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 smallerb. hotter and fainterc. more luminous and biggerd. less luminous and red

A hydrogen burning shell is created near the helium core because

a. helium diffuses into the shellb. hydrogen diffuses into the corec. core is hot and densed. both a. and b.

If we observe a star cluster which has all the starsof main sequence present, this cluster is

a. oldb. youngc. was born as a result of supernova explosiond. both a. and c.

Missing Mass

• 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

• 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!

• 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

• 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

D. Indicates the existence of dark energy in the Universe

C. Proves the expansion of the Universe

An Expanding Universe

• 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

• 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

• 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

Here, is the change in wavelength, and is the original wavelength of the photon

• This is equivalent to:

=z

galaxiesbetween distance Average

galaxiesbetween distance averagein Change=z

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 FriedmannDied at the age 27Fred Hoyle

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

A. Penzias and R. Wilson

Alpher, R. A., H. Bethe and G. Gamow. “The Origin of Chemical Elements,” Physical

Review, 73 (1948), 803

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

• 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…