EFEBHO relies on novel methodological approaches moving along three different routes:
We plan to take advantage of pulsation diagnostics that are independent of distance and reddening (luminosity amplitudes and periods [Bailey diagram], period ratios of double-mode pulsators [Petersen diagram]) to constrain the physical properties of RRLs in different stellar environments (field vs stellar systems). We have already used this approach to trace the role played by nearby dwarf galaxies in the Halo mass assembly (Musella+12; Fiorentino+15,+17, see Fig. 3). Moreover, we also found that the period ratio of double-mode RRLs can be used to constrain RRL metallicities (Coppola+15). Note that, typical limiting magnitudes for photometric investigations are five magnitudesfainter than spectroscopic ones. Photometric diagnostics will provide iron estimates well beyond V~20.5 mag (≳ 130 kpc in distance), i.e. the limiting magnitude for spectrographs available at the 8-10m class telescopes. Photometric iron estimates will be available for a RRL sample that is more than ten times larger than the current spectroscopic catalog (~10000 vs ~150000). Therefore, we developed three new metallicity diagnostics based on photometric indices. a) new metallicity estimates for ~2400 field RRab variables that use the shape of both optical and MIR light curves (Fourier parameters). Our calibration covers more than 3 dex in iron abundance (HR sample) and the comparison with spectroscopic iron abundancesindicates an accuracy of ~0.35 dex over the entire metallicity range (Mullen+21, submitted). b) new algorithm (REDIME) to provide simultaneous estimates of distance, reddening and metallicity by using optical and NIR mean magnitudes (Bono+19). c) the inversion of optical and NIR PLZ relations (Marconi+15) to estimate the Iron Distribution Function (IDF) of RRLs in the Sculptor dSph galaxy (Martínez-Vázquez+19) and in ω-Cen (Braga+17).
Galactic chemical evolution, and in particular, the [X/Fe] vs [Fe/H] plane is one of the most effective diagnostics to study the formation timescale of the various Galactic components. Matteucci+86 suggested that the duration of the inner Halo formation was of the order of ~1 Gyr from fitting the [alpha/Fe] vs. [Fe/H] diagram (alpha includes O, Mg, Si). This is a consequence of the time-delay model, which relies on the role played by different supernovae (SN) in contributing to the chemical enrichment (Matteucci+12). In this theoretical framework, core collapse SN restore on very short timescales their nucleosynthesis products, mainly the alpha-elements, while SN Ia restore the bulk of Fe on much longer timescales. The same HR spectra will be adopted to measure neutron-capture elements, indeed, both s- and r-process elements can be soundly adopted to trace the Halo chemical enrichment history (Spitoni+16, see Fig. 4). Galactic Archeology is the playground within which we plan to perform a detailed comparison between theory (Cescutti+15; Palla+20) and observations. This paradigm can be adopted for all chemical species we can measure on RRL spectra and it brings forward independent estimates of the fraction of in situ and ex situ Halo stars (chemical tagging).
The modelling of the Galactic spheroid will move along three different but complementary approaches: Jeans/phase-space modelling, N-body simulations, and hydrodynamical simulations. In the Jeans approach we will model the stellar Halo as an overall multi-component axisymmetric equilibrium system, by using the most recent version of our code JASMINE2 (Caravita+20). This code was designed to build multi-component systems, thus it is the natural tool to describe the MW components, embedded in the potential of the various mass components (bulge, disk, dark matter halo, stellar haloes). This analysis will be complemented by the analytical modelling of multi-component systems along the lines described in Ciotti+21. Coupling the numerical and analytical approach, we will test the consistency of the structural properties of the stellar halo with the information provided by the observed kinematic fields, thus restricting the parameter space to models with compatible structure and dynamics. The resulting model will be further tested and explored by direct integrations of stellar orbits in the derived potentials. Finally, we will develop a complementary line of investigation to build halo models. They will be based on the novel modelling technique derived from the action-based phase-space distribution functions (Pascale+19).