Spin mode reconstruction in Lagrangian space

Galaxy angular momentum directions (spins) are observable, well described by the Lagrangian tidal torque theory, and proposed to probe the primordial universe. They trace the spins of dark matter halos, and are indicators of protohalos properties in Lagrangian space. We define a Lagrangian spin parameter and tidal twist parameters and quantify their influence on the spin conservation and predictability in the spin mode reconstruction in $N$-body simulations. We conclude that protohalos in a more tidal twisting environments are preferentially more rotation-supported, and more likely to conserve their spin direction through the cosmic evolution. These tidal environments and spin magnitudes are predictable by a density reconstruction in Lagrangian space, and such predictions can improve the correlation between galaxy spins and the initial conditions in the study of constraining the primordial universe by spin mode reconstruction.