The formation processes that led to the current Galactic stellar halo are still under debate. Previous studies have provided evidence for different stellar populations in terms of elemental abundances and kinematics, pointing to different chemical and star formation histories (SFHs). In the present work, we explore, over a broader range in metallicity (-Fe H 0.5), the two stellar populations detected in the first paper of this series from metal-poor stars in DR13 of the Apache Point Observatory Galactic Evolution Experiment (APOGEE). We aim to infer signatures of the initial mass function (IMF) and the SFH from the two α-to-iron versus iron abundance chemical trends for the most APOGEE-reliable α-elements (O, Mg, Si, and Ca). Using simple chemical-evolution models, we infer the upper mass limit (M up ) for the IMF and the star formation rate, and its duration for each population. Compared with the low-α population, we obtain a more intense and longer-lived SFH, and a topheavier IMF for the high-α population.

For the first time, we obtain chemical evolution models (CEMs) for Tucana and Cetus, two isolated dwarf spheroidal galaxies (dSphs) of the Local Group. The CEMs have been built from the star formation histories (SFHs) and the metallicity histories, both obtained independently by the LCID project from deep color-magnitude diagrams. Based on our models, we find that the chemical histories were complex and can be divided into different epochs and scenarios. In particular, during 75% of the SFH, the galaxies behaved as closed boxes and, during the remaining 25%, either received a lot of primordial gas by accretion or they lost metals through metal-rich winds. In order to discriminate between these two scenarios, abundances ratios in old stars are needed. At t∼4.5 Gyr, the galaxies lost most of their gas due to a shortstrong, well-mixed wind. We obtain very similar CEMs for both galaxies, although Cetus is twice as massive as Tucana. We conclude that the star formation in both galaxies began with only 1.5% of the baryonic mass fraction predicted by ΛCDM.

We use semi-analytical methods to obtain detailed chemical evolution models (CEMs) for the dwarf spheroidal (dSph) galaxy Tucana. Published star formation rates and the age–metallicity relationship are used to constrain the observables. The results show that Tucana: (i) behaved like a closed box for 75 per cent of its life, (ii) had either a primordial-gas accretion or a metal-rich wind during 15 per cent of its life (between 0.5 and 2.0 Gyr), and (iii) lost 95 per cent of its gas through a well-mixed wind at t ∼ 4.5 Gyr. Specifically, we find two CEMs: the metal-dilution model and the metal-loss model, which differ mainly during the range 0.5–2.0 Gyr. In order to discriminate between these CEMs, we compare the predicted [Xi/Fe]–[Fe/H] trends, which differ less than the average error of the observed trends for other dSphs of the Local Group. Furthermore, the models predict very different metallicity distribution functions. Therefore, an observational metallicity distribution function for Tucana is essential in order to discriminate between the metal-dilution and the metal-loss scenarios. In addition, because the difference of [Xi/Fe] between the two models is less than the average of the errors observed for others dSph and ultra-faint dwarf galaxies of the Local Group, greater precision is required in future observations, so that the errors are less than the difference between the models, thus enabling discrimination between them.