Halo Spin from Primordial Inner Motions
  The standard explanation for galaxy spin starts with the tidal-torque theory
(TTT), in which an ellipsoidal dark-matter protohalo, which comes to host the
galaxy, is torqued up by the tidal gravitational field around it. We discuss a
complementary picture, using the relatively familiar velocity field, instead of
the tidal field, whose intuitive connection to the surrounding, possibly
faraway matter arrangement is more obscure. In this 'spin from primordial inner
motions' (SPIM) concept, implicit in TTT derivations but not previously
emphasized, the angular momentum from the gravity-sourced velocity field inside
a protohalo largely cancels out, but has some excess from the aspherical
outskirts. At first, the net spin scales according to linear theory, a sort of
comoving conservation of familiar angular momentum. Then, at collapse, it is
conserved in physical coordinates. Small haloes are then typically subject to
secondary exchanges of angular momentum. The TTT is useful for analytic
estimates. But a literal interpretation of the TTT is inaccurate in detail,
without some implicit concepts about smoothing of the velocity and tidal
fields. This could lead to misconceptions, for those first learning about how
galaxies come to spin. Protohaloes are not perfectly ellipsoidal and do not
uniformly torque up, as in a naive interpretation of the TTT; their inner
velocity fields retain substantial dispersion. Furthermore, quantitatively,
given initial conditions and protohalo boundaries, SPIM is more direct and
accurate than the TTT to predict halo spins. We also discuss how SPIM applies
to rotating filaments, and the relation between halo mass and spin, in which
the total spin of a halo can be thought of as a sum of random contributions.
