Of?
Protons, Neutrons and Electrons: The Stuff of Life
You, this computer, the air we breathe, and the distant stars are all made up of protons, neutrons and electrons. Protons and neutrons are bound together into nuclei and atoms are nuclei surrounded by a full complement of electrons. Hydrogen is composed of one proton and one electron. Helium is composed of two protons, two neutrons and two electrons. Carbon is composed of six protons, six neutrons and six electrons. Heavier elements, such as iron, lead and uranium, contain even larger numbers of protons, neutrons and electrons. Astronomers like to call all material made up of protons, neutrons and electrons "baryonic matter".
Until about twenty years ago, astronomers thought that the universe was composed almost entirely of this "baryonic matter", ordinary stuff. However, in the past decade, there has been ever more evidence accumulating that suggests there is something in the universe that we can not see, perhaps some new form of matter.
The Dark Matter Mystery
By measuring the motions of stars and gas, astronomers can "weigh" galaxies. In our own solar system, we can use the velocity of the Earth around the Sun to measure the Sun's mass. The Earth moves around the Sun at 30 kilometers per second (roughly sixty thousand miles per hour). If the Sun were four times more massive, then the Earth would need to move around the Sun at 60 kilometers per second in order for it to stay on its orbit. The Sun moves around the Milky Way at 225 kilometers per second. We can use this velocity (and the velocity of other stars) to measure the mass of our Galaxy. Similarly, radio and optical observations of gas and stars in distant galaxies enable astronomers to determine the distribution of mass in these systems.
The mass that astronomers infer for galaxies including our own is roughly ten times larger than the mass that can be associated with stars, gas and dust in a Galaxy. This mass discrepancy has been confirmed by observations of gravitational lensing, the bending of light predicted by Einstein's theory of general relativity.
HST Image of a gravitational lens
Text Link for an HST press release describing this image.
By measuring how the background galaxies are distorted by the foreground cluster, astronomers can measure the mass in the cluster. The mass in the cluster is more than five times larger than the inferred mass in visible stars, gas and dust.
Candidates for the Dark Matter
What is the nature of the "dark matter", this mysterious material that exerts a gravitational pull, but does not emit nor absorb light? Astronomers do not know.
There are a number of plausible speculations on the nature of the dark matter:
• Brown Dwarfs: if a star's mass is less than one twentieth of our Sun, its core is not hot enough to burn either hydrogen or deuterium, so it shines only by virtue of its gravitational contraction. These dim objects, intermediate between stars and planets, are not luminous enough to be directly detectable by our telescopes. Brown Dwarfs and similar objects have been nicknamed MACHOs (MAssive Compact Halo Objects) by astronomers. These MACHOs are potentially detectable by gravitational lensing experiments. If the dark matter is made mostly of MACHOs, then it is likely that baryonic matter does make up most of the mass of the universe.
• Supermassive Black Holes: these are thought to power distant quasars. Some astronomers speculate that there may be copious numbers of black holes comprising the dark matter. These black holes are also potentially detectable through their lensing effects.
• New forms of matter: particle physicists, scientists who work to understand the fundamental forces of nature and the composition of matter, have speculated that there are new forces and new types of particles. One of the primary motivations for building "supercolliders" is to try to produce this matter in the laboratory. Since the universe was very dense and hot in the early moments following the Big Bang, the universe itself was a wonderful particle accelerator. Cosmologists speculate that the dark matter may be made of particles produced shortly after the Big Bang. These particles would be very different from ordinary "baryonic matter". Cosmologists call these hypothetical particles WIMPs (for Weakly Interacting Massive Particles) or "non-baryonic matter".
WMAP and Dark Matter
By making accurate measurements of the cosmic microwave background fluctuations, WMAP is able to measure the basic parameters of the Big Bang model including the density and composition of the universe. WMAP measures the density of baryonic and non-baryonic matter to an accuracy of better than 5%. It is also able to determine some of the properties of the non-baryonic matter: the interactions of the non-baryonic matter with itself, its mass and its interactions with ordinary matter all affect the details of the cosmic microwave background fluctuation spectrum.
