The “dark matter” that comprises a still-undetected
one-quarter of the universe is not a uniform cosmic fog, says a
University of California, Berkeley, astrophysicist, but instead forms
dense clumps that move about like dust motes dancing in a shaft of

In a paper submitted this week to Physical Review D, Chung-Pei Ma, an
associate professor of astronomy at UC Berkeley, and Edmund
Bertschinger of the Massachusetts Institute of Technology (MIT),
prove that the motion of dark matter clumps can be modeled in a way
similar to the Brownian motion of air-borne dust or pollen.

Their findings should provide astrophysicists with a new way to
calculate the evolution of this ghost universe of dark matter and
reconcile it with the observable universe, Ma said.

Dark matter has been a nagging problem for astronomy for more than 30
years. Stars within galaxies and galaxies within clusters move in a
way that indicates there is more matter there than we can see. This
unseen matter seems to be in a spherical halo that extends probably
10 times farther than the visible stellar halo around galaxies. Early
proposals that the invisible matter is comprised of burnt-out stars
or heavy neutrinos have not panned out, and the current favorite
candidates are exotic particles variously called neutrilinos, axions
or other hypothetical supersymmetric particles. Because these exotic
particles interact with ordinary matter through gravity only, not via
electromagnetic waves, they emit no light.

“We’re only seeing half of all particles,” Ma said. “They’re too
heavy to produce now in accelerators, so half of the world we don’t
know about.”

The picture only got worse four years ago when “dark energy” was
found to be even more prevalent than dark matter. The cosmic account
now pegs dark energy at about 69 percent of the universe, exotic dark
matter at 27 percent, mundane dark matter – dim, unseen stars – at 3
percent, and what we actually see at a mere 1 percent.

Based on computer models of how dark matter would move under the
force of gravity, Ma said that dark matter is not a uniform mist
enveloping clusters of galaxies. Instead, dark matter forms smaller
clumps that look superficially like the galaxies and globular
clusters we see in our luminous universe. The dark matter has a
dynamic life independent of luminous matter, she said.

“The cosmic microwave background shows the early effects of dark
matter clumping, and these clumps grow under gravitational
attraction,” she said. “But each of these clumps, the halo around
galaxy clusters, was thought to be smooth. People were intrigued to
find that high-resolution simulations show they are not smooth, but
instead have intricate substructures. The dark world has a dynamic
life of its own.”

Ma, Bertschinger and UC Berkeley graduate student Michael
Boylan-Kolchin performed some of these simulations themselves.
Several other groups over the past two years have also showed similar

The ghost universe of dark matter is a template for the visible
universe, she said. Dark matter is 25 times more abundant than mere
visible matter, so visible matter should cluster wherever dark matter

Therein lies the problem, Ma said. Computer simulations of the
evolution of dark matter predict far more clumps of dark matter in a
region than there are clumps of luminous matter we can see. If
luminous matter follows dark matter, there should be nearly
equivalent numbers of each.

“Our galaxy, the Milky Way, has about a dozen satellites, but in
simulations we see thousands of satellites of dark matter,” she said.
“Dark matter in the Milky Way is a dynamic, lively environment in
which thousands of smaller satellites of dark matter clumps are
swarming around a big parent dark matter halo, constantly interacting
and disturbing each other.”

In addition, astrophysicists modeling the motion of dark matter were
puzzled to see that each clump had a density that peaked in the
center and fell off toward the edges in the exact same way,
independent of its size. This universal density profile, however,
appears to be in conflict with observations of some dwarf
galaxies made by Ma’s colleague, UC Berkeley professor of astronomy
Leo Blitz, and his research group, among others.

Ma hopes that a new way of looking at the motion of dark matter will
resolve these problems and square theory with observation. In her
Physical Review article, discussed at a meeting earlier this year of
the American Physical Society, she proved that the motion of dark
matter can be modeled much like the Brownian motion that botanist
Robert Brown described in 1828 and Albert Einstein explained in a
seminal 1905 paper that helped garner him the 1921 Nobel Prize in

Brownian motion was first described as the zigzag path traveled by a
grain of pollen floating in water, pushed about by water molecules
colliding with it. The phenomenon refers equally to the motion of
dust in air and dense clumps of dark matter in the dark matter
universe, said Ma.

This insight “let’s us use a different language, a different point of
view than the standard view,” to investigate the movement and
evolution of dark matter, she said.

Other astronomers, such as UC Berkeley emeritus professor of
astronomy Ivan King, have used the theory of Brownian motion to model
the movement of hundreds of thousands of stars within star clusters,
but this, Ma said, “is the first time it has been applied rigorously
to large cosmological scales. The idea is that we don’t care exactly
where the clumps are, but rather, how clumps behave statistically in
the system, how they scatter gravitationally.”

Ma noted that the Brownian motion of clumps is governed by an
equation, the Fokker-Planck equation, that is used to model many
stochastic or random processes, including the stock market. Ma and
collaborators are currently working on solving this equation for
cosmological dark matter.

“It is surprising and delightful that the evolution of dark matter,
the evolution of clumps, obeys a simple, 90-year-old equation,” she

The work was supported by the National Aeronautics and Space Administration.



Chung-Pei Ma can be reached at (510) 642-4850 or

A video simulation of the evolution of dark matter is available on
Ma’s Web site,