National Center for Computational Sciences

By: Leo Williams

Astrophysicists simulate the dark matter that cradles a galaxy

Sometime in the early 1930s, the eminent Swiss astronomer Fritz Zwicky noticed something very odd as he was looking to the skies: Galaxies move around each other too fast.

Zwicky was scrutinizing a group of eight galaxies orbiting one another more than 350 million light years away in the Coma Galaxy Cluster. Thanks to Newton and Einstein, he understood the balance of forces necessary to keep the galaxies in this dance. Like a yo-yo swung by a child, they need both the centrifugal force pushing them outward and the string—in this case gravity—pulling them back in. Too much force inward and the system collapses; too much outward and the galaxies fly apart.

Every object with mass exerts a gravitational pull on other objects—from a yo-yo to a galaxy. Zwicky’s problem was that the galaxy cluster he was observing appeared to have too little mass, and therefore too little gravity, to hold together. The galaxies should have flown off into space. To solve this problem, he and his colleagues concluded that these and all galaxies must be dominated by matter that they couldn’t see. They called it dark matter.

Armed with a knowledge of how gravity works and extensive observations of planets, stars and galaxies, scientists have in fact concluded that less than one-fifth of the matter in the universe is visible. The remainder, dark matter, has no interaction with regular matter except through the force of gravity. Nevertheless, there is so much dark matter in the universe that its gravitational force controls the lives of stars and galaxies.

What, then, would dark matter look like if we could see it? A team led by astrophysicist Piero Madau of the University of California–Santa Cruz (UCSC) has taken a substantial step toward answering this question. Using the power of Oak Ridge National Laboratory’s (ORNL’s) Jaguar supercomputer, Madau’s team has run the largest simulation ever of dark matter evolving over billions of years to envelop a galaxy such as our own Milky Way. This envelope is known as a dark matter halo.

Madau and his collaborators—including Juerg Diemand and Marcel Zemp, both of UCSC, and Michael Kuhlen of the Institute for Advanced Study in Princeton, New Jersey—reviewed the simulation and their findings in the journal Nature. Their paper, entitled “Clumps and Streams in the Local Dark Matter Distribution,” appears in the August 7 issue.

The simulation followed a galaxy worth of dark matter through nearly the entire history of the universe, dividing the dark matter into more than a billion separate parcels. It was a staggering job, tracking 9,000 trillion trillion trillion tons of invisible stuff spread across 176 trillion trillion trillion square miles as it evolved over 13 billion years. Each parcel of dark matter was 4,000 times as massive as the sun.

Hypothetical particles with real gravity

Scientists don’t know exactly what dark matter is. Candidates include hypothetical particles such as the neutralino, the sterile neutrino, the axion, or some other weakly interacting massive particle (or WIMP). Fortunately, researchers don’t need to know what dark matter is in order to simulate it. All they need to know is that dark matter interacts with other matter only through gravity and that it is cold, meaning it is made up of particles that were moving slowly when galaxies and clusters began to form. Using initial conditions provided by observations of the cosmic microwave background, Madau and his team were able to simulate dark matter through a computer application called PKDGRAV2, developed by a group of numerical astrophysicists at the University of Zurich, which ignored visible matter and focused entirely on the gravitational interaction between a billion dark matter particles. The project had a major allocation of supercomputer time through the Department of Energy’s Innovative and Novel Computational Impact on Theory and Experiment (or INCITE) program, and it used about 1 million processor hours on the Jaguar system, located at ORNL’s National Center for Computational Sciences.

“The computer was basically just computing gravity,” Madau explained. “You have to compute the gravitational force between 1 billion particles, and to do that is very tricky. You’re following the orbits of these particles in a gravitational potential that is varying all the time. The code allows you to compute with very high precision the gravitational force due to the particles that are next to you and with less and less precision the gravitational force due to the particles that are very far away, because the gravity becomes weaker and weaker with distance.”

Dark matter is not evenly spread out, although researchers believe it was nearly homogeneously distributed right after the Big Bang. Over time, however, it became bunched and clumped as gravity pulled it together, first into tiny clumps more or less the mass of Earth. These clumps were pulled together into larger clumps, which were pulled together into still larger clumps, and so on until they combined to form halos of dark matter massive enough to host galaxies.

One key question, then, is whether the smaller clumps would remain identifiable or would smooth out within the larger galactic halos. The answer required a state-of-the-art supercomputer such as Jaguar, which at the time of the simulations in November 2007 was capable of nearly 120 trillion calculations a second. Because they did not have the resolution to resolve any unevenness, smaller simulations showed the dark matter smoothing out, especially in the galaxy’s dense inner reaches. Madau’s billion-cell simulation, however, provided enough resolution to verify that subclumps and sub-subclumps do indeed survive, even in the very inner regions where our solar system is located.

“You expect a hierarchy of structure in cold dark matter,” Madau explained. “What you don’t know is what sort of structure will survive the assembly because as these subclumps come together, they are subject to tidal forces, and they can be stripped and destroyed. So their existence in the field had been predicted. The issue was whether they would survive as assembled together to bigger and bigger structures.”

“What we find,” he continued, “is the survival fraction is quite high.”

Madau’s team will be able to verify its simulation results using the National Aeronautics and Space Administration’s Gamma-Ray Large Area Space Telescope (GLAST). Launched on June 11, 2008, GLAST will scan the heavens to study some of the universe’s most extreme and puzzling phenomena: gamma-ray bursts, neutron stars, supernovas, and dark matter, just to name a few. While dark matter particles cannot themselves be detected by GLAST (direct detection of dark matter is being pursued by large underground detectors), researchers believe that dark matter particles and antiparticles may be annihilated when they bump into each other, producing gamma rays that can be observed from space. The clumps of dark matter predicted by Madau’s team should bring more particles together and thereby produce an increased level of gamma rays. In fact, Madau and his colleagues have produced a second paper, “The Dark Matter Annihilation Signal from Galactic Substructure: Predictions for GLAST,” which is scheduled for publication in the September 10, 2008, issue of Astrophysical Journal.

A second verification comes from an effect known as gravitational lensing, in which the gravity exerted by a galaxy along the line of sight bends the light traveling from faraway quasars in the background. If the dark matter halos of galaxies are as clumpy as this simulation suggests, the light from a distant quasar should be broken up, like a light shining through frosted glass.

“We already have some data there,” Madau noted, “which seems to imply that the inner regions of galaxies are rather clumpy. The flux ratios of multiply imaged quasars are not as you would predict with a smooth intervening lens potential. Instead of a smooth lens, there is substructure that appears to be affecting the lensing process. Our simulation seems to produce the right amount of lumpiness.”

While this simulation may help explain why the universe is as it is, it leaves other questions unanswered. For example, Madau noted that while dark matter in the galaxy is very clumpy, that same feature is not found in visible matter. In fact, the Milky Way is orbited by far fewer dwarf galaxies than might be predicted by the simulation.

“We see as many as 20 dwarf galaxy satellites of the Milky Way that are luminous,” he explained, “and we estimate that there may be a hundred or so. But we predict thousands of relatively massive clumps. So one issue is, why are most of those clumps dark? It seems that we’re not very efficient at forming stars, and so there must be some sort of threshold where stars can only form in more massive potential.”