WMAP determined that the universe is flat, from which it follows that the mean energy density in the universe is equal to the critical density (within a 2% margin of error). This is equivalent to a mass density of 9.9 x 10-30 g/cm3, which is equivalent to only 5.9 protons per cubic meter. Of this total density, we now know the breakdown to be:
• 4% Atoms, 23% Cold Dark Matter, 73% Dark Energy. Thus 96% of the energy density in the universe is in a form that has never been directly detected in the laboratory. The actual density of atoms is equivalent to roughly 1 proton per 4 cubic meters.
• Fast moving neutrinos do not play any major role in the evolution of structure in the universe. They would have prevented the early clumping of gas in the universe, delaying the emergence of the first stars, in conflict with the new WMAP data.
• The data places new constraints on the Dark Energy. It seems more like a "cosmological constant" than a negative-pressure energy field called "quintessence". But quintessence is not ruled out.
Other Interesting Sites and Further Reading:
On dark matter:
• Visit the dark matter page at the Berkeley Cosmology Group.
• A list of popular books on dark matter and the Big Bang.
• A recent introductory html article by David Spergel on searching for dark matter. This article is geared towards physics undergraduates and will appear in "Some Outstanding Problems in Astrophysics", edited by J.N. Bahcall and J.P. Ostriker.
On MACHOs:
• OGLE home page: The Warsaw experiment searching for MACHOs.
• MACHO home page: The Berkeley/Livermore/Australia search for MACHOs.
On gravitational lensing:
• HST Gravitational Lensing Home Page.
Clustering of galaxies
Clusters of galaxies fall into two morphological categories: regular and irregular. The regular clusters show marked spherical symmetry and have a rich membership. Typically, they contain thousands of galaxies, with a high concentration toward the centre of the cluster. Rich clusters, such as the Coma cluster, are deficient in spiral galaxies and aredominated by ellipticals and S0s. The irregular clusters have less well-defined shapes, and they usually have fewer members, ranging from fairly rich systems such as the Hercules cluster to poor groups that may have only a few members. Galaxies of all types can be found in irregular clusters: spirals and irregulars, as well as ellipticals and S0s. Most galaxies are to be found not in rich clusters but in loose groups. The Galaxy belongs to one such loose group—the Local Group.
The Local Group
The Local Group contains seven reasonably prominent galaxies and perhaps another two dozen less conspicuous members. The dominant pair in the group is the Milky Way and Andromeda, both giant spirals of Hubbletype Sb and luminosity class II. The distance to the Andromeda system was first measuredby Hubble, but his estimate was too low by a factor of two because astronomers at that time did not recognize the distinction between variable stars belonging to Population II (like those studied by Shapley) and Population I (those studied by Hubble). Another spiral in the Local Group—M33, Hubble type Sc and luminosity class III—is notable, but the rest are intermediate to dwarf systems, either irregulars or ellipticals. Most of the mass of the Local Group is associated with the Milky Way and Andromeda, and with a few exceptions the smaller systems tend to congregate about one or the other of these galaxies. The size of the Local Group is therefore larger only by about 50 percent than the 2 × 106 light-years separating the Milky Way system and the Andromeda galaxy, and the centre of mass lies roughly halfway between these two giants.
The Andromeda galaxy is one of the few galaxies in the universethat actually has a velocity of approach with respect to the centre of the Galaxy. If this approach results from the reversal bythe mutual gravitational attraction of a former recession, then the total mass of the Local Group probably amounts to a few times 1012 solar masses. This is greater than the mass inferred for the optically visible parts of the galaxies and is another manifestation of the dark matter problem.
Neighbouring groups and clusters
Beyond the fringes of the Local Group lie many similar small groups. The best studied of these is the M81 group, whose dominant galaxy is the spiral galaxy M81. Much like the Andromeda and Milky Way systems, M81 is of Hubble type Sb and luminosity class II. The distance to M81, as well as to the outlying galaxy NGC 2403, can be determined from various stellar calibrators to be at a distance of 107 light-years. It is not known whether NGC 2403 and its companion NGC 2366 are truly bound to M81 or whether they are an independent pair seen by chance to lie near the M81 group. If they are bound to M81, then a measurement of their velocity along the line of sight relative to that of M81 yields, by an argument similar to that used for the Andromeda and Milky Way galaxies, an estimate of the gravitating mass of M81. This estimate equals 2 × 1012 solar masses and exceeds by an order of magnitude what is deduced from measurements of the rotation curve of M81 inside its optically visible disk.
