Verifying the consistency relation for the scale-dependent bias from local primordial non-Gaussianity

We measure the large-scale bias of dark matter haloes in simulations with non-Gaussian initial conditions of the local type, and compare this bias to the response of the mass function to a change in the primordial amplitude of fluctuations. The two are found to be consistent, as expected from physical arguments, for the three halo-finder algorithms which use different spherical overdensity (SO) and friends-of-friends methods. On the other hand, we find that the commonly used prediction for universal mass functions, that the scale-dependent bias is proportional to the first-order Gaussian Lagrangian bias, does not yield a good agreement with the measurements. For all halo finders, high-mass haloes show a non-Gaussian bias suppressed by 10-15 per cent relative to the universal mass function prediction. For SO haloes, this deviation changes sign at low masses, where the non-Gaussian bias becomes larger than the universal prediction.