Spring 2023 ASTR 3740 Clicker Questions

Spring 2023 ASTR 3740 Homepage

Spring 2023 ASTR 3740 Relativity and Cosmology: Clicker Questions

Fri 2023 Jan 20 (no credit)

How did El-Badry et al. 2022 conclude that a binary system discovered by the Gaia satellite contained a 10 solar mass black hole?
A. X-ray observations revealed an accreting x-ray binary.
B. The orbital elements from Gaia indicated a massive object, but optical observations showed no correspondingly massive star.
C. Optical observations revealed a gravitationally lensed system.
Will you get an A in this class?
A. Yes, I am at least 90% sure of it.
B. I think I have a better than 50% chance.
C. I care more about learning stuff than about my grade.
In this class, I am most interested in learning about:
A. Relativity.
B. Black Holes.
C. Cosmology.
D. Mathematics.
E. All of the above.

Mon 2023 Jan 23:

Why do JWST (James Webb Space Telescope) and HST (Hubble Space Telescope) images look so different?
A. JWST's wavebands are in the infrared (1-20μm) whereas HST's are in the optical (0.2-0.8μm, or 200-800nm)?
B. JWST has higher angular resolution than HST.
C. JWST has a broader field of view than HST.

Does spacetime have an existence independent of objects in it? (No right answer).
A. Yes.
B. No.
C. Something else.

Which of the following is an inertial frame (a frame with respect to which objects move in straight lines in the absence of forces)? (No right answer).
A. The frame of an object in free-fall.
B. The frame of an object at rest in this room.
C. The frame of a person on a roller coaster.
D. The frame of an electron in an atom.
E. All of the above.

Which conservation law is not associated with a symmetry of spacetime?
A. Conservation of energy.
B. Conservation of momentum.
C. Conservation of angular momentum.
D. Conservation of velocity of center of mass.
E. Conservation of electric charge.

Wed 2023 Jan 25:

The north-pointing jet in the radio galaxy Centaurus A appears brighter than the south-pointing jet. The north-pointing jet appears:
A. Blueshifted, brighter, and speeded up.
B. Redshifted, dimmer, and slowed down.

On this spacetime diagram, how fast is Cerulean moving relative to Vermilion, in units of the speed of light?
A. 0.
B. 1/2.
C. 1.
D. 2.
E. The information on the diagram is insufficient to answer the question.

If the postulates of special relativity are correct, would the light have moved differently if Cerulean, not Vermilion, had emitted the light?
A. Yes.
B. No.

Fri 2023 Jan 27:

The multiply-lensed supernova AT2016jka at redshift \(z = 1.95\) was a probable Type 1a (thermonuclear) supernova, whose light curve is powered by the radioactive decay \(^{56}\textrm{Ni} \overset{6~\textrm{day}}{\longrightarrow} {}^{56}\textrm{Co} \overset{111~\textrm{day}}{\longrightarrow} {}^{56}\textrm{Fe}\) with 6 and 111 day half-lives. Should the observed lightcurve of AT2016jka show:
A. Slower decay than 6 and 111 days;
B. A decay rate of 6 and 111 days;
C. Faster decay than 6 and 111 days?

What is the solution to the challenge problem? (How can Vermilion and Cerulean both be at the center of the lightcone?)
A. In special relativity, reality depends on the observer, and it is possible for two logically inconsistent things to occur.
B. Light moves differently depending on who emits it.
C. Clocks run at different rates depending on velocity.
D. Observers moving at different velocities have different notions of simultaneity (“now”).

Two circular hoops of the same size start at rest. Hoop A starts moving at near the speed of light towards hoop B. Which hoop passes inside the other?
A. A.
B. B.
C. Neither.

Spacetime diagram

If Cerulean were moving as shown relative to Vermilion, which line would be a “now line” for Cerulean?
A.
B.
C.
D.
E.

Mon 2023 Jan 30:

What sets the frequency of a gravitational wave “chirp” from a merging pair of black holes/neutron stars?
A. The orbital frequency of the merging pair.
B. The temperature of the merging pair.
C. The distance of the merging pair.
D. Hawking radiation from the merging pair.

a 3D cube

A cube. Are the lengths of its sides all equal?
A. Yes.
B. No.

In the Lorentz transformation movie, what is being varied?
A. The speed \(c\) of light.
B. The position \(x(t)\) as a function of time \(t\) of Cerulean relative to Vermilion.
C. The velocity \(v\) of Cerulean relative to Vermilion.

Wed 2023 Feb 1:

If the aether existed, then the motion of the Earth around the Sun would cause the (classical) difference between light travel times along the two arms of the interferometer to be \((v_\textrm{⊕}/c)^2 \approx 10^{-8}\) (notes 1.18-1.24). Approximately how long would the path length have to be to see a change by one fringe as the apparatus rotated?
A. \(1\) wavelength.
B. \(10^4\) wavelengths.
C. \(10^8\) wavelengths.
D. Something else.

