The Universe The Universe is everything. All us, the room, the U.S. the earth, the solar system, all the other stars in the Milky way galaxy, all the other galaxies... everything. How big and how old is the universe? Let s ask a question that goes back a long time. (It is sometimes called Oberon s paradox) Why is the night sky dark where there are no stars? Does this tell us anything about the universe. Can the universe be infinity large and old? If the universe were infinitely old and large, in any direction you look in the night sky you would see a star. Light from that star would have reached us after some time so the night sky if the universe were infinitely old and large would have reached us and the night sky would be bright. This relies on the purely mathematical concept of infinity. But if the universe is not infinite, what if you go to the edge. What is on the other side? If it is not infinitely old, how did it get here and what happened before it started? As we will see, the universe is not infinite in size or age. The Solar system, Stars and Galaxies If you watch the sky at night for a while, you will notice several things. There are a few points of light that move with the respect to the general background of stars. They have peculiar motion. These are the planets and as we know, orbit the sun and form the solar system. The peculiar motion is due to the fact the earth is in orbit around the sun along with the other planets. The other obvious feature of the night sky is all the stars. They appear to be fixed. In fact they do move but on a time scale so slow that generations of humans would not notice their movement. Even with a good telescope, you can not resolve i.e., see any size or structure in the stars. This tells us that stars are far away.
Another feature is the diffuse band of light across the sky. This is the Milky way and the diffuse light is from star light that has scattered off interstellar dust between the stars. With a telescope, you might also see some object that have a shape. Some are blobs. Some are spirals. They are very faint. Until the 20 th astronomers argued about what they were. We now know they are other galaxies like our own Milky way. They are very very far away. Distances Astronomical distances are normal measured in two units: Light year. The distance light travels in one year. It is a very big distance. A light year is 9.5 x 10 12 km or 5.9 x 10 12 miles. A light year is not a unit of time! Parsec. A parsec is 3.26 light year or 3.1 x 10 13 km. We will see why this unit is often used below. One way to measure distances to distance objects is parallax. If you view an object from one angle and then another, the object appears to shift. The top part of the diagram above shows the Earth at two different times,
and the triangle formed with a nearby star and these two positions of the Earth. The bottom part shows two pictures of the nearby star projected onto more distant stars taken from the two sides of the Earth s orbit. A parsec is the distance of an object that appears to shift one arc second from one side of the earth s orbit (say June) to the other side (December). An arc second of angle is very small. There are 360 o in a circle. Each degree can be divided into 60 minutes of arc and each minute of arc into 60 arc seconds of angle. (3600 arc seconds in one degree!). One arc second is about as small an angle as you can easily measure. The atmosphere smears out the image of a star. With special equipment, 0.03 arc seconds can be measured but it is not easy. Using parallax, the distance to stars within about 30 parsec (100 light years)have been measured. 100 light years is a very big distance but is small compared to objects we can see in the sky. The Alpha Centuri complex is the nearest star to the solar system and is about 4.6 light years away. This method was first used by Friedrich Bessel in 1838. Another important method of measuring distance involves a special type of stars call Cepheid variable stars. Cepheid variable stars are pulsating stars, named after the brightest member of the class, Delta Cephei. Because the stars are very young, they pulse over weeks or months. (This has nothing to do with stars twinkling. Twinkling is due to the earth s atmosphere.) The period of the increase and decrease in the intensity is related to the total (absolute) intensity of light output by the star. How does this allow distances to be measure? If you know the in intensity, you can use: Intensity = 1 distance 2 to find the distance to the star if you measure the intensity of light from the star. Cepheid variable stars can be used to measure distances at any distance to you see one because they are very bright, even in another galaxy.
A major task of the Hubble space telescope is to measure Cepheid variable stars. The distance from Cepheid variable stars can be cross checked against distanced measured by parallax. Another indirect method of measuring distance is red shift. In 1929 Hubble published a claim that the radial velocities of galaxies are proportional to their distance. The red shift of a galaxy is a measure of its velocity, When the light from a star is analyzed, the spectral lines from an element, say hydrogen, are shifted towards the red. This is due to the Doppler shift. The light from all very distant objects are shifted to the red. It looks like everything is moving away from us!. When modern measurements of distance are plotted vs the red-shift you get something like: This tells us that the speed an object is moving away from us is a measure of the distance to that object. Actually, Hubble s original data had some mistakes and was controversial for years. One reason it took years for other scientist to accept, is the implication that the universe is expanding! If you accept Hubble s data, then you accept the fact the universe is expanding. This implies the universe is not finite. How does something infinite expand? If something is expanding, you can project back in time to where it started and thus the universe can not be infinitely old.
