Copyright by Athena Ranice Stacy 2011 - The University of Texas at ...

with respect to the sink is denoted by rI. ˙Nion is the number of ionizing
photons emitted per second, and αB is the case B recombination coefficient.
We use αB = 1.3 × 10 −12 cm 3 s −1 for He iii recombinations to He ii, and
αB = 2.6 × 10 −13 cm 3 s −1 for He ii and H ii recombinations to the ground
state (Osterbrock and Ferland 2006).
The emission rate of H i, He i and He ii ionizing photons is given by
Nion
˙ = πL∗
σSBT 4 ∞
eff νmin
Bν
dν , (3.2)
hν
where h is Planck’s constant, σSB the Stefan-Boltzmann constant, and νmin the
minimum frequency required for ionization of the relevant species (H i or He ii).
For simplicity we do not distinguish between the H ii and He ii regions. We
assume the sink emits a blackbody spectrum Bν with an effective temperature
Teff, which depends upon the evolving stellar radius and luminosity.
As described in Greif et al. (2009), the integral on the right-hand side
of the ionization front equation is discretized by the following sum:
rI
0
nen+r 2 dr
i
ne,in+,ir 2 i ∆ri , (3.3)
where ∆ri is the radial extent of each bin i, and the sum ranges from the
sink particle to the current position of the I-front. The left hand side of the
ionization front equation is similarly discretized by:
nnr 2 I
drI
dt
1
∆t
62
i
nn,ir 2 i ∆ri , (3.4)