NLTE AND LTE Lick indices for red giants from [Fe/H] 0.0 TO −6.0 AT SDSS AND IDS spectral resolution

Abstract

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 < Teff < 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[subscript n], from multi-variate linear regression for I with terms up to third order in the independent variable pairs (Teff, [M/H]) and (V - K, [M/H]), and compare them to the fitted C[subscript n] values of Worthey et al. at IDS spectral resolution. For this fitted I data-set we present tables of LTE partial derivatives, [partial derivative]I/[partial derivative]Teff [vertical bar][M/H], [partial derivative]I/[partial derivative][M/H] [vertical bar] Teff, [partial derivative]∣/[partial derivative](V - K) [vertical bar][M/H], and [partial derivative]I/[partial derivative][M/H] [vertical bar](V - K), that can be used to infer the relation between a given difference, [delta]I, and a difference [delta]Teff or [delta](V - K), or a difference [delta][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 Teff and [M/H] values. As an example of the impact on stellar parameter estimation, for late-type giants of inferred Teff [greater than or similar to] 4200 K, an Fe-dominated I value computed in LTE that is too strong might be compensated for by inferring a Teff value that is too large.