  This is the second of two papers examining Spitzer Infrared Spectrograph
(IRS) observations of the ultraluminous X-ray source (ULX) in Holmberg II. Here
we perform detailed photoionization modeling of the infrared lines. Our
analysis suggests that the luminosity and morphology of the [O IV] 25.89 $\mu$m
emission line is consistent with photoionization by the soft X-ray and far
ultraviolet (FUV) radiation from the accretion disk of the binary system and
inconsistent with narrow beaming. We show that the emission nebula is
matter-bounded both in the line of sight direction and to the east, and
probably radiation-bounded to the west. A bolometric luminosity in excess of
10$^{40}$ erg s$^{-1}$ would be needed to produce the measured [O IV] flux. We
use modeling and previously published studies to conclude that shocks likely
contribute very little, if at all, to the high-ionization line fluxes observed
in the Holmberg II ULX. Additionally, we find that the spectral type of the
companion star has a surprisingly strong effect on the predicted strength of
the [O IV] emission. This finding could explain the origin of [O IV] in some
starburst systems containing black hole binaries.
