We test the integrated galactic initial mass function (IGIMF) on the chemical evolution of 16 ultra-faint dwarf (UFD) galaxies discussing in detail the results obtained for three of them: Boötes I, Boötes II and Canes Venatici I, taken as prototypes of the smallest and the largest UFDs. These objects have very small stellar masses (∼ 10 3 − 10 4 M ) and quite low metallicities ([Fe/H]< −1.0 dex). We consider three observational constraints: the present-day stellar mass, the [α/Fe] vs. [Fe/H] relation and the stellar metallicity distribution function. Our model follows in detail the evolution of several chemical species (H, He, α-elements and Fe). We take into account detailed nucleosynthesis and gas flows (in and out). Our results show that the IGIMF, coupled with the very low star formation rate predicted by the model for these galaxies (∼ 10 −4 − 10 −6 M yr −1 ), cannot reproduce the main chemical properties, because it implies a negligible number of core-collapse SNe and even Type Ia SNe, the most important polluters of galaxies. On the other hand, a constant classical Salpeter IMF gives the best agreement with data. We suggest for all the UFDs studied a very short infall time-scale and high galactic wind efficiencies. Comparing with Galaxy data we suggest that UFDs could not be the building blocks of the entire Galactic halo, although more data are necessary to draw firmer conclusions.

We introduce a new set of zoom-in cosmological simulations with sub-pc resolution, intended to model extremely faint, highly magnified star-forming stellar clumps, detected at z = 6.14 thanks to gravitational lensing. The simulations include feedback from individual massive stars (in both the pre-supernova and supernova phases), generated via stochastic, direct sampling of the stellar initial mass function. We adopt a modified delayed cooling feedback scheme, specifically created to prevent artificial radiative loss of the energy injected by individual stars in very dense gas (n ∼ 103 − 105 cm−3). The sites where star formation ignites are characterised by maximum densities of the order of 105 cm−3 and gravitational pressures Pgrav/k &gt;107 K/cm3, corresponding to the values of the local, turbulent regions where the densest stellar aggregates form. The total stellar mass at z = 6.14 is 3.4$\times 10^7~\rm M_{\odot }$, in satisfactory agreement with the observed stellar mass of the observed systems. The most massive clumps have masses of $\sim 10^6~\rm M_{\odot }$ and half-mass sizes of ∼100 pc. These sizes are larger than the observed ones, including also other samples of lensed high-redshift clumps, and imply an average density one orders of magnitude lower than the observed one. In the size-mass plane, our clumps populate a sequence that is intermediate between the ones of observed high-redshift clumps and local dSph galaxies.

By means of 3D hydrodynamic simulations, we study how Type Ia supernovae (SNe) explosions affect the star formation history and the chemical properties of second generation (SG) stars in globular clusters (GC). SG stars are assumed to form once first generation asymptotic giant branch (AGB) stars start releasing their ejecta; during this phase, external gas is accreted by the system and SNe Ia begin exploding, carving hot and tenuous bubbles. Given the large uncertainty on SNe Ia explosion times, we test two different values for the “delay time”. We run two different models for the external gas density: in the low-density scenario with short delay time, the explosions start at the beginning of the SG star formation, halting it in its earliest phases. The external gas hardly penetrates the system, therefore most SG stars present extreme helium abundances (Y &gt; 0.33). The low-density model with delayed SN explosions has a more extended SG star formation epoch and includes SG stars with modest helium enrichment. On the contrary, the high-density model is weakly affected by SN explosions, with a final SG mass similar to the one obtained without SNe Ia. Most of the stars form from a mix of AGB ejecta and pristine gas and have a modest helium enrichment. We show that gas from SNe Ia may produce an iron spread of ∼0.14 dex, consistent with the spread found in about $20\%$ of Galactic GCs, suggesting that SNe Ia might have played a key role in the formation of this sub-sample of GCs.