The fitted line in this graph has a slope of 73.8 ± 2.4 (km/s)/mpc and is called Hubble s Constant. Something at a million parsecs is moving away from us a 73.8 km/s. If you look at the dimensions of Hubble s constant, you will see that is is velocity/distance which is one over time. If you convert km to parsec and cancel the kilometers out, you have approximately one over the age of the universe. It works out to 13.6 billion years! Stars Before we continue with the universe, let s consider how a star is born and what happens during a stars life. Star Formation The universe is primarily hydrogen. When enough hydrogen collects in one place under the influence of gravity, the hydrogen is pulled into a large mass. Eventually, when the hydrogen is pulled tightly together under the influence of gravity, it starts to fuse. It takes temperatures of 10 million degrees Celsius to start the fusion process. The heat from the fusion creates an outward pressure which balances the inward pull of gravity. As long as the star can burn hydrogen by fusion to overcome gravity, it will survive. pressure pressure gravity gravity gravity pressure gravity pressure
Fusion and the elements Four hydrogen nuclei (protons) can fuse into helium: 4 protons 4 He + 2 positron + 2 neutrinos + Energy The energy is released because helium is slightly less massive than four protons. This mass difference is converted to energy by E = m c 2 We would not be here (life does not form in just hydrogen and helium!) if that was all that happens. The helium can also fuse to carbon: 3 4 He 12 C + Energy Similar processes can build up Oxygen ( 4 He 4 + 12 C) and all the other elements up to 56 Fe Why 56 Fe and not higher? Using a mass spectrometer the mass of most of the elements have been carefully determined. From the famous equation E = m c 2 and knowing the mass of the proton and neutron, one can determine the binding energy of a nucleon (proton or neutron). This is how much energy it takes to remove a nucleon from the nucleus. It is somewhat like the escape velocity from a gravitational field. As you can see from the plot, Fe 56 is the most stable nucleus. Below Fe 56 or above the nucleons are less tightly bound. This explains both the energy
released in an atomic bomb (fission or splitting of the uranium nucleus) and the energy release from fusion (stars or the hydrogen bomb). 56 Fe is the most stable of the elements so the release of energy and the fusion process stops at 56 Fe These higher mass fusions beyond carbon only occur when the temperature is very high (billions of degrees). This requires a star which is several times larger than our Sun. Death of a Star - Gravity will Finally Win After a star converts most of its hydrogen to helium, the helium core contracts under the influence of gravity. This increases the temperature of the core and the helium starts to burn along with the un-burnt hydrogen outside the core. The star expands to become a red giant. Our Sun will reach this stage in about 5 billion years. The helium will fuse into 12 C. For stars of the Sun s size and smaller, the temperature can not get large enough to fuse the helium into more massive elements. After burning the helium in the red giant state, the star will shed its outer layer and shrink into a white dwarf under the influence of gravity. The nuclei in a white dwarf can no longer fuse so a white dwarf is really a burn out star. The white dwarf will eventually cool and become a stellar cinder. For stars several times more massive than the Sun, the carbon will continue to fuse into heavier elements up to 56 Fe. 56 Fe is the most stable nucleus. The 56 Fe core of the star collapses catastrophically under gravity. When the nuclei as compressed together, the core rebounds violently in a great explosion. Such a stellar explosion is called a supernova. It is during this brief time when the star explodes that the elements heavier than 56 Fe are formed. All the gold, silver, uranium, etc on the earth were formed in supernova explosions. The core at the center of the supernova is compressed so tightly that the electrons and protons are driven together to form neutrons in a neutron star: proton + electrons neutron + neutrino In effect, the core becomes a giant nucleus made entirely of neutrons.
Black Holes If the stellar core in a supernova explosion is more massive than 3-5 Suns, the core will continue to collapse under the influence of gravity. When this massive object collapses to a diameter of 20 km, it becomes a black hole. If you will remember back to when we talked about gravity, we discussed escape velocity. This is the speed where an object can escape the gravitation field of a planet. In a black hole, the escape velocity is larger than the speed of light. Thus light (or anything else) can not escape from the black hole. The point around the collapsed object where gravitation force is so large that light can not escape is called the event horizon. Once inside the event horizon, an object is lost to our universe since it can never escape. Mass Event Horizon radius Earth 0.8 cm Jupiter 2.8 m 1 Solar Mass 3 km 10 Solar Mass 30 km 100 solar Mass 300 km General Relativity We discussed general relativity earlier. This is the extension to special relativity when you consider non-inertial frames of reference. (Special relativity is limited to reference frames that move with constant velocity with respect to one another.) Einstein published his theory of general relativity in 1915 which turns out to be a theory of gravity where Newton s law of gravity breaks down. Besides explaining the bending of light by gravity and the precession of the orbit of the planet Mercury, general relativity explains how mass bends space-time. Instead of a flat 4-dimensional Euclidean geometry, space-time becomes 4-dimensional non-euclidean. A straight line is not the shortest path between two points. Shortest paths are called geodesics.
