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 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 ~t_0/3, or 55-70 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 degrees in the TTT prediction at t_0, such that the linear spatial correlations of spins on scales >~ 1 Mpc/h 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.