Chapter 20
Dark Matter, Dark Energy, and
the Fate of the Universe
Unseen Influences
Dark Matter: An undetected form of mass that emits little or
no light but whose existence we infer from its gravitational
influence
Dark Energy: An unknown form of energy that seems to be
the source of a repulsive force causing the expansion of the
universe to accelerate
Contents of Universe
• “Normal” Matter:
~ 4.4%
– Normal Matter inside stars:
– Normal Matter outside stars:
• Dark Matter:
• Dark Energy
~ 0.6%
~ 3.8%
~ 25%
~ 71%
What is the evidence for dark
matter in galaxies?
Newton’s Description of Gravity
Yields
𝐹 = 𝑚𝑎
𝐺𝑚1 𝑚2
𝑟2
= 𝑚1 𝑎 =
𝑣=
𝑣2
𝑚1
𝑟
𝐺𝑚
𝑟
Where m is the mass contained inside of the
radius r
Orbital velocity
Orbital velocity curve if most of
the mass was at the center of the
galaxy.
Radius
𝑣=
𝐺𝑚
𝑟
The Mass of the Milky Way
If all mass was concentrated in the center,
Rotation curve would follow a modified
version of Kepler’s 3rd law.
Rotation Curve = orbital velocity
as function of radius.
The Mass of the Milky Way (II)
Total mass in the disk of
the Milky Way:
Approx. 200 billion solar
masses
Additional mass in an
extended halo:
Total: Approx. 1 trillion
solar masses
Most of the mass is not
emitting any radiation:
dark matter!
Mass within Sun’s
orbit:
1.0 x 1011 MSun
Total mass:
~1012 MSun
The visible
portion of a
galaxy lies
deep in the
heart of a
large halo of
dark matter
We can
measure
rotation
curves of
other spiral
galaxies
using the
Doppler
shift of the
21-cm line
of atomic H
Astronomers calculate a mass to light ratio.
Galaxy luminosity is measured to estimate the amount of
mass in the stars.
Total mass is found from motion. Orbital velocities of the
gas clouds and stars. If total mass is larger than that
attributed to stars difference must be due to dark matter.
Spiral galaxies all tend to have flat rotation curves
indicating large amounts of dark matter :10x as much
dark matter as normal or 90% of mass is dark
Slowest
Fastest
Remember the motion of stars in
elliptical galaxies is more
random than in spirals so you
cannot get an orbital velocity
curve. There is also very little H2
in elliptical galaxies.
Broadening of spectral lines in
elliptical galaxies tells us how
fast the stars are orbiting.
Different parts of the galaxy
have similar spectral broadening.
These galaxies also have dark
matter
What is the evidence for dark
matter in clusters of galaxies?
Fritz Zwicky did this in the 1930s
• Treating galaxy clusters as orbiting the
common center of mass
• Measures speed of the whole cluster
• Found individual speeds of the galaxies
around the center of mass
• Calculated the mass of clusters
• He found dark matter to be ~50x that of
normal matter
Result was too radical for others to accept.
Now with the spiral galaxy data and other independent
methods confirming this result it has been accepted.
Clusters contain
large amounts of Xray emitting hot gas
Temperature of hot
gas (particle
motions) tells us
cluster mass:
85% dark matter
13% hot gas
2% stars
Gravitational lensing, the bending of light rays by
gravity, can also tell us a cluster’s mass
All three methods of measuring cluster mass indicate
similar amounts of dark matter
Does dark matter really exist?
Our Options
1. Dark matter really exists, and we are observing
the effects of its gravitational attraction
2. Something is wrong with our understanding of
gravity, causing us to mistakenly infer the
existence of dark matter
Because gravity is so well tested, most astronomers
prefer option #1
What might dark matter be made
of?
A bit of terminology
Baryons: protons and neutrons
Normal matter is sometimes called baryonic matter
Nonbaryonic matter is the other stuff. What ever it may
be.
Two Basic Options
• Ordinary Dark Matter (MACHOS)
– Massive Compact Halo Objects:
dead or failed stars in halos of galaxies
• Extraordinary Dark Matter (WIMPS)
– Weakly Interacting Massive Particles:
mysterious neutrino-like particles
The
Best
Bet
MACHOs
occasionally
make other
stars appear
brighter
through
lensing
MACHOs
occasionally
make other
stars appear
brighter
through
lensing
… but not
enough
lensing
events to
explain all
the dark
matter
Why Believe in WIMPs?
• There’s not enough ordinary matter
• WIMPs could be left over from Big Bang
• Models involving WIMPs explain how galaxy
formation works
What is the role of dark matter in
galaxy formation?

Gravity of dark matter is what caused protogalactic clouds
to contract early in time
WIMPs
can’t
contract to
center
because
they don’t
radiate away
their orbital
energy
Dark matter is
still pulling
things together
After correcting
for Hubble’s
Law, we can see
that galaxies are
flowing toward
the densest
regions of space
What are the largest structures in
the universe?
Maps of galaxy positions reveal extremely large structures
nearby: superclusters and voids; and a near uniform
distribution on the larger scale.
Time in billions of years
0.5
2.2
5.9
8.6
13.7
13
35
70
93
140
Size of expanding box in millions of lt-yrs
Models show that gravity of dark matter pulls mass into
denser regions – universe grows lumpier with time
Structures in galaxy maps look very similar to the ones
found in models in which dark matter is WIMPs
Will the universe continue
expanding forever?
Two Options
• The density of the universe is large enough
that gravity will cause the universe to
collapse back on itself.
• The universe will expand forever.
• Normal matter only contributes about 0.5%
of the matter density needed to cause the
universe to collapse
Fate of
universe
depends
on the
amount
of dark
matter
Lots of
dark matter
Critical
density of
matter
Not enough
dark matter
Amount of dark matter
is ~25% of the critical
density suggesting fate
is eternal expansion
Not enough
dark matter
But expansion
appears to be
speeding up!
Dark
Energy?
Not enough
dark matter
Brightness of distant white-dwarf supernovae tells us how
much universe has expanded since they exploded
An accelerating universe best fits the supernova data, and
puts the age of the universe just under 14 billion years old.