D2L Questions (Midterm II)

C. 20,000 solar luminosities

According to figure 8.1 (Maoz, p. 218), what is the luminosity of a Cepheid with a period of 10 days? A. 10,000 solar luminosities B. 1000 solar luminosities C. 20,000 solar luminosities D. 2,000 solar luminosities

B. Star formation rate per square kpc D. Surface gas density mass per square pc

According to the assigned reading, which two quantites are correlated, according to the Kennicutt-Schmidt Law? A. Surface atomic hydrogen density mass per square pc B. Star formation rate per square kpc C. Surface molecular hydrogen density mass per square pc D. Surface gas density mass per square pc E. Star formation rate F. Total gas mass

0.9 meters Read Section 10.4.

According to the discussion in Ryden, Section 10.4, the portion of the universe currently visible to us today was once confined to a sphere of physical radius ____ meters. (To be automatically scored, you need to provide the exact same number and metric units -- meters -- she produces; I mainly would like you to read this section for the general idea of the extreme nature of the inflation model, a feature which this length comparison captures pretty succinctly.) Be sure to input the units: "meters" or you will not receive full credit.

If you attempted to answer this question, I gave credit for it. But do take a look at the plot in the book. This plot (and plots similar to it) is one of the most important plots of correlation when it comes to trying to understand and model galaxy evolution: it unambiguously indicates that black holes must be very important in the growth of galaxies and vice versa.

According to the reading, what property of galaxies correlates the best (most tightly) with the mass of the central black hole? Which sub-part of Figure 3.45 shows this correlation? It is essential to use complete sentences to answer this question so I know what you are talking about.

B. 3 light-hours

A significant change in a quasar's luminosity over the course of 3 hours implies a maximum size of the quasar emission line region of A. 3 parsecs B. 3 light-hours C. 3 hours E. 3 light-years

NOTE: Dispersion is not the same as range (which can be strongly affected by outliers). You did have to read more than just the caption to understand this plot - the context of the plot is the orbits of stars. So "rotational velocity" is the velocity inferred from the mean redshift along the line of sight ("towards" or "away") relative to the mean redshift of the galaxy, as a function of radius. The "Rotation" is that mean rotation speed of the disk where the stars are, so there is a systematic rotation of the disk, as measured from the average velocity of all the stars at the same radial location in the disk. The "velocity dispersion" describes how the different stars with the same radial offset have a slightly different redshift. So it is the width of the distribution of velocities σ_v=(Σ(v_i−(v-bar))^2/(N−1))^(1/2) stars at a given radius in the galaxy disk. The rotation velocity is not how fast stars are rotating. If you answered that way, you might get a small amount of credit for looking at the figure but very little more because really, the question wanted you to understand the context of the figure, which does require reading both the caption and the reading.

Figure 3.42 has two panels. What is the difference between the quantities plotted in the upper and lower panels? In addition to reporting the labels, explain the difference to a friend, in your own words.

B. 5 cm^-1

Figure 8.1 has strange frequency units (cm^-1, inverse centimeters.) If the peak of the CMB spectrum is 2 mm, what is the "frequency" in inverse centimeters? (Hint: it should also be approximately the peak of this figure) A. 0.5 cm^-1 B. 5 cm^-1

angular diameter distance -- proper distance -- luminosity distance

For convenience, let's assume the universe is flat (kappa=0). Put the following cosmic distances corresponding to a given redshift in order of size, from smallest to largest. - luminosity distance - angular diameter distance - proper distance

18000 K

For this problem, assume today the CMB temperature is 3 K. What is the temperature in Kelvin of the CMB radiation at redshift 6,000. Enter your answer rounded off to two significant figures.

A. Equation 6.17 applies if the lens is located halfway between the observer and the lensed background source.

Gravitational lensing is introduced in Maoz Ch. 6.1.4; This question is based on the reading pp. 164-166 up through equation 6.17. Review that text and answer this question. Equation 6.17 follows from 6.16 under what conditions? A. Equation 6.17 applies if the lens is located halfway between the observer and the lensed background source. B. Equation 6.17 applies only if the gravitational lens is a point source. C. Equation 6.17 applies only in the case of very strong gravitational fields. D. Equation 6.17 applies for all distances between the source and the lens.

F. t^(-1/2)

How does the radiation temperature T depend on time t during the radiation-dominated epoch (prior to about 50,000 years after the Big Bang)? T is proportional to .... A. t^(2/3) B. t C. t^(-2/3) D. 1/t E. t^(1/2) F. t^(-1/2)

C. r_c(t) = r_c,0 a(t) (increases as the universe expands)

How does the radius of curvature (the hypothetic characteristic scale associated with the curvature of space) r_c change as the universe expands with scale factor a if space is isotropic and homogeneous? A. r_c(t) = r_c,0 (remains constant as the universe expands) B. r_c(t) = r_c,0 / a(t) (decreases as the universe expands) C. r_c(t) = r_c,0 a(t) (increases as the universe expands)

A. T is proportional to 1/a

How does the temperature of the radiation background change with scale factor a? A. T is proportional to 1/a B. T is proportional to a^2 C. T is proportional to a D. T is proportional to 1/a^2

B. COBE measured the spectrum of the CMB to be the most perfect black-body spectrum found in nature, characterized by a temperature of 2.725. D. The dipole feature in the COBE sky data showed that we are moving with respect to the radiation from the Big Bang, at about 600 km/s towards Hydra. E. The rms fluctuations in the CMB measured by COBE were about 1 part in 100,000.

