Reading: Chapters 2 and 4 of Sparke & Gallagher
The rules: Collaborative work is encouraged. This homework can be done in consultation with your fellow classmates, the AI, or the professor. However, everyone must submit their own solutions to get credit, and all help should be acknowledged (a single sentence mentioning the others in your study group is sufficient). Show your work.
1. [5 pts] Use the data of Tables 1.2 - 1.6 to estimate approximate spectral types for the brightest stars in the LMC, in the right panel of Figure 4.5.
2. [10 pts] The Carina dwarf spheroidal galaxy has a velocity dispersion (sigma) three times less than that at the center of the globular cluster Omega Centauri, while Carina's core radius is 50 times greater. (a) Use the virial theorem to show that Carina is about six times as massive as Omega Centauri. (b) Using the luminosity listed in Table 4.2, compare the M/L of Carina with that of Omega Centauri.
3. [15 pts] The Sagittarius dwarf spheroidal galaxy is now about 20 kpc from the Galactic center. (a) Find the mass of the Milky Way within that radius, assuming that the rotation curve remains flat with V(R) = 200 km/s. (b) Show that this dwarf galaxy would need a mass of about 6 x 109 Msun if stars at 5 kpc from its center are to remain bound to it. (c) What mass-to-light ratio (M/L) in the V band would this require?
4. [10 pts] Show that if stars are made from gas that is initially free of metals, so that Z(0) = 0, the closed box model predicts that when all the gas is gone, the mean metal abundance of stars is exactly p.
5. [10 pts] Explain why most of the galaxies nearest to us do not follow Hubble's law.