# A Strömgren sphere and neutral time

1. May 15, 2009

### TFM

1. The problem statement, all variables and given/known data

A Strömgren sphere is the ionized region surrounding a strong ionizing source. Its size is determined by there being a balance between the rate of ionization and the rate of recombination. Consider such a sphere of radius $$R_S$$ = 10 pc and internal density $$n_e = 10^6 m^{-3}$$, and with a central ionizing source of $$10^{49} photons s^{−1}$$.

a)

How long will it take to become neutral once the ionising star has switched off?

b)

Suppose that the sphere expands at a rate equal to the sound speed in a 10^4 K gas. How long will it take to expand to a radius of 100 pc? ($$v_s^2\approx 3kT/m_H$$)

2. Relevant equations

3. The attempt at a solution

Okay I have done part b), getting an answer of about 5.6 million years, but I have a small query regarding part a).

I know that the charge loss will be $$10^49 atoms s^{-1}$$
because this is the photon rate when it is in equilibrium, which means this rate is equal to the rate at which atoms become neutral. I also know that I need to work out the volume of the sphere, and thus the number of particles in it.

However, i am slightly uncertain how to work out how many particles are actually ionised before the star is turned off.

?

TFM

Last edited: May 15, 2009