SCI 190 Handout on Astrophysics and Cosmology

Astrophysics is a branch of astronomy that applies the theories and techniques of physics to the study of celestial objects. For the large and massive objects in our universe, the most important force is gravity, and the base of our present theoretical understanding is Einstein's theory of gravitation and Einstein's theory of general relativity. Other ideas of physics are also used in astrophysics, such as the use of emission spectrum from stars to determine their composition, or doppler shifts in the emission spectrum to determine the speed of stars with respect to the Earth.

Cosmology is the study of the organization and structure of the universe and its evolution. Cosmology studies the universe as a whole and seeks to find answers to questions such as how the universe was formed, why does it look the way it does, and what will happen to it in the future. It looks for answers to what seems to be impossible questions, such as "Has the universe always existed, or did it have a beginning in time?" "If it had a beginning, what came before that?" "Is it finite or infinite?" "If it is finite, what is out there beyond it?"

Stars and Galaxies

When we give distances on Earth, we usually use meters and kilometers. Even for the distance between the Earth and the moon, which is 384,000km, these units are reasonable. But the size of galaxies is much, much larger and the unit typically used to measure these distances is the light-year (ly). One light-year is the distance light travels in one year. (Remember that light, and in fact all electromagnetic radiation, travels at 300,000,000 = 3x10^8m/s.) One light year is approximately 10,000,000,000,000km. (1 ly ~ 1x10^13km) In these units, the size of our solar system is about 0.001ly, and the closest star to us, other than the Sun, is Proxima Centauri, which is 4.3ly away.

On a clear and moonless night, thousands of stars of varying degrees of brightness can be seen from Earth, as well as the elongated cloudy stripe known as the Milky Way. The elongated cloudy stripe is actually composed of countless individual stars that are part of our Galaxy. Our Galaxy is a spiral-armed galaxy that is flat like a disc, and has a central bulging nucleus as depicted on page 2. Our Galaxy is about 100,000ly in diameter and 2000ly thick, with the central bulge about 6000ly thick. Our Galaxy contains about 100 billion stars and our Sun is just one of them. Our Sun is a little more than half way out from the galactic center and orbits the galactic center once every 200 million years.

Our Milky Way Galaxy

Shown above are two views of our Milky Way Galaxy, one from above and one from the side.

Using powerful telescopes such as the Hubble space telescope, which is in orbit about the Earth, billions and billions of other galaxies can be seen beyond our Milky Way Galaxy. The nearest one is the Andromeda galaxy, which is over 2 million light years away. When we look up and see the Andromeda galaxy, what we see is the light that left the Andromeda galaxy over 2 million years ago. What does the Andromeda galaxy look like today? We won't know for over 2 million years, since light leaving the Andromeda galaxy will not arrive on Earth for over 2 million years. In this way, astronomers are able to look back into the past. The farther away a star or galaxy is, the 'older' the light is that reaches the Earth. The orbiting Hubble space telescope can see more clearly galaxies farther away than other telescopes because it is above the Earth's atmosphere and its images are free from distortions that are caused by the Earth's atmosphere. The Hubble space telescope has seen galaxies as far away as 14 billion light years, which means it has looked back into the past 14 billion years.

Stellar Evolution

Stars are born, it is believed, when gaseous clouds (mostly hydrogen) contract due to the pull of gravity. These collapsing clouds of gas are called protostars. As the particles of each protostar accelerate inward due to gravity, their kinetic energy increases. When the kinetic energy is high enough, the repulsion between hydrogen atoms can be overcome and nuclear fusion can begin. The dominant early reaction for young stars is the fusing of hydrogen into helium. This is a nuclear reaction and cannot take place until the average kinetic energy is high enough to correspond to a temperature of 10 million degrees Kelvin. Remember that temperature is just a measure of the average translational kinetic energy, so it is reasonable to just give a temperature for the star rather than the average translational kinetic energy. The process of gravitational collapse yields the highest temperatures in the center of the star where the particles have fallen the farthest and gained the most kinetic energy. (Our sun has a core temperature in the tens of millions of degrees while its surface temperature is about 6000K.)