Identify the Nobel-award winning results that were achieved by the COBE space mission. Choose all that apply. A. COBE discovered the CMB radiation. B. COBE measured the spectrum of the CMB to be the most perfect black-body spectrum found in nature, characterized by a temperature of 2.725. C. COBE discovered that the light from the CMB is polarized. D. The dipole feature in the COBE sky data showed that we are moving with respect to the radiation from the Big Bang, at about 600 km/s towards Hydra. E. The rms fluctuations in the CMB measured by COBE were about 1 part in 100,000.

A. Why is the temperature of the cosmic microwave background so uniform across the entire sky? B. Why is the universe so close to being geometrically flat? E. What is the origins of the tiny fluctuations (one part in 100,000) that we observe in the cosmic microwave background? The answer to this question, and how inflation simultaneously solves not only all these questions should be your main aim for the reading for today. Inflation also resolves the particle physics question: "Where are all the magnetic monopoles?" Alan Guth actually developed the idea to resolve that question. But we don't have time to look into monopoles (and their cousins, cosmic strings.)

Identify the questions that were unanswered by the original Big Bang theory. (For reference, the original Big Bang theory is that the universe started out as a hot dense place and has been expanding ever since.) A. Why is the temperature of the cosmic microwave background so uniform across the entire sky? B. Why is the universe so close to being geometrically flat? C. Why is the abundance of helium in the universe as high as 25% everywhere? D. Why is there a cosmic microwave background? E. What is the origins of the tiny fluctuations (one part in 100,000) that we observe in the cosmic microwave background?

3.4

If instead of an O6V star (as used in the example), you want to estimate the ionized region around a compact star cluster of 40 of the same kind of stars. How much larger (by what factor) would this region be in linear dimension (its radius R_S), assuming it's otherwise surrounded by gas of the same uniform ambient ISM density (10^-7 m^-3) as in the example equation 16.20? Be sure to use at least 2 significant figures in your answer. Your answer will just be a number representing the factor, since every version of this question will have a slightly different number. (Note that this problem is not asking you to re-calculate the size itself.)

5.2x10^2 km/s The typical random speed of a proton in a cluster of galaxies is similar to a random speed of a galaxy in a cluster of galaxies.

If the average random one-dimensional (Line of Sight) kinetic energy of a proton in a gas of ionized hydrogen is approximately equal to kT/2, what is the random speed in km/second associated with a temperature of (3.3x10^0) million Kelvin? (Enter units 'km/s')

0.24

If the efficiency of converting gravitational potential energy to radiative energy is expressed as an "efficiency" parameter times the rest mass energy (mc^2) in the accretion onto a black hole, what is the estimated accretion rate ("M-dot") onto an AGN radiating 11 x 10^37 W, in units of solar masses per year for an assumed efficiency (eta) of 8%? (The actual efficiency is ~ 1/12 using approximations, and 5.7%, if a general relativistic potential is used; use the efficiency, 1/12, corresponding to Equation 7.38 here.)

13.0

If the universe expanded at a constant rate, the age of the universe would be exactly 1/H0. Compute this time in Gigayears if H0 = 75.0 km/s/Mpc. Provide your answer with at least three significant figures for reliable grading. (If you're close the quiz should score it correctly.) Hint: 1 Gigayear = 1 billion years = 10^9 years Remember D2L doesn't understand scientific notation.

A. about the same as what we would measure

If the universe is uniformly expanding, what (similarly-defined) Hubble constant would an observer in another galaxy measure for the galaxies they can see? Assume that for this observer, the same amount of time has elapsed since the Big Bang as for us today. A. about the same as what we would measure B. significantly smaller than what we would measure C. significantly larger than what we would measure D. completely unknown since they are in a different galaxy

C. 10 times farther

If you have two supernova, but one of them peaks at a brightness 100 times as faint as the other, how much farther away is the first supernova? A. 100 times farther B. 10,000 times farther C. 10 times farther

300 Mpc

If you measure a redshift of 0.07 and you knew (from other sources) that the Hubble constant is 70 km/sec/Mpc, how far away is this source in Mpc? (For redshifts << 1 you can use the small redshift approximation to estimate the recession velocity such that v=cz.)

D. have gravity Radiation not only responds to the curvature of spacetime, it affects it itself.

In General Relativity, radiation (photons) A. travel faster than the speed of light B. travel slower than the speed of light C. are shifted to shorter wavelengths when they travel out of deep gravitational potential wells D. have gravity

B. hydrogen is 100% ionized

In Ryden, when X=1 ... A. the gas is 100% hydrogen B. hydrogen is 100% ionized C. hydrogen is 100% neutral

Angular size in negatively curved space (hyperbolic) -- Angular size in flat space -- Angular size in positively curved space (spherical)

In a flat universe, in the limit the angular size of a galaxy (D) << its distance (d) (i.e. D<<d), then the angular size of a galaxy is D/d. However, in curved universes, the angles are no longer exactly proportional to 1/d. For a galaxy at the same physical size and same distance but in universes of different curvature (we are humans, we can imagine these things!), put the angular sizes in order from SMALLEST to LARGEST. -Angular size in positively curved space (spherical) -Angular size in negatively curved space (hyperbolic) -Angular size in flat space

A. radiation pressure balances gravity The Eddington luminosity represents the estimate of the maximum luminosity an AGN can have, and it is directly proportional to its black hole mass. So a measurement of the luminosity of an AGN can provide an estimate of the lower limit of the mass of its black hole. Note many AGN are not radiating at their maximum possible levels. The radiation pressure on the electrons balances the inward gravitational force on the proton.

