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Units to cover: 79, 80, 81, 82, 83, 84
As a star converts most of its hydrogen in its core into
helium, the star gets
a. less luminous and smaller
b. hotter and fainter
c. more luminous and bigger
d. less luminous and red
A hydrogen burning shell is created near the helium core
because
a. helium diffuses into the shell
b. hydrogen diffuses into the core
c. core is hot and dense
d. both a. and b.
If we observe a star cluster which has all the stars
of main sequence present, this cluster is
a. old
b. young
c. was born as a result of supernova explosion
d. both a. and c.
Missing Mass
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In Unit 73, we calculated the mass of
the Milky Way by measuring the orbital
velocities of dwarf galaxies in orbit
around our galaxy
We can also count the number of stars
in the galaxy, and estimate the galactic
mass. The two numbers do not agree!
Rotation curves do not show the
expected decrease in stars’ orbital
velocities with distance from the
galactic center, so there must be much
more mass present in our galaxy
Astronomers cannot find a large
majority of this mass!
Astronomers call the missing mass dark
matter
Many galaxies have flat rotation curves!
Dark matter is not unique to the Milky Way!
Figure 78.03
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99 percent of the stars in a galaxy are
within 20 kpc of the center
Gas extends far out into the disk, but is not
very massive!
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Galaxies are now thought to be embedded
in a dark matter halo that surrounds the
entire galaxy
Unfortunately, dark matter cannot be
detected directly.
Dark Matter in Clusters of Galaxies
• Missing mass is also a problem
in clusters of galaxies!
– Not enough visible mass to hold
the clusters together by
gravitation, and to keep hot gas
in their vicinity
– Cluster mass must be 100 times
greater than the visible mass!
– Once again, dark matter seems
to be the solution
Gravitational Lenses
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Dark matter warps space just like ordinary matter
does
The path of light rays bends in the presence of
mass
A galaxy or other massive object can bend and
distort the light from objects located behind it,
producing multiple images
This is called gravitational lensing
Gravitational lensing of light by clusters of galaxies
A. Indicates the existence of dark matter
B. Proves that the Universe has large positive curvature
C. Proves the expansion of the Universe
D. Indicates the existence of dark energy in the
Universe
An Expanding Universe
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The expansion of the Universe is not like
the explosion of a bomb sending fragments
in all directions
Space itself is expanding!
We can detect photons that appear to have
moved at different speeds through space
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Rather, the speed of light is constant, and it
is space that was moving relative to the
photon
If each galaxy is like a button attached to
a rubber band, an ant walking along the
band as it is stretched will appear to have a
velocity slower than it really does. The
buttons (galaxies) are fixed relative to
space, but space itself is moving.
One More Analogy
• The expansion of the universe and the
increasing distance between galaxies is
similar to the increase in distance
between raisins in a rising loaf of raisin
bread.
• The raisins are fixed relative to the
dough, but the dough expands,
increasing the space between them.
• Problem with these analogies – loaves
and rubber bands have edges!
– We have seen no ‘edge’ to the Universe;
there are an equal number of galaxies in
every direction!
– Also, galaxies can move relative to space,
as sometimes gravity can accelerate one
galaxy toward another faster than space
expands!
The Meaning of Redshift
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As light waves travel through
space, they are stretched by
expansion
This increases the wave’s
wavelength, making it appear
more red!
An objects redshift, z, is
z


Here,  is the change in
wavelength, and  is the original
wavelength of the photon
• This is equivalent to:
z
Change in average distance between galaxies
Average distance between galaxies
The Age of the Universe
• Thanks to the Hubble Law, we can
estimate the age of the universe
• At some point in the distant past,
matter in the universe must have
been densely packed.
• From this point, the universe would
have expanded at some high speed
to become today’s universe
• Assuming a constant expansion
over time, we find that the age of
the universe is around 14 billion
years.
Static Universe and Big Bang
Alexander Friedmann
Fred Hoyle
Died at the age 27
Light from the Big Bang
• Every time we look at the
night sky, we are looking
back in time
• Can we see light from the
Big Bang?
– Almost!
G. Gamow
Alpher, R. A., H. Bethe and G. Gamow. “The
Origin of Chemical Elements,” Physical Review,
73 (1948), 803
A. Penzias and R. Wilson
The Last Scattering Epoch
• Minutes after the Big Bang, the
Universe was opaque
– High temperatures kept all matter
ionized
– Photons could only travel a short
distance before being absorbed
• After 400,000 years, the Universe
cooled enough for electrons and
ions to recombine, allowing light
to pass
• Now the Universe was
transparent!
Light from the Early Universe
• So what should light from 400,000
years after the Big Bang look like?
– It should have a spectrum that
corresponds to the temperature of the
Universe at that time, 3000 K.
– Expansion of space will stretch this
light, however
• The Universe has expanded by a factor
of 1000 since this time, so the
wavelength will have stretched by the
same amount
– Spectrum will correspond to a
temperature of 3K.
• This light from the early Universe has
been found, and is called the Cosmic
Microwave Background
Clumpiness in the CMB
A Timeline of the Universe
The Origin of Helium
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Immediately after the Big
Bang, only protons and
electrons existed
Shortly after the BB,
temperature and density was
high enough for deuterium to
form by fusion
After 100 seconds or so,
temperature cooled enough so
that deuterium could fuse into
helium nuclei
The temperature continued to
cool, and fusion stopped after a
few minutes.
Big Bang theory predicts that
around 24% of the matter in the
early universe was helium,
which matches what we see.
The Epoch of Inflation
• Modern technology allows
us to test theories back to a
time 10-33 seconds after the
Universe Birth (UB).
• Physics as we know it
ceases to function at 10-43
seconds after the UB, called
the Plank Time
• Using particle colliders,
scientists have uncovered a
number of clues about what
happened in the early
universe, after the Plank
time
• The early universe
underwent a period of very
rapid expansion
• By 10-33 seconds, the universe expanded from
the size of a proton to the size of a basketball
• This expansion is called inflation
Expansion Forever? Or Collapse?
• The fate of the universe is ultimately
controlled by its total amount of
energy
– Energy of expansion (positive)
– Gravitational energy that can slow the
expansion (negative)
– Binding energy
• If the total energy is positive or
zero, the expansion continues
forever
• If the total energy is negative, the
expansion will halt, and the
universe will contract and
eventually collapse.
Dark Energy
• Dark energy may provide the solution
to the mystery
• Dark energy remains constant
everywhere, regardless of the
universe’s expansion
• Provides an outward push to accelerate
expansion
• Dark energy must make up
around 70% of all of the
energy in the universe
• Much work remains to be
done on this frontier…