by George Rhee
The Distribution of Mass and Light
Comparing theory with observations is somewhat like comparing two maps. One map has been given to us (by theorists Fig. 5.6) and contains the location of buried treasures, the other map has been made by us from direct observations of our surroundings (Fig. 5.5). To find the treasure we have to find features that are present in both maps and match them up. The theorists give us a a map of what the surroundings of an average observer should look like. We cannot actually find our Coma galaxy cluster of galaxies in the theorists map, but there should be somewhere a cluster of galaxies that resembles Coma. There will also be a number of halos in the simulation comparable to the number of Milky Way halos that we see in the data, but the locations will not match. Nevertheless by doing statistical studies of the two maps we can learn alot about the distribution of stars and dark matter in our universe.
Fig. 5.6The model universe from computer simulations. The left-hand image shows the dark matter distribution in the cosmic web. The right-hand image shows the expected distribution of visible light when the halos in the left hand image are populated with stars following a plausible star formation recipe (Credit: Volker Springel (Heidelberg University) and the Virgo Consortium)
The surveys provide us with a census of galaxies. We have redshifts and colors of half a million galaxies. We can use these data to estimate the mass in stars within each galaxy. The theories do not readily predict this number but they do predict how many dark matter halos of any given mass are present at any time. The idea is to find out the mass of the dark matter halo associated with the galaxies that we observe in the surveys.
We can also obtain significant results from the observations alone. We can calculate the fraction of atoms located inside stars by estimating the total mass of stars in the survey volume. Remarkably only 3.5% of the baryons present in the universe are actually found inside stars. In other words, the processes that formed galaxies are not efficient, most of the atoms in the universe are not located in stars. When you look up at the night sky, the stars that you see account for 3.5% of the atoms in the universe which in turn account for 4.6% of the total density of the universe!
Most stars in the universe are found in galaxies with a similar stellar mass to the Milky Way. There is a problem with trying to match up observed galaxies in a survey with halos in a simulation. The model produces too many low mass and high mass halos if we fix it so that the right number of Milky Way mass galaxies are produced.
If we remove the assumption that the amount of visible matter (stellar mass) is proportional to the amount of dark matter in a galaxy we can match the numbers of observed galaxies in the maps to the observed number of halos of given mass in the simulation. We can then estimate the relative amounts of visible and dark matter in galaxies of different mass.
Review
In this chapter we saw how systematic surveys of the sky have revealed the largest known structures in the universe. From the field of biology a book entitled “The Beak of the Finch” illustrates the value of survey work in science. It describes the work of scientists on a small island in the Galapagos. They studied over a period of decades the population of finches on the island and got to see evolution in action. They showed how a difference in beak size of a fraction of a millimeter could mean life or death for a finch during hard times when food is scarce. This study was able to see natural selection taking place in real time in a bird population. The work consisted of repeating exactly the same observations year after year, measuring beak sizes and putting metal bands on birds. However the insights obtained from this work are intriguing and wonderful.
The same is true in astronomy. Many new insights come as a result of survey work. The work is inherently boring and repetitive. We point our telescope and measure some galaxy redshifts then point it somewhere else and measure some more redshifts, on and on, night after night. It is out of such work that the realization came that there are enormous voids in space, regions empty or almost empty of galaxies. Surveys are important because we study the universe in a controlled matter. It is hard to draw conclusions about a sample of galaxies that were selected because they seemed interesting to the author, on the other hand if we select all galaxies in the sky brighter than some limit and study their properties our conclusions will have some meaning.
As with so much of astronomy, this field has made great use of technological developments. With new spectrographs we can measure the redshifts of 500 galaxies in an hour or so. It seems every decade or two things improve such that what used to take a few months now can be done in one night of observing. This is of importance because we need large numbers of galaxy redshifts to map out the matter distribution in the universe.
There is a simple satisfaction at simply knowing our surroundings in space. When I was a small child, the universe was the neighborhood on the scale of a few hundred yards. I remember an old house falling apart in a wooded area nearby that was forbidden territory. That was my frontier beyond which lay the unknown. Eventually I expanded my horizons well beyond this. In that same way I find it interesting to simply know where we live on a cosmic scale. Over there in Coma is a huge cluster of galaxies, over in Perseus lies a big filament of galaxies that covers half the sky and so on. By making these maps we can study our neighborhood and compare it to others.
We have seen that we can map out the universe nearby over a large area of the sky, and we can probe the distant universe by studying distant galaxies in a small part of the sky. Both these approaches are equally important. The nearby surveys map out the mass nearby. The distant galaxy surveys give us the chance to study the evolution of galaxies. We can see if the galaxies looked different in the past. What was the rate of star formation at high redshifts compared to today in a given volume of space? Do galaxy shapes and sizes look different at redshift one than they do today?