In estimating the Eddington Luminosity limit, we want to find the black hole mass such that A. radiation pressure balances gravity B. gas pressure balances gravity C. magnetic turbulence balances gravity

C. electrons Learning goal: understand the physical process generating most of the X-ray emission in a hot plasma between the galaxies of a massive cluster of galaxies.

In the hot gas, the process of emitting X-rays is called thermal bremsstrahlung. Bremsstrahlung in German means "braking radiation." What particle is emitting this radiation? (Consider what particle does the most accelerating during the process of generating radiation in this process.) A. quarks B. protons C. electrons D. cosmic rays

B. found for ellipticals D. Stellar luminosity scales to velocity dispersion to some power H. The width of absorpton lines in the aggregate sum of many stellar spectra is required.

Let's organize the various major scaling relations by name what what scales with what. Which of the following statements apply to the Faber-Jackson relation? A. found for spirals B. found for ellipticals C. Stellar luminosity scales to rotation speed to some power D. Stellar luminosity scales to velocity dispersion to some power E. Luminosity, effective radius, and central surface brightness are correlated with each other F. Measured with 21-cm emission line studies G. Measured with H-alpha emission line studies H. The width of absorpton lines in the aggregate sum of many stellar spectra is required.

A. found for spirals C. Stellar luminosity scales to rotation speed to some power F. Measured with 21-cm emission line studies G. Measured with H-alpha emission line studies

Let's organize the various major scaling relations by name what what scales with what. Which of the following statements apply to the Tully - Fisher relation? A. found for spirals B. found for ellipticals C. Stellar luminosity scales to rotation speed to some power D. Stellar luminosity scales to velocity dispersion to some power E. Luminosity, effective radius, and central surface brightness are correlated with each other F. Measured with 21-cm emission line studies G. Measured with H-alpha emission line studies H. The width of absorpton lines in the aggregate sum of many stellar spectra is required.

B. found for ellipticals E. Luminosity, effective radius, and central surface brightness are correlated with each other

Let's organize the various major scaling relations by name what what scales with what. Which of the following statements apply to the the fundamental plane? (Section 3.4.3) A. found for spirals B. found for ellipticals C. Stellar luminosity scales to rotation speed to some power D. Stellar luminosity scales to velocity dispersion to some power E. Luminosity, effective radius, and central surface brightness are correlated with each other F. Measured with 21-cm emission line studies G. Measured with H-alpha emission line studies H. The width of absorpton lines in the aggregate sum of many stellar spectra is required.

To get full credit on this question you needed to correctly identify the units as density of galaxies per unit luminosity, in addition to correctly naming the distribution function as the galaxy luminosity function (the specific form is the Schechter function). L_star is very similar to the Milky Way's luminosity. The IMF expressed in 5.20 is a simple power-law with no cut-off; the luminosity function has an exponential function at a characteristic luminosity L_star. If you said one was a function for star masses and the other was for galaxies, well, that is trivially true (it's got a different name too) but what it is a distribution function of does not have anything to do with the mathematical form of the expression, which was what the question asked you to compare.

Maoz, Ch. 7, Equation 7.31 Use brief sentences: (a) What is the name of the function in that equation, and what are the units of ϕ(L∗) , (b) How does the luminosity L∗ (pronounced "L-Star") compare to the luminosity of the Milky Way? (c) How does the mathematical form of this function (Equation 7.31) differ from the mathematical form of the stellar IMF discussed in Maoz Ch. 5 (Equation 5.20)?

flat -- 0 positively curved (spherical) -- +1 negatively curved (hyperbolic) -- -1

Match the curvature constant kappa (κ) to the appropriate curved space time -flat -positively curved (spherical) -negatively curved (hyperbolic) 0 +1 -1

negatively curved (hyperbolic), infinite -- α+β+γ=π−A/r_c^2 flat, infinite -- α+β+γ=π positively curved (spherical), finite size -- α+β+γ=π+A/r_c^2

Match the features of a triangle, with angles α, β, γ and area A with the curved space. For this problem the radius of curvature is r_c, , and angles are in units of radians. α+β+γ=π α+β+γ=π+A/r_c^2 α+β+γ=π−A/r_c^2 -negatively curved (hyperbolic), infinite -flat, infinite -positively curved (spherical), finite size

Contains stars over 8 billion years old. -- Both ellipticals and spirals Surface brightness scales like -r1 (exponential law) -- Spirals Surface brightness scales like -r1/4 (de-Vaucoleurs law) -- Giant Ellipticals Most common giant galaxy in a cluster of galaxies -- Giant Ellipticals Most common giant galaxy outside of clusters -- Spirals Is primarily made up of old stars -- Giant Ellipticals Most common type of giant galaxy in the recent (nearby) universe (Redshift < 0.2) -- Spirals Milky Way is one -- Spirals Has a prominent disk -- Spirals

Match the galaxy type with the description. Choose the best match for each category. The categories here are about giant (massive) galaxies, not dwarfs. Giant Ellipticals Spirals Both ellipticals and spirals -Contains stars over 8 billion years old. -Surface brightness scales like -r1 (exponential law) -Surface brightness scales like -r1/4 (de-Vaucoleurs law) -Most common giant galaxy in a cluster of galaxies -Most common giant galaxy outside of clusters -Is primarily made up of old stars -Most common type of giant galaxy in the recent (nearby) universe (Redshift < 0.2) -Milky Way is one -Has a prominent disk

