Prospects for direct detection of black hole formation in neutron star mergers with next-generation gravitational-wave detectors

A direct detection of black hole formation in neutron star mergers would provide invaluable information about matter in neutron star cores and finite temperature effects on the nuclear equation of state. We study black hole formation in neutron star mergers using a set of $\mathrm{190}$ numerical relativity simulations consisting of long-lived and black-hole-forming remnants. The postmerger gravitational-wave spectrum of a long-lived remnant has greatly reduced power at a frequency $f$ greater than $f_{\mathrm{peak}}$, for $f\gtrsim 4\mathrm{kHz}$, with $f_{\mathrm{peak}}\in [2.5,4]\mathrm{kHz}$. On the other hand, black-hole-forming remnants exhibit excess power in the same large $f$ region and manifest exponential damping in the time domain characteristic of a quasinormal mode. We demonstrate that the gravitational-wave signal from a collapsed remnant is indeed a quasinormal ringing. We report on the opportunity for direct detections of black hole formation with next-generation gravitational-wave detectors such as Cosmic Explorer and Einstein Telescope and set forth the tantalizing prospect of such observations up to a distance of 100 Mpc for an optimally oriented and located source with an SNR of 4.

Figure 1

Typical strain profiles for three binary neutron star mergers that form distinctive remnants. The systems are placed at a distance of 100 Mpc. The sensitivity curves of two proposed next-generation observatories [55, 90] are shown with solid and dashed black curves. The tinted backgrounds, orange and violet, denoted by “M” and “H,” indicate the frequency bands used to define ${\rho }_M$ and ${\rho }_H$, respectively, as per the text, while the green background denoted by “I” represents the inspiral. The long-lived and delayed collapse remnants show the unmistakable f-mode peak. This feature is absent in the prompt collapse merger which instead has a prominent peak near the fundamental quasinormal mode of the remnant BH. The delayed collapse case also has excess power at these frequencies, though not as elevated as the prompt collapse case.

Figure 2

The time domain gravitational polarizations for the $(l,m)=(2,2)$ mode, $h_{22}$, of the prompt collapse BNS merger shown in Fig. 1 with the peak of the $h_{22}$ taken as the reference for the time coordinate. Inset: the complete waveform including the inspiral and the ringdown while the main part of the figure illustrates the ringdown signal. The dashed lines in this part are the NR data while the solid lines portray the best-fit QNM model. The vertical line shows the start time for the QNM model which is defined as the time at which the mismatch between the NR data and the QNM model is minimum. It can be seen that the QNM fit worsens at late times. This is due to numerical noise as can be seen by noting that the mean of the NR data at late times is no longer zero.

Figure 3

The ratios of the SNRs in the $f_H$ and $f_M$ frequency bands, ${\rho }_H/{\rho }_M$, as a function of the mass ratios of the binaries. The long-lived remnants are shown in green (circle) while the BH forming cases are plotted in red (triangle). The results for the 40 km Cosmic Explorer detector are shown in the left panel, while the right panel shows that for the Einstein Telescope.

Figure 4

Total mass and mass ratio for the simulations considered in this study. Each simulation is classified according to the merger outcome: prompt or delayed BH formation, or no BH formation within simulation time (long-lived remnants). Note that many simulations share the same total mass and mass ratio, but differ in the choice of EOS, so that there are fewer than 152 points.

Figure 5

An example of a long-lived remnant with significant power in the $f_H$ band. Left: the time domain strain of the postmerger waveform showing the two GW polarizations. Right: the spectrum corresponding to the strain on the left panel.

Figure 6

An example of a delayed collapse remnant with equal component masses of $1.35M_{\odot }$ and employing SFHo EOS. Left: the time domain strain of the full postmerger waveform (green) and a section of the postmerger with the ringdown excised out. Right: the spectrum corresponding to the strain in the left panel.

Figure 7

SNRs of long-lived and BH-forming binaries in the frequency ranges $f_H\in [4096,8192]\mathrm{Hz}$ (top panel) and $f_M\in [2048,4096]\mathrm{Hz}$ (bottom panel) assuming optimal orientation and sky position at a distance of 40 Mpc.