Testing Tidal-Torque Theory: I. Spin Amplitude and Direction

We evaluate the success of linear tidal-torque theory (TTT) in predicting galactichalo spin using a cosmological N -body simulation with thousands of well-resolved haloes. The proto-haloes are identified by tracing today’s haloes back to the initial conditions. The TTT predictions for the proto-haloes match, on average, the spin amplitudes of today’s virialized haloes if linear growth is assumed until ∼ t0/3, or 5570 per cent of the halo effective turn-around time. This makes it a useful qualitative tool for understanding certain average properties of galaxies, such as total spin and angular-momentum distribution within haloes, but with a random scatter of the order of the signal itself. Non-linear changes in spin direction cause a mean error of ∼ 50◦ in the TTT prediction at t0, such that the linear spatial correlations of spins on scales ≥ 1 hMpc are significantly weakened by non-linear effects. This questions the usefulness of TTT for predicting intrinsic alignments in the context of gravitational lensing. We find that the standard approximations made in TTT, including a second order expansion of the Zel’dovich potential and a smoothing of the tidal field, provide close-to-optimal results.