  We perform general-relativistic hydrodynamical simulations of dynamical
capture binary neutron star mergers, emphasizing the role played by the neutron
star spin. Dynamical capture mergers may take place in globular clusters, as
well as other dense stellar systems, where most neutron stars have large spins.
We find significant variability in the merger outcome as a function of initial
neutron star spin. For cases where the spin is aligned with the orbital angular
momentum, the additional centrifugal support in the remnant hypermassive
neutron star can prevent the prompt collapse to a black hole, while for
antialigned cases the decreased total angular momentum can facilitate the
collapse to a black hole. We show that even moderate spins can significantly
increase the amount of ejected material, including the amount unbound with
velocities greater than half the speed of light, leading to brighter
electromagnetic signatures associated with kilonovae and interaction of the
ejecta with the interstellar medium. Furthermore, we find that the initial
neutron star spin can strongly affect the already rich phenomenology in the
postmerger gravitational wave signatures that arise from the oscillation modes
of the hypermassive neutron star. In several of our simulations, the resulting
hypermassive neutron star develops the one-arm ($m=1$) spiral instability, the
most pronounced cases being those with small but non-negligible neutron star
spins. For long-lived hypermassive neutron stars, the presence of this
instability leads to improved prospects for detecting these events through
gravitational waves, and thus may give information about the neutron star
equation of state.