Is the Michelson-Morley apparatus in this room large enough to detect motion of the Earth through the aether?
A. Yes.
B. No.

On your way out to Alpha Cen, you appear to me, watching you through a telescope on Earth, to move at what speed?
A. 0;
B. ½ c;
C. Near c;
D. 2 c;
E. Near infinite speed.

On your way back from Alpha Cen, you appear to me, watching you through a telescope on Earth, to move at what speed?
A. 0;
B. ½ c;
C. Near c;
D. 2 c;
E. Near infinite speed.

If the round-trip time is 8 years from my (Earth) perspective, then the round-trip time from your (traveler's) perspective is:
A. Practically no time.
B. Less than 8 years.
C. 8 years.
D. More than 8 years.

Mon 2023 Feb 6:

Hubble Space Telescope observations of the jet in M87 show blobs emerging at 6c. This suggests that:
A. The jet is moving faster than c.
B. Special Relativity is wrong.
C. The blobs are not parcels of matter, but rather waves of brightness passing along the jet.
D. The jet is pointed almost towards us, and is moving at close to c.
E. The jet is pointed away from us, and is moving at close to c.

Why is a second jet not observed in M87?
A. There is no second jet.
B. Aberration bends the second jet out of view.
C. The second jet is relativistically dimmed out of view.
D. The second jet is relativistically redshifted out of view.
E. The second jet is behind the quasar, which obscures it.

What is a 4-vector in special relativity?
A. Any set \(\{ t , x , y , z \}\) of 4 quantities.
B. A set \(\{ t , x , y , z \}\) of 4 quantities that transform in a certain way under Lorentz transformations.
C. Something else.

How does the rest mass m of a spacecraft change with its velocity v?
A. It increases.
B. It stays the same.
C. It decreases.

Is the energy-momentum \(p^i \equiv E ( 1 , \pmb{n} )\) of a photon a 4-vector?
A. Yes.
B. No.

Wed 2023 Feb 8:

“The Lorentz Transformation, which is considered as constitutive for the Special Relativity Theory, was invented by Voigt in 1887 [who mistakenly thought the transformations applied to all waves, including sound as well as light], adopted by Lorentz in 1904, and baptized by Poincaré in 1906. Einstein probably picked it up from Voigt directly.” — W. Engelhardt. Why does Einstein, not Lorentz, get credit for discovering special relativity?
A. Lorentz derived the equations, but did not attempt to apply them to reality.
B. Lorentz made some mathematical mistakes, which Einstein corrected.
C. Lorentz thought that matter (electrons) contracts as it moves through the aether, whereas Einstein said there is no aether.
D. Nowadays physicists do in fact attribute special relativity to Lorentz, not Einstein.
E. History is unfair.

Fri 2023 Feb 10:

On a spacetime diagram, the worldline of a person must point:
A. vertically upward;
B. at less than 45° from vertical;
C. at 45° from vertical;
D. horizontally;
E. in any direction.

If light is a wave, what is waving?
A. The aether.
B. Spacetime.
C. Empty space.
D. Electric and magnetic fields.

In Problem Set 2 on the twin paradox, your twin watches you on Earth through a telescope. At the moment that the twin accelerates at Alpha, the twin sees your clock:
A. Run at the same slowed-down rate both before and after accelerating.
B. Suddenly change from 2 years to 8 years.
C. Suddenly speed up.
D. Suddenly slow down.
E. Change from running forward to runing backward.

Which would you most like to review (which do you understand least well)?
A. The postulates of special relativity.
B. The paradoxes of special relativity.
C. 4-vectors and Lorentz transformations.
D. Energy-momentum in special relativity.
E. Something else.

Pole-in-the-barn paradox: Will the spaceship fit inside the space station?
A. Yes.
B. No.

Wed 2023 Feb 15:

To observe the most energetic phenomena in the Universe, what spectral band of light would be most promising?
A. Radio.
B. Infrared.
C. Optical.
D. Ultraviolet.
E. X-rays.

The Newtonian gravitational potential satisfies \(\phi = - \frac{G M}{r^2}\) at distance \(r\) from a point or spherical mass \(M\). Why can't that be correct, in special relativity?

Gravity is a \(1/r^2\) force like the electromagnetic force. Why was it not possible to modify gravity to behave like electromagnetism?
A. Like masses attract, whereas like charges repel.
B. A wave of gravity carries energy (and momentum), so must interact with itself, whereas a wave of electromagnetism carries no charge, so does not interact with itself.
C. Electromagnetism is based on a \(U(1)\) symmetry, implying only a single conserved quantity (charge), whereas gravity is associated with all symmetries of spacetime, implying several conserved quantities (energy, momentum, angular momentum...).
D. The many symmetries of gravity imply that it is a more complicated force than electromagnetism.
E. All of the above.

Fri 2023 Feb 17:

The weak Principle of Equivalence states that gravitational mass = inertial mass. Does Newtonian gravity satisfy the weak Principle of Equivalence?
A. Yes.
B. No.

