ANSWERS for EXAM 1:
1. Photometric technique, Light Curve technique, transit technique
2. The kuiper belt is just outside the orbit of neptune
3. Direct imaging technique
4. Higgs particle
5. Just proper motion
6. Gravitational drag from the disk, planet-planet encounter,
planet-star encounter. Our solar system doesn't have a disk, but
planet-planet encounters and planet-star encounters (if one happens to
go through our solar system) may certainly cause this to happen.
7. Jupiter's orbital period is many years (~10) and to
confirm an exoplanet discovery we generally wish to see multiple
orbital periods. Thus, it inherently takes a large amount of time to
find exoplanets with large periods (large semi-major axis).
8. Minimum mass. Due to the effect of inclination, we don't
measure the true velocity of the star, just one component of it. This
is always smaller or equal to the true velocity, so we always measure
the minimum mass.
9. They will most likely stick together and fall into the star.
10. Run out of disk. Orbital resonances. Magnetic fields.
11. To measure a proper motion, we need to take an image of
the object over time, and then see how it moves. To measure radial
velocity we need to take a spectrum of the object and measure the
doppler shift.
12. gravity, electromagnetic, weak force, and strong force
13. Core accretion theory says that small pieces of the disk
start sticking together, forming a core, which then furthermore
accretes from the disk. In the disk instability model, one region of
the disk starts to collapse and directly forms a planet with almost no
further accretion.
14. Planet A has a surface gravity that is 8 times larger
than Planet B.
15. When a gas cloud collapses, it will spin faster due to
conservation of angular momentum. Also, because it is gas, the
material collides with itself easily. These collisions tend to make
the particles end up in a similar configuration, either by constant
collisions to make all particles get in line or by sending some
particles into the center. Thus, the final configuration is a disk,
where there are no more collisions.
16. Jovian planets are made from mainly hydrogen and
helium. Hydrogen and helium can not condense close to a star because
they are too light. They must form further from the star where the
temperture is lower. Once a planet can accrete H and He, it can grow
very large since there is so much of that material.
17. The first is that Kepler detects an eclipse. This tells
us that the system is edge-on. Second, Kepler measures the period,
which tells us the distance the planet is from the star. Third, Kepler
measure the shape of the eclipse (depth and length) which tells us the
radius of the planet.
18. First, if a mini black hole is made in the LHC, it will
evaporate on very short timescales due to Hawking radiation. Thus, it
will not be able to grow. Second, a black hole made in the LHC will
likely be traveling so fast that it will escape from the Earth very
quickly. Third, there have been much more energetic collisions in the
Earth's atmosphere since the beginning, and the Earth still exists!
So, we are safe.
19. Heisenberg Uncertainty Principle states that in a short
amount of time (small uncertainty), the uncertainty on the energy
increase. Thus, you might be able to have huge energy fluctuations in
small time intervals. Since energy is equated with mass, then the
energy fluctuations can lead to mass fluctuations. This then causes
the creation of a pair of particles (they come in 2 since you have to
conserve charge and spin). This is what we call virtual particles.
ANSWERS for EXAM 2:
1) event horizon; infinite density
2) proper motion of stars
3) The effects of gravity are the same as the effects of acceleration
4) 3 km
5) WIMPS, most likely a neutralino
6) If you are weightless, or feel no accelerations
7) 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).
8) Heisenberg Uncertainty Principle states that in a short
amount of time (small uncertainty), the uncertainty on the energy
increase. Thus, you might be able to have huge energy fluctuations in
small time intervals. Since energy is equated with mass, then the
energy fluctuations can lead to mass fluctuations.
9) Seeing rapid variations in brightness implies that the object has to be
smaller than the light travel time across it. If the object were larger,
then the light from one side would get blended with the light from the
other side, and we wouldn't see variations. For quasars, the variations are
short (weeks), which means the actual size is small.
10) 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.
11) Quasars, which are actively feeding black holes, peaked in the universe
before the time when star formation peaked. We also see quasars as some of
the earliest objects in the universe, when galaxies did not have time to
form yet. Thus, there is some evidence that black holes came first.
12) When two dark matter particles collide, they annihilate each other
(since they are their own anti-particle). When they annihilate they form a
gamma-ray photon. Thus, a telescope that can see X-rays or gamma-rays could
see this increased signature coming from where dark matter particles
exist in large numbers (the middle of a galaxy, for example).
