Consider a neutral hydrogen cloud of mass = 200 , temperature T = 21.5K, and density n = 106 atoms/m3. To answer all questions below, you will also need the following information: - There are 4 spiral arms in the Milky Way galaxy (MW); - The cloud is on a circular orbit, 3.2 kpc from the centre of the MW; - Relative speed of the cloud with respect to spiral arms is 50 km/s.

QUESTION: Every time the cloud passes through a spiral arm, its density, n , increases by a factor of 4.

Therefore, the Jeans mass also changes according to (1).

a. What the cloud's Jeans mass after the first pass through the spiral arm?

b. After the second pass?

c. How many passes of the cloud through spiral arms are needed to make the cloud collapse?