First direct comparison of nondisrupting neutron star-black hole and binary black hole merger simulations

We present the first direct comparison of numerical simulations of neutron star-black hole and black hole-black hole mergers in full general relativity. We focus on a configuration with nonspinning objects and within the most likely range of mass ratio for neutron star-black hole systems ($q=6$). In this region of the parameter space, the neutron star is not tidally disrupted prior to merger, and we show that the two types of mergers appear remarkably similar. The effect of the presence of a neutron star on the gravitational wave signal is not only undetectable by the next generation of gravitational wave detectors, but also too small to be measured in the numerical simulations: even the plunge, merger and ringdown signals appear in perfect agreement for both types of binaries. The characteristics of the post-merger remnants are equally similar, with the masses of the final black holes agreeing within $\delta M_{\mathrm{BH}}<5\times {10}^{-4}{M}_{\mathrm{BH}}$ and their dimensionless spins within $\delta {\chi }_{\mathrm{BH}}<{10}^{-3}$. The rate of periastron advance in the mixed binary agrees with previously published binary black hole results, and we use the inspiral waveforms to place constraints on the accuracy of our numerical simulations independent of algorithmic choices made for each type of binary. Overall, our results indicate that nondisrupting neutron star-black hole mergers are exceptionally well modeled by black hole-black hole mergers, and that given the absence of mass ejection, accretion disk formation, or differences in the gravitational wave signals, only electromagnetic precursors could prove the presence of a neutron star in low-spin systems of total mass $\sim 10M_{\odot }$, at least until the advent of gravitational wave detectors with a sensitivity comparable to that of the proposed Einstein Telescope.

Figure 1

Normalized constraint violation during the 4 NsBh inspirals. $\Vert C\Vert$ is defined as in Eq. (71) of 40. The top axis (in $ms$) assumes $M_{\mathrm{NS}}=1.4M_{\odot }$.

Figure 2

Evolution of the time derivative of the coordinate separation between the center of the black hole and the center of the neutron star for the 4 NsBh simulations. The inset zooms on the early time behavior.

Figure 3

Dominant (2, 2) mode of the gravitational waveform for the NSBH system at low, medium and high resolutions, as well as for the ‘adaptive’ run. The insert zooms on the time of merger.

Figure 4

Phase error in the (2, 2) mode of the gravitational waveform. The dashed curves show the difference between the fixed resolution simulations and the adaptive simulation without time and phase shifts, while the solid curves show the same phase differences, but after matching the waveforms in the interval $675<t/M<2175$. The solid blue curve shows the difference between the adaptive simulation and the BBH results (with arbitrary shifts).

Figure 5

Measurement of the rate of periastron advance as a function of the orbital frequency for a NSBH system of mass ratio $q=6$, compared with a fit valid for BBH systems [25], and the results from first-order self-force calculations [25, 47]. All values are normalized by the rate of periastron advance for a point particle around a Schwarzschild black hole. The dashed lines show the uncertainty in the fit to the BBH results.

Figure 6

Tidal quadrupole during the inspiral of the adaptive run. Left: Amplitude of the tidal quadrupole $Q$, best fit $Q_{\mathrm{Tide}}$ to the expected evolution of the equilibrium tide (proportional to $d^{-3}$, where $d$ is the binary separation), and residual $Q_{\mathrm{osc}}$ from that fit. Right: Fourier transform of $Q_{zz}/I_{00}$, composed of a power-law component (equilibrium tide) and an oscillatory component at 1.5 kHz (assuming $M_{\mathrm{NS}}=1.4M_{\odot }$).

Figure 7

Matter distribution (in blue) and location of the apparent horizon (in grey) after 5% of the neutron star material has been accreted onto the black hole. Even at merger, the neutron star remains remarkably compact.

Figure 8

Dominant (2, 2) mode of the gravitational waveform for the NSBH (adaptive run) and BBH mergers. The insert zooms on the time of merger. A time and phase shifts have been applied to the BBH waveform in order to minimize the phase difference with the NSBH results in the interval $675<t/M<2175$.

Figure 9

Amplitude of the gravitational wave spectrum for optimally oriented binaries located at 100 Mpc. The aLIGO curve is the Zero-Detuned High Power noise curve of Ref. 52. BBH results are shown in black and NSBH results in red for the dominant mode ($l=2$, $m=2$, solid curves), and the two largest subdominant modes ($l=2$, $m=1$, dashed curves and $l=3$, $m=3$, dash-dotted curves). The amplitude $h_{\mathrm{opt}}$ is defined as $h_{\mathrm{opt},lm}(f)=\sqrt{5/4\pi }{f}^{1/2}{h}_{lm}(f)$.