Homework # 3, due 24 Feb
1. Calculate the size of a Stromgren sphere in a gas of density 103 cm−3 surrounding an O3 star. This is the volume of gas nearly completely ionized by
the star. Assume the recombination rate of protons and electrons to form
neutral hydrogen is
dne
= −2 × 10−13 ne np
dt
T
104 K
−3/4
cm−3 s−1 .
If the star suddenly turned on, estimate how long it would take for the
Stromgren sphere to come into radiative equilibrium.
Also calculate the size of such a sphere surrounding a solar G2 star.
2. Suppose the number density of stars normal to the Galactic plane varies as
n(z) = n0 exp(−z/zh ). Suppose you do a survey of G2 stars in the direction of
the North Galactic Pole complete to a magnitude mv = 30.
What value would you obtain for V/V max ?
3. Compute expressions for the potential and kinetic energies of the singular
isothermal sphere. Assume the temperature is 20 K. Suppose the sphere’s
boundary is where it’s pressure is the same as that of the warm phase in the
ISM.
What is the radius of the sphere if its mass is 10 M ?
What will happen if the sphere cools uniformly?