Information about the last stages of a binary neutron star inspiral and the final merger can be extracted from quasiequilibrium configurations and dynamical evolutions. In this article, we construct quasiequilibrium configurations for different spins, eccentricities, mass ratios, compactnesses, and equations of state. For this purpose we employ the SGRID code, which allows us to construct such data in previously inaccessible regions of the parameter space. In particular, we consider spinning neutron stars in isolation and in binary systems; we incorporate new methods to produce highly eccentric and eccentricity-reduced data; we present the possibility of computing data for significantly unequal-mass binaries with mass ratios q ≃ 2; and we create equal-mass binaries with individual compactness up to C ≃ 0.23. As a proof of principle, we explore the dynamical evolution of three new configurations. First, we simulate a q ¼ 2.06 mass ratio which is the highest mass ratio for a binary neutron star evolved in numerical relativity to date. We find that mass transfer from the companion star sets in a few revolutions before merger and a rest mass of ∼10 −2 M ⊙ is transferred between the two stars. This amount of mass accretion corresponds to ∼10 51 ergs of accretion energy. This configuration also ejects a large amount of material during merger (∼7.6 × 10 −2 M ⊙ ), imparting a substantial kick to the remnant neutron star. Second, we simulate the first merger of a precessing binary neutron star. We present the dominant modes of the gravitational waves for the precessing simulation, where a clear imprint of the precession is visible in the (2,1) mode. Finally, we quantify the effect of an eccentricity-reduction procedure on the gravitational waveform. The procedure improves the waveform quality and should be employed in future precision studies. However, one also needs to reduce other errors in the waveforms, notably truncation errors, in order for the improvement due to eccentricity reduction to be effective.

Binary neutron stars in circular orbits can be modeled as helically symmetric, i.e., stationary in a rotating frame. This symmetry gives rise to a first integral of the Euler equation, often employed for constructing equilibrium solutions via iteration. For eccentric orbits, however, the lack of helical symmetry has prevented the use of this method, and the numerical relativity community has often resorted to constructing initial data by superimposing boosted spherical stars without solving the Euler equation. The spuriously excited neutron star oscillations seen in evolutions of such data arise because such configurations lack the appropriate tidal deformations and are stationary in a linearly comoving-rather than rotating-frame. We consider eccentric configurations at apoapsis that are instantaneously stationary in a rotating frame. We extend the notion of helical symmetry to eccentric orbits, by approximating the elliptical orbit of each companion as instantaneously circular, using the ellipse's inscribed circle. The two inscribed helical symmetry vectors give rise to approximate instantaneous first integrals of the Euler equation throughout each companion. We use these integrals as the basis of a self-consistent iteration of the Einstein constraints to construct conformal thin-sandwich initial data for eccentric binaries. We find that the spurious stellar oscillations are reduced by at least an order of magnitude, compared with those found in evolutions of superposed initial data. The tidally induced oscillations, however, are physical and qualitatively similar to earlier evolutions. Finally, we show how to incorporate radial velocity due to radiation reaction in our inscribed helical symmetry vectors, which would allow one to obtain truly non-eccentric initial data when our eccentricity parameter e is set to zero.