Gravitational scattering of two neutron stars

Abstract

We present the first numerical relativity simulations of the gravitational scattering of two neutron stars. Constraint-satisfying initial data for two equal-mass nonspinning sequences are constructed at fixed energy and various initial angular momenta (impact parameter) and evolved with Einstein equations through the scattering process. The strong-field scattering dynamics are explored up to scattering angles of $220^\circ$ and the threshold of dynamical captures. The transition to bound orbits is aided by significant mass ejecta up to baryon mass ${\sim}0.1M_\odot$. A quantitative comparison with predictions of the scattering angle from state-of-the-art effective-one-body and post-Minkowskian calculations indicates quantitative agreement for large initial angular momenta although significant discrepancies in the tidal contribution emerge toward the capture threshold. Gravitational waveforms and radiated energy are in qualitative agreement with the analogous black hole problem and state-of-the-art effective-one-body predictions. Toward the capture threshold waveforms from scattering dynamics carry a strong imprint of matter effects, including the stars' $f$-mode excitations during the close encounter. Overall, our simulations open a new avenue to study tidal interactions in the relativistic two-body problem.

Figures (3)

• Figure 1: Snapshots of SLy simulations with $J_\text{in}/M^2=1.192,1.248,1.664$ (upper row) and MS1b simulations with $J_\text{in}/M^2=1.313,1.382,1.658$ (lower row) both at $E_\text{in}/M\simeq1.034$. Each panel shows the rest-mass density (color map) and the 3-metric conformal factor (contours at $0.5, 0.55, 0.6, 0.65, 0.75, 0.8, 0.85, 0.9, 0.93$) on the orbital plane and shortly after the close encounter. The star trackers are plotted with red and blue solid lines up to the snapshots and discontinuous from then on. Smaller initial angular momenta result in scattering with a closer passage and eventually to a dynamical capture (merger).
• Figure 2: Scattering angle as a function of the initial angular momentum for the two simulation series. Data refer to the highest resolution set of simulations. Top: total scattering angle $\chi^{\rm NR}$ for neutron stars and black holes with same initial energy $E_\text{in}/M \simeq 1.034$ and angular momenta $J_\text{in}/M^2$. Middle: scattering angle for the BH-BH sequence and comparison to the tidal-free term $\chi^{\rm NR}_{\rm free}$ from neutron star scattering (see main text) and to TEOBResumS-Dalí and 4PM result in expanded or EOB-resummed form. Bottom: tidal contribution to the scattering angle (computed by subtracting the BH-BH data) and comparison with TEOBResumS-Dalí (PN NNLO tides) and PM calculations up to NNLO.
• Figure 3: Gravitational waveform amplitude (top) and frequency (bottom) for the SLy NS-NS with $J_\text{in}/M^2=1.248$ (solid blue, extracted at $R=400{{\rm M_{\odot}}}$), for the BH-BH case with same $J_\text{in}$ (black, extracted at $R=100{{\rm M_{\odot}}}$) and for EOB NNLO tides (dashed light blue). The EOB initial angular momentum is chosen such that the peak of the EOB frequency matches the NS-NS one. The blue shaded area corresponds to the numerical uncertainty for the NS-NS case linked to resolution and extraction radius.