Accurate evolutions of inspiralling neutron-star binaries: assessment of the truncation error

We have recently presented an investigation in full general relativity of the dynamics and gravitational-wave emission from binary neutron stars which inspiral and merge, producing a black hole surrounded by a torus (Baiotti et al 2008 Phys. Rev. D 78 084033). We discuss here in more detail the convergence properties of the results presented in Baiotti et al (2008 Phys. Rev. D 78 084033) and, in particular, the deterioration of the convergence rate at the merger and during the survival of the merged object, when strong shocks are formed and turbulence develops. We also show that physically reasonable and numerically convergent results obtained at low resolution suffer however from large truncation errors and hence are of little physical use. We summarize our findings in an 'error budget', which includes the different sources of possible inaccuracies we have investigated and provides a first quantitative assessment of the precision in the modelling of compact fluid binaries.