Suppose you watch this scene while falling freely. According to the Principle of Equivalence, what kind of trajectory will the cannonball follow from your perspective (relative to you)?
A. A vertical line.
B. A straight line.
C. A curved (parabolic) line.

Standing on the surface of the Earth, you hold a negative mass object in your hand. According to the Principle of Equivalence, which way does the negative mass object fall when you drop it?
A. Down to the floor.
B. It justs hangs there in mid-air, falling neither down nor up.
C. Up to the ceiling.
D. None of the above.

You are in flat space. You swing a clock on a rope in a circle around you, so that the clock is moving at near the speed of light relative to you. According to Special Relativity, the clock will appear to you to tick:
A. Slow;
B. At the same rate as your own clock;
C. Fast;
D. None of the above.

In the situation of the previous question 40, the object therefore appears to you (according to Special Relativity):
A. Redshifted;
B. Neither redshifted nor blueshifted;
C. Blueshifted.

Mon 2023 Feb 20:

In this situation, according to Special Relativity, does B see the light from A to be redshifted or blueshifted?
A. B sees the light to be redshifted (lower energy) compared to A.
B. B sees the light to have the same energy as A.
C. B sees the light to be blueshifted (higher energy) compared to A.

On this 2-dimensional map, the shortest distance between Boulder (40^oN 105.25^oW) and Dushanbe, Tajikstan (38.5^oN 68.75^oE) over the Earth's surface is:
A. A straight line;
B. A curved line.

The distance squared \(d r^2\) between points separated by vertical distance \(d z\) and angle \(d \phi\) on the surface of a 2D cylinder of radius \(R\) is given by (\(z\), \(\phi\) are called cylindrical coordinates):
A. \(d r^2 = d z^2 + d \phi^2\)
B. \(d r^2 = R^2 ( d z^2 + d \phi^2 )\)
C. \(d r^2 = ( d z + R \, d \phi )^2\)
D. \(d r^2 = d z^2 + R^2 \, d \phi^2\)
E. \(d r^2 = - d z^2 + R^2 \, d \phi^2\)

In the previous question 44, the metric \(g_{ij}\) of the cylindrical spacetime with respect to cylindrical coordinates \(z\), \(\phi\) is:
A. \(\left(\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\right)\)
B. \(\left(\begin{array}{cc} R & 0 \\ 0 & R \end{array}\right)\)
C. \(\left(\begin{array}{cc} R^2 & 0 \\ 0 & R^2 \end{array}\right)\)
D. \(\left(\begin{array}{cc} 1 & 0 \\ 0 & R \end{array}\right)\)
E. \(\left(\begin{array}{cc} 1 & 0 \\ 0 & R^2 \end{array}\right)\)

In general, does the metric have to be symmetric (\(g_{ij} = g_{ji}\))?
A. Yes.
B. No.

In general, does the metric \(g_{ij}\) have to be diagonal (\(g_{ij} \neq 0\) only if \(i = j\))?
A. Yes.
B. No.

Wed 2023 Feb 22:

Will the probe fall into the black hole?
A. Yes.
B. No.

How do you know that a spacetime is globally flat?
A. In free fall, all spacetimes are globally flat.
B. Geodesics are straight lines.
C. Geodesics that are initially parallel remain parallel.
D. The spacetime is embedded in a higher dimensional spacetime.

Can spacetime be curved inside a region where there is no mass (but there may be mass outside the region)?
A. Yes.
B. No.

What aspect of the Schwarzschild metric tells you that the geometry is stationary (independent of Schwarzschild time \(t\))?
A. All metric components \(g_{\mu\nu}\) are independent of time \(t\).
B. The metric is diagonal.
C. The metric is spherical.
D. The spacetime is empty (a vacuum).

The Schwarzschild metric is \[ d s^2 = - ( 1 - r_s/r ) \, dt^2 + {dr^2 \over 1 - r_s/r} + r^2 ( d\theta^2 + \sin^2\!\theta \, d\phi^2 ) \] where \(r_s = 2 G M / c^2\) is the Schwarzschild radius, the horizon radius.

What aspect of this metric tells you that the geometry is spherically symmetric?

Fri 2023 Feb 24:

On this unstable circular orbit, if we accelerate forwards, we will:
A. Fall into the black hole;
B. Remain on the unstable circular orbit;
C. Leave the black hole, going far away from it.

Will the probe fall into the black hole?
A. Yes.
B. No.

Does it make sense to talk about (massive) observers at rest at the horizon, \(r = r_s\), of a Schwarzschild black hole?
A. Yes.
B. No.

Mon 2023 Feb 27:

What is the proper circumference of a circle at radius \(r\) in the Schwarzschild geometry?
A. \(r\).
B. \(\pi r\).
C. \(2\pi r\).
D. The proper circumference depends on the choice of coordinates.

Which of the Schwarzschild coordinates \(t , r , \theta , \phi\), if any, is timelike inside the horizon, \(r < r_s\)?
A. \(t\);
B. \(r\);
C. \(\theta\);
D. \(\phi\);
E. None of the above.

