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Problem 4 : As discussed in class, recent observations of stars within 0.1 pc of the center of our galaxy show that they move with speed approximately 300 km/sec. a. (20 points) Assuming circular orbits about the galactic center, calculate the mass within 0.1 pc of the center. Express your answer in terms of solar masses. As we’ve discussed many times in class, for a mass m moving with speed v in a circular orbit of radius r about a much larger mass M, F=ma is written as v2 GMm -------------- = m ----r r2 which tells us that the “mass in the middle” is 36 6 v2r M = -------- = 4.2 ×10 kg = 2.1 ×10 solar masses G b. (5 points) Argue that it is very unlikely for this mass to be made up of ordinary stars. From Table A4-1, the nearest star to us is 1.31 pc, so the local density of stars is something less than one per cubic parsec. This is consistent with one of our past studio exercises (on interstellar reddening) where we were told that the local density of stars is something like 0.1 per cubic parsec. If the center of our galaxy were made up of ordinary stars, this problem suggests a stellar density of 2 million per 0.13 cubic parsecs, or about 20 billion times the local stellar density. This would be like having several suns within the size of our solar system, which is much larger than we see anywhere else in the galaxy. Instead, we believe the center of our galaxy is occupied by a giant black hole. Problem 3 (25 points): Five galaxies are listed. (All are Messier objects). Five answer columns are also listed, corresponding to the five descriptive phrases listed below. Put a check (✓) in the corresponding box if that descriptive phrase applies to that galaxy. (One point for each box.) Galaxy M31 A C ✓ D ✓ ✓ M32 M77 B ✓ M82 M87 ✓ E ✓ ✓ ✓ ✓ ✓ ✓ ✓ A.) Spiral galaxy B.) Elliptical galaxy C.) Active galaxy D.) Significant (typical or greater) star formation in progress E.) Member of the local group Note that Appendix 1 lists the Messier objects, including their type. Note also that M82 is a “starburst” galaxy, which the text associates with being an “active galaxy”. If you didn’t check box C for M82, you’ll still get credit if you explained why not. Problem 2 (25 points): Use Zeilik Table 24-1 and Figure 24-2 to determine the distance to the Seyfert galaxy Markarian 79. Clearly indicate the values you assume for any other parameters. According to the figure caption, the prominent emission lines in Figure 24-2 are Hβ, and two lines of OIII. These can be associated with the lines listed in Table 24-1 if we allow for some redshift: Line Hβ OIII OIII λ0 4861 4959 5007 λ 5050 5150 5200 z=(λ−λ0)/λ0 0.0391 0.0385 0.0386 Each line is consistent with a redshift z ≈ 0.039. According to Hubble’s Law, the distance to the galaxy is given by Equation 22-3c, namely cz d = ----- = 156 Mpc H where we’ve assumed a value of H = 75 km/sec•Mpc. Problem 1: The spectral type of a certain main sequence star is precisely determined to be F5. Its apparent visual magnitude is 14.90 and its apparent blue magnitude is 15.85. a. (20 points): Find the distance to the star, accounting for interstellar reddening. Table A4-3 (in the appendix) tells us that an F5 star has absolute visual magnitude MV=3.4 and an intrinsic color index B−V=0.45. The observed color index is taken from the apparent magnitudes given, namely B−V=15.85−14.90=0.95, where the difference between intrinsic and observed is due to interstellar reddening. The “color excess” is CE=0.95−0.45=0.50 (Zeilik Eq.19.3) and the total visual absorption is AV≈3×CE=1.5 (Eq.19.4). We can then determine the distance from m V – M V = 5 log d – 5 + A V (Eq.19.2), and therefore logd = (14.90−3.4+5−1.5)/5 = 3 or d = 10 3 pc = 1 kpc b. (5 points): Does it seem that you are viewing the star through a dense dust cloud, or simply through the average interstellar medium? Explain your answer. It appears that we are viewing this cloud through the average interstellar medium. From the average amount of dust in the galactic disk, we expect to see between one and two magnitudes of visual absorption per kpc. (See class notes, or Zeilik page 369.) In this problem, the absorption is 1.5 magnitudes over 1 kpc, which is just what you’d expect if there were no extra-dense clouds in the way. Exam #3 79205 Astronomy Fall 1996 NAME: Solution Key You have two hours to complete this exam. There are a total of four problems and you are to solve all of them. All the problems are worth the same number of points. You may use your textbook (Zeilik), workbook (Hoff), and class notes and handouts, or other books. You may not share these resources with another student during the test. Indicate any figures or tables you use in your calculations. Show all Work! GOOD LUCK! Problem Score Worth 1. 25 2. 25 3. 25 4. 25 Total Score: 100