ANSWERS to EXAM 1:
1) gamma rays
2) the light travel time from the Sun, about 8 minutes
3) gravity
4) The effects of gravity are the same as acceleration
5) the race car driver, until they crash...
6) When two particles collide or when a high energy photons interacts
with an atom, that process can excite an electron to a higher orbit in
the atom. A short time later, that electron falls back down into a
ground state. When it falls back down it releases a photon.
7) mass and motion
8) a central singularity, a spherical shell of material just outside
the event horizon, or a new state of matter within the event horizon
9) Due to its limited size LIGO cannot measure black holes that are
too much more massive than these. The problem is that with a very long
gravity wavelength, LIGO would only see a small fraction of it and
hence not be sensitive. For smaller black holes, they are definitely
in the LIGO data stream, but these first mergers were large enough
that they had a huge signal compared to the smaller ones.
10) When a system (like a galaxy) forms stars, it will form stars over
a variety of masses, small mass to high mass. The high mass stars burn
their fuel much quicker, which causes them to both be very bright and
live a short amount of time. Also, more massive stars produce more
blue light since they have more energetic collisions between
particles. Thus, when a system has recent star formation, i.e. young,
it appears blue, and then eventually fades to red as it gets old.
11) gravity waves travel at the speed of light, so there is no more
action at a distance.
12) Pulsars detect gravity waves by having us observe their orbit
getting smaller. We infer this is happening due to them creating
gravity waves. LIGO absorbs some of the energy from the gravity wave
and thus provides a direct measure of the wave. Therefore, LIGO is a
direct measure and considered a clear confirmation.
13) We think GR breaks down since inside of a black hole, the
calculations show that all mass goes into a central point of infinite
density. Infinite density implies zero radius, and having an object
with a radius of zero makes no sense.
14) Why is a LIGO detector in the shape of an L, and why are
there two LIGO detectors?
15) Photons are more easily reflected if the particle size if closer
to their wavelength. The sky is blue since particles in the air
scatters blue light more than red light. This happens over the whole
sky. At sunset, the sunlight is passing through a lot of atmosphere
into our eyes in a direct path; most of the light is scattered out of
that path except for the red light. We cannot see into the middle of
the Milky Way since dust in the galaxy scatters most of the light away
from our sightline.
16) Consider an object orbiting another object (e.g. a spaceship
orbiting the Earth). That object feels weightlessness. Equivalence
Principle then implies that there are no accelerations. Therefore, it
is moving with constant velocity, and therefore traveling in a
straight line. Thus, the orbit is a straight line, which implies
spacetime is curved.
17) The two observations that Einstein used are the precession of
Mercury and the bending of starlight by the Sun. For Mercury, the
elliptical orbit would take it closer and then further away from the
Sun. As it got closer, spacetime was curved more, and it would appear
to travel a little further than if it were not curved. This additional
movement causes it to precess. For the Sun, it was predicted that a
star behind the Sun would appear in a different place than if the Sun
were not in the path, since the Sun warps spacetime. This star
movement was measured during an eclipse of the Sun, since you cannot
see the stars when the Sun is up.
18) We first take a spectrum of an object which divides the light up
into the constituent wavelengths (like a prism). Then there are
characteristic wavelengths from each object, mainly since they are made
up of similar elements (e.g. hydrogen). By measuring the position of
these observed wavelengths, we can compare to the wavelengths at rest
and determine how much they have been doppler shifted.
19) Comparing to light paths: in a stationary frame the light path is
shorter than in the moving frame. If speed of light is a constant in
any frame, then, since distance = c x time, time in the moving frame
much be larger, implying the clock must be running slower.
20) For the graph, the axis are time on the horizontal and distance
(relative, or strain) on the vertical. The curve is a low-amplitude
sinusoid starting out, but then increases in amplitude and
frequency. It then suddenly goes down to a low amplitude and
eventually goes to flat-line. If two stars of the same mass as the BHs
came together, LIGO would not see much at all. It would start out the
same as the BHs, but since the stars are so large, they would merge
before they got to the point of increasing the amplitude or decreasing
the period.
ANSWERS to EXAM 2:
1) gravity (or the mutual gravitational attraction of the matter in
the universe)
2) gravity
3) gravity
4) Heisenberg Uncertainty Principle
5) dark energy and the anthropic principle
6) The speed stays the same; the wavelength gets bluer.
7) mass
8) two BHs to LIGO; inner edge to X-ray; young stars to color;
distance to spectrum; MW black hole to adaptive optics; fusion rate to
neutrino telescope
9) The particle detectors are built underground (or in a
mountain). The idea is to use the Earth as a shield for the background
of fast-moving particle that get into the detector. The earth's
atmosphere is producing showers of particles due to events in the
upper atmosphere. The particles from these showers get into detectors
on the earth surface.
10) From X-ray observations, we find black holes not at the center of
a galaxy, so they might be many of them at large radii. Also, the
masses we find, including the two measurements from gravitational
waves, is consistent with expectations for having many black holes at
large radii in a galaxy. This unseen mass could then account for the
dark matter.
11) In isolation the material in a galaxy is more or less in a stable
orbit, so it doesn't interact with anything and maintains its
radius. As galaxies merge, the material interacts, losses velocity and
falls towards the center.
12)
13) Ways to increase the amount of structure include: making the dark
matter colder, making the universe older, decreasing the amount of
dark energy, increasing the strength of gravity, having dark matter
interact.
14) The black holes that are the engines for the quasars did not go
anywhere. They just stopped accreting. One reason for why they do not
exist locally is because they used up all of their fuel (or expelled
it from the galaxy).