21-cm line -- Neutral hydrogen X-ray emission and absorption -- X-ray emission and absorption H-alpha emission (in other galaxies); quasar absorption lines. -- Ionized gas

Match the halo gas to the detection method 21-cm line X-ray emission and absorption H-alpha emission (in other galaxies); quasar absorption lines. Coronal gas Neutral hydrogen Ionized gas

D. 0.7 Note the curvature contribution can also be written in terms of a ratio with the critical density (or critical energy density). The Einstein equations require that the sum of all these Omega's equal 1, identically. So if the sum of Omega_matter+ Omega_radiation+ Omega_Lambda > 1 then Omega_curvature is <0 (negative); if that sum is < 1 then Omega_curvature is > 0 (positive). But for most practical cases (in the universe we are living in) the curvature is zero, within our measurement uncertainties.

Omega_X is the ratio of the mass-energy density of x to the critical mass -energy density (for this discussion, it is written as ρc^2 or (3 H(t)^2 c^2)/(8πG) If the universe is geometrically flat, then the sum of Omega_radiation, Omega_matter, and Omega_Lambda is = 1. At the present time, Omega_radiation is insignificant (very tiny), and all the tests we've made indicate that the universe is indeed geometrically very flat. This means that if Omega_matter = 0.3, then Omega_Lambda must be ____ A. 0.3 B. 0 C. 1 D. 0.7 E. Impossible to say

Parallax -- Cepheids -- Tully Fisher, surface-brightness fluctuations, globular cluster and planetary nebular luminosity functions -- Type 1a supernovae and (to a lesser extent) S-Z effect in clusters

Put the following techniques in order, for techniques used to establish distances from near to far. In an exam, be able to explain how these techniques work. - Cepheids - Parallax - Tully Fisher, surface-brightness fluctuations, globular cluster and planetary nebular luminosity functions - Type 1a supernovae and (to a lesser extent) S-Z effect in clusters

Radiation dominated era -- The expansion of the universe is slowing down, because of matter constitutes the largest component of energy density during this epoch. -- The expansion of the universe is slowing down, because of matter constitutes the largest component of energy density during this epoch. For a test: Be able to estimate the transitions between these epochs in terms of scale factor and redshift, starting from values for Omega_radiation, Omega_matter and Omega_DarkEnergy. Equation (16) describes the timing of this transition. The universe has been increasingly dark-energy dominated since z~0.75. Radiation caused the deceleration of the expansion of the universe prior to z~4000. (p. 163) During the early part of this epoch, the universe cools enough to allow neutral hydrogen to survive. Later on, galaxies and stars begin to assemble.

Put these three epochs of the universe in chronological order (first occurring to last). - The expansion of the universe is speeding up, because dark energy is the largest component of the energy density of the universe during this epoch. - Radiation dominated era - The expansion of the universe is slowing down, because of matter constitutes the largest component of energy density during this epoch.

A. Radiation slows the expansion of the universe. C. Dark energy (Lambda>0) speeds up the expansion of the universe. D. Matter slows the expansion of the universe.

Qualitatively, identify the main effects of the contents of the universe on its expansion. This question is intended to help you get a qualitative understanding of the reading, and not get lost in the equations. A. Radiation slows the expansion of the universe. B. Radiation speeds up the expansion of the universe. C. Dark energy (Lambda>0) speeds up the expansion of the universe. D. Matter slows the expansion of the universe. E. Matter speeds up the expansion of the universe. F. Dark energy (Lambda>0) slows the expansion of the universe.

C. Both of these explanations are true. Quasars are both rare and were more common in the past.

Quasars are generally found only at large distances. This fact implies that ... A. Quasars were more common in the past. B. Quasars are very rare in the local universe. C. Both of these explanations are true. Quasars are both rare and were more common in the past.

(My Answer) When looking at M87, the place astronomers looked to solve this issue was at the OII, or singly ionized oxygen, emmission line at 3727 Angstroms (pg.146, Section 3.8.2). The emmison line came from using a slit and spectroscopy to obtain a spectrum of the M87 core using Hubble (Fig 3.43). The most important aspect of the OII emission line was how much it had broadened. Astronomers were able to take this value and estimate the Black Hole to mass of 3*10^9 Solar masses. This was done converting the boradening to charactersitic velocity dispersion and solving for mass since the radius is known.

Summarize, according to the assigned reading, how the black hole mass in M87 was estimated using the Hubble Space Telescope. Use specifics from the text and figure captions to identify exactly what emission line was observed and what measurements were made to complete the mass estimate.

B. a lot less helium

Suppose neutrons decayed to protons a lot more rapidly than 880 seconds. This alternative universe would have: A. a lot more helium B. a lot less helium C. about the same amount of helium

A. 180 degrees / l

The CMB sky (no matter what its pattern) can be decomposed into a sum of spherical harmonics with terms numbered from l=0 to infinity. The "ell" (l) corresponds to an angular size of A. 180 degrees / l B. 360 degrees / l C. l degrees

1.5x10^9

The Schwarzschild radius, in kilometers, for a black hole of (5.0x10^8) solar masses is ______. (Round your answer to the nearest 2 significant figures.)

