PHYS0003/PHYS1650 - Nature of the Universe Assignment 4 Due date: 5:00pm, November 26, 2014 Please submit to the assignment box in first floor of CYMP Buld. Give answers and explanations for the following questions. 1. (15 marks) (a) Name two differences between open clusters and globular clusters. (b) What can we learn by studying the H-R diagram of stars in a cluster that we cannot learn by studying single stars? 2. (10 marks) The total mass of a binary system can be estimated with the following formula a3 (1) total mass = 2 P where a is the average distance between the two stars in AU’s and P is the orbiting period in years, and the total mass will be in the unit of solar masses. (a) Look up the average distance between the two stars of Sirius, which is a binary system. Also look up their period. (b) Estimate the total mass. 3. (5 marks) (a) Is it easier to discover visual binaries that are closed to us or far away from us? Why? (b) Is it easier to discover spectroscopic binaries that are high in orbital speed or low in orbital speed? Why? 4. (10 marks) Suppose the period-luminosity relation of Cepheid variables is given by log10 L = 1.1 log10 P + 2.5 , (2) where L is the average luminosity in the unit of solar luminosity and P is period in units of days. Derive the relation for absolute magnitude M in the form M = A log10 P + B , (3) and find the unknowns A and B. Hint: the absolute magnitude of the Sun is 4.8. 5. (10 marks) What is the source of energy in a protostar? At what point does a protostar become a star? 6. (10 marks) An interstellar cloud of hydrogen has a radius of ten parsecs and a density of 109 hydrogen atoms per cubic meter. Calculate the total mass of interstellar matter in the cloud. 7. (10 marks) (a) Why do we call 12 C a catalyst in the CNO cycle? (b) For each helium nucleus produced, does the p-p chain or the CNO cycle produce more energy? Why? 8. (5 marks) Why an extreme massive star, say 1000 solar masses, cannot be formed? (This is a difficult question.) 9. (10 marks) Observationally, how can astronomers distinguish between Type Ia and Type II supernovae? 10. (15 marks) Sgr A* is a radio-luminous object at the center of our Milky Way Galaxy. One method to calculate the mass of Sgr A* is to measure the orbital velocity of the surrounding gas clouds. (a) Given the measured velocity of 260kms−1 of a gas cloud located 0.3pc from Sgr A*, what is its inferred mass M? (Hint: Using the following results from Newtonian mechanics M = v 2 r/G where v is the orbital velocity of the cloud, r its distance from the central object and G = 6.67 × 10−11 Nm2 kg−2 the gravitational constant.) (b) Hence, what is the Schwarzschild radius of Sgr A*, the central object? (c) The observational limit is that its size is at most 20pc. Can we conclude that it is a black hole?