Cosmic Dawn

by George Rhee

  If the number of particles is 10 billion, 1010, then to compute the force on one of the particles we must carry out 10 billion minus one calculations. To compute the forces on all the particles we must carry out 1020 computations. One of the objectives of people writing the computer programs that carry out these simulations is to see if they can speed up the computations. One ingenious trick is to note that particles far away from the point at which we are trying to calculate the gravitational force can be treated as one particle if they are clumped together. For example I can treat the planet Pluto and its moon as one object when I calculate their pull on me. Pluto and its moon are so close together compared to their distance from me that they pull me in essentially the same direction so I can treat them as one point object. One might argue that this is an approximation and that we want the exact answer in science. The art of being a good astronomer is the art of approximation, of knowing what simplifying assumptions to make to render a problem more tractable. We do this in everyday life. When someone asks me how long a drive I have to work, I say about 20 miles. I could say 22.145 miles but I would get some strange looks. I say 20 or so miles because that is the accuracy that is required in ordinary conversation..

  We know what the universe looks like today from the maps shown in the previous chapter. We know how dark matter clumps will grow thanks to the simulation techniques described above. We can only run our simulations forward in time so we have to know the dark matter distribution at early times to set up the starting point of our simulations.

  How to Start a Model Universe

  To start a computer simulation we must specify the initial velocities and positions of the particles whose evolution we are to follow from the past to the present day. The initial conditions can be thought of as specifying how the density of the early universe varied from one location to the next. We characterize the variations in density using a statistical description and then make a specific density distribution from the description. The idea behind this is that we can run several versions of a model universe that are statistically similar to see the effect of random variations in density. These models are the same on average but differ in the exact locations that the galaxies form.

  To start our simulation we need to know the size of the small variations in density in the universe before galaxies and stars formed. We have a reliable estimate from observations of the cosmic background radiation intensity from one part of the sky to the next. The WMAP satellite has accurately measured these. From these variations we can estimate the variations in density of the dark matter from one location to the next when the universe was only 400,000 years old. In other words we have a reliable way to determine the starting conditions for our simulation when the density variations were very small. We want to know if we can reproduce all this complex structure we see today using this set of very simple initial conditions. Amazingly the answer seems to be yes, which means we understand something about the role of gravity in structure formation. Note however that we do not understand the origin of the variations. We do have some plausible ideas as to their cause but we do not have any direct evidence for the mechanism.

  Once we have run a dark matter simulation we need to see if it matches the real world. Unfortunately we only have observations of the light emitted by galaxies, not the dark matter itself. We thus have to first find a way to estimate where the stars and galaxies will form in the simulation and then compare these light-emitting regions to the maps produced by the galaxy surveys.

  Matching the Models to the Real World

  The simplest way to compare the distribution of galaxies in the real world and the simulations would be to compare pictures and judge by eye. This is not as naive as it sounds, the eye is actually very good at discriminating between pictures. I don’t think we yet have a computer algorithm that can tell the difference between a genuine Rembrandt and a fake. A more objective method is to calculate some numbers from the data and see if they match numbers computed from the models. The galaxy distributions form a sponge like structure known as the cosmic web. It is not easy to quantify sponginess to compare two sponges but it can be done.

  For example we can calculate how many galaxy clusters are present in a galaxy survey and compare that with the number of clusters seen in a simulated volume of the universe. We can use the models to mimic observational data. We then compare the results by applying statistical tests to real and model data and see if they match.

  At the other extreme we know that there are large regions of space (tens of millions of light years across) that are empty of galaxies. We can see if we find similar sized voids in the simulations.

  In the universe, the rich get richer and the poor get poorer. By this we mean that a structure that is only very slightly denser than its surroundings in the early universe will become increasingly overdense as time passes. Similarly, a region that is slightly less dense will become increasingly less dense. Gravity like capitalism accentuates differences. Another feature of the gravitational instability is that the overdense regions which are not perfectly spherical become increasingly elliptical or elongated with time. This explains the formation of filaments that constitute the cosmic web. The underdense regions on the other hand become increasingly spherical with time. The voids or empty regions observed in galaxy surveys do in fact turn out to have a roughly spherical shape. The matter distribution resembles a sponge. The low density regions, the holes in the sponge, are somewhat spherical while the high density regions form a connecting network of filaments and sheets with large massive objects forming at the intersections of filaments.

  Our ability to make simulations has improved at a similar pace to our ability to carry out observations. Computers have enabled us to carry out surveys of galaxies over large areas of the sky and to great distances in reasonable amounts of time. Similarly, computers have enabled us to carry out simulations with sufficient resolution that we can say something about galaxies and their distribution in space. Astronomy is driven by improvements in technology as well as new physical insights. The improvements in technology show no signs of abating. Computers keep improving at a staggering pace and new telescopes and better detectors enable us to make observations of better quality and quantity.