How would you solve for the evolution of the radius \(r ( t )\) as a function of Schwarzschild time \(t\) for radial \((d \theta = d \phi = 0)\) geodesics of light in the Schwarzschild geometry?
A. Set \(d s^2 = 0\) and solve for \(d r / d t\).
B. Since \(d s^2 = 0\) for light, no proper time goes by on a lightwave, so there are no geodesics.
C. Solve Einstein's equations.
D. The geodesic depends on the frequency of the photon.
E. It depends on the choice of coordinates.

In Finkelstein (1958) coordinates, radially infalling light moves at \(45^\circ\) in a spacetime diagram. Is it possible to choose coordinates so that outgoing as well as infalling light moves at \(45^\circ\)?
A. Yes.
B. No.

Wed 2023 Mar 1:

What will happen at the horizon of the Schwarzschild black hole at the moment you free-fall through it?
A. You will freeze at the horizon, your time slowing infinitely.
B. You will be engulfed in blackness.
C. You will be tidally torn apart.
D. You will encounter an infinitely bright light.
E. Nothing special.

You and a friend are falling toward a Schwarzschild black hole at the same time, though at different locations in longitude and latitude. As you both continue to approach the singularity, will you ever meet?
A. Yes.
B. No.

What lies on the other side of the antihorizon (red line)?
A. Nothing.
B. A white hole and another “parallel” universe.
C. The invisible interior of the star that collapsed to a black hole long ago.

Mon 2023 Mar 6:

Vote for your favorite quiz question.

From a safe distance, you watch a spherical, pressureless star collapse to a black hole. What will you see?
A. The star will appear to freeze when at the horizon radius, and never collapse.
B. The star will appear to branch into a wormhole and white hole, before becoming a black hole.
C. The star will appear to collapse to a singularity.

When the mass of a black hole increases, its horizon expands. Does the horizon appear to engulf stuff that previously fell through the horizon?
A. Yes, stuff that previously fell into the black hole disappears.
B. No, stuff that previously fell into the black hole remains frozen at the horizon, appearing to expand with the horizon.

If, as seen by an outside observer, a star collapsing to a black hole appears never to collapse through its horizon, even unto the end of the Universe, does the star ever actually collapse?
A. Yes.
B. No.

If a collapsing star somehow stopped collapsing before falling inside its horizon, would it have a horizon?
A. Yes.
B. No.

Wed 2023 Mar 8:

Which is the most common type of point source detected by the Fermi Gamma-ray Space Telescope (≥ GeV)?
A. Supernova remnant.
B. Pulsar (rotating neutron star).
C. High-mass X-ray binary system (containing a high-mass star accreting on to a white dwarf, neutron star, or black hole).
D. Active Galactic Nucleus.
E. Blazar (type of Active Galactic Nucleus in which the jet from the supermassive black hole is pointed directly at us).

What happens when we reach the inner horizon of a real astronomical black hole?
A. Nothing special.
B. We will be tidally torn apart.
C. The outside Universe will appear redshifted and dimmed to invisibility.
D. The outside Universe will appear exponentially blueshifted, bright, and speeded up.
E. We will enter a wormhole.

Is the singularity of the ideal mathematical solution for a Reissner-Nordström black hole gravitationally attractive or repulsive (what does the river model for RN black holes say)?
A. Attractive.
B. Repulsive.
C. Neither.

Fri 2023 Mar 10:

If nothing can escape from a black hole, how can its gravity escape?
A. Gravity is a curvature of space, and does not need to escape.
B. The gravity does not escape, but the tidal force does escape.
C. Gravity does not escape from a black hole: a person outside the BH experiences the gravity of the matter that long ago collapsed to, or fell into, the BH.
D. Gravity travels faster than light.

Is the ring singularity of the ideal mathematical solution for a Kerr black hole gravitationally attractive or repulsive?
A. Attractive.
B. Repulsive.
C. Neither.

From the point of view of an observer outside the outer horizon of a white hole, is the white hole gravitationally attractive or gravitationally repulsive (what does the river model say)?
A. Attractive.
B. Repulsive.
C. Neither.

Mon 2023 Mar 13:

What does the arrowed blue line in the Penrose diagram of the Schwarzschild geometry represent?
A. A possible worldline of a person (timelike line).
B. A possible worldline of light (lightlike line).
C. A possible “now” line, a line of simultaneity (spacelike line).

The horizon lines in the Penrose diagram are:
A. Timelike.
B. Lightlike.
C. Spacelike.

What will happen if you pass through the X-point at the intersection of ingoing and outgoing horizons, in the exact mathematical solution? Can this happen in a real astronomical black hole?

Wed 2023 Mar 15:

What is the significance of the fact that the neutron stars in the Hulse-Taylor binary are both near 1.4M_☉ (1.4414M_☉ and 1.3867M_☉)?
A. They formed from the collapse of a white dwarf that reached the Chandrasekhar limit of 1.4M_☉.
B. 1.4M_☉ is the maximum mass of a neutron star.
C. Pulsars are rotating neutron stars.
D. At 1.4 solar masses, a neutron star is pulsationally unstable.
E. Neutron stars that massive will form a black hole when they merge.

