Gravitational-Wave Detector for Postmerger Neutron Stars: Beyond the Quantum Loss Limit of the Fabry-Perot-Michelson Interferometer

Advanced gravitational-wave detectors that have made groundbreaking discoveries are Michelson interferometers with resonating optical cavities as their arms. As light travels at a finite speed, these cavities are optimal for enhancing signals at frequencies within the bandwidth, beyond which, however, a small amount of optical loss will significantly impact the high-frequency signals. We find an elegant interferometer configuration with an “$\mathsf{L}$ resonator” as the core, significantly surpassing the loss-limited sensitivity of dual-recycled Fabry-Perot-Michelson interferometers at high frequencies. Following this concept, we provide a broadband design of a 25-km detector with outstanding sensitivity between 2 and 4 kHz. We perform Monte Carlo population studies of binary neutron-star mergers, given the most recent merger rate from the GWTC-3 catalog and several representative neutron-star equations of state. We find that the new interferometer configuration significantly outperforms other third-generation detectors by a factor of 1.7 to 4 in the signal-to-noise ratio of the postmerger signal. Assuming a detection threshold with signal-to-noise $\text{ratio}>5$ and for the cases we explore, the new design is the only detector that robustly achieves a detection rate of the neutron-star postmerger larger than one per year, with the expected rate between $\mathcal{O}(1)$ and $\mathcal{O}(10)$ events per year.

Popular Summary

In 2017, gravitational waves were detected from the coalescence of two neutron stars for the first time. The mergers of binary neutron stars and their aftermath create extreme conditions for studying dense-matter physics, well beyond the ability of terrestrial high-energy experiments. However, current gravitational-wave detectors are sensitive mainly to the inspiral part of neutron-star coalescence, and so an abundance of information encoded in the postmerger signal is lost. Here, we prototype a detector design that will allow future observatories to study postmerger physics.

The LIGO and Virgo gravitational-wave detectors are based on the famous Michelson interferometer. Laser light injected into the device is divided by a beam splitter and sent down two perpendicular arms. Mirrors at the end of each arm reflect the light back to be recombined. Any minute change in the lengths of the arms—by a passing gravitational wave, for example—will create observable interference effects.

We show that by simply flipping the beam splitter, we obtain an $\mathsf{L}$-shaped resonator that naturally resonates signals at 2 to 4 kHz—the frequency band needed to observe postmerger gravitational waves. We carry out a design based on this new interferometer, and it has outstanding performance for observing postmerger signals.

This design represents a paradigm shift, and it has by far the most promising potential to serve as the detector probing postmerger neutron-star phenomena—the most violent and energetic processes with matter. We envision many experimental and theoretical efforts will follow this direction for detector development, together with science case studies from the broad gravitational-wave community.

Figure 1

Schematic of the FPMI interferometer and the $\mathsf{L}$ resonator. They are both sensitive to 2 degrees of freedom of motion: naming $\text{common}+\text{mode}$ indicated by red arrows, and differential $-$ mode (gravitational-wave mode) indicated by black arrows.

Figure 2

The relative response of the $\mathsf{L}$ resonator and FPMI interferometer to the differential mode. The $\mathsf{L}$ resonator outperforms at $c/4L$ and $3c/4L$ with a relative amplification of $4/T_{\mathrm{ITM}}$, where $T_{\mathrm{ITM}}$ is chosen as 0.014. In contrast, the FPMI interferometer outperforms around frequency 0 Hz and $c/2L$.

Figure 3

The schematic of the new interferometer comprised of the $\mathsf{L}$ resonator and a central Michelson interferometer. It also includes a power recycling mirror (PRM) and signal extraction mirror (SEM). Constant phase squeezing is injected from the dark port.

Figure 4

Strain sensitivity of the 25-km new detector in comparison to A+ [51, 52], NEMO [21], ET [53], the “postmerger” tuned CE-20-km and the CE-40-km [54, 55] detectors. The sensitivity of ET corresponds to the combined three 10-km triangular configurations. The new detector gives superior sensitivity in the frequency range of 2–4 and 8–10 kHz. The parameters of the new detector are listed in Table. 1.

Figure 5

Detailed quantum-noise budget of the new detector (solid lines). The SEC loss limit of the postmerger tuned CE-20-km detector (dashed line) is included for comparison. At 3 kHz, the SEC loss limit of the new detector is orders of magnitude lower than that of the postmerger tuned CE-20-km detector. The output loss limits the quantum noise of the new detector.

Figure 6

Noise budget of the 25-km new detector. Above 20 Hz, the sensitivity of the new detector is limited by quantum shot noise. Instead of frequency-dependent squeezing, only constant phase squeezing is applied. The seismic noise. Newtonian noise and suspension thermal noise include both arm cavity and central Michelson noise. We present the BS and ITM coating and substrate noise separately. The noise budget is modeled by the software pygwinc [63].

Figure 7

The postmerger waveform of binary neutron stars in various of equations of state with peak mode frequency ranging from 2 to 4 kHz. The source distance is assumed to be 100 Mpc. Each neutron star in the binary is assumed to have equal mass $1.35M_{\odot }$. The black solid line represents the sensitivity of the new detector.

Figure 8

Number of events with SNR greater than 5 (top) and the SNR of the loudest event (bottom), both are assuming one year of observing time. They are obtained from the median values in the Monte Carlo simulations. The upper ends of the error bars correspond to the case with the merger rate being $295.7{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$, the lower ends correspond to $21.6{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$, and the symbols correspond to $105.5{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$.

Figure 9

Horizon distance for detecting the dark-matter-induced neutron-star collapse signal with different detector sensitivities, assuming the threshold SNR is 5.