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QUALIFIER EXAM SOLUTIONS 1. Cosmology (Early Universe, CMB, Large-Scale Structure)

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QUALIFIER EXAM SOLUTIONS 1. Cosmology (Early Universe, CMB, Large-Scale Structure) Draft version June 20, 2012 Preprint typeset using LATEX style emulateapj v. 5/2/11 QUALIFIER EXAM SOLUTIONS Chenchong Zhu (Dated: June 20, 2012) Contents 1. Cosmology (Early Universe, CMB, Large-Scale Structure) 7 1.1. A Very Brief Primer on Cosmology 7 1.1.1. The FLRW Universe 7 1.1.2. The Fluid and Acceleration Equations 7 1.1.3. Equations of State 8 1.1.4. History of Expansion 8 1.1.5. Distance and Size Measurements 8 1.2. Question 1 9 1.2.1. Couldn't photons have decoupled from baryons before recombination? 10 1.2.2. What is the last scattering surface? 11 1.3. Question 2 11 1.4. Question 3 12 1.4.1. How do baryon and photon density perturbations grow? 13 1.4.2. How does an individual density perturbation grow? 14 1.4.3. What is violent relaxation? 14 1.4.4. What are top-down and bottom-up growth? 15 1.4.5. How can the power spectrum be observed? 15 1.4.6. How can the power spectrum constrain cosmological parameters? 15 1.4.7. How can we determine the dark matter mass function from perturbation analysis? 15 1.5. Question 4 16 1.5.1. What is Olbers's Paradox? 16 1.5.2. Are there Big Bang-less cosmologies? 16 1.6. Question 5 16 1.7. Question 6 17 1.7.1. How can we possibly see galaxies that are moving away from us at superluminal speeds? 18 1.7.2. Why can't we explain the Hubble flow through the physical motion of galaxies through space? 19 1.7.3. Can galaxies with recession velocities v > c slow down until v < c? 19 1.8. Question 7 19 1.8.1. How does nucleosythesis scale with cosmological parameters? 20 1.8.2. How do we determine primordial densities if D is easily destroyed in stars? 20 1.8.3. Why is there more matter than antimatter? 20 1.8.4. What are WIMPs? 20 1.9. Question 8 20 1.9.1. Describe systematic errors. 21 1.9.2. Describe alternate explanations to the SNe luminosity distance data, and why they can be ruled out? 22 1.9.3. Can SNe II be used as standard candles? 23 1.10. Question 9 23 1.10.1. What is the fate of the universe, given some set of Ωs? 23 1.10.2. How do we determine, observationally, the age of the universe? 24 1.10.3. Is Λ caused by vacuum energy? 25 1.11. Question 10 25 1.11.1. What are the consequences of these numbers on the nature of the universe? 26 1.11.2. How do we determine Ωr from the CMB? 26 1.11.3. How are other values empirically determined? 26 1.11.4. What are the six numbers that need to be specified to uniquely identify a ΛCDM universe? 27 1.11.5. Why is h often included in cosmological variables? 27 1.12. Question 11 27 1.12.1. What are the possible fates the universe? 28 1.13. Question 12 29 [email protected] 2 1.13.1. How does the CMB power spectrum support the inflation picture? 31 1.13.2. Derive the horizon size at recombination. 31 1.13.3. Why is the CMB a perfect blackbody? 31 1.13.4. How is the CMB measured? 32 1.13.5. Why did people use to think CMB anisotropy would be much larger than it is currently known to be? 32 1.13.6. What is the use of CMB polarization? 32 1.14. Question 13 32 1.14.1. Why is BAO often used in conjunction with CMB? 35 1.14.2. What is the BAO equivalent of higher-l CMB peaks? 35 1.15. Question 14 35 1.15.1. How is weak lensing measured? 36 1.15.2. Can strong lensing be used to determine cosmological parameters? 36 1.16. Question 15 36 1.16.1. What caused inflation? 37 1.16.2. How does inflation affect the large scale structure of the universe? 37 1.16.3. Is inflation the only way to explain the three observations above? 37 1.17. Question 16 37 1.17.1. Is the anthropic principle a scientifically or logically valid argument? 38 1.18. Question 17 38 1.18.1. Describe galaxy surveys. 39 1.18.2. What about three or higher point correlation functions? 39 1.19. Question 18 40 1.20. Question 19 40 1.20.1. What about He reionization? 