OBJECTIVES With the EFEBHO cutting-edge methodologies and datasets, we will address several long-standing

problems concerning the early Halo and Bulge formation. In the following we explain how we will answer our three

fundamental questions.

Q1 – Halo mass distribution

The density profile and the halo flattening are key parameters to investigate the properties of the stellar and dark matter

halos. Our preliminary findings based on the EFEBHO RRL photometric catalog are shown in Fig. 5. Our best fit was

performed by using an Einasto profile with an effective radius reff~8.9 kpc and a concentration index n~3.8. These

values indicate a Halo density profile more concentrated when compared with previous studies (Deason+11; Sesar+11;

Xue+15). However, the comparison with literature values is hampered by the fact that they cover a limited range in

Galactocentric distances, i.e. up to ~70 kpc whereas our data reach up to 140 kpc (Fig. 5).

Q1.1 EFEBHO will compare the RRL density profile with those predicted by a suite of numerical simulations (Auriga)

and by N-body simulations plus hydrodynamical modeling of the interstellar medium. This comparison will allow us to

address the Halo duality. We will be able to discern between the purely dissipation-less and the dissipative theoretical

frameworks. In particular, we will take advantage of a suite of high resolution magneto-hydrodynamical simulations

calculated with the moving-mesh code AREPO (Auriga models, Grand+17) to reconstruct the full Galactic formation

scenario. By inspecting the merging histories of those numerical siblings, we will follow the time evolution of the Einasto

parameters, metallicity gradients, and kinematical properties.

Q1.2 The main aim of this experiment is to compare the observed RRL density profile with predicted ones associated to

old stellar populations. The N-body/hydrodynamical simulations will be constructed using a broad variety of dark matter

haloes and accretion histories. Note that co-evolution studies suggest a tight correlation between old and global Halo

density profiles. Thus, the RRL density profile will allow us to constrain the shape of the dark matter Halo.

 Q2 Fraction of in situ and ex situ Halo RRLs

We plan to investigate the location of the knee, i.e. the point at which the [alpha/Fe] ratio shows a steady decrease as a

function of the iron content. This feature is typically associated with the phase at which SN Ia start to contribute

significantly to the iron enrichment. Fig. 6 shows preliminary results concerning the [alpha/Fe] ratio only based on Halo

RRLs suggesting an almost steady decrease as a function of the iron content.

Q2.1 Following Fiorentino+15 we plan to compare new Halo and dwarf galaxy/GC catalogs (see Methodologies).

Furthermore, we will use new pulsation predictions, based on nonlinear convective hydrodynamical models together with

new synthetic HB models (Salaris+20) covering a broad range in metal content and in helium abundance

(Marconi+15,+18,+21). The EFEBHO multi-wavelength catalogs will offer the unique opportunity to use both theoretical

and empirical multi-band diagnostics (PLZ relations) to estimate accurate individual RRL distances. Once individual

distances have been fixed, we plan to invert select PLZ relations to estimate individual iron abundances. Therefore, we

can derive new and homogeneous IDFs of old stellar populations and compare them with spectroscopic measurements

(Kirby+15) of RGs covering a broad range in age. This means the opportunity to constrain on a quantitative basis the

chemical enrichment history in dwarf galaxies and their contribution to the Halo. Furthermore, we plan to provide a new

and homogeneous calibration of the Fourier parameters for both RRab and RRc variables. Optical and NIR light curves

of Halo and dwarf RRLs will allow us to estimate RRL individual metallicities with Fourier parameters, and in turn, to

investigate the IDF up to the Sculptor galaxy group (Da Costa+10), i.e. well beyond the Local Group. It is worth

mentioning that we plan to develop a new machine learning approach to simultaneously take into account multi-band

luminosity amplitudes and Fourier parameters.

Q2.2 The Halo chemical enrichment traced by RRLs will be constrained by using novel predictions of different [X/Fe] vs

[Fe/H] planes. At variance with previous work (Brusadin+13; Spitoni+16), we aim at constructing a stochastic model,

following the approach described in Cescutti08. The stochastic model takes into account the spread observed in s- and

r-process element abundance ratios, allowing for the division of the Halo into many independent regions. The star

formation history (SFH) in these regions is fixed by the assumed infall/outflow laws and star formation efficiency. The

mass of newborn stars is generated stochastically by a random function with a weighted initial mass function.

Moreover, we also plan to build chemical models for dwarf galaxies which might have been accreted by the Halo. Dwarf

galaxies are known to evolve with a lower star formation rate (SFR) than larger galaxies and this implies, according to

the time-delay model, different patterns in [X/Fe] vs [Fe/H] planes. The time-delay model (Matteucci+12) predicts that in

the early SF phases the core-collapse supernovae are responsible for the production of alpha elements and part of the

iron. Subsequently, when SNIa (white dwarfs in binaries) start restoring the bulk of Fe, the [alpha/Fe] ratio decreases

and the metallicity at which this occurs depends on the SFR. This means that the knee in the [alpha/Fe] ratio, in galaxies

with lower SFR, occurs at metallicities lower than in the solar vicinity. The contrary occurs in spheroids (ellipticals,

bulges) where the SFR was much higher. The same applies to s-process elements. Indeed, these elements show a

different behaviour at low [Fe/H], at variance with the [alpha/Fe] ratios which show a difference at high [Fe/H]. The HR

sample will allow us to measure alpha, iron peak and neutron capture elements and to develop a new LR spectroscopic

diagnostic rooted on the Magnesium b triplet to trace the alpha-element abundances for Halo RRLs (~10,000).

Q2.3 Our preliminary results (see Fig. 7) show an IDF across the Halo quite flat with [Fe/H]=-1.53 dex and a constant

spread σ=0.48 dex. A steady increase in the mean iron content takes only place for |Z|≲ 6-8 kpc. Our findings do not

show a transition between inner and outer Halo and pave the way to a number of questions. Why does the Halo mean

iron abundance and its standard deviation are so homogeneous? Why does the metallicity gradient only show up at

small distances from the Galactic plane? Are the metal-rich RRLs alpha-enhanced or alpha-poor? To answer these

questions, EFHEBO will perform a thorough comparison between chemical models, pulsation predictions and

observations in order to provide a comprehensive view of the Halo chemical enrichment history.

Q3. Bulge structure and chemical enrichment

Concerning the Bulge we plan to apply the model by Matteucci+20 to study the evolution of s- and r-process elements.

The Bulge evolution is strictly related to the Halo, since it was likely formed by the gas collapsing during the formation of

the inner Halo. Indeed, to explain the Halo chemical enrichment, gas outflow is required (Prantzos03; Brusadin+13).

Most of the Bulge models (Matteucci+90; Cescutti+11; Matteucci+20) have confirmed that to reproduce the metallicity

distribution function of Bulge stars, the majority of the Bulge should have formed on a short timescale. The comparison

between predictions and data will allow us to reconstruct the early formation of both Halo and Bulge. There is mounting

evidence in the recent literature of RRLs located in the Solar neighbourhood with thin disc kinematics and chemistry

(Zinn+20; Prudil+20; Iorio+21). This working hypothesis is quite controversial, because the age of candidate disk RRLs

seems to be ~5-6 Gyr. However, RRLs have never been identified in intermediate-age clusters. In case this finding were

supported by new and independent measurements, field RRLs would become the perfect stellar tracer, since they would

be ubiquitous across the entire Galaxy.

Bibliography