George Lake, University of Washington
Galaxies come in two basic flavors, ellipticals and spirals. The elliptical galaxies are dense and slowly rotating while the spiral galaxies are more diffuse and rapidly rotating. There are numerous schemes for classifying galaxies with well-justified additional complexities. However, this simple "theorist's cartoon" already highlights the big problem: Why do the compact ones rotate slowly while the bigger ones rotate rapidly. It takes just a few minutes of playing on a piano stool to see why this is a problem. Start rotating with your arms out. When you pull them in, you spin fast. How did elliptical galaxies become so compact without spinning rapidly?
Hubble's tuning-fork classification of galaxies was brilliant and insightful . He saw that there were relatively featureless galaxies that always had the same radial brightness profiles and elliptical isophotes (lines of constant surface brightness). They were distinguished only by the eccentricity of their isophotes which never got flatter than about 2:1. Then there were spiral galaxies that showed greater diversity. They had disks with spiral arms. The arms could be tightly wound or relatively open. They often had central bulges of varying prominence. The prominence of the bulge and the winding of the spirals tends to go hand in hand. The larger the bulge-to disk ratio (B/D), the more tightly wrapped are the spiral arms (go to the tuning fork to compare.) There is a parallel sequence of barred spiral galaxies, ones where the spiral arms seem to connect to a strong linear feature, the bar, in the center of the disk.
This leads to a more refined cartoon for theorists. There are bulges that can live alone or in disks. The ratio of disk-to-bulge looks like the simplest physical parameter to target for an explanation of the diversity of galaxies. Sometimes the bulge lives alone as an elliptical galaxy. Sometimes it is wed to disk of varying importance to make a spiral galaxy. There are numerous other features to explain. Star formation is still occurring in disks but stopped long ago in the ellipticals. Ellipticals are preferentially located in great clusters of galaxies.
Why make things hard? There are two kinds of galaxies, ellipticals and spirals. So let's have two kinds of clouds make them, compact ones that don't spin rapidly and diffuse ones that spin a lot. Further, the blue stars of a disk look younger than the red stars of the bulge.
How about just saying that there were two epochs of galaxy formation? What's the problem with either of those ideas?
Those ideas certainly had their adherents a decade ago. But, the problem is that we think we know something about the way that galaxies formed. We don't need to know very much, just that they started as little fluctuations that grew. It doesn't matter what exotic mechanism made the little fluctuations. It could be some quantum process in the early Universe, it could be explosions that occurred a billion years after the big bang, it could be some wandering super-duper, super-conducting, super-colliding, super-stringy super-stuff that generated the little fluctuations. Indeed, the reason that there are so many wild ideas for the origin of little fluctuations is that what comes later depends so little on how they started!
The evolution of little fluctuations is remarkably simple. The only assumption is that the initial fluctuations didn't single out any particular scale. That is, the fluctuations on a scale of a few galaxies are comparable to the fluctuations on a scale of a single galaxy.
Figures 2 and 3 show why we think this is a good assumption. In these figures, we compare N-body simulations from initial conditions that are scale free (panel a), simulations that single out a single scale (panel b) and the observed Universe (panel c). Figure 2 shows the comparison at the depth of the Center for Astrophysics catalog of nearby galaxies. Figure 3 gives a deeper view by comparing larger simulations to the recent Cambridge Automatic Plate Measuring Machine (APM) survey. Here, we see the real distribution of galaxies looks like the scale free fluctuations. Galaxies themselves are clear imprints and that's one of the problems we still have to explain.
So, once upon a post recombination epoch (that's when all the matter recombined to make atoms rather than being a plasma of electrons and protons), there were these little fluctuations that could grow. They expanded with the rest of the Universe, but the extra little bit of mass retarded their expansion. As their expansion was retarded, they became progressively more dense relative to the Universe and the expansion was slowed evermore. Eventually, they reached maximum expansion. After that occurred, the protogalaxy collapses by a factor of two to reach an appropriate balance between the kinetic energy and the gravitational potential energy.
