Quadratic shape biases in three-dimensional halo intrinsic alignments

Understanding the nonlinear relation between the shapes of halos or galaxies and the surrounding matter distribution is essential in accurate modeling of their intrinsic alignments. In the perturbative treatment, such nonlinear relation of the intrinsic alignments appears as higher-order shape bias parameters. In this paper, we present accurate measurements of the quadratic shape bias parameters by combining the \emph{full three-dimensional} power spectrum of the intrinsic alignments (i.e., without any projection) with the quadratic field method. In order to benefit from the full three-dimensional power spectrum we employ the spherical tensor decomposition of the three-dimensional shape field and measure their power spectra for the first time. In particular, we detect the vector and tensor power spectra in this basis, which cannot be explained by the widely-used nonlinear alignment model. Further, by cross-correlating the three-dimensional halo shape field with the quadratic shape bias operators from the initial condition of the same simulation to cancel cosmic variance, we effectively extract bispectrum information and detect quadratic shape bias parameters in the intrinsic alignments with high significance for the first time. We also compare these measurements with the prediction where quadratic shape biases are dynamically generated from the linear Lagrangian shape bias through the large-scale bulk flow. We find general agreement for all three biases with small deviations, which in practice could be negligible for the current photometric surveys. This implies that the advection prediction for the higher-order shape biases can be used as a prior in the cosmological analyses of intrinsic alignments.