Testing tidal-torque theory - I. Spin amplitude and direction

We evaluate the success of linear tidal-torque theory (TTT) in predicting galactic-halo spin using a cosmological N-body simulation with thousands of well-resolved haloes. The protohaloes are identified by tracing today's haloes back to the initial conditions. The TTT predictions for the protohaloes match, on average, the spin amplitudes of the virialized haloes of today, if linear growth is assumed until , t 0 /3, or 55 -70 per cent of the halo effective turnaround 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 , 508 in the TTT prediction at t 0 , such that the linear spatial correlations of spins on scales $ 1 h 21 Mpc 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.