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Unformatted text preview: NS 209 What is there in the universe, beyond the Milky Way Final Exam A 11 June 2007  16:0018:00 Instructor: Emrah Kalemci Surname: Name: Student No: Problems (62 pts) Short answer (10 pts) Multiple choice (48 pts) Total (120 pts): Instructions: 32 multiple choice questions (1.5 pts each), 10 point short answer questions 2 problems (62 pts), over 120. i)You MUST use the key below for multiple choice questions. ii)Wrong answers do not cancel right answers, feel free to guestimate the answers iii) All double answers erased. iv) No calculators! Some useful information: H o = 70 km/s/Mpc c=3 x 10 5 km/s pc = 3 x 10 13 km 1 AU = 1.5 x 10 8 km ly = 10 13 km radian = 57.3 o . ρ critical = 1026 kg/m 3 (9 x 1027 kg/m 3 is the actual value, but you may use 1026 kg/m 3 to aid computation) Problem 1. a. Assume supernovae type Ia are standard candles with constant peak luminosity of 3.6 x10 36 Watts. If such a supernova explosion was detected with a flux of (1/π) 1011 Watts/m 2 , what is the distance to this quasar in Mpc? (15 pts) Luminosity = Flux x 4 π (distance) 2 . 3.6 x10 36 Watts = (1/π) 1011 Watts/m 2 x 4 π (distance) 2 . (distance) 2 = 9 x 10 46 m 2 , distance = 3 x 10 23 m = 10 Mpc b. Draw a sphere with a radius from the sun to the galaxy with the supernova explosion (shown by the line denoted with d in the figure). Assume that the normal matter and dark matter is homogeneously distributed in this sphere, calculate the dark matter mass inside this sphere in kg. Use Ω dm =0.20 for dark matter. Take π = 3. (15 pts) Volume = 4/3 x π x d 3 = 4 x 27 x 10 69 m 3 . = 1.08 10 71 m 3 . ρ dm = ρ critical x Ω dm = 0.2 x 1026 kg/m 3 . The dot at the center depicts Sun Mass = 0.2 x 1026 kg/m 3 x 1.08 10 71 m 3 . and the other dot depicts the Galaxy = 2.2 x 10 46 kg. with Sn Type 1a d 2. Of matter and radiation, which dominated the universe and by what factor in density (assuming a flat universe with critical density) at the start of decoupling? Take z ~ 1000, it is actually 1100, but to aid computation you can use 1000. Assume today, Ω matter ~1 (including dark matter) and Ω radiation ~ 5x105 . For this problem only assume cosmological constant is zero, and matter dominates the density, even for today. You can use the figure for hints. a. Find the current matter and radiation density using the critical density and Ω values given above. (5 pts) today: ρ matter = 1026 kg/m 3 . ρ radiation = 5 x1031 kg/m 3 . b. Determine how density changes with the size of the universe for matter and radiation. DO NOT forget the cosmological redshift for radiation. For a photon, E = hc/λ where E is energy, h is the Planck constant and λ is the wavelength which increases linearly with the size of the universe....
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 Fall '09
 MehmetYali

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