15) head-on collision between a dark matter particle and a normal
particle
16) The Weakly-Interacting part is due to the need to keep dark matter
dominate at large radii in a galaxy; otherwise it would fall in by
interacting with itself and losing velocity. The Massive part is
because we need dark matter to be cold, which implies moving at a slow
velocity. Otherwise it becomes hard to form structure and galaxies
would not exist. The Particle part is based primarily on theoretical
models that try to match how the universe appears to what happens in
the models. Also, the Bullet Cluster provide additional need for dark
matter being a particle.
17) DAMA sees a yearly modulation in their recoil rate of the nuclei in
their experiment. They attribute this modulation since the orbit of the
Earth sometimes is moving against the dark matter flow (and hence has
increased rate) and sometimes going with it (giving a lower rate of
interaction).
18) The first step involves the cloud starting to collapse due to
gravity. As it is getting smaller, the 2nd step involves the cloud
spinning up due to conservations of angular momentum. For the 3rd
step, if there are strong particle interactions and collisions, the
system will flatten into a disk.
To not make a disk, you could modify it by not having spin, not having
gas, or making stars from the gas as it collapses. You could also make
the cloud out of dark matter and then it would not interact and form a
disk.
19) From the strength of the lensing, measured by the size of the
arcs, we can estimate the total mass in the cluster. We then measure
the amount of light in all of the galaxies and convert that light to
mass we can see. We then compare the total mass to the mass in
galaxies, and we find that we are missing mass which is the dark
matter.
20) If the particle is too low mass, then it would be hot and hard to
clump together to form galaxies. If the particle to too massive, it
will form structure that is too large and may even cause the universe
to collapse back in on itself. If the interaction rate is too large,
then it will fall into the centers of galaxies like normal matter, and
we would not have a preference for dark matter being at large radii as
seen in rotation curves. If the interaction rate is too low, we just
would not be able to detect the particle, but there are no obvious
consequences from the astronomy side. For the graph, the exclusion
zone is above the line.
ANSWERS to EXAM 3:
1) CMB
2) it decreases
3) distance and velocity
4) fainter
5) if it didn't end, then structure would not have formed and we would
not be here
6) gravity has more of an influence in this case than dark energy
7) V=H0xD: V is velocity and we measure that by taking a spectrum with
a spectrograph and getting the redshift. D is distance, which we get
from seeing how bright something is (taking an image) and knowing how
bright it is supposed to be through a calibration. H0 comes from
plotting V and D against each other and seeing what the relationship
is.
8) The horizon problem is that opposite sides of the universe are
effectively at the same temperature, yet they are separated by too
large a distance for information to have traveled between them given
the speed of light. Inflation solves this having the universe undergo
an accelerated expansion (faster than the speed of light) thereby
making the universe a lot smaller in the past, so these sides could
have come into equilibrium.
9) We do not have a physical explanation for the values of the
constants in our universe. However, their values are perfectly tuned
for our existence, and any small deviations would have us not
exist. The way to accommodate this fine tuning is to have an infinite
number of possibilites, i.e. the multiverse, and we can only live in
the one that is perfect for us.
10) The observations are measuring the relative amount of the elements
in the early universe, which include studying stars that are very old
(thus, pristine material). The theory comes from using our
understanding of nuclear reactions at very high temperature and high
densities that can produce those abundances. The theory relies on the
density of normal matter. Thus, the relative abundances then imply 4%
normal matter according to theory.
11) Since 7 Byr is about half the age, the wavelength would be
approximately half as large (more energy). Thus, around 0.5cm.
12) Uncertainty in energy (or position) times uncertainty in time (or
momentum) is larger than a constant.
13) From the CMB we measure the average spot size of the clumps. This
spot size gives us the circumference. We then compare that
circumference to 2*pi*R.
14) c, a, f, e, d, b
15) cosmological constant (or energy of empty space), a new particle,
or misunderstanding of gravity, or a pull from other Hubble Volumes,
or oscillating universe.
16) There are some objects we see now that are moving away from us at
faster than the speed of light. The reason for this is that we are
seeing those objects a long time ago (due to finite speed of light)
when the universe was a lot smaller and was not expanding away from us
faster than the speed of light at that time.
17) Given the considered size of the universe at that time, Einstein
thought it should have collapsed due to gravity. Since that didn't
happen, he included a term that would perfectly balance gravity. It is
a blunder since Einstein missed the opportunity to discover that the
Universe is expanding from theoretical considerations. He basically
missed that his model of the cosmological constant placed the universe
in an unstable configuration.
18) For the Cepheid, we need to measure a velocity and we do that by
getting a spectrum. We then get the distance assuming they are
standard candles. We measure their period by taking images of how the
light varies over time. The period is then related to the intrinsic
brightness. We can then measure how bright they appear to us. With the
intrinsic and observed, we get the distance. Then distance and
velocity give expansion rate.
19) Since our universe is expanding faster than the speed of light,
then light leaving the back of your head could never make it around
the whole universe. If the universe in the future stopped expanding
and began contracting, then the light could make it all the way
around.
20) The Heisenberg Uncertainty Principle leads to fluctuations in
spacetime. These manifest as energy fluctuations which lead to over
and under dense regions. These would normally average out, but during
inflation these regions were greatly separated and got froze into
bumps in the matter distribution (and hence CMB).
21) Nothing in the Big Bang model. In the multiverse model, it was an
infinite bubbling sea of quantum fluctuations in spacetime. In the
cyclic model, it is our universe oscillating forever in size.
22) With cosmic time on the horizontal axis (time=0 on the left) and
expansion rate on the vertical axis, after an initial rapid expansion
due to inflation it would look like a parabola. The minimum is where
the present day would be located. The decrease since time=0 is due to
the effects of gravity slowing down the expansion. The increase beyond
present time is due to dark energy.