B. much smaller than the co-moving radial coordinate distance

The angular diameter distance for the CMB at z=1000 is A. much larger than its co-moving radial coordinate distance B. much smaller than the co-moving radial coordinate distance C. about the same distance as its co-moving radial coordinate distance

5.8x10^7 K

The average energy of an x-ray photon coming from the hot gas trapped in the gravitational potential well of the Chandra-Newton cluster is (5.0x10^0) keV. If E ~ kT, what is the characteristic temperature of the hot gas in Kelvin? This D2L question will ask for 3 inputs: a number between 1.00 and 9.99, an exponent for the power 10, and a physical unit. (Hint: the unit should be K for Kelvin). Use values for constants like k or the conversion of eV to Joules or ergs with 3-4 significant figures. Maoz has a list of physical constants in the front of his book, right after the Preface.

E. That the fraction of the total mass of galaxies in gas plus stars is constant.

The baryonic Tully Fisher relation has less dispersion than the original Tully Fisher relation, and applies over a wider range of galaxy masses. What does this fact imply? (Read pp. 128-129+). A. That the sum of the mass in stars and in gas is constant from galaxy to galaxy. B. That the the gas fraction of the total mass in these galaxies is constant. C. That the stellar fraction of the total mass in these galaxies is constant. D. That the mass in stars is correlated with the mass in gas. E. That the fraction of the total mass of galaxies in gas plus stars is constant.

A. angular size distance

The cosmic distance D appropriate to multiply by the angular size (in radians) to get the physical size (e.g. d_(physical size) = DΘ A. angular size distance B. luminosity distance C. actual distance D. proper distance

C. luminosity distance

The cosmic distance you should use relating the (bolometric) luminosity to the (bolometric) flux of an object, in the expression L=4π d^2 F A. lookback time distance B. angular diameter distance C. luminosity distance D. proper distance

True

The cross section of a free electron to a photon is much larger than the cross section of that electron when it is bound to a proton. True or False?

Radiation (and relativistic matter) -- 1/3 Non-relativistic matter -- 0 Dark energy that behaves like a "cosmological constant" -- -1

The equation of state can be written most generally by P=wρ . Match the quantity w to the corresponding thing: - Radiation (and relativistic matter) - Non-relativistic matter - Dark energy that behaves like a "cosmological constant" 1/3 0 -1

C. D_A ~ R_H/ z (for z ~ 1100)

The horizon distance (RH= the co-moving radial coordinate distance of an object on our cosmic horizon) using current cosmological parameters is 14,000 Mpc. The redshift of the CMB is about z=1100. What is the angular-diameter distance to the surface of last scattering (where the CMB photons last interacted with matter, approximately) A. D_A ~ R_H * z (for z=1100) B. D_A ~ R_H (for z=1100) C. D_A ~ R_H/ z (for z ~ 1100)

C. quarks and anti-quarks The source (or mechansm) of the asymmetry is yet unknown.

The huge asymmetry between matter and anti-matter and the large ratio of photons to baryons today are the result of what tiny asymmetry in the early universe? A. neutron and protons B. neutrinos and anti-neutrinos C. quarks and anti-quarks D. hydrogen and helium

C. Omega_M + Omega_Lambda

The location of the first peak the CMB power spectrum (in terms of angular separation, or equivalently, "ell" (l) ) is most dependent on .... A. the Hubble constant H0 B. Omega_Lambda - Omega_M/2 C. Omega_M + Omega_Lambda D. Omega_Lambda E. Omega_M

A. quasars See p. 207 for a brief overview of the "zoo" of AGN.

The most luminous AGN are A. quasars B. Seyfert galaxies C. BL-lac objects D. radio galaxies

B. a billion (1E9)

The ratio of photons to baryons in the universe is about A. one millionth (1E-6) B. a billion (1E9) C. one billionth (1E-9) D. a million (1E6)

D. (a-dot)/(a) This definition is the first step to understanding how the contents of the universe affect the evolution of its expansion. This is a very good cosmological fact to remember.

The scale factor a(t) changes from 0 at the moment of the Big Bang (t=0) to 1.0 today (t=t0). There is a direct relationship between a and redshift z : a = 1/(1+z). The Hubble parameter H(t) is equal to A. ((a-dot)/(a))^2 B. a C. a-dot D. (a-dot)/(a)

C. Gamma = Gamma_full * X

The scattering rate is derived in Equation 9.16. But that rate only applies when the universe is 100% ionized. So for this question, let's call that rate Gamma_full. How would the scattering rate be different if we correctly accounted for X? A. Gamma = Gamma_full / X B. Gamma = Gamma_full/ (1.0-X) C. Gamma = Gamma_full * X D. Gamma = Gamma_full (1.0 - X)

0.445

This question follows on from the one previous but very likely with a DIFFERENT MASS difference (1.00 MeV), so pay attention; you will need to compute the neutron to proton ratio for a different mass difference for this question. Compute the ratio of neutrons to protons for this mass difference (1.00 MeV), as you did for the previous question. But now, estimate what the maximum value of the mass of Helium over the total mass of baryons will be if ALL the neutrons left when the universe is 0.8 MeV are incorporated into helium nuclei. The solution to this problem is worked on in Section 9.3, Ryden. The key is to calculate f, the ratio of neutrons to protons; pp. 171-174.

epoch of recombination is the moment when ... -- when the number density of ionized hydrogen (free protons) equals the number density of neutral hydrogen atoms epoch of photon decoupling is the moment when... -- when the time between photon-electron scattering events is longer than the age of the universe at that moment in time. epoch of last scattering is the moment when... -- when an average CMB photon last interacted with an electron

To clarify the discussion of physical ideas in section 9.2, Ryden makes a distinction between three moments in the history of the universe. They happen close in time, but not exactly at the same time. Match the name of the epoch to the physical condition that defines it. - when the number density of ionized hydrogen (free protons) equals the number density of neutral hydrogen atoms - when an average CMB photon last interacted with an electron - when the time between photon-electron scattering events is longer than the age of the universe at that moment in time. - epoch of recombination is the moment when ... - epoch of photon decoupling is the moment when... - epoch of last scattering is the moment when...

