Measuring the tidal response of structure formation: anisotropic separate universe simulations using treepm

Abstract

ABSTRACT We present anisotropic ‘separate universe’ simulations that modify the N-body code gadget4 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 non-linear response of the matter power spectrum to a spatially uniform trace-free tidal field up to wavenumber $k = {7\, h\, {\rm Mpc}^{-1}}$. Together with the response to a large-scale overdensity measured in previous work, this completely describes the non-linear 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, RK ≈ 0.5 for $k \ge 3\, h\, {\rm Mpc}^{-1}$ up to the scale where we consider our simulations reliable, $k \le 7\, h\, {\rm Mpc}^{-1}$. 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 that increases with halo mass.