The M81 group also has a few normal galaxies with classificationssimilar to those of galaxies in the Local Group, and it was noticed by some astronomers that the linear sizes of the largest H II regions (which are illuminated by many OB stars) in these galaxies had about the same intrinsic sizes as their counterparts in the Local Group. This led Allan Sandage and the German chemist and physicist Gustav Tammann to the (controversial) technique of using the sizes of H II regions as a distance indicator, because a measurement of their angular sizes, coupledwith knowledge of their linear sizes, allows an inference of distance.
This method can be used, for example, to obtain the distance to the M101 group, whose dominant galaxy M101 is a supergiant spiral—the closest system of Hubble type Sc and luminosity classI. Since Sc I galaxies are the most luminous spiral galaxies, with very large H II regions strung out along their spiral arms, determining the distance to M101 is a crucial step in obtaining the absolute sizes of the giant H II regions of these important systems. The sizes of the H II regions in the companion galaxies of M101 compared with the calibrated values for nearby galaxiesof the same class yield a distance to the M101 group of approximately 2 × 107 light-years.
Having calibrated the sizes of the giant H II regions in M101, Sandage and Tammann could then obtain the distances to 50 field Sc I galaxies. Once this had been done, it became possible to measure the absolute brightnesses of Sc I galaxies, and it was ascertained that all such systems have nearly the same luminosity. Since Sc I galaxies like M101 or M51 can be recognized on purely morphological grounds (well-organized spiral structure with massive arms dominated by giant H II regions), they can now be used as “standard candles” to help measure the distances to irregular clusters that contain such galaxies (e.g., the Virgo cluster containing the Sc I galaxy M100).
The Virgo cluster is the closest large cluster and is located at a distance of about 5 × 107 light-years in the direction of the constellation Virgo. About 200 bright galaxies reside in the Virgo cluster, scattered in various subclusters whose largest concentration (near the famous system M87) is about 5 × 106 light-years in diameter. Of the galaxies in the Virgo cluster, 68 percent are spirals, 19 percent are ellipticals, and the rest are irregulars or unclassified. Although spirals are more numerous, the four brightest galaxies are giant ellipticals, among them M87.Calibration of the absolute brightnesses of these giant ellipticals allows a leap to the distant regular clusters.
The nearest rich cluster containing thousands of systems, the Coma cluster, lies about seven times farther than the Virgo cluster in the direction of the constellation Coma Berenices. The main body of the Coma cluster has a diameter of about 2.5 × 107light-years, but enhancements above the background can be traced out to a supercluster of a diameter of about 2 × 108 light-years. Ellipticals or S0s constitute 85 percent of the bright galaxies in the Coma cluster; the two brightest ellipticals in Comaare located near the centre of the system and are individually more than 10 times as luminous as the Andromeda galaxy. These galaxies have a swarm of smaller companions orbiting them and may have grown to their bloated sizes by a process of “galactic cannibalism” like that hypothesized to explain the supergiant elliptical cD systems (see above).
The spatial distribution of galaxies in rich clusters such as the Coma cluster closely resembles what one would expect theoretically for a bound set of bodies moving in the collective gravitational field of the system. Yet, if one measures the dispersion of random velocities of the Coma galaxies about the mean, one finds that it amounts to almost 900 km/sec. For a galaxy possessing this random velocity along a typical line of sight to be gravitationally bound within the known dimensions ofthe cluster requires Coma to have a total mass of about 5 × 1015 solar masses. The total luminosity of the Coma cluster is measured to be about 3 × 1013 solar luminosities; therefore, the mass-to-light ratio in solar units required to explain Coma as a bound system exceeds by an order of magnitude what can be reasonably ascribed to the known stellar populations. A similar situation exists for every rich cluster that has been examined in detail. This dark matter problem for rich clusters was known to the Swiss astronomer Fritz Zwicky as early as 1933. The discovery of X-ray-emitting gas in rich clusters has alleviated the dynamic problem by a factor of about two, but a substantial discrepancy remains.
