# Strömgren Sphere of Sun

I have a homework problem:

The Sun emits $\sim5 x 10^{23}$ photons per second with $hν > 13.6$ $eV$. If the density of hydrogen atoms in interplanetary space is $n =$ $109 m^{-3}$, what is the size of the Stromgren sphere? Assume a recombination coefficient $α = 2.6 x 10^{-19} m^3s^{-1}$.

From Wikipedia, I was able to get to

$$R_S = \left( \frac{3S_*}{4\pi n^2 \beta_2} \right)^\frac{1}{3}$$

And I know $\beta_2 = \frac{\alpha}{T}$, but I have no idea what the $S_*$ is. Wikipedia describes it as a source of flux, which is obviously the sun, but I cannot figure out anything else about it. I'm actually quite sure that the professor would have given us a different equation, but he never went over it, so I don't know. Anyone know how to solve this?

• In astronomy, S is usually flux. Here is it probably total watts put out by the star. The wikipedia article is sloppy in not defining its terms or linking to a page defining these. Oct 29 '13 at 0:36

Fundamentally, this is just balancing rates to find an equilibrium. On one side, you have the ionization rate, $5\times10^{23}\ \mathrm{s}^{-1}$, often denoted $Q$. On the other side you should write, as a function of $R_\mathrm{s}$, the rate of recombinations in the entire volume given the density of $\mathrm{H}^+$ and $e^-$. No $\beta$'s or $S$'s required.