The amount of available scientific data doubles every year. In astronomy this is due more to the increase in the available detector area than the actual collecting area of telescopes. Part of the challenge is to make the survey data available to the astronomical community and also to the general public. The Sloan Digital Sky Survey developed a web tool called Skyserver to access the data. This tool has had about one billion hits in the last decade. It has had over one million distinct users. An associated project was the galaxy zoo project where 40 million galaxy classifications were made by the general public. Three hundred thousand people participated in this project. The data explosion resulting from astronomical survey projects requires new tools to extract the information. This is one of the new frontiers of research in what has been called the age of surveys.
The fact that galaxies are distributed in a cosmic web extending for billions of light years raises the question of origins. How did the cosmic web come into existence and why do some huge regions of space contain no galaxies at all? It is these questions that we turn to in the next chapter.
Further Reading
A Grand and Bold Thing: An Extraordinary New Map of the Universe Ushering In A New Era of Discovery. Ann K. Finkbeiner, New York, Simon & Schuster. 2010.
Mapping the Universe: The Interactive History of Astronomy. Paul Murdin, London, Carlton Books, 2011.
George RheeAstronomers' UniverseCosmic Dawn2013The Search for the First Stars and Galaxies10.1007/978-1-4614-7813-3_6© Springer Science+Business Media, LLC 2013
6. How Did Galaxies Come into Existence?
George Rhee1
(1)Department of Physics & Astronomy, University of Nevada, Las Vegas, Nevada, USA
Abstract
How can we understand the origin of galaxies? The problem is not unlike that of the origin of life on earth. We see a wide variety of species in the world today. The fossil records tells us that species were different in the past. At very early times only very simple single celled organisms existed. Biologists studying the origin of life must ask themselves how so much complexity and diversity emerged from simple beginnings. They must also
ask what got the process going in the first place.
The largest structure revealed to date is a huge filament consisting of thousands of galaxies. This structure known as the Sloan Great Wall is about 1.4 billion light years across. Like scientists studying the origin of life on earth, astronomers want to understand the origin of galaxies and the large structures that they are part of. We want to understand how so much complexity emerged from the early universe which was almost featureless.
If the matter was evenly disposed throughout an infinite space, it could never convene into one mass; but some of it would convene into one mass and some into an other, so as to make an infinite number of great masses scattered at great distances from one to another throughout all that infinite space. And thus might the Sun and fixed stars be formed.
Isaac Newton, Letter to Richard Bentley, 1692
How can we understand the origin of galaxies? The problem is not unlike that of the origin of life on earth. We see a wide variety of species in the world today. The fossil records tells us that species were different in the past. At very early times only very simple single celled organisms existed. Biologists studying the origin of life must ask themselves how so much complexity and diversity emerged from simple beginnings. They must also ask what got the process going in the first place.
The largest structure revealed to date is a huge filament consisting of thousands of galaxies. This structure known as the Sloan Great Wall is about 1.4 billion light years across. Like scientists studying the origin of life on earth, astronomers want to understand the origin of galaxies and the large structures that they are part of. We want to understand how so much complexity emerged from the early universe which was almost featureless.
Observations of the cosmic background radiation tell us that when the universe was a few hundred thousand years old no stars or galaxies existed, the density of matter was almost perfectly smooth. The density of matter varied from one place to the next by less than one part in a 100,000. How then did the complex structures and galaxies described in the previous chapter emerge from the early universe?
We present the solution to this puzzle in this chapter. We begin by discussing the mechanism by which gravity amplifies small density variations present in the early universe. To properly model the emergence of the cosmic web we need to use computers. We start with an almost totally smooth matter distribution and use computers to model how this distribution changes due to the effect of gravity in an expanding universe. We discuss how by adding gas to the dark matter calculations we can gain more insight into the process of galaxy formation.
The Gravitational Instability: How the Rich Get Richer
What would happen to a part of the universe that was very slightly denser than its surroundings when the universe was only 400,000 years old? This region will expand slightly slower than a region of average density because of the gravitational force caused by the small excess of matter. Since the region expands more slowly, the density in this region is dropping slower than that of its surroundings. This in turn means that the density of the region relative to its surroundings is increasing.
As an analogy let us consider two cars. Car A uses gas at a rate of 10 miles per gallon. Car B uses gas at a rate of 20 miles per gallon. The two cars fill up their gas tanks with 10 gallons of gas and start on a journey. After 20 miles, car A has 8 gallons left and Car B has 9 gallons left. Car B has about 1. 1 times as much gas left as car A. Twenty miles further car A has 6 gallons left and car B has 8 gallons left, car B now has 1. 3 times as much gas in its tank as car A. By the time the two cars have gone 8 miles car A has three times as much gas in its tank as car B. Although both cars have less and less gas in their tanks, the relative amount of gas of car B to car A keeps increasing.