Superclusters
In 1932 Harlow Shapley and Adelaide Ames introduced a catalog that showed the distributions of galaxies brighter than 13th magnitude to be quite different north and south of the plane of the Galaxy. Their study was the first to indicate that the universe might contain substantial regions that departed from the assumption of homogeneity and isotropy. The most prominent feature in the maps they produced in 1938 was the Virgo cluster, though already apparent at that time were elongated appendages that stretched on both sides of Virgo to a total length exceeding 5 × 107 light-years. This configuration is the kernel of what came to be known later—through the work of Erik Holmberg, Gérard de Vaucouleurs, and George O. Abell—as the Local Supercluster, a flattened collection of about 100 groups and clusters of galaxies including the Local Group. The Local Supercluster is centred approximately on the Virgo cluster and has a total extent of roughly 2 × 108 light-years. Its precise boundaries, however, are difficult to define inasmuch as the localenhancement in numbers of galaxies above the cosmological average in all likelihood just blends smoothly into the background.
Also apparent in the Shapley-Ames maps were three independent concentrations of galaxies, separate superclusters viewed from a distance. Astronomers now believe superclusters fill perhaps 10 percent of the volume of the universe. Most galaxies, groups, and clusters belong to superclusters, the spacebetween superclusters being relatively empty. The dimensions ofsuperclusters range up to a few times 108 light-years. For larger scales the distribution of galaxies is essentially homogeneous and isotropic—that is, there is no evidence for the clustering of superclusters. This fact can be understood by recognizing that the time it takes a randomly moving galaxy to traverse the long axis of a supercluster is typically comparable to the age of the universe. Thus, if the universe started out homogeneous and isotropic on small scales, there simply has not been enough time for it to become inhomogeneous on scales much larger than superclusters. This interpretation is consistent with the observation that superclusters themselves look dynamically unrelaxed—that is, they lack the regular equilibrium shapes and central concentrations that typify systems well mixed by several crossings.
Statistics of clustering5
The description of galaxy clustering given above is qualitative and therefore open to a charge of faulty subjective reasoning. To remove human biases it is possible to take a statistical approach, a path pioneered by the American statisticians Jerzy Neyman and Elizabeth L. Scott and extended by H. Totsuji and T. Kihara inJapan and by P.J.E. Peebles and his coworkers in the United States. Their line of attack begins by considering the correlation of the angular positions of galaxies in the northern sky surveyed by C.D. Shane and C.A. Wirtanen of Lick Observatory, Mount Hamilton, Calif. If the intrinsic distribution in the direction along the line of sight is assumed to be similar to that across it, then it is possible to derive from the analysis the two-point correlation function that expresses the joint probability for finding two galaxies in certain positions separated by a distance r. Of special interest is the enhancement in the probability above a random distribution of locations well represented, up to scales of about 5 × 107 light-years, as a simple power law, (r/r 0)−1.8, with r 0 equal to about 2 × 107 light-years. Beyond 5 × 107 light-years, the enhancement drops more quickly with distance than r −1.8, but the exact way it does this is somewhat controversial.
To summarize, then, when one knows a galaxy to be present, there is a considerable statistical enhancement in the likelihood that other galaxies will be near it for distances of 5 × 107 light-years or less, whereas at much larger distances the probability drops off to the expectation for a purely random distribution in space. This result provides a quantitative expression for the phenomenon of galaxy clustering. A similar power-law representation seems to hold for the correlation of galaxy clusters; this provides empirical evidence for the phenomenon of superclustering.
In addition to angular positions, it is possible to derive empirical information about the large-scale distribution of galaxies in the direction along the line of sight by examining the redshifts of galaxies under the assumption that a larger redshift implies a greater distance inaccordance with Hubble's law. A number of groups have carried out such a program, some in fairly restricted areas of the sky and others over larger regions but to shallower depths. A primary finding of such surveys is the existence of huge holes and voids, regions of space measuring hundreds of millionsof light-years across where galaxies seem notably deficient or even totally absent. The presence of holes and voids forms, in some sense, a natural complement to the idea of superclusters, but the surprising result is the degree of the density contrast between the large-scale regions where galaxies are found and those where they are not.
