Equation of state effects and one-arm spiral instability in hypermassive neutron stars formed in eccentric neutron star mergers

We continue our investigations of the development and importance of the onearm spiral instability in long-lived hypermassive neutron stars (HMNSs) formed in dynamical capture binary neutron star mergers. Employing hydrodynamic simulations in full general relativity, we find that the one-arm instability is generic in that it can develop in HMNSs within a few tens of milliseconds after merger for all equations of state in our survey. We find that mergers with stiffer equations of state tend to produce HMNSs with stronger m = 2 azimuthal mode density deformations, and weaker m = 1 components, relative to softer equations of state. We also find that for equations of state that can give rise to double-core HMNSs, large m = 1 density modes can already be present due to asymmetries in the two cores. This results in the generation of l = 2, m = 1 gravitational wave modes even before the dominance of a one-arm mode that ultimately arises following merger of the two cores. Our results further suggest that stiffer equations of state give rise to HMNSs generating lower m = 1 gravitational wave frequencies. Thus, if gravitational waves from the onearm instability are detected, they could in principle constrain the neutron star equation of state. We estimate that, depending on the equation of state, the onearm mode could potentially be detectable by second generation gravitational wave detectors at similar to 10 Mpc and by third generation ones at similar to 100 Mpc. Finally, we provide estimates of the properties of dynamical ejecta, as well as the accompanying kilonovae signatures.