Numerical overcooling in shocks
  We present a study of cooling in radiative shocks simulated with smoothed
particle hydrodynamics (SPH) 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 onto galaxy
haloes, cold accretion and thermal feedback from supernovae or active galactic
nuclei. To avoid numerical overcooling of accretion shocks onto haloes that
should develop a hot corona requires a particle or cell mass resolution of 10^6
M_sun, 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.
