Constraining the metallicities, ages, star formation histories, and
  ionizing continua of extragalactic massive star populations
  We infer the properties of massive star populations using the far-ultraviolet
stellar continua of 61 star-forming galaxies: 42 at low-z observed with HST and
19 at z~2 from the Megasaura sample. We fit each stellar continuum with a
linear combination of up to 50 single age and single metallicity Starburst99
models. From these fits, we derive light-weighted ages and metallicities, which
agree with stellar wind and photospheric spectral features, and infer the
spectral shapes and strengths of the ionizing continua. Inferred light-weighted
stellar metallicities span 0.05-1.5 Z$_\odot$ and are similar to the measured
nebular metallicities. We quantify the ionizing continua using the ratio of the
ionizing flux at 900\AA\ to the non-ionizing flux at 1500\AA\ and demonstrate
the evolution of this ratio with stellar age and metallicity using theoretical
single burst models. These single burst models only match the inferred ionizing
continua of half of the sample, while the other half are described by a mixture
of stellar ages. Mixed age populations produce stronger and harder ionizing
spectra than continuous star formation histories, but, contrary to previous
studies that assume constant star formation, have similar stellar and nebular
metallicities. Stellar population age and metallicity affect the far-UV
continua in different and distinguishable ways; assuming a constant star
formation history diminishes the diagnostic power. Finally, we provide simple
prescriptions to determine the ionizing photon production efficiency
($\xi_{ion}$) from the stellar population properties. $\xi_{ion}$ has a range
of log($\xi_{ion})=24.4-25.7$ Hz erg$^{-1}$ that depends on stellar age,
metallicity, star formation history, and contributions from binary star
evolution. These stellar population properties must be observationally
determined to determine the number of ionizing photons generated by massive
stars.
