In Problem B of the Qualification Round, you estimated the number of stars in the Milky Way by assuming a constant density of stars throughout the galaxy. However, the density of stars is not constant and varies significantly across dierent regions. (a) Name the three regions A, B, C marked in the horizontal Milky Way drawing below. A B C Scientists have developed a basic model for the MilkyWay to describe the density distribution of stars (r) at distance r from the center by evaluating the three regions A, B, C: (r) = exp A r RA + exp B r RB + exp C r RC The model parameters have the values below: = 104 stars/(light-year)3 RA = 20 light-years RB = 12 103 light-years RC = 5 104 light-years A = 21, B = 3, C = 8 (b) Create a double logarithmic plot of the density distribution (r) with respect to r. (c) Using this model, calculate the number of stars in the Milky Way (r 130,000 light-years). Note: Assume that the Milky Way has a constant thickness of 1,000 light-years.