So far, the process looks the same for galaxies and clusters of galaxies. But, there is something very special about galaxies. When you look out at clusters of galaxies, membership of an individual galaxy is a little ambiguous. When you look at stars within a galaxy, it's easy to tell which galaxy the star belongs to. The reason that galaxies look so different is that after they first recollapsed, the gas in them radiated like mad and they kept collapsing. This process of energy loss by the gas is called dissipation. When we look at the very largest elliptical galaxies as well as whole clusters of galaxies, we see that there is hot gas in these systems that is trying its darndest to do the same thing today. It is failing where galaxies succeeded for two reasons: 1) it is less dense and 2) it is too hot. Gas cools by the particles undergoing collisions that result in the loss of energy. The higher the density the more frequent the collisions which easily explains the first reason. That the process is so temperature sensitive owes to nature of the inelastic collisions that lead to energy loss. The characteristic temperature of the diffuse hot gas in the Milky Way is a million degrees. At this temperature, some material exists as atoms and some as a free plasma. The transition from atoms to free plasma occurs by collision. The transition back to an atom releases a photon. So collisions lead to radiative cooling. When the temperature shifts ever higher to tens of millions of degrees in a big elliptical galaxy or even a hundred million degrees in a cluster of galaxies, there are no atoms. Collisions are nearly all from free plasma to free plasma and it is very rare that any photons are created to take energy away from the plasma. Occasionally, such a collision will produce an X-ray. The slow trickle of energy away from the plasma in ellipticals and clusters is seen by X-ray observatories orbiting the earth.
However, the time scale for their cooling to occur is longer than the age of the Universe, so the gas is stuck for the time being. Starting with scale-free fluctuations, galaxies are the largest objects where the gas could radiate away energy making a system that was dense enough to form stars.
With the assumption of scale-free fluctuations, it is remarkably easy to determine just how much galaxies collapsed owing to dissipation. In the scale-free scenario, the surface density of galaxies in groups of 2 galaxies is just a little brighter than that of groups with 4 galaxies and so on. By looking at the progression, we can extrapolate back to what would have been the surface brightness of a single galaxy if it had formed as part of the hierarchy of clustering without dissipation. By determining the enhancement in the surface brightness over what is predicted in the absence of dissipation, we can determine how much they collapsed during dissipation. This calculation is extremely robust. All we are doing is to first find the ratio between the surface brightness of a typical galaxy to the typical surface brightness of a small group of galaxies. Since surface brightness increases as the square of the collapse factor, we take the square root of the ratio we just determined to find the collapse factor. We find that galaxies have surface brightnesses 100 times that of groups, which leads us to conclude that they collapsed by a factor of 10 as they dissipated. That factor of ten is called the collapse factor. The final square root in the calculation means that it's hard to make a big mistake. If our initial ratio was wrong by 20%, our final answer is still good to 10%.
The spin of galaxies provides a second way to measure their collapse factor. As protogalaxies expanded and started to recollapse, they exerted mutual tides that started them spinning a small amount. Those tidal torques are all that are needed to explain the spin of present-day galaxies. Knowing that the fluctuation in the numbers and positions of nearby galaxies is comparable to the fluctuations that made a single galaxy enables us to calculate the average torque on a galaxy. Once again, it's not the details of the fluctuations that are important, only that the fluctuations on the scale of a few galaxies was about the same as the fluctuations on the scale of a single galaxy. Once we know how much the protogalaxies were spinning, we then determine the collapse factor needed to explain a galaxy's spin today. Remember that if you start spinning on a piano stool and pull in your arms, you spin faster. The faster you want to spin, the more you pull in your arms---this is analogous to changing your "collapse factor".
That simple theory works great for spirals. We find that when a tidally torqued protogalaxy collapses by a factor of 10, it makes a flat, spinning disk. This is a remarkable victory for the theory. But, before we close the books, let's look at ellipticals. When we compare their surface brightnesses with groups, we would conclude that they collapsed a little more than spirals, say a factor of 20 rather than 10. Alas, when we compare their spin to tidal torques, we conclude that they didn't collapse at all.
Things worked too well for spirals to give it all up. So the typical approach up through the mid-80's was to apply band-aids to the walking wounded theory. The easiest band-aid would be to find that there was a spread in the initial angular momentum from tidal torques. I can count dozens of papers by respected colleagues that tried one new idea after another to make that work. However, for every "new idea", there was a careful calculation that showed it just didn't work.
Ok, let's try the band-aid and splint approach. Let's use what we've described to make disks and find a new way to form elliptical galaxies. Guided by the fact that they don't spin much, let's suppose that they didn't dissipate. That would mean that they must be dense because they formed at very early times when the Universe itself was dense. At those early times, we find that there is a different cooling mechanism. A hot plasma can transfer energy directly to the cosmic background radiation, the relic radiation of the Hot Big Bang.
So now we have what I call the stranger or creationist theory of galaxy formation. We split the problem in two. We need two vastly different kinds of fluctuations, one set to make ellipticals just 50 million years after the Big Bang and another set of fluctuations that kicks in 2 billion years later to make the spirals and clusters of galaxies (recall that the arguments for spiral formation relied on continuity with the clustering hierarchy). Also, don't forget that ellipticals are in clusters and spiral galaxies have bulges in the middle, so the new mystery fluctuations have to come with a mechanism to make sure that the disks know where the bulges are and the biggest bulges (the ellipticals) know where the clusters are going to form 2 billion years later. Finally, since ellipticals were born in the early Universe without dissipation, they didn't cool by the plasma-atom cooling process and we no longer have any reason to single out the size of galaxies.
By now, I hope that you are as unhappy with that scheme as I was in the early 1980's. I was convinced that there had to be a better way. I thought I had a good half-baked idea or two about how to make things work. If only there was some way to build intuition about just what happen. The problem is that our simple arguments show that it happened at a redshift of at least 3 or 4. At that redshift, quasars are all we see. They have to fit in with galaxy formation, but are too inscrutable to build intuition. What about some numerical simulations?
Back in the mid 1970's, Richard Larson of Yale University did some marvelous simulations of galaxy formation. His simulations had a high degree of symmetry and a number of knobs to adjust the initial angular momentum, rates of cooling, the rates of star formation and the like. They showed how some output might be related to an input, but the cosmological context wasn't strong enough. There will also too many knobs to twiddle. I recall discussing these simulations with my thesis advisor J. P. Ostriker back in the late '70's. While we both appreciated their importance, his comment was that "there are so many knobs to twiddle he should have been able to make flowers and trees".
This highlights the dual simplicity and complexity of the problem. It's not hard to specify the initial conditions. The physics is just Newtonian gravity and atomic cooling. The problem is that galaxies have 1011 stars or 1068 atoms. The computers available to astronomical researchers in the 1970's were not up to any believable representation of such systems.
In January of 1984, I attended a meeting on "Halos of Galaxies" in Tucson and heard an interesting talk by a Canadian colleague, Ray Carlberg. We had both been postdocs at the Institute of Astronomy in Cambridge England back in 1980-81. He had made a fresh run at the Larson simulations of galaxies. He gave a very convincing talk about how many of the knobs that could be twiddled in these simulations were either well-determined or unimportant. The big problem that remained was getting enough computer time to relax some of the heavy handed assumptions and do more realistic simulations. Among the many problems were the inability to handle systems with arbitrary shapes and the difficulty in simulating enough particles. Computer time was so precious that everyone started at maximum expansion---the galaxies were "dropped". If anything important happened during the expansion phase, it was missed. There was never enough computer time to explore the parameter space of initial conditions to find out what really mattered.
Back in 1984, I was a Member of Technical Staff (MTS) at AT&T Bell Labs. Industry is very different than a University. At that time, researchers at American Universities had extremely limited access to supercomputers. The less powerful University mainframes weren't justified unless they were saturated with jobs. It was a terrible time to do large scale computing at Universities.
At Bell Labs, there was a big shiny Cray that was justified by being nearly empty. That way, when someone wanted to design a new communications processor, there were sufficient resources to get the job done in a short time. They would load the machine up for a job that took days---and they didn't have to wait a month for it to finish. The AT&T device designers were doing the job in a fraction of the time of their competitors. [The chips for the No. 5 ESS switch were designed and fabricated in less than a year, without the ever-at-the-ready Cray it would have taken 5 years.] It made good business sense to keep a nearly empty Cray around. The basic researchers at the lab could buy "stand-by" time for just $100/hour when the going market rate for an hour was $6,000! With the Cray being 200--600 times faster than the University VAXes, it was a great opportunity. That factor of 200--600 was the difference between walking and taking the Concorde.
So off we went to simulate. We started our protogalaxies in expansion and followed them through turnaround and collapse. We calculated the mutual gravity of particles with a kludgey scheme for atomic cooling. We simulated both light and dark matter. Only the light matter could cool, the dark matter experienced only gravity. We got hooked on simulating. We could let things get flat like disks, barred like the spirals, we could see spiral arms form and dissolve. We could alter a few simple input parameters and see the Hubble sequence.
We quickly burned up the entire computer allocation of the Physical Research Lab. We got access to the entire allocation by an accounting mistake. I had to get some of it put back and get more time. A friendship with a systems programmer led to the cutting of a deal with Nils-Peter Nelson who ran the Cray. If I stayed out of everyone's way, I could have all the time I could eat. He called this an NSF grant--Nelson Slush Fund.
Back we ran to compute more and more galaxies. The lab bought a bigger two-headed Cray. We were happy to shake it down, running 700 hours of jobs in 320 hours of wall clock time. By the time we finished we'd set a record for the use of Cray time on a scientific problem unrelated to national defense. [The record may still hold. One thing for sure is that the problem is still unrelated to national defense.]
Given the half-baked ideas that we started with, we were lucky that we ran a lot of simulations without thinking too much. But, now it was time to reflect on a file cabinet of graphics.
We found something most remarkable. It didn't matter what the initial spin of a galaxy was. We could take two galaxies with the same initial spin and turn one into a diffuse rapidly rotating spiral and the other into a compact slowly rotating elliptical galaxy. So, what happen to the simple physical rules that govern spinning piano players? The trick was a braking mechanism for the spin. If the initial conditions were such that the collapse was smooth, then all the particles settled into a nice spiral disk. But, if we let lumps form on small scales, those lumps would rattle around and transfer their spin outward to the dark matter. What was left was a nice elliptical galaxy. Remarkably, in the case of the elliptical galaxy, some of the material was thrown to large radii and never became dense enough to form stars. Ellipticals are observed to have envelopes of hot gas that would emit the X-rays seen by the orbiting X-ray observatories, Einstein and Ginga.
We finally had a physical control parameter for the Hubble sequence-- the presence or absence of substructure during collapse. We executed this mechanism by changing the random motions of particles. The substructure could grow when the initial conditions were "cold". It was suppressed by the random motions when the protogalaxies were "warm". This result was published in two papers in the October 1988 issue of The Astronomical Journal.
We still needed a cosmological context for our mechanism. We couldn't just point to ellipticals and say "there's a cold one" or "look at that great spiral over there, it's dark matter must have been really hot". The trick is that "hot" and "cold" are relative terms rather than absolute. "Hot" is just hot enough to prevent the growth of substructure. A collapse is "hot" if the random velocities of the particles at the time of maximum expansion is greater than 20% of the final velocity dispersion after it has settled down into its present state. Lower random velocities are "cold". When I was pondering this problem, an article by Adrian Meisels titled "The Hubble Sequence of Masses" made me jump out of my chair. He showed that there is a systematic progression of characteristic velocities across the Hubble Sequence. Broadly, the current velocities in elliptical galaxies are twice that in spirals. So if the initial random velocities of the dark matter had just the right universal value, galaxies with velocities as large as elliptical galaxies would have undergone "cold" collapses, while those galaxies with velocities as small as spiral galaxies would have been "hot".
