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 one-arm 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 one-arm instability are detected, they could in principle constrain the neutron star equation of state. We estimate that, depending on the equation of state, the one-arm mode could potentially be detectable by second generation gravitational wave detectors at ∼10 Mpc and by third generation ones at ∼100 Mpc. Finally, we provide estimates of the properties of dynamical ejecta, as well as the accompanying kilonovae signatures.