Tidal Resonance in Binary Neutron Star Inspirals: A High-Precision Study in Numerical Relativity

We investigate the tidal resonance of the fundamental (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>f</a:mi></a:mrow></a:math>) mode in spinning neutron stars, robustly tracing the onset of the excitation to its saturation, using numerical relativity for the first time. We performed long-term (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mo>≈</c:mo><c:mn>15</c:mn></c:mrow></c:math> orbits) fully relativistic simulations of a merger of two highly and retrogradely spinning neutron stars. The resonance window of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>f</e:mi></e:math> mode is extended by self-interaction, and the nonlinear resonance continues up to the final plunging phase. We observe that the quasicircular orbit is maintained throughout since the dissipation of orbit motion due to the resonance is coherent with that due to gravitational waves. The <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>f</g:mi></g:math>-mode resonance causes a variation in the stellar spin of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mo>≳</i:mo><i:mn>6.3</i:mn><i:mo>%</i:mo></i:math> in the linear regime and much more as <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mo>∼</k:mo><k:mn>33</k:mn><k:mo>%</k:mo></k:math> during the later nonlinear regime. At the merger, a phase shift of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mo>≲</m:mo><m:mn>40</m:mn><m:mtext> </m:mtext><m:mtext> </m:mtext><m:mi>rad</m:mi></m:math> is rendered in the gravitational waveform as a consequence of the angular momentum and energy transfers into the neutron star oscillations.