Week 1 (Oct 3) In-Class Problem

Due Oct 7, 2022 by 11:59pm
Points 10
Submitting a text entry box or a file upload

October 3rd - Note, there is no class on October 5th! This is a (rare) one-problem week!

Problem 1:

The total mass of neutral gas in the Galaxy is ~ 4 $LaTeX: \times$ $\times$ $LaTeX: 10^{9} M_{\odot}$ $10^{9} M_{\odot}$ . Assume that this material is uniformly distributed in a disk of radius $LaTeX: R_{\rm disk}$ $R_{\rm disk}$ = 15 kpc and thickness H = 200 pc, and that it is a mixture of H and He with He/H=0.1 (by number). Assume ionized hydrogen to be negligible in this problem.

(a) What is the average number density of hydrogen nuclei within the disk?

(b) If 0.7% of the neutral interstellar mass is in the form of dust in spherical particles of radius a = 1000 $LaTeX: \unicode{8491} = 0.1 \mu m$ $\unicode{8491} = 0.1 \mu m$

and density 2 g $LaTeX: cm^{-3}$ $cm^{-3}$ , what is the mean number density of dust grains in interstellar space?

(c) Now assume that 30% of the gas and dust mass is in spherical molecular clouds of radius 15 pc and mean density $LaTeX: n(H_{2}) = 100 cm^{-3}$ $n(H_{2}) = 100 cm^{-3}$ . What would be the mass of one such cloud? How many such molecular clouds would there be in the Galaxy?

(d) With 30% of the material in molecular clouds as in (c), above, what is the expectation value for the number of molecular clouds that will be intersected by the line of sight to the Galactic center, assumed to be 8.5 kpc away? [Hint: the number of molecular clouds in the Galaxy is large, and they occupy a small fraction of the volume, so think of this as a Poisson process", where the presence or absence of each molecular cloud on the line-of-sight is treated as an independent event (like the number of radioactive decays in a fixed time interval).]