This explains how the universe can be finite, if very large, and you don t find a brick wall with a end of the universe sign. The mass in the universe curves space and time back on itself. It is analogous to getting in a plane and flying in a straight line. Eventually, you go all the way around the earth and come back to where you started. Of course the earth is a two dimensional surface where as in general relativity, the universe is a four dimensional system. As a side note about general relativity, astronomy now routinely uses the bending of light by massive astronomical object to view very distant (early) galaxies. A massive galaxy was recently used to to image (focus) the light from a galaxy formed in the first billion years after the big bang shortly after stars and galaxies formed. Cosmology Evidence suggest that the Universe come into being 12-15 billion years ago in a primordial explosion called the Big Bang. Cosmology and Sub-atomic Particles What makes up the universe? We now know that the universe is made up of 12 particles. In addition there are four forces which are felt by the exchange of another group of 6 particles. All of matter is made up of 6 quarks and 6 leptons and their antiparticles. The 6 quarks are labeled up, down, charmed, strange, top and bottom and have a very large range of masses. Normal matter (protons and neutrons) are combinations of 3 up or down quarks. All the other baryons (3 quark objects) and mesons (quark anti-quark objects) that have been discovered are combinations of these six quarks. Quarks can not exist individually but must combine in twos and threes. The six leptons are the electron, muon, tau and a neutrino associated with each. The electron is the only lepton in normal matter. Neutrinos are mass-less or almost so. Recent experiments indicate neutrinos have the mass of the proton). The muon is 200 times heavier and the tau is more than twice the mass of a proton. a very very small mass. The electron is very light ( 1 2000
The four forces are: The strong force is very strong, but very short-ranged. It acts only over ranges of 10 15 meters and is responsible for holding the quarks together in a nucleon. The residual of this force holds the composite nucleon together. This force is carried by the gluon The electromagnetic force causes electric and magnetic effects such as the repulsion between like electrical charges or the interaction of bar magnets. It is long-ranged, but much weaker than the strong force. It can be attractive or repulsive, and acts only between pieces of matter carrying electrical charge. This force is carried by the photon or a particle of light. The weak force is responsible for radioactive decay and neutrino interactions. It has a very short range and, as its name indicates, it is very weak. This force is carried by the W ± and Z 0 The gravitational force is weak, but very long ranged. Furthermore, it is always attractive, and acts between any two pieces of matter in the Universe since mass is its source. The graviton is responsible for gravity. It has not been observed.
The Time-line of the Universe Understanding how quarks, leptons and the four forces work lets us project back to what happened in the early moments of the big bang. Before 10 43 second after the big bang, the laws of physics break down. The four forces are all the same (unified). At about 10 43, gravity separates from the other forces. The temperature is 10 32 K. The universe is a soup of quarks, anti-quarks and photons in equilibrium. At t=10 35 sec, (T=10 27 K) Strong Force separates from the electromagnetic and weak forces which are still unified. From 10 35 to 10 33 seconds the universe expands by a factor of 10 50. This time is called the inflation period. It explains why the universe we see today is so uniform. AT 10 12 seconds (T=10 15 K) the electromagnetic and weak forces separate. The universe is still a quark lepton soup. Photons are in equilibrium with electrons and positron. At 10 6 sec (T=10 13 K) free quarks form protons and neutrons. At about 3 minutes (T=10 9 K) some protons and neutrons combine to form deuterium, helium and traces of other light elements. Most of the protons remained and neutrons decayed to protons and electrons via β decay.