2.220 MeV

To within 3 significant figures, and the appropriate units (so that the number in front of the units is somewhere between 0.1 and 999) what is the binding energy quoted by Barbara Ryden for an deuteron? Your grade on this question will depend on entering the correct number AND units.

Positively curved universes with R_c < R_H. -- We don't see "sky-filling" galaxies; and we don't see periodicities in the galaxy or CMB distribution. Negatively curved universes with R_c < R_H. -- Galaxies remain resolved, at ~ 1 arcsecond in size, even when they are over half the distance to our cosmic horizon.

We know the universe is pretty flat just by looking, that is, it is pretty easy to rule out radii of curvature R_c < R_H, the distance to our cosmic horizon (~4000 Mpc). But the arguments against strongly positively curved universes are different from those against strongly negatively curved universes. Match the arguments against strong curvature to the appropriate direction. Since there are only two options here, please read the feedback to make sure you guessed the correct answer for the correct reason. -Positively curved universes with R_c < R_H. -Negatively curved universes with R_c < R_H. -We don't see "sky-filling" galaxies; and we don't see periodicities in the galaxy or CMB distribution. -Galaxies remain resolved, at ~ 1 arcsecond in size, even when they are over half the distance to our cosmic horizon.

It is bigger than the Schwarzchild radius by a factor of (c/sigma_v)^2, where sigma_v is the typical velocity dispersion of the galaxy, and is measured from the stars. It's basically the radius at which the gravitational influence of the black hole is the same as that of the rest of the matter in the galaxy, and inside which, the black hole mass matters, and outside which, the black hole mass becomes a less and less important contribution to the total amount of matter inside the orbits.

What defines the "black hole radius of influence" in the assigned reading from the Schneider text? How big is it in comparison to the Schwarzchild radius (the event horizon)? A brief 1-2 sentences are all that are requested here.

3.8x10^-4

What is the parallax angle (in arcseconds) of a star at a distance of (2.6x10^3) parsecs? Express to 2 significant digits.

C. about 2 mm This wavelength of light is strongly absorbed by atmospheric water. That's why CMB experiments prefer to be in high and dry locations (like Antarctica) or in space.

What is the peak wavelength of the CMB? A. about 7.35 cm B. about 10 microns C. about 2 mm D. about 1 Angstrom

4.284

What is the redshift of gas if you measure the Lyman alpha emission line at 642.0 nm? (The rest-frame wavelength of Lyman alpha is 121.5 nm.) Enter your solution with at least 4 significant figures. (Wavelengths are generally straightforward to measure to the nearest 0.1 nm, if not better.)

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What is the scale factor a when z=5.1? Provide your answer with at least 2 significant figures. For the midterm and final, it will be useful to remember the definition of redshift and the relationship between scale factor a and redshift z.

B. Concentrated in the center Right - v proportional to 1 /sqrt (r) is a "Keplerian" orbit, like in our solar system, where 99.9% of the mass is in the center.

Where is the mass in a system where the orbital velocity decreases like 1 / sqrt (r)? A. Spread throughout the system. B. Concentrated in the center

A. Spread throughout the system. A "flat" rotation curve means that the orbital velocities of gas (or stars) do not decrease even as you look at gas with larger and larger orbits. That pattern indicates there is lots of matter at these large radii.

Where is the mass in a system where the orbital velocity does not change with r ? A. Spread throughout the system. B. Concentrated in the center

A. 75 km/s/Mpc

Which Hubble constant implies the shortest inferred age of the universe? (Assume all other cosmological quantities are identical - same matter and dark matter densities.) A. 75 km/s/Mpc B. 65 km/s/Mpc C. 70 km/s/Mpc D. The inferred age does not depend on the Hubble's constant

A. A cosmic microwave background from the entire sky.

Which piece of evidence best supported the idea of a hot Big Bang universe, that started out has a hot dense place? A. A cosmic microwave background from the entire sky. B. Hubble discovered galaxies that were farther from us were also receding from us more quickly. C. The sky is dark at night.

B. Why is the night sky dark?

Which question does Olber's paradox attempt to address? A. How old is the Universe? B. Why is the night sky dark? C. Why is the fraction of helium to hydrogen 25% by mass in the universe? D. Why is the daytime sky on Earth blue?

