Introduction to Astrophysics II, 29:120
Winter, 2006-2007
Fifth Homework Set...February 22, 2007. Due March 1, 2007

You know the story by now. Do it!

(1) A spectral class A0V star is 2 kiloparsecs distant in the galactic plane. How much is its light attenuated at a wavelength of 5000 Å  relative to the case if there were no interstellar extinction?

(2) Astronomers like magnitudes. What is the apparent magnitude of the star in problem # 4, including the effect of interstellar extinction?

(3) A common measure of the color of a star is the difference in its B and V magnitudes, B-V. What is B-V for the star in problem #4?

(4) For purposes of simplification, assume that the extinction of the light of the above star (yea, we're still talking about the same star) is due predominantly to particles with the size for which $Q_{ext}$ is a maximum.
(a) What is the size of the particles that are primarily attenuating the light at 5000 Å?
(b) What is the number density of these grains in the interstellar medium?

(5) Problem 12.2 from the textbook

(6) Assume that a spectral class O5V star radiates like a blackbody. Calculate its Lyman luminosity in photons/sec ($N$ in equation 12.21). You will probably have to use Mathcad or some other numerical scheme to come up with an answer. Be sure to make it clear what you are doing. Hint: You will have to do some searching, in the book or elsewhere, for some of the data that you need.

(7) Assume that the star in problem # 6 is placed in a cloud of hydrogen gas with a density of 10 cm$^{-3}$. What is the radius of the HII region which is produced?

(8) Assume that the dominant star in the Rosette Nebula (NGC 2237) is an O5V star. Using data you can find on the Rosette, calculate the mean density in the HII region.