Cosmological simulation in tides: power spectra and halo shape responses, and shape assembly bias

Abstract: The well-developed separate universe technique enables accurate calibration of the response of any observable to an isotropic long-wavelength density fluctuation. The large-scale environment also hosts tidal modes that perturb all observables anisotropically. As in the separate universe, both the long tidal and density modes can be absorbed by an effective anisotropic background, on which the interaction and evolution of the short modes change accordingly. We further develop the tidal simulation method, including proper corrections to the second order Lagrangian perturbation theory (2LPT) to generate initial conditions of the simulations. We measure the linear tidal responses of the matter power spectrum, at high redshift from our modified 2LPT, and at low redshift from the tidal simulations. Our results agree qualitatively with previous works, but exhibit quantitative differences in both cases. We also measure the linear tidal response of the halo shapes, or the shape bias, and find its universal relation with the linear halo bias, for which we provide a fitting formula. Furthermore, analogous to the assembly bias, we study the secondary dependence of the shape bias, and discover for the first time dependence on halo concentration and axis ratio. Our results provide useful insights for studies of the intrinsic alignment as source of either contamination or information. These effects need to be correctly taken into account when one uses intrinsic alignments of galaxy shapes as a precision cosmological tool.