At 300,000 year (3000 K) electrons and nuclei combine into neutral atoms. The universe becomes transparent. The radiation given off at this point is the origin of the Cosmic Background Radiation. Around 500 million years after the big bang, early stars and galaxies form. Today (13.6 billion years) the universe has cooled to 2.7 above absolute zero. Nucleosynthesis in the Big bang At about 3 minutes after the big bang, the free neutrons and protons collided. A few of these collisions resulted in deuterium being formed. Some of the resulting deuterium collied with other neutrons to form 3 He. This provides even more evidence for the big bang. Deuterium and 3 He can be observed in the spectra of interstellar gas clouds. Stars don t normally produce deuterium because there are no free neutrons. Even if it did form in normal stellar fusion, the deuterium would fuse (burn) in the normal stellar fusion process. The observed ratios for primordial Deuterium and 3 He to normal Hydrogen correspond to almost exactly the amount you would expect from the big bang. Cosmic Background Radiation After the big bang occurred and neutral atoms formed, the universe was very hot. Like any black-body it has a characteristic shape called a black-body distribution. Over the 12-15 billion years the universe has existed, the universe has cooled and the temperature of the background radiation has cooled. In 1965, Arno Penzias and Robert Wilson detected a microwave background while working at Bell labs in New Jersey. They were trying to improve microwave transmission for phone and TV communications. After a lot of work they showed the background signal was not from any local source but was coming uniformly from all points in the sky.
They only looked at a small part of the entire black-body spectrum but showed that it corresponded to a source at a temperature of 3 K. It is the radiation left over from the big bang. In the mid-1990 s, an instrument called FIRAS on the COBE satellite made an incredible precise measurement of the cosmic background radiation which is shown in this plot: (note the error bars on the data are 400σ. The data fits a black-body curve to better than 25 parts in 10,000 along the entire curve!) In 2001, the Wilkinson Microwave Anisotropy Probe (WMAP) satellite was launched. It could measure the tiny variation in the cosmic microwave background. These tiny variation show why parts of space are nearly empty and other parts contain clusters of galaxies.
In the last couple of years, the Planck satellite has returned an even more detail view of the cosmic microwave background radiation. This data may help to explain why the inflation period happened in the early stages of the Big Bang. Where s the Mass - Dark Matter For a few decades, astronomers and astrophysicists have been adding up the matter in the universe and finding that only about 5% of what they expect is visible. This is a problem that is currently being vigorously investigated. While this missing matter problem does not effect the validity of the big bang theory, it raises lots of questions about our understanding of the universe. The most compelling evidence for dark matter is the rotation rate of galaxies in galaxy clusters. The spin rate of clusters
of galaxies should depend only of the amount of material in the cluster. These clusters rotate at rates that is consistent with more than 10 time the material that we see as stars and gas in the cluster. Roughly 20% is thought to be dark matter Currently there are two ideas about what makes up the dark matter: WIMPS (Weakly Interacting Massive Particles) and MACHOS Massive Astrophysical Compact Halo Objects). MACHOS are non-luminous objects that make up the halos around galaxies. MACHOS are thought to be primarily red dwarf stars (what would result if our own sun collapsed) and black holes. Like many astronomical objects, their existence had been predicted by theory long before there was any proof. The existence of red dwarfs was predicted by theories that describe star formation. Recent results on MACHOS show that only about 20% of the missing matter can be MACHOS. WIMPS are subatomic particles. The weakly interacting part of the name says they particles are extremely difficult to detect like the neutrino. If they exist, billions of these particles would be passing through you every second. Some have proposed that WIMPS could be neutralinos, the counterpart to the neutrino in super-symmetry particle physics unification theories. The neutrino was proposed earlier as a dark matter particle but it is now clear that if the neutrino has mass, it is much too small to account for the missing matter. Experiments currently under way at the LHC at Cern should give us a better idea if the missing matter is a strange new subatomic particle. Where s the Mass - Dark Energy Roughly 70% of the missing mass of the universe is thought to be dark energy. Remember from E=mc 2 that mass is energy and energy has mass. Dark energy is thought to permeates all of space and tends to increase the rate of expansion of the universe. Not only is the universe expanding but there is an expansion of this rate of expansion (acceleration). If the acceleration continues indefinitely, the final result will be that galaxies outside of our local area (local super-cluster) will move outside of
our event horizon i.e., they will no longer be visible, because their apparent velocity becomes greater than the speed of light. Don t worry... this would require many times of the current age of the universe. In the late 1990s observations of type Ia supernovae were used to measure the rate of expansion of the universe, Essentially, a type Ia supernova is well understood and can be used as a standard candle. With the Doppler shift of the light from the supernova, the expansion rate of the universe can be deduced. These observations have been corroborated by several independent sources including information from more recent cosmic microwave background radiation maps using the WMAP satellite. The nature of this dark energy is a matter of speculation. It is very defuse (low density) and homogeneous. It could be energy associated with the vacuum energy of space-time. It could be that general relativity is wrong on the scale of galactic clusters. It is more likely something new we have never imagined.