The conception of the universe common to all Chinese philosophy is neither materialistic nor animistic (a belief system centring on soul substances); it can be called magical or even alchemical. The universe is viewed as ahierarchically organized mechanism in whichevery part reproduces the whole. Man is a microcosm (small universe) corresponding rigorously to this macrocosm (large universe); his body reproduces the plan of the cosmos. Between man and universe there exists a system of correspondences and participations that the ritualists, philosophers, alchemists, and physicians have described but certainly not invented. This originally magicalfeeling of the integral unity of mankind and the natural order hasalways characterized the Chinese mentality, and the Taoists especially have elaborated upon it. The five organs of the body and its orifices and the dispositions, features, and passions of man correspond to the five directions, the five holy mountains, the sections of the sky, the seasons, and the elements (wu-hsing), which in China are not material but more like five fundamental phases of any process in space-time. Whoever understands man thus understands the structure of the universe. The physiologist knows that blood circulates because rivers carry water and that the body has 360 articulations because the ritual year has 360 days. In religious Taoism the interior of the body is inhabited by the same gods as those of the macrocosm. An adept often searches for his divine teacher in all the holy mountains of China until he finally discovers him in one of the “palaces” inside his head.
Return to the Tao
The law of the Tao as natural order refers to the continuous reversion of everything to its starting point. Anything that develops extreme qualities will invariably revert to the opposite qualities: “Reversion is the movement of the Tao” (Lao-tzu). All being issues from the Tao and ineluctably returns to it; Undifferentiated Unity becomes multiplicity in the movement of the Tao. Life and death are contained in this eternal transformation from Non-Being into Being and back to Non-Being,but the underlying primordial unity is never lost.
For society, any reform means a type of return to the remote past; civilization is considered a degradation of the natural order, and the ideal is the return to an original purity. For the individual,wisdom is to conform to the rhythm of the universe. The Taoist mystic, however, not only adapts himself ritually and physiologically to the alternations of nature but creates a void inside himself that permits him to return to nature's origin. Lao-tzu, in trance, “wandered freely in the origin of all beings.” Thus, in ecstasy he escaped the rhythm of life and death by contemplating the universal return. “Having attained perfect emptiness, holding fast to stillness, I can watch the return of the ever active Ten Thousand Beings.” The number 10,000 symbolizes totality.
Change and transformation
All parts of the universe are attuned in a rhythmical pulsation. Nothing is static; all beings are subjected to periodical mutations and transformations that represent the Chinese view of creation. Instead of being opposed with a static ideal, change itself is systematized and made intelligible, as in the theory of the five phases (wu-hsing) and in the 64 hexagrams of the I Ching (Classic of Changes), which are basic recurrent constellations in the general flux. An unchanging unity (the permanent Tao) was seen as underlying the kaleidoscopic plurality.
Chuang-tzu's image for creation was that of the activity of the potter and the bronze caster: “to shape and to transform” (tsao hua). These are two phases of the same process: the imperceptible Tao shapes the universe continuously out of primordial chaos; the perpetual transformation of the universe by the alternations of Yin and Yang, or complementary energies (seen as night and day or as winter and summer), is nothing but the external aspect of the same Tao. The shaping of the Ten Thousand Beings by the Supreme Unity and their transformationby Yin and Yang are both simultaneous and perpetual. Thus, the saint's ecstatic union is a “moving together with the Tao; dispersing and concentrating, his appearance has no consistency.” United with the permanent Tao, the saint's outer aspect becomes one of ungraspable change. Because the gods can become perceptible only by adapting to the mode of this changing world, their apparitions are “transformations” (pien-hua); and the magician (hua-jen) is believed to be one who transforms rather than one who conjures out of nothing.
Concepts of man and society
Wu-wei
The power acquired by the Taoist is te, the efficacy of the Tao in the realm of Being, which is translated as “virtue.” Lao-tsu viewedit, however, as different from Confucian virtue: