Lesson 6

6 :: “Dark Matter, Dark Energy, and Other Things

That Refuse to Be Seen”

An exploration of the observational evidence for the ubiquitous — but unobserved — dark matter and dark energy.

(Formerly) Dark Matter

Many forms of material were once “dark matter.” We are just starting to detect planets around other stars directly and for several years we “saw” them only through their gravitational tug on their central stars. Cool gas that radiates light only in the radio range was invisible before the creation of radio detectors, and the hot intra-cluster gas in galaxy clusters was invisible until X-ray satellites were placed in orbit. Currently, mankind has the electromagnetic spectrum, including light in colors ranging from high-energy gamma rays to extremely long radio waves, blanketed with detectors.

Invisible Pull

The universe is a dark and wondrous place. From our vantage point on Earth, we can see only the smallest fraction of its volume, and our particle accelerators allow us to create only the lowest-mass particles. Still, what little we can see offers us vast theoretical — and even philosophical — challenges. Sometimes what we can’t actually see challenges scientists the most. For astronomers and cosmologists these invisible enigmas take the form of dark matter and dark energy.

Dark matter takes many forms. For a while Neptune was a large piece of dark matter, because at its most basic level dark matter is just matter that we haven’t yet observed, except through the motions of other objects. Thanks to gravity, every body with mass pulls on every other body. Toy cars and black holes are each equally bound by this reality. In the years following the 1781 discovery of Uranus, astronomers noticed that its orbit did not follow the course they predicted. Two separate mathematicians, John Couch Adams and Urbain Jean Joseph Le Verrier, looked at the discrepancies in Uranus’s orbit and calculated where a planet would have to be to cause the deviations. Their calculations led to astronomers finding Neptune in 1846.

Over the years, deviations in orbital speed and orbital shapes have led astronomers to speculate on the existence of lots of unseen material (see sidebar). To understand this better, let’s talk about gravity and orbits. An object, such as a planet, tends to stay in motion in a straight line unless a force acts on it. The force of gravity pulls on planets and causes them to curve around stars. The amount of pull depends on the size of the star. If our sun were twice its size, the Earth would have to orbit much faster to stay at its current distance from the sun because the sun’s gravity would pull much harder.

The orbiting object doesn’t really care how the mass inside its orbit is distributed. If the Earth orbited a cloud of jellybeans with the same mass as the sun, its orbit would not change. Objects actually orbit a system’s center of mass — the point on which a system balances. A large spherical cloud of jellybeans and the spherical sun with the same total mass will exert the same gravitational tug on planets. (It would just be a lot colder here with the jellybeans!)

Our own Milky Way is mathematically similar to a cloud of jellybeans. Our sun, going around the galaxy, doesn’t orbit a single high-mass object. Instead, it orbits millions of stars and clouds of gas and dust. The combined mass of all the objects inside the orbit of the sun determines how fast the sun orbits.

Ideally, we can “weigh” the amount of mass interior to different regions of a galaxy by measuring the velocities of the stars and gas located at different radii. Vera Rubin, now at the Smithsonian Center for Astrophysics, was one of the pioneers in this study. She painstakingly measured the velocities of galaxies at different radii and realized that the mass of a galaxy does not necessarily drop with radius. This was surprising because the amount of light that galaxies give off goes down with radius, and people assumed that the light distribution and mass distribution would be the same.

Let’s consider a few toy models to better understand the problem. First, consider the case in which the majority of mass in a galaxy is in the galactic bulge (see Figure 6-1). In this case the orbital velocities of stars would drop off with radius, with the outer stars orbiting significantly more slowly than the inner stars. Next, let’s consider the case in which the majority of the mass in the galaxy is evenly distributed throughout the disk of the galaxy. In this case, outer stars would orbit much faster (see Figure 6-1)


Figure 6-1: The Galaxy consists of three major parts: the bulge, disk, and halo. The small structures in the halo are globular clusters. (Graphic by Pamela L. Gay, copyright 2002)


Figure 6-2: The orbital velocity of stars in a disk of material increases with radius. The orbital velocity of stars orbiting outside a central concentration of mass decreases with radius. (Graphic by Pamela L. Gay, copyright 2002)

Plots of how fast stars orbit galaxies at different radii are called galaxy rotation curves (see http://burro.astr.cwru.edu/JavaLab/RotcurveWeb/back_RC.html). Actual rotation curves, calculated out to the furthest visible edges of galaxies, all show measured velocities leveling off (and sometimes gradually increasing) in the outer disks of the galaxies. This implies that the actual mass distribution and the visible (luminous) material distribution are different. To account for the observed motions of stars and gas, a galaxy must have a halo of dark material that is 70 to 90 percent of the galaxy’s total mass.

Galaxies aren’t the only harbors of dark matter. Similar research techniques, using galaxies instead of stars, have determined that galaxy clusters are also approximately 90 percent dark matter. Dark matter is everywhere — in galaxies, in galaxy clusters, and probably permeating all of space. Scientists currently believe that 90 percent of all mass in the universe is dark. To truly understand the universe, astronomers need to figure out what dark matter is made of. Astronomer Don Winget of the University of Texas offered up the solution of assuming one Acme brick in each solar-sized volume of space. Unfortunately, although this solution would match observations, the real source of dark matter is not likely to take on such a mundane form.

Looking for Knowledge in the Dark

I saved the subject of dark matter for the end of this course because to understand the problem you need to think about nucleogenesis, particle physics, and inflation. Matter comes in two forms — baryonic and non-baryonic. Baryons are particles made of three quarks, such as the proton and the neutron (see http://hyperphysics.phy-astr.gsu.edu/hbase/particles/hadron.html#c6). Non-baryonic dark matter includes neutrinos and weakly interacting massive particles (WIMPs) that have not yet been discovered but which are predicted by the standard model. Baryonic matter makes up everything that we can see (stars, dust, and galaxies).

In a flat universe, the total matter density, omega, is one. Omega is divided into two parts representing the baryons and non-baryons. As near as observers can tell from adding up all visible luminous mass, baryons alone produce a matter density of just 0.1. This low value agrees with the predictions of big bang nucleosynthesis. The amount of deuterium (produced during nuclear reactions) in the universe would differ according to the baryonic density of the early universe. In stars, deutrium is part of an intermediate step and is completely used up during the reactions. The only sources of lasting deuterium are human laboratories and the big bang.

If the matter density of the universe at the time of the big bang had been higher than 10 percent, the deuterium produced would all have been converted into helium. Since we observe natural deuterium in gas clouds — and even in our terrestrial oceans, — we know that the early universe must have a baryonic mass density of 10 percent or less.

This means that the remaining universe must be made of non-baryonic dark matter. Non-baryonic dark matter is divided into two types: hot and cold. Hot dark matter was extremely energetic in the early universe (and was thus hot) and cold dark matter was less energetic in the early universe (and was thus cold). The temperature distribution of the dark matter determined the rate at which galaxies formed. If the overall distribution of dark matter had been hot, the dark matter would have slowed — and perhaps prevented — the formation of the galaxies. If dark matter had been strictly cold, galaxies would have formed too quickly and the universe would have been much more clumped than we observe. It seems that dark matter is a mixture of both hot and cold particles. Cosmologists believe the majority of the dark matter is cold non-baryonic material.

This is a problem. We understand what baryonic dark matter might be — loose planets freed from their stars; black holes that give off no light; brown dwarfs that are too small to ignite light-producing nuclear reactions– and we understand what might make up hot dark matter, namely, neutrinos with mass. However, we have never detected anything that might be cold dark matter and we can only guess at its possible sources.

Perhaps dark matter consists of the super-symmetric particles predicted in the standard model. Perhaps it is made of massive strings. Whatever the answer, it is safe to say that dark matter consists of particles on the edge of our current understanding that we have not yet discovered in high-energy supercolliders.

The Dark Matter Rap

If you think physicists and cosmologists don’t have a sense of humor, be sure to check out “The Dark Matter Rap” by David Weinberg, quoted on pages 122 and 126 of our course text, The Whole Shebang.

Dark Energy

Dark energy, or vacuum energy, is perhaps even more of a mystery than dark matter. Einstein included a cosmological constant in his theory of relativity that referred to a universal acceleration caused by “vacuum energy.” He initially included this unobserved term in his equations to counteract the gravitational deceleration of cosmic expansion, essentially trying to make the universe stand still. When it was discovered that the universe is expanding, Einstein tried to erase the cosmological constant and vacuum energy with it.

Since around 1998, observations of supernovae have begun to show us that Einstein’s greatest “mistake” was no mistake at all. The acceleration of the expansion of the universe has been observed from Type 1a supernovae. When astronomers measure the distance and redshift of supernovae they find that the velocity of supernovae is less than expected at large distances. This implies that the universe was expanding somewhat more slowly in the past than it is now.

Scientists believe that the energy that permeates all of space — called “vacuum energy” — causes this acceleration. Vacuum energy fills all the empty spaces in the universe and is a constant of the universe, with a constant value. The constant value makes it impossible to hold up some sort of meter to space and measure the value of the vacuum energy. Instead, like dark matter, it is possible to measure the vacuum energy of space only from its effects on visible matter. Because we see the universe’s expansion accelerating, we know (or at least posit) that there is a dark invisible energy pushing outwards.

An accelerating universe adds a new twist to our cosmic geometry. It is now possible to live in a universe with a flat geometry that will continue to accelerate outwards forever. “Death by ice would suffice,” and it certainly seems to be the likely fate of our evolving universe. As the universe continues to expand and all the stars die and their white dwarf ashes cool, all energy will fade away, leaving a cold black universe.

Some say the world will end in fire; Some say in ice. From what I’ve tasted of desire I hold with those who favor fire. But if it had to perish twice, I think I know enough of hate To know that for destruction ice Is also great And would suffice. — Robert Frost, “Fire and Ice”

I started this lesson by saying that the universe is a dark and wondrous place. I close with the observation that it is filled with energy and matter that is now — and might always be — undetectable by humans. To detect a particle, a detector has to interact with what is being detected. This is what happens when light (photons) entering a camera trigger chemical reaction in film. If the universe is filled with weakly interacting massive particles, how do we know we can build a detector with which they will interact? Like a man in a constantly moving elevator who cannot determine his velocity, we are surrounded by a constant energy that we cannot measure. We know the mass is there. We know the energy is there. For now we must be content to outline the invisible with descriptions gleaned from the visible.

Moving Forward

In the next lesson we’ll depart from our exploration of the most distant past and the most distant future, and instead look into our own origins (quite a recent event from a cosmological perspective) and the cosmic history that allowed us to be here.

Assignment: Finding Our Way in the Dark

Read the Chapter 5 of The Whole Shebang: A State-of-the-Universe(s) Report by Timothy Ferris. In this chapter (and in Lesson 7) we discover that galaxies and galaxy clusters are rotating faster then expected. The existence of dark matter can explain this. Some fringe scientists have also attempted to explain it by changing the law of gravity so that at great distances there is an extra term — an extra kick to accelerate stars and galaxies in large systems. The scientific community has been reluctant to consider these theories of “Modified Newtonian Dynamics” (MOND). Do you find it more reasonable to say that there is a bunch of material out there that we can’t (and might never) observe, or that gravity has an extra term that applies only at distances too great for us to test in a laboratory? Come to the Message Board to discuss your answers.

For more information on MOND, see http://www.astro.umd.edu/~ssm/mond/litsub.html.

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