We haven't completely rid ourselves of tooth fairies. Is there an independent way to determine this magic velocity? How would the dark matter have acquired this Universal Random Velocity? Is it the only way to make this scheme work? I'll take those three questions in turn.
One of the things that Ray and I found from our extensive simulations was that the initial random velocities of a collapse determine the overall density profile of the system. The random velocity creates a pressure that resists formation of high densities in the middle. So if we can measure the central densities and core radii (the place where the density falls to half the central value) of the dark matter, we determine the initial random velocities. These quantities are determined by mapping the current velocities in galaxies. The first time my computer showed me that the data fit our predictions, they had to scrape me off the ceiling.
Oddly, the magic random velocity is just that expected for a neutrino that would "close the Universe", In recent years, the Inflationary model of the Universe has achieved a high degree of success. In this model, the Universe was flattened by a phase of rapid expansion during the first 10-39 seconds of the Big Bang. The result should be an exquisitely balanced Universe whose density causes it to teeter on the precipice between being bound and unbound. It will expand forever, but any overdensity---no matter how tiny---will ultimately collapse. Unfortunately, the "normal matter" that makes up you and me and the stars has less than a tenth of the density required. Neutrinos have long been a prime candidate for the dark matter needed to keep the Universe from expanding into boring emptiness or recollapsing to a meaningless singularity. However, neutrinos are difficult dark matter candidates. They tend to spoil the formation of galaxies and make it all too easy to form even bigger and larger structures than the Great Attractors and Great Walls that we see. In figures 2 and 3, panel b) is what the Universe should look like with neutrinos as dark matter.
One alternative for the magic dispersion is that the dark matter was originally very cold, but it acquired the random velocities from the growth of small puffy substructure that dissolves. That's tricky, since the growth or suppression of small scale structure was the reason we turned to the idea of a magic random velocity.
Let's return to the basics of our mechanism---the growth or suppression of substructure---to find an alternative to the magic dispersion. Substructure doesn't arise magically, it grows from small seed fluctuations. Ray and I assumed that the seeds would always be there and used random velocities as a way of regulating their growth. Sometime later this year, a paper by Neal Katz (now at MIT) and James Gunn (Princeton) will appear in the The Astrophysical Journal that promotes an alternative scheme: the dark matter is cold and the strength of the seeds is allowed to vary. Ellipticals form when the seeds are strong. Spirals result from protogalaxies that were exceedingly smooth. As well as the differences in initial conditions, Katz used a code with more spatial resolution, more particles and he tried to clean up the algorithms for both dissipation and star formation.
Our friendly competition did much better numerical simulations. The astute reader will have noticed an absence of illustrations showing our model spirals and ellipticals. Frankly, they looked good but not great. The simulations done by Katz look GREAT. He has kindly provided the photos for figure 4 which compares the formation of a spiral (on the right) to an elliptical (on the left). Each frame specifies a viewing angle and a "redshift" (the redshift maps to time, the higher the redshift the longer away and farther ago). The top 8 frames are taken in the initial equatorial plane. The lumps cause the final galaxy to precess a bit, so the final equatorial plane of the galaxy is different. The bottom two frames change the viewing angle slightly to give edge-on views of the galaxies. In these pictures, the dark matter is blue and the "gas" is red. In the simulation of the elliptical galaxy, there is a considerable difference in the distribution of stars and gas, so in that case, Katz shows the stars in yellow. During the formation of the spiral, some lumps do form. However, they are relatively "soft" and dissolve quickly. The more persistent lumps in the elliptical are responsible for it's final structure.
Since I'm in the position to have last word, I'll use it to say that all subsequent work has agreed on the importance of substructure for determining the Hubble sequence. By using velocity dispersions to control substructure, Ray and I were able to find a compelling cosmological context and conduct a test using the present day mass distributions in galaxies. The seed scheme has some distinct attractions, but is not as far along.
One thing is clear, galaxies form in the dark.