41 2. Extragalactic Astronomy (Galaxies and Galaxy Evolution, Phenomenology) 43 2.1. Question 1 43 2.1.1. What does the Hubble sequence miss? 44 2.1.2. What is the Tully-Fisher relationship? 45 2.1.3. What is the fundamental plane? 45 2.1.4. What other criteria could be used for galaxy classification? 45 2.2. Question 2 45 2.2.1. Why can't we simply use the inner 10 kpc data derived from 21-cm line emission and a model of the halo to determine the mass of the halo? 46 2.2.2. How is the total mass of an elliptical galaxy determined? 46 2.3. Question 3 47 2.3.1. Is He and metals ionized? Is any component of the IGM neutral? 47 2.3.2. What are the properties of these neutral H clouds? Can they form galaxies? 48 2.4. Question 4 48 2.5. Question 5 50 2.5.1. How are SMBHs formed? 52 2.5.2. What correlations are there between the properties of the SMBH and the host galaxy? 52 2.6. Question 6 52 2.7. Question 7 53 2.7.1. What determines the emission spectrum of an AGN? 54 2.7.2. Are there backgrounds at other wavelengths? 54 2.8. Question 8 54 2.8.1. What are cold flows? 55 2.8.2. What is feedback? 55 2.8.3. What is downsizing? 56 2.9. Question 9 56 2.9.1. What are cooling flows? 57 2.10. Question 10 57 2.11. Question 11 59 2.11.1. Describe population synthesis. 60 2.11.2. What do the spectra of real galaxies look like? 60 2.12. Question 12 60 2.12.1. What have we learned about high-z galaxies from LBGs? 62 2.12.2. Are there other \breaks" that could be used to detect galaxies? 62 2.12.3. Can we find Lyman-break galaxies at low redshifts? 62 2.13. Question 13 62 2.13.1. What is the cause of the various emission features of AGN? 64 2.14. Question 14 64 3 2.14.1. Are there non-EM backgrounds? 66 2.15. Question 15 66 2.15.1. Where are most AGN located? 69 2.15.2. What evidence is there that AGN are powered by supermassive black holes? 69 2.16. Question 16 69 2.16.1. How are high-z cluster found? 71 2.17. Question 17 71 2.18. Question 18 73 2.18.1. What are SZ surveys conducted with? 74 2.18.2. What is the kinematic SZ effect? 74 3. Galactic Astronomy (Includes Star Formation/ISM) 75 3.1. Question 1 75 3.1.1. What is the IMF useful for? 75 3.1.2. Is there a universal IMF? 75 3.1.3. Why are the lower and upper limits of the IMF poorly understood compared to that of the middle (several M stars)? What constraints are there? 76 3.1.4. What's the difference between a field and stellar cluster IMF? 77 3.1.5. How do you determine an a present-day mass function (PDMF) from an IMF? 77 3.2. Question 2 77 3.2.1. What Orbits are Allowed in an Axisymmetric Potential? 78 3.2.2. How did each population of stars gain their particular orbit? 78 3.2.3. Orbits in Elliptical Galaxies 79 3.2.4. What are the different populations in the galaxy, and what are their ages and metallicities? 80 3.2.5. What is the spheroid composed of (globular clusters?)? 80 3.3. Question 3 80 3.3.1. What errors are in your analysis? 80 3.3.2. Can you give some real statistics for SNe Ia? 81 3.4. Question 4 81 3.4.1. What stars are collisional? 82 3.4.2. Gas is collisional. Why? 82 3.5. Question 5/6 82 3.5.1. How does H2 form? 82 3.5.2. Why is H2 necessary for star formation? 83 3.5.3. How do Population III stars form? 83 3.6. Question 7 84 3.6.1. What observational differences are there between GCs and dSphs? 84 3.6.2. What is a Galaxy? 84 3.7. Question 8 85 3.7.1. How does velocity dispersion increase over time? 85 3.7.2. Why is the mean [Fe/H] not -1 at the birth of the MW? 86 3.8. Question 9 87 3.9. Question 10 88 3.9.1. Given a cross-section, how would you calculate the amount of extinction? 90 3.9.2. What percentage of the light is absorbed (rather than scattered) by the light? 90 3.9.3. Why is dust scattering polarized? 90 3.9.4. What is the grain distribution of the ISM? 91 3.10. Question 11 91 3.10.1. Under what conditions does the above formulation of dynamical friction hold? 92 3.10.2.
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