  Crunching Big Numbers: The State of the Art

  The Virgo consortium, an international collaboration of a dozen scientists in the UK, Germany, Netherlands, Canada the USA and Japan has produced some of the most detailed computer simulations. To carry out these calculations they use computers that have more than 3,000 cores with 14 TB of memory and 600 TB disk storage. The simulations can take anything from a week to several months on a 100 or more processors.

  We can run a large-scale simulation and zoom in on the result to find interesting examples of clusters of galaxies (Fig. 6.1). To get a better picture we can rerun the simulation of a smaller volume centered on the interesting cluster. There are a number of properties of galaxies in clusters that differ from galaxies outside clusters. For example the proportion of elliptical galaxies relative to spiral galaxies is much higher in clusters. The star formation rate of galaxies in clusters seems to be different at different redshifts and so on. Almost all the galaxies in clusters are less than a tenth of a cluster diameter in size. We want to have the big picture (cluster) but also see the small picture (galaxies) in sufficient detail to see if it is influenced by the big picture. In order to do this we need more particles in the cluster region than are provided by the large scale simulation. We thus run a smaller sized simulation with as many particles as the big simulation. The large scale simulations consist of a cube 700 million light years on a side, the smaller simulations correspond to a cube 2 million light years on a side.

  Fig. 6.1A zoom through the Virgo consortium Millennium-II Simulation of dark matter evolution. The images all correspond to a moment in time. The dark matter density is color coded so that high density regions are white and low density regions are black. The simulation follows about 10 billio
n particles in a cube roughly 500 million light years on a side. The units shown in the figure are Megaparsecs where 1 parsec is about 3 light years. The bottom three boxes zoom in on a structure comparable in mass to the Coma cluster an aggregation of many thousands of galaxies. The images show how halos are embedded in larger structures that constitute the cosmic web (Credit: Michael Boylan-Kolchin, Volker Springel, Simon D. M. White, Adrian Jenkins, and Gerard Lemson (2009) Monthly Notices of the Royal Astronomical Society, 398 1150B, by permission of Oxford University Press on behalf of the Royal Astronomical Society)

  If you search the world wide web under the heading “N-body simulations” you will find many sites that contain images and movies produced using these computations. The movies give insight into the growth of the three dimensional structures as they form. Looking at this material you see structure arise out of the almost uniform early universe. It is remarkable that astrophysicists have solved key elements of this problem. The more mathematically minded and adventurous readers can find computer codes on the web and run their own simulations. For example, you can make an elliptical galaxy and have it collide with another one and watch the results. The point is that the codes have been written and all you have to do is to type in a few simple instructions to run the program and get results.

  So far in this chapter we have emphasized the role of gravity in determining the large scale structure of the universe. The visible parts of the universe are visible because of the presence of gas that emits and absorbs light. To understand galaxy formation we must include the physics of gas. This involves more than gravity, since the gas, unlike the dark matter, responds to pressure and can dissipate energy by radiation.

  The Effect of Gas: A Study in Dissipation

  None of the simulations described above can produce stars and galaxies. The models simulate the collapse of lumps of dark matter due to gravity. They can also include the behavior gas, on large scales. In order to compare simulations with observations we need a scheme for labeling as visible some of the gas in the simulations. One has to specify under which conditions (density, temperature, composition) gas will turn into stars. Gas made of atoms and molecules is different from dark matter in that it can emit and absorb light. The details of these physical processes are quite complex and not always well established. One uses a prescription rather than actually simulating the star formation process. This is currently the only way to compare cosmological simulations to observations. This simplistic approach is supported by observations of galaxies which reveal a threshold gas density for star formation. The star formation rate increases as the gas density increases. These relations between star formation and gas density are found for very nearby galaxies; we do not know if they hold at high redshifts. Simulations including gas are made for cubes 300 million light years on a side with about 300 million dark matter particles and 300 million gas particles initially. As the simulation is run, the dark matter particles remain unchanged but the gas particles get converted to stars. The smallest structures that can be seen in these simulations are about 20,000 light years in size. We are still a long way from simulating the formation of galaxies and the formation of stars inside those galaxies using the basic equations of physics, hence the need for star formation recipes. Current simulations can produce quite realistic looking galaxies. Figure 6.2 shows a simulated galaxy including gas physics and star formation and a real galaxy image.

