  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.
