Astronomy 104: Homework Set 5 Due: Monday, March 16, 2015 (Assignment covers Destinations 10, 11, 12, 13) 1. Calculate the Schwarzschild radii for the following objects assuming they have been converted into black holes (Destination 10): a) You. b) The Earth. c) The Sun. d) The Galaxy. 2. Use the web to find the following information about any globular cluster other than M 92: Total luminosity, approximate total number of stars, age, chemical abundance, distance from Sun, distance from Galactic Center. Be sure you identify a globular cluster and not an open cluster like the Pleiades. There are over 20 of them in Messier’s catalog and nearly 200 overall within our Galaxy alone. You may have to estimate some of these based on the information you find on the web. 3. Identify the most luminous, reddest red giant in the HR diagram of a globular clusters shown in Figure 11.5 of the text. What is the radius of this star? Give your result in both Solar Units and AU. 4. The atomic weights of Al28, Fe56 and Cd112 (those are Aluminum, Iron and Cadmium) are 27.982, 55.935 and 111.903 atomic mass units, respectively. Imagine fusing two of these Al nuclei into one Fe nucleus. Then imagine fusing two of these Fe nuclei to make one Cd nucleus. Which of these two reactions is exothermic (produces energy) and which endothermic (consumes energy)? Given what you observe from these comparisons, explain under what conditions Fe and Cd might be able to form in stars. 5. Use the data in the following table for the questions below. Reading through Destination 13 will help you put the questions in this problem in context. R (pc) Density_1 (𝑴⊙ /𝒑𝒄𝟑 ) Density_2 (𝑴⊙ /𝒑𝒄𝟑 ) 5000.00 8500.00 12000.00 20000.00 40000.00 80000.00 120000.00 200000.00 2.05E-07 2.51E-08 6.36E-09 8.27E-10 5.15E-11 3.19E-12 6.26E-13 8.04E-14 3.62E-08 7.52E-09 2.69E-09 5.84E-10 7.30E-11 9.10E-12 2.69E-12 5.78E-13 a) Plot the logarithm (base 10) of the mass density vs. the logarithm (base 10) of the radial distance from the center of a galaxy for both density profiles listed in the table. b) In a log-log plot like the one you produced, a straight light implies a power-law profile. Do the data for each of the density laws you plotted follow a straight line? c) Determine the slope of the line that best fits each of the two density profiles. Keeping in mind that the Bulge of our Galaxy has a power-law slope of about −4 and the Halo has a power-law slope of about −3, which density profile from the table, number 1 or number 2, is most likely from the galaxy’s bulge population, and which is most likely from its halo? d) At what radius from the galaxy center does the halo population (the one with slope −3) become more dominant than the bulge population (the one with the slope −4). HINT: At what value of R do the lines cross? You will read off log(R) but give the actual value of R in pc.