In the first ever detected merger of two black holes, GW150914, the starting masses of the black hole pair were 29M_☉ and 36M_☉, but the mass of the resulting single black hole was 62M_☉, which is less than the sum 65M_☉ of the original pair. Where did the energy in the missing 3M_☉ go to?
A. A supernova.
B. A jet.
C. Gravitational waves.
D. They disappeared inside the black hole.
E. In general relativity, mass-energy is not conserved.

If a gravitational wave is a wave of spacetime curvature, then doesn't the wave also affect the lengths of rulers (and rates of clocks), so how can LIGO detect gravitational waves?
Hint: what is spacetime curvature?

As GW150914 approached the merger climax, the separation between wave peaks was a bit less than 0.01 seconds. What was the approximate wavelength of the gravitational waves detected?
A. About 10^–3 times the size of a proton nucleus.
B. About the size of a proton nucleus.
C. About the size of an atom.
D. About the wavelength of visible light.
E. About the size of the merging black hole system (about 0.01 lightseconds, or 1000 km).

Why does the detection of a burst of gamma rays 1.8 seconds after the gravitational wave signal in GW170817 imply that the speed of gravitational waves is the speed of light?
A. Because gamma-rays are a kind of gravitational wave.
B. Because general relativity predicts that gravitational waves move at the speed of light.
C. Because the signal travelled the same distance, 130 million lightyears, in the same time.
D. Because extremely energetic particles must move at the speed of light.
E. Actually, the fact that the gamma-ray signal was delayed by 1.8 seconds implies that gravity moves slightly faster than light.

Fri 2023 Mar 17:

A more massive black hole produces Hawking radiation with longer wavelength. Therefore a more massive black hole produces Hawking radiation that is _____ energetic, and therefore has a _____ Hawking temperature.
A. Equally, equal.
B. Less, lower.
C. More, lower.
D. Less, higher.
E. More, higher.

Wien's law is \(\lambda_{\rm peak} T = 3 ~{\rm mm}~{\rm K}\). A 10 solar mass black hole has a Schwarzschild radius of 30 km. Approximately what is the Hawking temperature of a 10 solar mass black hole?
A. \(10^{-7}~{\rm K}\).
B. \(3~{\rm K}\).
C. \(10~{\rm K}\).
D. \(30~{\rm K}\).
E. \(10^{7}~{\rm K}\).

What is the Hawking entropy of the 4 million solar mass black hole at the center of the Milky Way? How does this compare to the entropy in the CMB (the number of photons in the observable Universe)?
A. The entropy of the Milky Way black hole is larger.
B. The entropy of the CMB is larger.
C. The entropies are comparable.
Mathematica notebook hawk.nb

Does an infaller continue to see Hawking radiation when they fall through the horizon?
A. Yes, from the (true, event) horizon.
B. Yes, from the past horizon (the redshifted, dimming surface of the star that collapsed long ago).
C. B, and also from the sky above.
D. No.

What will Hawking radiation look like (a) at the horizon, (b) near the singularity? Will the temperature (the characteristic frequency of Hawking radiation) be:
A. About zero.
B. Similar to the Hawking temperature seen from outside.
C. Somewhat higher than the Hawking temperature seen from outside.
D. Huge.

Mon 2023 Mar 20:

The tidal force at radius \(r\) outside a spherical mass \(M\) (e.g. a black hole) goes as \(G M / r^3\). What kind of black hole can you fall into without being torn apart at or outside its horizon?
A. A stellar-massed black hole (3 to 100 solar masses);
B. A supermassive black hole (\(\geq 10^6\) solar masses);
C. All black holes tear you apart at their horizons.
What is the density of a black hole that tears you apart at its horizon? What is its mass?
Mathematica notebook tide.nb

What is the source of energy that heats up the accretion disk in an x-ray binary to the point that it emits x-rays?
A. Chemical energy.
B. Nuclear fission.
C. Nuclear fusion.
D. Gravity (gravitational binding energy).
E. Friction.

What do astronomers take as the most convincing evidence that Cygnus-X1 contains a black hole?
A. It emits x-rays.
B. It produces a relativistic jet.
C. It contains more than 3 solar masses in a region smaller than a white dwarf star.
D. It gravitationally lenses the region around it.
E. It shows gravitational redshifting.

Approximately how many stellar-mass (3-100 solar masses) black holes are there in our Galaxy?
A. \(10^2\).
B. \(10^4\).
C. \(10^6\).
D. \(10^8\).
E. \(10^{10}\).
STSci

In a gravitational wave, what is waving?
A. The aether.
B. Spacetime.
C. Empty space.
D. Tidal forces.

Not the right answer.

