We lack a “canonical” model of the Galactic stellar Halo, i.e. a comprehensive framework of the physical mechanisms behind its early formation and evolution. The most popular theories date back to Eggen+62 who suggested a dissipative collapse and to Searle+78 who suggested a dissipation-less mechanism. The latter scenario is supported by Cold Dark Matter cosmological simulations suggesting that the Halo formed from the aggregation of protogalactic fragments- small galaxies form first and then merge to form larger galaxies (Monachesi+19). The discovery of stellar streams and the merging of a massive dwarf galaxy like Sagittarius (Ibata+94) provided further support to this hierarchical mechanism. Now in the Gaia era, the fine structure of the Halo is clearly emerging (Das+16; Iorio+19). New signatures of major/minor mergers have been found in the inner Halo: Gaia Enceladus (Helmi+18) and Sequoia (Myeong+19). Furthermore, we lack quantitative constraints on the possible correlation between Bulge and Halo mass and their merger histories (Bell+17). In order to attack the early Halo formation and to quantitatively establish the fraction of stars that formed in situ from those that were accreted we plan to use four observables: Pulsation properties- RRL pulsation properties are relics of the environment from which they originate (Fabrizio+19), standard candles (Marconi+21) and crucial ingredients to trace stellar parameters (Marconi+18). The comparison between period and luminosity amplitude distributions of the RRLs in nearby dwarf galaxies, globular clusters (GCs) and in the field provides firm constraints on the role that these systems played in building up the Halo. Fiorentino+17, by using more than 20000 field RRLs, found that the Halo was mainly formed either in situ or by the accretion of a few massive dwarf galaxies. EFEBHO plans to use the full parameter space of RRLs as solid beacons to probe the Halo and as a stepping stone to understand the Bulge, since their formations are tightly connected. Metallicity distributions- Accurate measurements of the elemental abundances in field stars are a powerful diagnostic to investigate their origin (in situ vs ex situ) and the formation timescale of the various Galactic components (Chiappini+97). Matteucci+86 suggested that the inner Halo formed on a timescale of ~1 Gyr using the [alpha/Fe] vs. [Fe/H] diagram (alpha includes O, Mg, Si). Furthermore, the Halo metallicity gradients and their spreads are key observables to trace back the Halo chemical enrichment. On the basis of Low Resolution (LR) spectra for 302 field RRLs, Layden94 found that the Halo iron gradient is quite flat over the 10-40 kpc range ([Fe/H]~-1.6 and σ=0.3 dex), but it becomes more metal-rich inside the solar circle (d ≲ 8 kpc). More recently, Xue+15 by using ~1800 Red Giant stars (RGs) also found evidence of a shallow metallicity gradient steadily decreasing by 0.1-0.2 dex from ~10 to ~100 kpc. In contrast, Conroy+19, based on High Resolution (HR) optical spectra of 4200 RGs, and Fernández-Alvar+17, based on HR near-infrared (NIR) spectra of 3900 RGs, found no evidence of a gradient over a wide range of Galactocentric distances (10-80 kpc). Halo density profile- A variation in the slope of the Halo density profile and/or in its flattening when moving from the inner to the outer Halo can be associated to a dichotomic formation mechanism. However, the current findings are controversial. On the one hand, Carollo+07 by using RGs and Kinman+12 by using RRLs suggested that the outer Halo is more spherical and its density profile is shallower than the inner Halo (Halo duality). On the other hand, Deason+11 by using Blue Horizontal Branch stars and Blue Stragglers found no change in the flattening as a function of the Galactocentric distance (see also Keller+08; Sesar+11). More recently, Xue+15 by adopting a global ellipsoidal stellar density model with an Einasto prole (Einasto65) found that a constant flattening provides a good fit of the entire Halo, while Iorio+18 found that the inner Halo is triaxial and that its flattening decreases outwards. Chemical-orbital properties- The coupling between chemical abundances and kinematics provides clues to the collapse and angular momentum evolution of the Halo. The current investigations are based on bright field RGs. Carollo+10 identified two Halo components: a more spherical and prograde inner Halo that is "more metal-rich” ([Fe/H]=-1.6 dex) and with highly eccentric orbits, and an outer Halo that is retrograde and "more metal-poor" ([Fe/H]=-2.2 dex). However, the properties of this dual Halo are poorly constrained and not always supported by subsequent investigations. Conroy+19 found an unimodal Iron Distribution Function (IDF) peaking at -1.2 dex, by using HR spectra for more than 4200 field RGs. We obtained a similar result using a homogeneous sample of ~5200 Halo RRLs (Crestani+21), but with a peak at [Fe/H]~-1.55 dex.
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