Our overdense region keeps getting less and less dense while its density relative to its surroundings keeps increasing. In the universe as in capitalism, the rich eventually get richer and the poor get poorer. Gravity thus acts as an amplifier, it enhances small differences in density that were present in the early universe. Regions that are initially slightly denser than their surroundings will subsequently form galaxies and clusters of galaxies. Conversely, regions of space that are initially less dense than average will become more and more empty forming the voids that we saw in the galaxy maps shown in Figs. 5.4 and 5.5.
At some point an overdense region will stop expanding and collapse to form a bound object such as our galaxy. There are many regions of varying sizes going through this process. The regions which gave rise to the first galaxies collapsed long ago at redshifts of 12 or higher (less than 400 million years after the Big Bang). Some of the larger regions bigger than clusters of galaxies are only just collapsing today.
To summarize, gravity causes slight variations in the density of the universe to increase with time. We believe it is this effect that leads to the formation of galaxies from a universe that is almost featureless. Of course the story does not end there. We would like to explain the properties of the cosmic web of galaxies. This simple model of the evolution of isolated overdense regions does not explain how a feature such as the Sloan Great Wall which is itself made up of thousands of galaxies could come into existence. To answer that question we use computers to simulate the gravitational interaction of hundreds of millions of particles.
Simulating the Universe Inside a Computer
Astronomers follow the evolution of dark matter using computer simulations. The calculations are based on the assumption that gravity is the only way that the particles influence each other. We can calculate the effects of gravity and predict the trajectories of particles in space using computers. The simplest calculation involves just two particles. At any given time if we know the positions of the particles we can calculate the strength of the gravitational force between them. If we also know the speeds at which the particles are moving, we can predict where the particles will be at any time in the future. If no force acts, the solution is very simple. The particles just keep going forever with whatever velocities they had initially. If the particles have mass they will affect each other’s motion due to the force of gravity. By calculating the force of gravity we can calculate the acceleration of the particles, that is to say, how their motion changes. By jumping from the present to a short time in the future we can predict the new velocities of the particles using Newton’s laws of motion. Knowing the velocities we calculate the new positions of the particles. So the simulation process consists of a repeating set of instructions. Note the location and velocities of all the particles, compute the forces, calculate the new velocities and location of the particles and repeat the process.
We can apply this method to the Earth’s orbit around the Sun. We give the program starting positions of the Earth and the Sun and the direction of the Earth’s motion. We can then compute where the earth will be a year and a half from today. The program cannot compute this in one step so it breaks down the task into a series of steps. We could, for example, compute the forces, velocities, and particle positions 500 times per orbit. If we did it 5,000 times per orbit the answers would be even more accurate.
How did Newton figure out the orbits of the planets since he had no computer? The analysis of motion in the solar system is considerably simplified by the fact that by ignoring the effect of the other planets on the Earth we get a pretty accurate answer. The reason Sir Isaac came up with the answer, is that this so-called two body problem can be solved exactly using equations. We can circumvent the computer because we can write the equation that describes an ellipse as a solution to the equations of motion of the planets. To put it simply, for certain problems we can write down the answer as a formula, for others we cannot. If I give a physicist the positions and velocities of 1,000 particles she cannot write down a simple formula for their future trajectories. We have to use a computer to perform the calculation. We are thus forced to break this problem down into a series of steps as described above.
With our computer code
we are not limited to problems that have simple solutions. We can turn gravity into a great video game. Just specify the starting conditions, also known as initial conditions, and let it roll. We could have three particles of equal mass for example. The program then calculates the force on particle one due to particle two and similarly the force on particle one due to particle three. With appropriate permutations we do the same for particles two and three. Notice that the number of force computations has now grown. In fact, the number of computations increases as the square of the number of particles in the simulation. Thus if we double the number of particles we have to spend four times as much time on the computations.
Astrophysicists need to perform simulations with very large numbers of particles. The reason for this is that the structure of galaxies is influenced by processes occurring on much larger scales. We want to see how the Sloan Great Wall was formed while at the same time seeing how the galaxies that make up the wall were formed. In order to get the full picture we need to know what happens on a scale of a billion light years as well as hundreds of light years at the same time. With the computing power of computers we are able to do this. An example of a state of the art supercomputer is the Blue Waters supercomputer funded by the National Science Foundation. When completed it will be able to carry out 1015 calculations per second. The iphone 4 can carry out about 40 million (4 ×107) calculations per second. The state of the art for dark matter simulations is currently the Bolshoi simulation which calculates the motion of about 10 billion particles of dark matter in a box 1 billion light years on a side.