As nuclear fusion begins in the core of the star, the star continues its gravitational collapse. What keeps a star from continuing to collapse due to gravity at this point in its evolution? The answer is radiation pressure. The process of nuclear fusion in the core, in which hydrogen is 'burned' to become helium, releases large amount of energy in the form of electromagnetic radiation. As this radiation moves out from the core of the star, it exerts an outward pressure on the particles of the star. When enough nuclear fusion takes place to create a radiation pressure that balances the gravitational collapse, the protostar becomes a star and its size becomes stable. Our Sun and other stars with similar masses take about 30 million years to stabilize and become a star. They have enough hydrogen to remain stable through hydrogen 'burning' for about 10 billion years, assuming our theories about stellar evolution are correct. Although most stars are billions of years old, there is evidence (and some beautiful pictures from the Hubble space telescope, http://hubble.stsci.edu) that stars are being born right this moment.

When the supply of hydrogen in the core is sufficiently depleted, the core contracts and heats up. This results in an increase in hydrogen fusion, which is an increase in radiation pressure, and the star expands into a red giant. A star entering the red giant phase can be thought of as having two regions, a core and an outer shell. In the core, a buildup of helium from the hydrogen 'burning' has reduced the radiation pressure, so gravitational collapse gets ahead and contracts the core. But as the core collapses, it heats up and the process of hydrogen 'burning' goes faster, creating more radiation pressure. The core will become stable again, but more dense and at a temperature ten to a hundred times hotter. The outer shell doesn't have the helium from the hydrogen burning, but it does see the increased radiation pressure from the core, so it expands until radiation pressure and gravitational collapse are balanced. Our Sun and the planets of our solar system are about 5 billion years old. Our Sun will enter the red giant phase in about another 5 billion years. When it does, it should expand until its radius is about equal to the distance from the Sun to the Earth. In the core of a red giant the temperature is ten to a hundred times hotter than it is in a star. At this temperature, not only does hydrogen 'burning' go faster, but there is also enough kinetic energy for other types of nuclear fusion. Helium can be fused into beryllium, and if the star is massive enough, elements all the way up to iron can be made.

What is the fate of a red giant? That depends on the size of the star. Stars with a mass a little larger than our Sun or smaller will run out of stuff to 'burn' and cool, becoming white dwarfs. The white dwarf will continue radiating away energy until it eventually becomes a black dwarf, a dark, cold piece of ash. More massive stars can continue to contract, due to their larger gravitational forces, until the atoms are crushed and the atomic nuclei are mashed up against each other. Under these high pressures, the electrons combine with the protons to form neutrons and the result may be a neutron star. Neutron stars are thought to be so dense as to have diameters of only a few kilometers (and masses greater than our Sun!!!) It is thought that one way in which a supernovae can be created happens when a neutron star undergoes its final collapse. When the atoms give way and it crushes to nuclear density, tremendous energy can be released in a short period of time. This cataclysmic event has enough energy to create virtually all of the elements of the period table.

Stars with masses much greater than our sun will continue to collapse even beyond the density of a neutron star, crushing not only the atoms, but the neutrons as well, pushing the quarks together. When this happens, a black hole is formed, an object whose gravitational attraction is so great that no matter or light can escape it. If our Sun had the same density as a black hole, it would be about the size of a golf ball. It is believed that there are black holes at the center of galaxies, and that our own Milky Way Galaxy has a black hole at its center with a mass estimated to be several million times that of our Sun.

