Beyond LIMD bias: a measurement of the complete set of third-order halo bias parameters

Abstract

We present direct measurements of cubic bias parameters of dark matter halos from the halo-matter-matter-matter trispectrum. We measure this statistic efficiently by cross-correlating the halo field measured in N-body simulations with specific third-order nonlocal transformations of the initial density field in the same simulation. Together with the recent Abidi & Baldauf (2018), these are the first measurements of halo bias using the four-point function that have been reported to date. We also obtain constraints on the quadratic bias parameters. For all individual cubic parameters involving the tidal field ${\mathcal{K}}_{ij}$, we find broad consistency with the prediction of the Lagrangian local-in-matter-density ansatz, with some indications of a positive Lagrangian coefficient $b_{\mathrm{td}}^L$ multiplying the time derivative of ${\mathcal{K}}_{ij}$. For the quadratic tidal bias ($b_{K^2}$), we obtain a significant detection of a negative Lagrangian tidal bias.

29 pages, 12 figures; v2: new renormalization procedure, added figure 12, results at higher redshifts on figs 1-5, added appendix B, C and F, clarifications throughout; v3: clarifications throughout, version accepted by JCAP

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