Introduction to Astrophysics II, 29:120
Winter, 2006-2007
Sixth Homework Set...March 2, 2007. Due March 8, 2007

(1) Calculate the frequencies of the $J=2 \rightarrow 1$ and $J=1 \rightarrow 0$ transitions of the CO molecule. What kind of telescope would you use to observe these spectral lines?

(2) Assume that the temperature in a molecular cloud is 6 K. Further assume that the intensity of a rotational transition is directly proportional to the population of a state, and that the statistical weights of rotational states are all unity. What is the ratio of the intensities of the $3 \rightarrow 2$ and $2 \rightarrow 1$ transitions of CO?

(3) Using insight from #2, explain how you would distinguish a cloud with $T=6$ K from one with $T= 15$ K. You do not need to carry out a calculation, but your explanation should be clear and use equations.

(4) What is the Jean's Mass for the gas in the Earth's atmosphere? How does that mass compare with the total mass of the Earth's atmosphere? A rough estimate for the mass of the Earth's atmosphere will do, jess fine.

(5) Calculate the time it takes for a free-falling, homologously-contracting cloud to go from its initial radius $r_0$ to $\frac{r_0}{2}$?

(6) A Giant Molecular Cloud (GMC, assumed spherical) has a mass of $5 \times 10^4 M_{\odot}$ and a radius of 10 parsecs. What is the change in gravitational potential energy as it contracts to $r = 5$ parsecs? Assuming that it is in virial equilibrium, where does this energy go?

(7) Assuming virial equilibrium, what is the temperature of a GMC with $5 \times 10^4 M_{\odot}$ and $r = 5$ parsecs? The molecular cloud can be assumed to be purely molecular hydrogen.

(8) # 12.9 from book