The LBT $Y_{\rm p}$ Project II: MODS Spectra, Physical Conditions, and Oxygen Abundances in Local Metal-Poor Nebulae
Empirically measuring the primordial He mass fraction, $Y_{\rm p}$, requires a significant number of low-metallicity nebulae with direct constraints on He/H and O/H abundances. This technique requires high-fidelity measurements of the gas-phase physical conditions, namely the electron temperature ($T_e$) and density ($n_e$). To this end, we present deep rest-optical spectroscopy for a sample of 62 low-metallicity ($\lesssim$ 20% solar O/H) galaxies acquired using the Multi-Object Double Spectrographs (MODS) on the Large Binocular Telescope (LBT) as part of the LBT $Y_{\rm p}$ Project. We discuss new fitting methods that recover the intensity of up to 61 H and He recombination lines, of which, up to 26 will be used to determine gas-phase He abundances, and we examine the emission line properties of the LBT $Y_{\rm p}$ Project sample. We assess different scaling relations in the low-metallicity interstellar medium (ISM), finding that $n_e$[Ar IV] measured in 31 targets is systematically larger than $n_e$[S II] or $n_e$[O II]. The larger densities are insufficient to significantly bias $T_e$[O III] or the O/H abundance. $T_e$[S III] and $T_e$[O III] are strongly correlated over a range of $\sim$10$^4$ K with very low scatter, and we calibrate new $T_e$[S III]-$T_e$[O III] scaling relations for use in other low-metallicity environments. We examine different $T_e$ measured in the low-ionization gas, finding significant scatter compared to $T_e$[O III]. The precision direct O/H derived in this analysis (median uncertainty $\sim$4%) are consistent with prior literature measurements, albeit with relatively large scatter. These data provide a key component necessary to empirically measure $Y_{\rm p}$ and the abundance patterns of other elements in the ISM.