I gave partial credit for an attempt on this question. However, the answer is that orbits of galaxies around other galaxies or inside clusters are velocities that have nothing to do with the expansion of the universe, but are always present. These motions cause "scatter" (in random plus and negative directions) in the Hubble diagram, in the inferred redshift. So inside the Local Group, galaxy relative motions are not due to redshift at all because all galaxies are orbiting the center of mass of the Local Group. Inside the Virgo Supercluster, there is some trend with redshift, but still much of the motion towards and away from us is part expansion and part real orbit speeds. A common speed inside a cluster of galaxies is around 1,000 km/s. But for galaxies with recession speeds > 10,000 km/s, orbital motions will create less scatter, proportionally, than galaxies that are closer. The observed random scatter will get higher again, for z~ 1 and beyond, because peak supernova apparent magnitudes become fainter and therefore less certain

Why is there more (proportional) scatter in the supernova data at redshifts 0.01-0.02 than there is at redshift 1? (Figure 6.5)

1.7x10^3

You measure the period of a Cepheid, and consult the calibration of the Cepheid Luminosity-Period relation, and find that the Luminosity of this Cepheid is (5.000x10^3) solar luminosities. If the average flux of this Cepheid is (5.6x10^-11) Watts per square meter, how far away is this Cepheid in parsecs? (1 parsec = 3.0856E16 meters; 1 solar luminosity = 3.828E26 Watts)

Hubble constant, H_0, matter-dominated universe -- 2/(3t_0) Horizon distance, matter-dominated universe -- 2 (c/H_0) Hubble constant, H_0, radiation-dominated universe -- 1/(2t_0) Horizon distance, radiation-dominated universe -- (c/H_0)

t_0 here is the current age of the universe. The Hubble constant is H_0 = H(t=t_0). While the universe is radiation-dominated, the scale factor a(t) = (t/t_0)^(1/2). While the universe is matter-dominated, the scale factor a(t)=(t/t_0)^(2/3). The Ryden textbook in Ch 5.3 derives some general relations for when the scale factor a(t) is a power-law with time. It is useful to recognize that the units of the Hubble parameter are inverse time (t^-1) and the units of a horizon size is distance. - 2/(3t_0) - (c/H_0) - 2 (c/H_0) - 1/(2t_0) - Hubble constant, H0, matter-dominated universe - Horizon distance, matter-dominated universe - Hubble constant, H0, radiation-dominated universe - Horizon distance, radiation-dominated universe

D. They are too low energy for modern technology. Cosmic neutrinos are an example of relativistic weakly-interacting dark matter. It's sometimes called "hot dark matter". The most stringent upper limits on the mass of neutrinos comes from astronomy, because if the neutrinos are massive, they suppress the formation of low-mass halos but not high-mass halos. We don't see this suppression in our universe, and so comparing observations to model predictions, astronomical observations limit the mass that can be associated with cosmic neutrinos, indirectly. The energy per neutrino is similar to the energy per CMB photon (the numbers of cosmic neutrinos are similar to the numbers of CMB photons). So an energy of 0.001 eV is far too low to trigger neutrino detectors with our current technology.

An amazingly exact prediction can be made for the energy density of cosmic neutrinos (about 1.68 x the energy density of the cosmic microwave background). These neutrinos have been streaming freely through the universe since about the first millisecond. The CMB is relatively easy to see. Why haven't we detected these cosmic neutrinos? A. They are too rare. B. They may switch types. C. Neutrinos are impossible to detect because they interact with nothing. D. They are too low energy for modern technology.

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At t~0.1 seconds, neutrinos still strongly coupled to protons and neutrons, and allowed them to switch identities. Because the mass of the neutron is higher than the mass of the proton, it was slightly easier to make protons than to make neutrons: (n_n)/(n_p) ≈ e^-(((m_n−m_p)c^2)/kT) . Suppose the mass difference, instead of being 1.29 MeV was 0.5 MeV. But also assume everything else was the same, including the time and energy when neutrinos basically stop interacting with matter, and cause the neutron-to-proton ratio to "freeze out" at kT ~ 0.8 MeV. If all the neutrons at this point make helium, what is the implied ratio of neutrons to protons at this point in time? (i.e. When the universe cools to 0.8 MeV, at about 1 second age.)

A. The temperature corresponds to a Planck spectrum where only a small fraction of the photons are capable of ionizing hydrogen. 1. The threshold for ionizing hydrogen is 13.6 eV. 2. The number of photons in the CMB outnumber the baryons by approximately a billion to one. (The ratio eta is the ratio of baryons to photons, and it is about 5.5E-10).

Carefully consider the discussion in Section 7.3. Identify the correct statement about the temperature of the universe when recombination happens. A. The temperature corresponds to a Planck spectrum where only a small fraction of the photons are capable of ionizing hydrogen. B. The temperature corresponds to a Planck spectrum where almost 100% of the photons are capable of ionizing hydrogen. C. The temperature corresponds to a Planck spectrum where 50% of the photons are capable of ionizing hydrogen.

A. Inflation, if it happened, happened over an incredibly infinitesimal span of time. D. Both inflation and dark energy would cause the universe to expand exponentially fast.

Choose the true statements. I've tried to phrase these to be agnostic about the reality of dark energy or inflation - I'm not asking you to confirm that either of these are "true", but there are things we can say about them that can be deemed true or false. A. Inflation, if it happened, happened over an incredibly infinitesimal span of time. B. Inflation, if it happened, happened over a very long span of time. C. Inflation and dark energy must be basically the same thing. D. Both inflation and dark energy would cause the universe to expand exponentially fast. E. The energy density associated with inflation is about the same as the energy density associated with dark energy today.

B. The trend of effective radius vs. absolute magnitude MB is different for giant ellipticals than it is for dwarf ellipticals. D. As dwarf ellipticals increase in luminosity, their central surface brightnesses also increase. F. cD galaxies have extended halos of light over and above the usual elliptical galaxy light profiles.