The inflationary instability at the inner horizon of a rotating black hole causes an exponentially huge growth in the density and interior mass of the black hole. Should the inflationary instability have any effect observable to an outside observer?
A. Yes, the mass and gravity of the black hole should appear to increase.
B. Yes, the inflationary instability would generate gravitational waves which the black hole would radiate away.
C. Yes, the inflationary instability would be able to drive jets emerging from the black hole.
D. Only if the instability creates a baby universe, in which case the baby universe would engulf our Universe.
E. No.

Mon 2023 Apr 3:

What are the units (time, length, mass) of the Hubble constant \(H_0\)?
A. Velocity.
B. Distance.
C. Time.
D. 1/Time.
What fundamental property of the Universe does \(H_0\) measure?
Why might the measurement of that property not be exact?

What is the largest region around us that has turned around from the Hubble expansion, and is not expanding?
A. The Solar System.
B. The Milky Way.
C. The Local Group of galaxies.
D. The Local Supercluster of galaxies.
E. The observable Universe.

Does the Universe have a center?
A. Yes (why?).
B. No (why?).

Wed 2023 Apr 5:

Why was it necessary to use a satellite (COBE) to obtain a clear view of the Cosmic Microwave Background?
A. Because the CMB comes from so far away.
B. Because astronomers observing from the ground would be cooked by microwaves.
C. Because water vapor in the atmosphere absorbs microwaves.
D. Because of interference from TV and other microwave communications.
E. Because scientists are in cahoots with NASA to fly big expensive missions.

Does galaxy clustering show a characteristic scale?
A. Yes.
B. No.

Fri 2023 Apr 7:

The announcement in 1998 of what remarkable observation ushered in the Standard ΛCDM Model of Cosmology?
A. The Universe is expanding.
B. The Universe is accelerating.
C. The Universe contains Dark Matter.
D. The detection of microwaves from the early Universe.
E. The Universe has a flat spatial geometry.

Galaxy clustering shows a characteristic scale of about 6,000 km/s, or equivalently 0.02c, or 100 Mpc, about a supercluster scale. What scale, in degrees, does that correspond to on the Cosmic Microwave Background (Kardashev)?
A. 0.01°.
B. 1°.
C. 30°
D. 180°

What does thermodynamic equilibrium mean? (Answer: A state of equilibrium in which there are no macroscopic flows of energy, momentum, number, or other conserved quantities.) What thing in the room you are sitting in is closest to thermodynamic equilibrium?
A. Your brain.
B. Your body.
C. The window.
D. The air conditioning.
E. The air.

The CMB was released at Recombination, when the temperature fell through 3000 Kelvin, at which point H in the Universe went from being ionized and opaque to neutral and transparent. The temperature of the CMB today is 3 Kelvin. By how much has the Universe expanded since Recombination?
A. \(10^2\).
B. \(10^3\).
C. \(10^4\).
D. \(10^6\).
E. \(10^{12}\).

Mon 2023 Apr 10

What set the characteristic scale (spatial length) of fluctuations in the CMB?
A. Quantum fluctuations at the Big Bang.
B. The horizon size (about 400,000 lyr) at recombination.
C. The scale of Local Groups of galaxies, about 1 Mpc.
D. The scale of galaxy superclusters, about 100 Mpc.

How can the uniformity of the temperature of the Cosmic Microwave Background (CMB) (to few \(10^{-5}\)) be construed as evidence for homogeneity and isotropy given that the CMB provides information only over a 2D surface on the sky?
A. If our Galaxy is typical, then observers everywhere in our Universe should see a uniform CMB.
B. The blackbody spectrum of the CMB implies that the Universe was simple and uniform.
C. Actually, it is the 3D distribution of galaxies that provides the strongest evidence.
D. The CMB cannot be construed as evidence for homogeneity and isotropy.

What is the length of the geodesic radius \(r_\parallel\) in terms of the radius \(R\) of the hypersphere, and the angle \(\chi\)?
A. \(R\).
B. \(\chi\).
C. \(R \chi\).
D. \(R \sin\chi\).
E. \(2\pi R\).

What is the length of the circumferential radius \(r\) in terms of the radius \(R\) of the hypersphere, and the angle \(\chi\)?
A. \(R\).
B. \(\chi\).
C. \(R \chi\).
D. \(R \sin\chi\).
E. \(2\pi R\).

Wed 2023 Apr 12

Where is the observer in this embedding diagram of the FLRW geometry?
A. At the center of the sphere.
B. At the north pole of the sphere.
C. At the end of the \(r_\parallel = R \chi\) line.
D. Anywhere on the surface of the sphere.
E. There is no observer in this diagram.

Why do astronomers use the cosmic scale factor \(a(t)\) rather than the radius \(R(t)\) of the Universe as a measure of the size of the Universe?
A. The radius \(R\) is defined only for a closed Universe.
B. Relative scales can be measured without knowing an absolute scale.
C. The Einstein equations determine the evolution only of \(a\), not \(R\).
D. Something else.

Does the critical density \(\rho_c\) defined by \(H^2 = \tfrac{8}{3} \pi G \rho_c\) vary with cosmic time \(t\)?
A. Yes.
B. No.

