NLTE and LTE Lick Indices for Red Giants from [Fe/H] 0.0 to -6.0 at SDSS and IDS Spectral Resolution

We investigate the dependence of the complete system of 22 Lick indices on overall metallicity scaled from solar abundances, [{{M}}/{{H}}], from the solar value, 0.0, down to the extremely metal-poor (XMP) value of -6.0, for late-type giant stars (MK luminosity class III, {log}g=2.0) of MK spectral class late-K to late-F (3750\lt {T}_{eff}\lt 6500 K) of the type that are detected as “fossils” of early galaxy formation in the Galactic halo and in extra-galactic structures. Our investigation is based on synthetic index values, I, derived from atmospheric models and synthetic spectra computed with PHOENIX in Local Thermodynamic Equilibrium (LTE) and Non-LTE (NLTE), where the synthetic spectra have been convolved to the spectral resolution, R, of both IDS and SDSS (and LAMOST) spectroscopy. We identify nine indices, that we designate “Lick-XMP,” that remain both detectable and significantly [{{M}}/{{H}}]-dependent down to [{{M}}/{{H}}] values of at least ∼ -5.0, and down to [{{M}}/{{H}}] ∼ -6.0 in five cases, while also remaining well-behaved (single-valued as a function of [{{M}}/{{H}}] and positive in linear units). For these nine indices, we study the dependence of I on NLTE effects, and on spectral resolution. For our LTE I values for spectra of SDSS resolution, we present the fitted polynomial coefficients, {C}_{{n}}, from multi-variate linear regression for I with terms up to third order in the independent variable pairs ({T}_{eff}, [{{M}}/{{H}}] ) and (V-K, [{{M}}/{{H}}]), and compare them to the fitted {C}_{{n}} values of Worthey et al. at IDS spectral resolution. For this fitted I data-set we present tables of LTE partial derivatives, \frac{\partial I}{\partial {T}_{eff}}{| }_[{{M}/{{H}}]}, \frac{\displaystyle \partial I}{\partial [{{M}}/{{H}}]}{| }_{T{eff}}, \frac{\displaystyle \partial I}{\partial (V-K)}{| }_[{{M}/{{H}}]}, and \frac{\partial I}{\partial [{{M}}/{{H}}]}{| }_(V-K), that can be used to infer the relation between a given difference, {{Δ }}I, and a difference {{Δ }}{T}_{eff} or {{Δ }}(V-K), or a difference {{Δ }}[{{M}}/{{H}}], while the other parameters are held fixed. For Fe-dominated Lick indices, the effect of NLTE is to generally weaken the value of I at any given {T}_{eff} and [{{M}}/{{H}}] values. As an example of the impact on stellar parameter estimation, for late-type giants of inferred {T}_{eff}≳ 4200 K, an Fe-dominated I value computed in LTE that is too strong might be compensated for by inferring a {T}_{eff} value that is too large.