Characterizing Extreme Emission Line Galaxies II: A Self-Consistent
  Model of Their Ionizing Spectrum
  Observations of high-redshift galaxies ($z >$ 5) have shown that these
galaxies have extreme emission lines with equivalent widths much larger than
their local star-forming counterparts. Extreme emission line galaxies (EELGs)
in the nearby universe are likely analogues to galaxies during the Epoch of
Reionization and provide nearby laboratories to understand the physical
processes important to the early universe. We use HST/COS and LBT/MODS spectra
to study two nearby EELGs, J104457 and J141851. The FUV spectra indicate that
these two galaxies contain stellar populations with ages $< \sim$ 10 Myr and
metallicities $\leq$ 0.15 Z$_\odot$. We use photoionization modeling to compare
emission lines from models of single-age bursts of star-formation to observed
emission lines and find that the single-age bursts do not reproduce
high-ionization lines including [O III] or very-high ionization lines like He
II or [O IV]. Photoionization modeling using the stellar populations fit from
the UV continuum similarly are not capable of reproducing the emission lines
from the very-high ionization zone. We add a blackbody to the stellar
populations fit from the UV continuum to model the necessary high-energy
photons to reproduce the very-high ionization lines of He II and [O IV]. We
find that we need a blackbody of 80,000 K and $\sim$60-70% of the luminosity
from the young stellar population to reproduce the very-high ionization lines
while simultaneously reproducing the low- intermediate-, and high-ionization
emission lines. Our self-consistent model of the ionizing spectra of two nearby
EELGs indicates the presence of a previously unaccounted-for source of hard
ionizing photons in reionization analogues.
