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We explore the co-evolution of the specific angular momentum of dark matterhaloes and the cold baryons that comprise the galaxies within. We study overtwo thousand central galaxies within the reference cosmological hydrodynamicalsimulation of the "Evolution and Assembly of GaLaxies and their Environments"(EAGLE) project. We employ a methodology within which the evolutionary historyof a system is specified by the time-evolving properties of the Lagrangianparticles that define it at z=0. We find a strong correlation between theevolution of the specific angular momentum of today's stars (cold gas) and thatof the inner (whole) dark matter halo they are associated with. This link isparticularly strong for the stars formed before the epoch of maximum expansionand subsequent collapse of the central dark matter halo (turnaround). Spheroidsare typically assembled primarily from stars formed prior to turnaround, andare therefore destined to suffer a net loss of angular momentum associated withthe strong merging activity during the assembly of the inner dark matter halo.Stellar discs retain their specific angular momentum since they are comprisedof stars formed mainly after turnaround, from gas that mostly preserves thehigh specific angular momentum it acquired by tidal torques during the lineargrowth of the halo. Since the specific angular momentum loss of the stars istied to the galaxy's morphology today, it may be possible to use our results topredict, statistically, the assembly history of a halo given the morphology ofthe galaxy it hosts.

The link between the assembly of the inner dark matter halo and the angular momentum evolution of galaxies in the EAGLE simulation