The assembly bias of dark matter haloes to higher orders

We use an extremely large volume ($2.4h^{-3}{\rm Gpc}^{3}$), high resolution N-body simulation to measure the higher order clustering of dark matter haloes as a function of mass and internal structure. We are able to measure clustering for haloes corresponding to rarer peaks than was possible in previous studies. We use a novel ``cross-moment'' counts-in-cells technique which suppresses discreteness noise. This allows us to extract, for the first time, halo bias parameters from linear up to fourth order. We find that for all orders measured, the bias parameters are strong function of mass for haloes more massive than the characteristic mass $M_{*}$. No theoretical model is able to reproduce this mass dependence closely. We also find that the bias parameters depend on the internal structure of the halo, even up to fourth order. Our results will provide useful inputs to theoretical models of galaxy clustering.