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We address the issue of numerical convergence in cosmological smoothedparticle hydrodynamics simulations using a suite of runs drawn from the EAGLEproject. Our simulations adopt subgrid models that produce realistic galaxypopulations at a fiducial mass and force resolution, but systematically varythe latter in order to study their impact on galaxy properties. We provideseveral analytic criteria that help guide the selection of gravitationalsoftening for hydrodynamical simulations, and present results from runs thatboth adhere to and deviate from them. Unlike dark matter-only simulations,hydrodynamical simulations exhibit a strong sensitivity to gravitationalsoftening, and care must be taken when selecting numerical parameters. Ourresults--which focus mainly on star formation histories, galaxy stellar massfunctions and sizes--illuminate three main considerations. First, softeningimposes a minimum resolved escape speed, $v_\epsilon$, due to the bindingenergy between gas particles. Runs that adopt such small softening lengths that$v_\epsilon \gt 10\,{\rm km s^{-1}}$ (the sound speed in ionised $\sim10^4\,{\rm K}$ gas) suffer from reduced effects of photo-heating. Second,feedback from stars or active galactic nuclei may suffer from numericalover-cooling if the gravitational softening length is chosen below a criticalvalue, $\epsilon_{\rm eFB}$. Third, we note that small softening lengthsexacerbate the segregation of stars and dark matter particles in halo centres,often leading to the counter-intuitive result that galaxy sizes {\em increase}as softening is reduced. The structure of dark matter haloes in hydrodynamicalruns respond to softening in a way that reflects the sensitivity of theirgalaxy populations to numerical parameters.

monthly notices of the royal astronomical society

Numerical convergence of hydrodynamical simulations of galaxy formation:  the abundance and internal structure of galaxies and their cold dark matter  haloes