  Fig. 6.2Which galaxy is real? A galaxy in a simulation (left) appears in all respects identical to a real galaxy (right) and background image from the Sloan Digital Sky Survey Collaboration. The simulation includes a star formation recipe and calculates the effect of interactions between the stars and the gas (Credit: Reprinted by permission from Macmillan Publishers Ltd: Nature, Geha, M. 2010, 463, 167, copyright (2010))

  A second approach is to run the dark matter simulation first and then retroactively add the effects of gas. Dark matter halos form by the merging of smaller halos to form larger ones. For a given halo that exists at the end of a simulation we can construct a merger history, namely locate all of the halos in the simulation that contributed mass to the halo in question. One then adds gas to these halos in the form of hot gas, cold gas and stars. Simple prescriptions are then used to determine how the baryons flow between these three components. For example, stars form out of the gas while supernova explosions return stellar baryons to the gas phase. By keeping track of all these processes one can predict what the stellar population of the final halo will be. It is then possible to predict the observables such as the colors and luminosities of the galaxies.

  These models produce catalogs of galaxies whose properties can be compared to the properties of galaxies in the surveys. For example we can measure the relative numbers of bright and faint galaxies in the models and the surveys. There are many more faint galaxies than bright galaxies and at the bright end there is a cutoff beyond which there are no bright galaxies. The relative numbers of bright and faint galaxies can currently be estimated out to redshifts of about eight (600 million years after the Big Bang) using Hubble Space Telescope observations.

  Cosmological simulations usually explain rather than predict astronomical observations. It is as if I tell you that I understand the stock market. To prove it, I can claim to explain all the available data on the S&P 500 index. However, I still have no idea what the index will do tomorrow. Physical science should be able to do better than that. Nevertheless the simulations are very useful as a guide to the complexities of galaxy formation.

  Prediction is not easy. One does not need to discuss simulations to make this point. The X-ray emission from clusters of galaxies could easily have been predicted before its discovery. The physics is so simple that it is set as a question in an introductory astronomy text. Yet, no one did predict the existence of a hot intracluster medium. Predicting the future is more difficult than predicting the past.

  The simulations have produced some beautiful results. They enable us to visualize the process of dark matter halo formation as it takes place. In cosmology, observations and theory are intertwined to their mutual benefit.

  Why Do Galaxies Rotate?

  The rising and setting of the Sun, the phases of the Moon and the seasons recur regularly because of the rotation of our planet and its moon. The moon rotates around the earth, the Earth revolves around the Sun, and of course the Earth revolves on its axis. As we have seen, the whole solar system revolves around the center of our galaxy. How did things start rotating in the first place?

  Scientist like to reason by analogy. If you have looked at a river flowing, you may have noticed the presence of eddies and turbulence in the flow of the water. Some researchers have argued that turbulence in the early universe would result in rotation. However, when examined in detail, this picture dues not work. The prevalent view of rotation in galaxies is that it arises due to tides. Tides arise because the force of gravity weakens with distance. Thus, the gravitational pull of the Moon on the Earth is stronger on the side of the Earth closest to the Moon. This effect results in a bulge in the oceans The surface of the Earth itself is distorted by tides of about one foot. That is the surface of the Earth rises and falls by about one foot every 12 h. This effect has been measured using a network of radio telescopes and a technique called Very Large Baseline Interferometry. The tidal effect is most pronounced for Io, one of Jupiter’s satellites where the tidal force due to Jupiter heats up the planet and causes the formation of active volcanos. The surface of Io rises and falls by several hundred feet due this effect.

  What of tides in the early universe? Imagine an egg-shaped clump of dark matter. This clump is not isolated. There is another clump of dark matter not too far away from it. Let us consider the gravitational force on our clump due to its neighbor. The end of our egg shaped clump that is closest to the neighbor will experience a stronger gravitational pull from the neighbor than the end that is furthest. This is what we mean by a tide. This effect will set the clump spinning.

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nbsp; The same effect could occur if you were to fall feet first in space towards a black hole or some such dense object. If your body were aligned perfectly with a line drawn from you to the center of the black hole, your body would remain aligned as you fall. You would experience a tidal force, since your feet being closer to the black hole want to move faster than your head. What if you are not perfectly aligned? What if your body is tilted at an angle to the line from you to the center of the black hole? The effect of the tidal force will be to set you spinning. One final analogy. Imagine a canoe with a rope at each end that lies parallel to the shore of a lake. You and your friend both pull on each rope and the canoe slowly moves towards the shore. If you pull harder than your friend, the canoe will start rotating, as well as moving towards the shore.

  Elliptical galaxies rotate very little while spiral galaxies rotate quite fast. Our calculations show that we can account for the spin of elliptical galaxies, but not that of spiral galaxies, using the tidal argument.

  The formation of rotating disks in spiral galaxies is more complex. The galaxies grow by mergers and the structure of the disk that eventually forms depends on how the star formation affects the gas during merger events. Mergers can also destroy disks and lead to the formation of elliptical galaxies as shown in Fig. 6.3. Simulations can currently form disk galaxies that look similar to actual spiral galaxies (Fig. 6.2) but there are still many elements of the formation process that need to be understood.