Understanding higher-order nonlocal halo bias at large scales by combining the power spectrum with the bispectrum

Understanding the relation between underlying matter distribution and biased tracers such as galaxies or dark matter halos is essential to extract cosmological information from ongoing or future galaxy redshift surveys. At sufficiently large scales such as the baryon acoustic oscillation (BAO) scale, a standard approach for the bias problem on the basis of the perturbation theory (PT) is to assume the "local bias" model in which the density field of biased tracers is deterministically expanded in terms of matter density field at the same position. The higher-order bias parameters are then determined by combining the power spectrum with higher-order statistics such as the bispectrum. As is pointed out by recent studies, however, nonlinear gravitational evolution naturally induces nonlocal bias terms even if initially starting only with purely local bias. As a matter of fact, previous works showed that the second-order nonlocal bias term, which corresponds to the gravitational tidal field, is important to explain the characteristic scale-dependence of the bispectrum. In this paper we extend the nonlocal bias term up to third order, and investigate whether the PT-based model including nonlocal bias terms can simultaneously explain the power spectrum and the bispectrum of simulated halos in N-body simulations. The bias renormalization procedure ensures that only one additional term is necessary to be introduced to the power spectrum as a next-to-leading order correction, even if third-order nonlocal bias terms are taken into account. We show that the power spectrum, including density and momentum, and the bispectrum between halo and matter in N-body simulations can be simultaneously well explained by the model including up to third-order nonlocal bias terms at k less than or similar to 0.1h/Mpc. Also, the results are in a good agreement with theoretical predictions of a simple coevolution picture, although the agreement is not perfect. These trend can be found for a wide range of halo mass, 0.7 less than or similar to M-halo [10(13) M-circle dot/h] less than or similar to 20 at various redshifts, 0 <= z <= 1. These demonstrations clearly show a failure of the local bias model even at such large scales, and we conclude that nonlocal bias terms should be consistently included in order to accurately model statistics of halos.