Measuring the Tidal Response of Structure Formation: Anisotropic Separate Universe Simulations using TreePM

Abstract: We present anisotropic "separate universe" simulations which modify the N-body code Gadget-4 in order to represent a large-scale tidal field through an anisotropic expansion factor. These simulations are used to measure the linear, quasi-linear and nonlinear response of the matter power spectrum to a spatially uniform trace-free tidal field up to wavenumber $k = 7 h \text{Mpc}<sup>{-1}$. Together with the response to a large-scale overdensity measured in previous work, this completely describes the nonlinear matter bispectrum in the squeezed limit. We find that the response amplitude does not approach zero on small scales in physical coordinates, but rather a constant value at $z=0$, $R_K\approx 0.5$ for $k \geq 3 h\text{Mpc}<sup>{-1}$ up to the scale where we consider our simulations reliable, $k \leq 7 h\text{Mpc}<sup>{-1}$ at $z=0$. This shows that even the inner regions of haloes are affected by the large-scale tidal field. We also measure directly the alignment of halo shapes with the tidal field, finding a clear signal which increases with halo mass.