TFM
May15-09, 11:31 AM
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.
?
Thanks in advanced,
TFM
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.
?
Thanks in advanced,
TFM