The LBT Y$_{\rm p}$ Project VI: Gas-Phase Chemical Abundance Patterns of Metal-Poor Nebulae
Through a combined rest-optical and NIR observing campaign, the Large Binocular Telescope Primordial He Abundance ($Y_{\rm p}$) Project has delivered a precision measurement of $Y_{\rm p}$. Given the stringent requirements to measure gas-phase He abundances, the optical spectra contain emission features from a plethora of metals in the Interstellar Medium (ISM). We present gas-phase N, O, Ne, S, Cl, Ar, K and Fe abundance patterns in 62 low-metallicity nebulae. We assess ionization correction factors for each element and select those that reproduce the observed ionic abundance trends. The Ne/O, S/O, and Ar/O abundances do not evolve with metallicity and agree with the solar ratios. Given the Type Ia enrichment of S and Ar, the solar S/O and Ar/O suggest extended star formation histories in local galaxies relative to high-$z$ galaxies at fixed O/H. We report the first ISM K abundances in low-metallicity extragalactic nebulae; both Cl/O and K/O are constant with O/H, indicating the production of these odd-Z elements follows that of $α$ elements. Consistent with prior analyses, gas-phase Fe/O is observed to decrease with O/H due to dust depletion; correcting for this produces an average [Fe/O]$=$$-$0.80, implying Fe-deficient stars capable of producing hard ionizing spectra. Finally, the metallicity-insensitive log(N/O) plateau from 50 nebulae is $-$1.43$\pm$0.10, consistent with previous works. Five galaxies have N/O significantly enhanced relative to the primary plateau, and we discuss their properties, mechanisms that could bias measurements of N/O, and nucleosynthetic progenitors that can produce enhanced N at low metallicity.