LAUSR

We study the effect of baryonic processes on the shapes of dark matter (DM) haloes from Illustris, a suite of hydrodynamical (Illustris) and DM-only (Illustris-Dark) cosmological simulations performed with the moving-mesh code {\sc arepo}. DM halo shapes are determined using an iterative method based on the inertia tensor for a wide range of $z=0$ masses ($M_{200} = 1 \times 10^{11} - 3 \times 10^{14} M_\odot$). Convergence tests shows that the local DM shape profiles are converged only for $r > 9\epsilon$, $\epsilon$ being the Plummer-equivalent softening length, larger than expected. Haloes from non-radiative simulations (i.e. neglecting radiative processes, star formation, and feedback) exhibit no alteration in shapes from their DM-only counterparts: thus moving-mesh hydrodynamics alone is insufficient to cause differences in DM shapes. With the full galaxy-physics implementation, condensation of baryons results in significantly rounder and more oblate haloes, with the median minor-to-major axis ratio $\left \approx 0.7$, almost invariant throughout the halo and across halo masses. This somewhat improves the agreement between simulation predictions and observational estimates of the Milky Way halo shape. Consistently, the velocity anisotropy of DM is also reduced in Illustris, across halo masses and radii. Within the inner halo ($r=0.15 R_{200}$), both $s$ and $q$ (intermediate-to-major axis ratio) exhibit non-monotonicity with galaxy mass, peaking at $m_* \approx 10^{10.5-11} M_\odot$, which we find is due to the strong dependence of inner halo shape with galaxy formation efficiency. Baryons in Illustris affect the correlation of halo shape with halo properties, leading to a positive correlation of sphericity of MW-mass haloes with halo formation time and concentration, the latter being mildly more pronounced than in Illustris-Dark.