Numerical overcooling in shocks

We present a study of cooling in radiative shocks simulated with smoothed particle hydrodynamics and adaptive mesh refinement codes. We obtain a similarity solution for a shock-tube problem in the presence of radiative cooling, and test how well the solution is reproduced in GADGET and FLASH. Shock broadening governed by the details of the numerical scheme (artificial viscosity or Riemann solvers) leads to potentially significant overcooling in both codes. We interpret our findings in terms of a resolution criterion, and apply it to realistic simulations of cosmological accretion shocks on to galaxy haloes, cold accretion and thermal feedback from supernovae or active galactic nuclei (AGN). To avoid numerical overcooling of accretion shocks on to haloes that should develop a hot corona a particle or cell mass resolution of 10(6) M-circle dot is required, which is within reach of current state-of-the-art simulations. At this mass resolution, thermal feedback in the interstellar medium of a galaxy requires temperatures of supernova-or AGN-driven bubbles to be in excess of 10(7) K at densities of n(H) = 1.0 cm(-3), in order to avoid spurious suppression of the feedback by numerical overcooling.