If the curvature constant is positive, \(\kappa > 0\) (closed geometry), is the density \(\Omega\) of the Universe:
A. \(= 0\);
B. \(> 0\) but \(< 1\);
C. \(= 1\);
D. \(> 1\);
E. Could be any of the above.

Fri 2023 Apr 14

If wavelengths expand with the Universe, \(\lambda \propto a\), how does the temperature \(T\) of the CMB change with scale factor \(a\)?
A. \(T \propto a\).
B. \(T \propto a^{-1}\).
C. \(T \propto a^{-2}\).
D. \(T \propto a^{-3}\).
E. \(T \propto a^{-4}\).

Observations indicate \(\Omega_{\rm m} \approx 0.3\) and \(\Omega_{\rm rad} = \Omega_\gamma + \Omega_\nu \approx 10^{-4}\) (note that \(\Omega_\nu / \Omega_\gamma = \tfrac{7}{8} \times \tfrac{4}{11} \times 3 = 0.95\) for relativistic neutrinos). At approximately what redshift \(1 + z\) did the Universe change from radiation-dominated to matter-dominated?
A. 3.
B. 30.
C. 300.
D. 3000.
E. It was never radiation-dominated.

Energy conservation in an FLRW universe implies \(\rho \propto a^{-n}\) with \(n = 3 ( 1 + p / \rho )\). What type of energy-momentum remains constant as the Universe expands?
A. Radiation (\(p / \rho = 1/3\), \(n = 4\)).
B. Matter (\(p / \rho = 0\), \(n = 3\)).
C. Curvature (\(p / \rho = -1/3\), \(n = 2\)).
D. Vacuum (\(p / \rho = -1\), \(n = 0\)).

According to the 2nd Friedmann equation \(\ddot{a} / a = \frac{4}{3} \pi G ( \rho + 3 p )\), what type of energy-momentum is at the borderline between attraction and repulsion?
A. Radiation (\(p / \rho = 1/3\)).
B. Matter (\(p / \rho = 0\)).
C. Curvature (\(p / \rho = -1/3\)).
D. Vacuum (\(p / \rho = -1\)).

Mon 2023 Apr 17:

In cosmology, the redshift \(z\) is related to cosmic scale factor \(a\) by \(1 + z \equiv \lambda_{\rm obs} / \lambda_{\rm emit} = a_0 / a\). The CMB was released at Recombination, when H transition from ionized (opaque) to neutral (transparent) at \(T \approx 3{,}000 ~{\rm K}\). The temperature of the CMB today is \(T \approx 3~{\rm K}\). At approximately what redshift did Recombination occur?
A. \(10^{-3}\).
B. 1.
C. 1000.
D. \(10^{12}\).
E. It depends on cosmological parameters such as \(\Omega_{\rm m}\) and \(\Omega_\Lambda\).

Why does the temperature 3,000 K at Recombination differ from the temperature 6,000 K of the Sun's photosphere?
A. The temperature at Recombination is redshifted compared to the Sun.
B. The Sun's photosphere is much denser than the density at Recombination.
C. The Sun is much hotter beneath its photosphere.
D. Whereas the Universe at Recombination was almost free of heavy elements, the Sun is 2% heavy elements (by mass), which absorb light at lower energies.

The horizon problem is: How can parts of the CMB more than about 1° apart have almost the same temperature? Why is this a problem?
Normally (that is, except during inflation when the Universe was dominated by vacuum energy), the Hubble parameter \(H\) given by \(H^2 = \frac{8}{3}\pi G \rho\) evolved with cosmic time \(t\) as:
A. \(H \propto t^{-2}\).
B. \(H \propto t^{-1}\).
C. \(H\) was constant.
D. \(H \propto t\).
E. \(H \propto t^2\).

Wed 2023 Apr 19:

Low-\(\ell\) harmonic peaks in the CMB power spectrum are spaced further apart than higher-\(\ell\) harmonics. Why?
A. Because lower harmonics are at larger scales where the curvature of the Universe is more apparent.
B. Because dark energy causes more acceleration at larger scales.
C. Because lower harmonics exited the horizon later, when the Universe was more matter-dominated, so the sound speed was lower.

During inflation when the Universe is dominated by vacuum energy, the Hubble parameter \(H\) given by \(H^2 = \frac{8}{3}\pi G \rho\) evolved as:
A. \(H \propto t^{-1}\).
B. \(H\) was constant.
C. \(H \propto a^{-1}\).

The expansion problem is: Why is the Universe expanding? Why is this a problem?

The flatness problem is: How come the Universe is so spatially flat? Why is this a problem?

Wed 2023 Apr 26:

The theoretically expected characteristic angular scale of fluctuations in the CMB depends mainly on the curvature \(\Omega_{\rm k}\). Does the scale also depend on the individual cosmological parameters \(\Omega_{\rm m}\) and \(\Omega_\Lambda\) at fixed curvature?
A. Yes.
B. No.