13) The WIMP miracle is the agreement between a theoretical
calculation and an observational constraint, which originally were not
related. The physicist calculate a mass and density of a particle
thought to be responsible for the electroweak force (a
WIMP). Astronomers calculate a density for the amount of dark
matter. The densities in both are remarkably similar.
14) When a galaxy first comes together, the baryons and dark matter are
distributed about the same. But then the baryons can easily interact
with each other - this interaction is through collisions which tends to
make them lose some of the their velocity and fall into the center.
Thus, the baryons are more centrally concentrated.
15) One way to detect a dark matter particle in the lab is through
recoil. A dark matter particle hits a nucleus of an atom; that direct
hit causes the nucleus to move a little, and a sensitive experiment
can detect this recoil.
16) The Bullet Cluster shows that the baryons (the gas) are not where most
of the mass in the cluster exists. Thus, there is no modification to the
laws of gravity that one can use to explain the situation. Since the dark
matter particle is non interacting it will fly right through itself when
the clusters collide. Thus, the particle nature is the best explanation.
17) At one lab (the LHC at CERN) neutrinos are generated in a collider
experiment. These neutrinos travel to another lab (in Italy), where
they are detected. With an accurate distance and an accurate timing
measure, one can then measure the speed at which they travel. The
result shows that they traveled slightly faster than the speed of
light. It could be wrong because they may not have measured the
distance accurately enough (they use the GPS system), or possibly the
time difference accurately.
18) 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.
19) When measuring the rotation of stars at the edge of a galaxy, they are
moving much faster than expected. One can take the amount of light that you
see and using Newton's Law calculate how fast the stars should be moving.
Since they are moving faster, there must be extra mass. This is the dark
matter.
ANSWERS for EXAM 3:
1) CMB and BBNS
2) dark energy about 72%, dark matter 24%, normal matter 4%
3) as the Universe evolves through time, it expands, and the expansion
causes it to cool
4) stars have yet to form, so there was no light
5) lights, my laser pointer, others?
6) inflation, elemental abundance, CMB released, first stars, mayo
7) 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.
Inflation solves this by making the universe a lot smaller in the
past, so these sides could have come into equilibrium.
8) The mutual gravitational attraction of the Milky Way and the
Andromeda galaxies was strong enough to overcome the expansion of
space.
9) matter had a stronger effect on the expansion rate earlier in the
Universe. The universe was smaller then, so objects were closer
together, so the gravity from the matter was stronger. Space was
smaller, so the effect of dark energy was less.
10) We know the total density is 1 from CMB observations. Normal
matter is 0.04 from BBNS. Dark energy is 0.73 from SN. If we subtract
these, then the stuff left is dark matter, which has to be
non-baryonic (since normal matter is accounted for).
11) 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 - that is why we can see them.
12) Nothing in the Big Bang model. In the multiverse model, it was an
infinite bubbling of quantum fluctuations in spacetime. In brane
cosmology, it was two branes on a collision course that gave rise to
our Universe.
13) Higgs boson; why we have more particles than anti-particles; Hawking
radiation; supersymmetric particle.
14) We look at the size of the hot and cold spots in the CMB. These
features are the structure seen in the Universe, and reflect the
amount of mass and expansion. They turn out to be the size that
suggest our universe is flat.
15) Before the CMB release, the photons had enough energy to knock
electrons from protons. The photons would then interact with the free
electrons. They were trapped and could not escape. As the universe
cooled (from expansion), the photons did not have enough energy to
knock of the electrons and all electrons found protons. The photons
were then free to travel.
16) 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 frooze into
bumps in the matter distribution (and hence CMB). This is the
structure.
17) Potential dark energy models include: 1) cosmological constant
which is the energy of empty space. If space has energy, it can then
push the objects apart. 2) modification of gravity. It is possible
that on large scales gravity becomes repulsive. 3) quintessence. This
would be a new field (or force) in the universe that would then be
mediated by a new type of particle. 4) hubble bubble. We line in an
underdense region of the whole universe and objects then stream away
from the center of the bubble. 5) brane cosmology. We would be in the
middle of two branes, and objects stream towards the outside.
18) It is a blunder since Einstein missed the opportunity to discover
that the Universe is expanding. He basically missed that his model of
the cosmological constant placed the universe in an unstable
configuration.
19) 0th is a point; 1st is a line; 2nd is a plane; 3rd is a cube; 4th
is a timeline; 5th is all possible timelines; 6th is connecting all
those timelines in a hyperplane; 7th is all possible timelines and
endings for our universe; 8th is including other universes with
different initial conditions; 9th is connecting all those different
universes; 10th is all possible timelines in all possible universes.