  Observations of both galaxies in the distant Universe and local starbursts
are showing increasing evidence for very hard ionizing spectra that stellar
population synthesis models struggle to reproduce. Here we explore the effects
of the assumed stellar initial mass function (IMF) on the ionizing photon
output of young populations at wavelengths below key ionization energy
thresholds. We use a custom set of binary population and spectral synthesis
(BPASS) models to explore the effects of IMF assumptions as a function of
metallicity, IMF slope, upper mass limit, IMF power law break mass and
sampling. We find that while the flux capable of ionizing hydrogen is only
weakly dependent on IMF parameters, the photon flux responsible for the He II
and O VI lines is far more sensitive to assumptions. In our current models this
flux arises primarily from helium and Wolf-Rayet stars which have partially or
fully lost their hydrogen envelopes. The timescales for formation and evolution
of both Wolf Rayet stars and helium dwarfs, and hence inferred population age,
are affected by choice of model IMF. Even the most extreme IMFs cannot
reproduce the He II ionizing flux observed in some high redshift galaxies,
suggesting a source other than stellar photospheres. We caution that detailed
interpretation of features in an individual galaxy spectrum is inevitably going
to be subject to uncertainties in the IMF of its contributing starbursts. We
remind the community that the initial mass function is fundamentally a
statistical construct, and that stellar population synthesis models are most
effective when considering entire galaxy populations rather than individual
objects.
