According to the current cosmological cold dark matter paradigm , the Galactic halo could have been the result of the assemblage of smaller structures .
Here we explore the hypothesis that the classical and ultra-faint dwarf spheroidal satellites of the Milky Way have been the building blocks of the Galactic halo by comparing their [ \alpha /Fe ] and [ Ba/Fe ] versus [ Fe/H ] patterns with the ones observed in Galactic halo stars .
The \alpha elements deviate substantially from the observed abundances in the Galactic halo stars for [ Fe/H ] values larger than -2 dex , while they overlap for lower metallicities .
On the other hand , for the [ Ba/Fe ] ratio the discrepancy is extended at all [ Fe/H ] values , suggesting that the majority of stars in the halo are likely to have been formed in situ .
Therefore , we suggest that [ Ba/Fe ] ratios are a better diagnostic than [ \alpha /Fe ] ratios .
Moreover , for the first time we consider the effects of an enriched infall of gas with the same chemical abundances as the matter ejected and/or stripped from dwarf satellites of the Milky Way on the chemical evolution of the Galactic halo .
We find that the resulting chemical abundances of the halo stars depend on the assumed infall time scale , and the presence of a threshold in the gas for star formation .
In particular , in models with an infall timescale for the halo around 0.8 Gyr coupled with a threshold in the surface gas density for the star formation ( 4 \mathrm { M } _ { \odot } \mathrm { pc } ^ { -2 } ) , and the enriched infall from dwarf spheroidal satellites , the first halo stars formed show [ Fe/H ] > -2.4 dex .
In this case , to explain [ \alpha /Fe ] data for stars with [ Fe/H ] < -2.4 dex we need stars formed in dSph systems .