Anewstar lights up inside a cloud of atomic hydrogen with a constant number density of n atoms per unit volume. The star emits ionizing photons at a rate of Q¤ photons per unit time. The ionizing photons begin carving out a growing “Str¨omgren sphere” of ionized gas inside the neutral gas . a. At a distance r from the star, what is the timescale ¿ion over which an individual atom gets ionized, if the ionization cross section is ¾ion? b. If the recombination coef cient is ® ´ h¾vi, what is the timescale ¿rec for an individual proton to recombine with an electron?