Testing tidal-torque theory - II. Alignment of inertia and shear and the characteristics of protohaloes

We investigate the cross-talk between the two key components of tidal-torque theory, the inertia (I) and shear (T) tensors, using a cosmological N-body simulation with thousands of well-resolved haloes. We find that the principal axes of I and T are strongly aligned, even though I characterizes the protohalo locally while T is determined by the large-scale structure. Thus, the resultant galactic spin, which plays a key role in galaxy formation, is only a residual due to ∼10 per cent deviations from the perfect alignment of T and I. The T–I correlation induces a weak tendency for the protohalo spin to be perpendicular to the major axes of T and I, but this correlation is erased by non-linear effects at late times, making the observed spins poor indicators of the initial shear field. However, the T–I correlation implies that the shear tensor can be used for identifying the positions and boundaries of protohaloes in cosmological initial conditions – a missing piece in galaxy formation theory. The typical configuration is of a prolate protohalo lying perpendicular to a large-scale high-density ridge, with the surrounding voids inducing compression along the major and intermediate inertia axes of the protohalo. This leads to a transient sub-halo filament along the large-scale ridge, whose subclumps then flow along the filament and merge into the final halo. The centres of protohaloes tend to lie in ∼1σ overdensity regions, but their association with linear density maxima smoothed on galactic scales is vague: only ∼40 per cent of the protohaloes contain peaks. Several other characteristics distinguish protohaloes from density peaks, e.g. they tend to compress along two principal axes while many peaks compress along three axes.