The Expanding Universe

Distant galaxies and stars display a redshift in their spectral lines. It is also observed that the farther away a star or galaxy is, the larger its redshift. The Doppler effect is used to interpret the redshift, with the conclusion that stars and galaxies are moving away from us. The observation that the farther away a star or galaxy is from us, the faster it is moving away from us, is consistent with the assumption that at some time in the past, all of the stars and galaxies were in the same place and were thrown outwards in a huge explosion called the Big Bang. By measuring a star's redshift and its distance from Earth, the amount of time since everything was in the same place can be calculated. The best measurements to date give a value of 14 billion years for the age of the universe and the inverse of this time is called the Hubble constant. Knowing that the distance an object travels in a time t is just its velocity times that time t (d=vt), and that the Hubble constant is just the inverse of the time (H = 1/t), we have a very simple relationship for the Hubble constant, namely v=Hd. By measuring the distance to stars and galaxies, and by calculating their speed relative to the Earth using their redshifts, we can find the Hubble constant. This is equivalent to finding the time it would take for an object moving at a speed (v) to move a distance (d) away from the Earth.

So we can calculate that 14 billion years ago the Earth and everything around it were in roughly the same spot, but surely the Earth isn't at the center of the universe? Heck, it's not even at the center of our Galaxy (which is a good thing since there is probably a massive black hole there). So an assumption must be made that there is nothing special about our little corner of the universe. This assumption is called the cosmological principle, and it states that the universe looks the same no matter which way we look or where we are. This assumption is only valid on a large scale, which for the universe is a size much bigger than our Galaxy. On a local scale (for Cosmology), this clearly isn't true; our Galaxy is a slowly rotating flat disc appearing different when we look at it from the side or from the top. The Cosmological principle is only assumed for really big things. So what does that imply for the Earth and everything around it? In the 14 billion years it took for everything around us to expand to where it is today, the Earth moved from the center of the universe to where it is today. We've certainly come a long way from the ideas of Aristotle with the Earth at the center of the universe. A view of the universe that was held until only a few hundred years ago!

The Cosmic Microwave Background

In 1964, additional evidence for the Big Bang theory of the universe was discovered in the form of electromagnetic radiation from outer space. Originally assumed to be noise, the electromagnetic radiation was found to be the same no matter which way into space you looked. Since our Galaxy looks different depending on which direction you look, it was assumed that the electromagnetic radiation was coming from outside our Galaxy, from the universe as a whole. It was also found to peak in the microwave region of the spectrum and have a distribution like that of every other emitter of radiation. (See Hewitt, pg 310 for the emission of radiant energy and radiation curves for emitters.) We know that everything with a temperature above absolute zero emits radiation and that the peak frequency of the radiation is just proportional to the temperature of the object. The peak wavelength for this radiation was at 7.35cm, which is in the microwave region of the electromagnetic spectrum, and this radiation is called the cosmic microwave background radiation. The peak frequency for the cosmic microwave background radiation is about 4 billion hertz, which corresponds to a temperature of 2.7K. In a sense, this is the average temperature of the universe, and it is very low because the universe has been expanding for a long time. Just like a hot gas that cools as it expands, the universe has cooled since the Big Bang until it is only 2.7K today.

The Standard Cosmological Model: The Early History of the Universe

It is now almost generally agreed among scientists that the evolution of the universe must have been determined in the first few moments of the Big Bang. In the last few decades, a convincing model of the origin and evolution of the universe has been developed. This model is called the standard cosmological model and has been made possible by experiments and advances in elementary particle physics at places such as Stanford's Linear Accelerator Center, Fermilab near Chicago, and CERN in Europe. By learning something about the way quarks behave inside neutrons and protons, we can make predictions for how quarks would have behaved just after the Big Bang. It's quite a stretch to go from something a billion times smaller than an atom (which is a billion times smaller than a CD) to something the size of the universe and predict how it might have behaved 14 billion years ago, but that is the beauty of physics.

In order to produce a universe as large as the one we observe today, both in size and mass, the Big Bang must have been huge. So huge in fact, that much of the very interesting features of the Big Bang happened very quickly, as the universe was rapidly expanding away from a single point and rapidly cooling. The two variables we will keep track of when we talk about the evolution of the universe are time and temperature. The standard cosmological model can only make predictions about the universe back until about 10^-43 seconds, when the temperature of the universe was about 1032K. We simply do not know enough about what might have happened before that because we have no good theory to predict the behavior of gravity at such a high temperature. It is believed that gravity must be quantized, but no good quantum mechanical theory for gravity has yet to be developed and experimentally verified. That is not to say that no theory exist, lots of theories exist, but none of them can be experimentally verified. Such is the nature of science.

