No cores in dark matter-dominated dwarf galaxies with bursty star formation histories

Measurements of the rotation curves of dwarf galaxies are often interpreted as requiring a constant density core at the centre, at odds with the "cuspy" inner profiles predicted by $N$-body simulations of cold dark matter (CDM) haloes. It has been suggested that this conflict could be resolved by fluctuations in the inner gravitational potential caused by the periodic removal of gas following bursts of star formation. Earlier work has suggested that core formation requires a bursty and extended star formation history (SFH). Here we investigate the structure of CDM haloes of dwarf galaxies ($M_{{\rm DM}} \sim 10^9-5\times10^{10}\,{\rm M}_\odot$) formed in the APOSTLE ('A Project of Simulating the Local Environment') and AURIGA cosmological hydrodynamic simulations. Our simulations have comparable or better resolution than others that make cores ($M_{{\rm gas}} \sim 10^4\,{\rm M}_\odot$, gravitational softening $\sim 150$ pc). Yet, we do not find evidence of core formation at {\it any} mass or any correlation between the inner slope of the DM density profile and temporal variations in the SFH. APOSTLE and AURIGA dwarfs display a similar diversity in their cumulative SFHs to available data for Local Group dwarfs. Dwarfs in both simulations are DM-dominated on all resolved scales at all times, likely limiting the ability of gas outflows to alter significantly the central density profiles of their haloes. We conclude that recurrent bursts of star formation are not sufficient to cause the formation of cores, and that other conditions must also be met for baryons to be able to modify the central DM cusp.