We analyze 11 years of Fermi-Large Area Telescope (LAT) data corresponding to the sky regions of seven dwarf irregular (dIrr) galaxies. DIrrs are dark matter (DM)-dominated systems, proposed as interesting targets for the indirect search of DM with gamma rays. The galaxies represent interesting cases with a strong disagreement between the density profiles (core versus cusp) inferred from observations and numerical simulations. In this work, we addressed the problem by considering two different DM profiles, based on both the fit to the rotation curve (in this case, a Burkert cored profile) and results from N-body cosmological simulations (i.e., Navarro-Frenk-White cuspy profile). We also include halo substructure in our analysis, which is expected to boost the DM signal by a factor of 10 in halos such as those of dIrrs. For each DM model and dIrr, we create a spatial template of the expected DM-induced gamma-ray signal to be used in the analysis of Fermi-LAT data. No significant emission is detected from any of the targets in our sample. Thus, we compute upper limits on the DM annihilation cross section versus mass parameter space. Among the seven dIrrs, we find IC10 and NGC6822 to yield the most stringent individual constraints, independently of the adopted DM profile. We also produce combined DM limits for all objects in the sample, which turn out to be dominated by IC10 for all DM models and annihilation channels, i.e., bb ̄, τ+τ-, and W+W-. The strongest constraints are obtained for bb ̄ and are at the level of σ 7×10-26 cm3 s-1 at mχ∼6 GeV. Though these limits are a factor of ∼3 higher than the thermal relic cross section at low weakly interacting massive particles masses, they are independent from and complementary to those obtained by means of other targets.