From 10^-43 seconds to 10^-35 seconds, the standard cosmological model predicts a temperature drop from 1032K to 1027K. At these temperatures, there is enough kinetic energy for the quarks to freely exist with the leptons. The quarks are going so fast that they cannot be bound into things like neutrons and protons. We call this era the Grand Unified Era where quarks and leptons are whizzing about in a dense soup.

From 10^-35 seconds to 10^-6 seconds (one millionth of a second), the standard cosmological model predicts a temperature drop from 1027K to 1013K. At these temperatures, there is not enough kinetic energy for the quarks to exist freely and they bind together to form hadrons (hadrons is the name for the class of particles that contains neutron, protons, and things like them). We call this era the Hadron Era.

From 10^-6 seconds to 10 seconds the standard cosmological model predicts a temperature drop from 1013K to 1010K. At these temperatures, there is not enough kinetic energy to form hadrons, but there is still enough energy to form leptons, such as electrons, which are lighter than neutrons and protons. We call this era the Lepton Era.

From 10 seconds to about 1 million years, the standard cosmological model predicts a temperature drop from 1010K to 3000K. At these temperatures, there is not enough kinetic energy to form even leptons, and by now most matter had disappeared through particle-anti-particle annihilations. The universe is still quite hot however and is dominated by radiation. We call this era the Radiation Era. It is believed that towards the end of the Radiation era the temperature of the universe had become low enough for electrons to combine with nuclei to form stable atoms.

From 1 million years to 14 billion years (the present), the standard cosmological model predicts a temperature drop from 3000K to 3K. As the universe expands and cools, the density of radiation is dropping. During this era in the evolution of the universe, the radiation density has dropped low enough that it is below the density of matter in the universe. We call this era the Matter-dominated Era. It is believed to be in this era that stars and galaxies formed, probably from self-gravitation around mass concentrations.

The Future of the Universe

The universe essentially has two fates, namely that there is enough mass in it for gravity to eventually halt the expansion and pull all of the matter back together in an event called the Big Crunch, or that there isn't enough mass in it to stop it from expanding forever, and it will continue expanding and cooling forever. The density of the universe that separates those two fates is called the critical density, and a universe that happens to have exactly that density would expand to some point and then stop, forever remaining that size. This third fate is unlikely, but then again, who really knows for sure what we will happen hundreds of billions of years in the future?

Primary Questions on Astrophysics and Cosmology

What is astrophysics?
What is cosmology?
What is the age of the universe?
What is the age of the Sun?
What is the age of the planet Earth?
What is a light-year?
Why do we say that looking through a telescope is like looking back in time?
What advantage does the Hubble space telescope have?
Where does the energy the Sun delivers to the Earth come from?
What do we think is the fate of our Sun?
What is the Big Bang?
What two pieces of evidence support the Big Bang theory of the universe?

Secondary Questions on Astrophysics and Cosmology

What does our Galaxy look like?
About how big is our Galaxy?
About how far away is the nearest star after our Sun?
About how far away are the nearest galaxies?
How is temperature related to kinetic energy?
What is a protostar?
What do we mean when we say a star 'burns' hydrogen?
What is radiation pressure?
What is a red giant?
Where do elements heavier than helium come from?
What determines whether a star becomes a white dwarf, a neutron star, or a black hole?
What is a supernovae?
What is a redshift?
What is the cosmological principle?
What is the cosmic microwave background?
What is the temperature of the universe and has it always been that temperature?
What is the standard cosmological model?
What is the future of the universe?
What do we mean by the critical density of the universe?

____________________________
Dr. Todd B. Smith
Physics Department
Science Center - Room 3
(in basement near KU)
229-2435
todd.smith@notes.udayton.edu