Consider Figure 3.10 and 3.11 in the Schneider chapter. (Figure 3.10 should be the plot of effective radius vs. absolute B magnitude, next to a plot of surface brightness vs. absolute B magnitude; Figure 3.11 is a plot of surface brightness as a function of radius.) Select the following statements that are true, based on the observations plotted in those graphs. A. cD galaxies surface brightness profiles follow r1/4 laws. B. The trend of effective radius vs. absolute magnitude MB is different for giant ellipticals than it is for dwarf ellipticals. C. Dwarf elliptical galaxies are scaled down versions of giant elliptical galaxies. D. As dwarf ellipticals increase in luminosity, their central surface brightnesses also increase. E. As giant ellipticals increase in luminosity, their central surface brightnesses also increase. F. cD galaxies have extended halos of light over and above the usual elliptical galaxy light profiles.

C. The highest-redshift data are the most important for discriminating between the 3 models.

Consider Figure 6.5 in the Ryden text (p. 120); which of the following statements is a reasonable inference from the the data and models in the figure? A. The scatter in the data points is largest around redshifts of 1. B. A flat, Lambda-only model is the best fit to the data C. The highest-redshift data are the most important for discriminating between the 3 models. D. The slope of the line can be used to estimate H0.

C. go down

Consider Figure 9.5 in Ryden. If the number of baryons to photons were higher, the predicted deuterium fraction would ... A. remain the same B. go up C. go down

C. the ratio of (105/172)^2. This plot is idealized, as if there were only luminous matter interior to about 5 kpc (or luminous matter was completely dominating the overall mass inside of 5 kpc, and there was no luminous matter outside of that radius.) The "enclosed mass" at 30 kpc includes both luminous and dark matter.

Consider figure 7.6 (p. 194) from the Maoz textbook. Assume the dashed curve is only for the luminous matter (if that were all that was there). What is the ratio of luminous matter within a radius of 30 kpc to the total amount matter inside 30 kpc? A. the ratio of (105/172)^3 B. the ratio of (105/172) C. the ratio of (105/172)^2. D. can't tell based on the plot E. 0 (zero)

157

Consider figure 7.6 in Maoz, p. 194. Assume that the rotation curve labeled "flat" is being observed edge-on (so the graph is showing you the maximum orbital speeds with no correction required for inclination). For the galaxy rotation curve marked "flat" (on the top of the plot), estimate the total enclosed mass in units of a billion solar masses at 22.0 kpc. Keep two significant figures in your answer. Hint 1: You will need to convert kpc to a distance appropriate to whether you prefer to work in MKS or cgs units. Hint 2: the answer will be a large number, even after you divide your result by a billion times the mass of the Sun.

C. BCD

Consider the mass to light ratios listed in Tables 3.1 and 3.2 of Schneider (in the PDF). Which galaxy type has the most blue light for its mass, at the extreme limit (All of the galaxy types are listed; when a range is provided in the table, use the extreme where the maximum amount of blue light per mass to break approximate ties.) A. Sb B. Sa C. BCD D. Im/Irr E. dSph F. S0 G. dE H. Sc I. Sd/Sm J. E K. cD

K. cD

Consider the mass to light ratios listed in Tables 3.1 and 3.2 of Schneider (in the PDF). Which galaxy type has the most dark matter for its mass, on average? (All of the galaxy types are listed.) A. Sb B. Sa C. BCD D. Im/Irr E. dSph F. S0 G. dE H. Sc I. Sd/Sm J. E K. cD

Empty Universe -- a(t)∝t Matter dominated (Omega_Matter=1) universe -- a(t)∝t^(2/3) Radiation dominated universe (as ours was prior to 10,000 years) -- a(t)∝t^(1/2) Dark-energy dominated universe (as ours may increasingly becomes) -- a(t)=e^(H_0(t−t_0))

Each kind of universe discussed in the text has a different flavor of expansion. Match the universe to the type of expansion it experiences. The scale factor a(t) has a different time dependence in each case. - a(t)=e^(H_0(t−t_0)) - a(t)∝t - a(t)∝t^(2/3) - a(t)∝t^(1/2) - Empty Universe - Matter dominated (Omega_Matter=1) universe - Radiation dominated universe (as ours was prior to 10,000 years) - Dark-energy dominated universe (as ours may increasingly becomes)

B. If the photons, electrons, and ions are in equilibrium they are at the same temperature T. C. To be in equilibrium, the photon-electron scattering timescale must be short compared to the age of the universe.

Equilibrium is a very useful concept in cosmology, but what are the requirements for equilibrium and what does it imply? Select the true statements that apply to equilibrium of photons, electrons, and baryons below: A. If the photons, electrons, and ions are in equilibrium they are all moving close to the speed of light. B. If the photons, electrons, and ions are in equilibrium they are at the same temperature T. C. To be in equilibrium, the photon-electron scattering timescale must be short compared to the age of the universe. D. To be in equilibrium, the photon-electron scattering timescale must be long compared to the age of the universe.

1.46

Estimate the gravitational mass of a cluster in units of 10^14 solar masses, located at a distance of 1.5 Gpc from Earth, with a gravitationally lensed "arc" offset by 20.0 arcseconds. (Be sure to divide out the 10^14 solar masses from your answer to get the right units for the D2L auto-grader.)