The dark matter deduced from its gravitational effects in galaxies and galaxy clusters could be:
A. Planets, black holes, primordial (mini) black holes;
B. Non-baryonic dark matter;
C. Neutrinos;
D. A or B;
E. Any of the above.

If the ratio of numbers of neutrons to protons is \(n/p = 1/7\) when weak interactions freeze out (10¹⁰Kelvin, 1 second), what is the helium fraction ⁴He/(H+⁴He) by mass?
A. 1/7 (14%).
B. 1/5 (20%).
C. 1/4 (25%).
D. 1/3 (33%).
E. 1/2 (50%).

Fri 2023 Apr 28:

The final will be mostly short answer questions, but there will be two longer essays on any of a range of topics. What essay question(s) would you like to see on the final? I encourage you to email me before Monday's in-class Review Session.
One of the short answer questions will be:
Write about one thing you were surprised to learn, and one thing you are still confused about.

Temperature is a measure of the mean energy per particle of a system in thermodynamic equilibrium. It is associated with the law of conservation of energy that follows from time translation symmetry of the laws of physics. When can an object be described by a temperature?
A. When all particles have the same energy.
B. When it is in thermodynamic equilibrium.
C. When energy is conserved.
D. When the laws of physics satisfy time translation symmetry.

Rocket fired from Earth

You fire a rocket from Earth. Which rocket wins the orbital race (which rocket returns first to the starting point)?
A. The rocket that stays on Earth.
B. The rocket that fires forwards.
C. The rocket that fires outwards.
D. The rocket that fires backwards.
E. The rocket that fires inwards.

Which of the following is not driven by gravity power?
A. Interstellar gas cools, contracts, heats up, forming protostars.
B. A protostar cools, contracts, heats up to the point that it ignites nuclear fusion.
C. A star burns by nuclear fusion.
D. The Fe core of an evolved massive star collapses to a neutron star or black hole, driving a supernova explosion.
E. An accretion disk around a stellar-sized or supermassive black hole heats to x-ray emitting temperatures as it spirals inward.

Mon 2023 May 1:

What essay question(s) would you like to see on the final?
What would you like to cover in the review today?

What is the best astronomical evidence for non-baryonic dark matter?
A. Laboratory detection of dark matter.
B. Galaxy rotation curves.
C. The Bullet cluster.
D. Dark matter in clusters of galaxies deduced from gravitational lensing.
E. The CMB power spectrum requires non-baryonic cold dark matter.

The Universe just prior to Recombination at \(1 + z \approx 1000\) and 400,000 years old is best described as:
A. A Big Bang.
B. Dominated by a dense, gravitationally repulsive, GUT-scale vacuum energy.
C. A dark, transparent void, dominated by non-baryonic cold dark matter.
D. An opaque, ionized, photon-baryon fluid close to thermodynamic equilibrium, with sound speed about \(c / \sqrt{3}\).
E. Stars were forming vigorously, and galaxies were beginning to cluster.

Friedmann's equations are Einstein's equations applied to the FLRW metric. Friedmann's equations show that that the Universe can have a closed or flat or open geometry, and it can be decelerating or coasting or accelerating. Is there a relation between the Universe's geometry and whether it is decelerating or accelerating?
A. A universe is closed if it is decelerating, open if accelerating.
B. A universe can be either closed or open and at the same time either decelerating or accelerating.

Wed 2023 May 3:

Would you vote in favor of making a baby Universe?
A. I think that it is immoral to attempt to make a baby Universe. I vote no.
B. If this is the only way that our Universe can reproduce, then I think society has a moral duty to make it happen. I vote yes.
C. I don't think society should waste resources attempting to make a baby Universe. I vote no.
D. I don't have a strong moral opinion, but I support the notion that society should attempt to make a baby Universe. I vote yes.
E. I don't really care either way. I probably won't bother to vote.

If society were presented with the one-time opportunity to make a baby Universe, what do you think the eventual outcome would be?
A. All out war between the yes and no factions.
B. Fierce political discussion, resolved by the democractic process.
C. Fierce political discussion, leading to deadlock.
D. Nothing. Society would not care, and would just go about its business.
E. C, but the hero and heroine wade in and break the deadlock.

You are the leader of the “No-baby-Universe” faction. You believe deeply that your cause is right. You strive for right. But your faction has lost the vote. What do you do?
A. Continue to argue non-violently for your cause.
B. Fight for right. Start a guerilla war.
C. Spread disinformation about your opponents and their theory of making baby Universes.
D. Something else.

How should the movie end?
A. As the science says: the people outside the black hole never know whether a baby Universe was made, or what might be the nature of that baby Universe.
B. The baby Universe should expand out into the old Universe, destroying it, and starting afresh.
C. Somehow there is an unexpected line of communication from inside the black hole to outside, that allows people outside the black hole to discover what happened.
D. Postpone the conclusion to a sequel.
E. Something else.

Spring 2023 ASTR 3740 Homepage

Updated 2023 May 3