Towards the design of gravitational-wave detectors for probing neutron-star physics

The gravitational waveform of merging binary neutron stars encodes information about extreme states of matter. Probing these gravitational emissions requires the gravitational-wave detectors to have high sensitivity above 1 kHz. Fortunately for current advanced detectors, there is a sizeable gap between the quantum-limited sensitivity and the classical noise at high frequencies. Here we propose a detector design that closes such a gap by reducing the high-frequency quantum noise with an active optomechanical filter, frequency-dependent squeezing, and high optical power. The resulting noise level from 1 to 4 kHz approaches the current facility limit and is a factor of 20 to 30 below the design of existing advanced detectors. This will allow for precision measurements of (i) the postmerger signal of the binary neutron star, (ii) late-time inspiral, merger, and ringdown of low-mass black hole–neutron star systems, and possible detection of (iii) high-frequency modes during supernovae explosions. This design tries to maximize the science return of current facilities by achieving a sensitive frequency band that is complementary to the longer-baseline third-generation detectors: the 10 km Einstein Telescope and 40 km Cosmic Explorer. We have highlighted the main technical challenges towards realizing the design, which requires dedicated research programs. If demonstrated in current facilities, the techniques can be transferred to new facilities with longer baselines.

Figure 1

Schematics showing the detector design (left) and the resulting sensitivity (right). The blue curve shows a possible intermediate step. The target sensitivity curve in red is around a factor of 30 below Advanced LIGO design at 3 kHz: a factor of 3 from 10 dB squeezing, 2 from high power, and 5 from detuned signal recycling with the optomechanical filter extending the improvement around the detune frequency. Sensitivity curves of Advanced LIGO plus $(\mathrm{A}+)$ [36], LIGO Voyager [34], Einstein Telescope [37], and Cosmic Explorer [38] are shown as references. A list of acronyms: PD for photodiode, IFO for interferometer, SQZ for squeezed light, and HF for high frequency detector.

Figure 2

The top panel shows the expected maximum SNR for detecting (2, 2) mode given different EOSs and detector sensitivities; the bottom panel shows the expected number of events with $\mathrm{SNR}\ge 5$ with a one-year observation. The error bar corresponds to the 90% confidence interval of the merger rate presented in Ref. [1], with a most probable rate of $1540{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$.

Figure 3

Stochastic GW background produced by the postmerger GW emissions of BNSs with a merger rate of $1540{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$. Transition regions between different plateaus correspond to dominant modes in the postmerger waveform, with the lowest-frequency one associated with the (2, 2) mode. The magenta and black dashed lines are the “power-law integrated” sensitivity curves defined in Ref. [64], with a one- and ten-year integration time, respectively.

Figure 4

The noise budget for the two cases of main interferometer: one assuming 1064 nm and LIGO-LF classical noise (upper panel), and the other assuming 2000 nm and LIGO Voyager classical noise (lower panel). The final sensitivity curves (total noise) were shown in Fig. 1 of the main text. The projected oscillator noise comes from the mechanical oscillator in the optomechanical filter. We have also included the contributions from the optical loss in the filter cavity, the signal-recycling cavity, and the output.

Figure 5

Displacement noises of the mechanical oscillator near 12 kHz resonant frequency (the reference frequency) before the control laser for the optomechanical filter is turned on, which will modify the mechanical susceptibility. Configurations of the optical spring cavity and optomechanical filter cavity were chosen to achieve a total noise level below the requirement in Eq. (a5).

Figure 6

A schematic showing the relevant four sidebands and their frequencies with respect to the carrier frequency ${\omega }_0$ and control laser frequency ${\omega }_0+{\omega }_m-{\mathrm{\Delta }}_{\mathrm{SR}}$ (${\mathrm{\Delta }}_{\mathrm{SR}}$ is the signal recycling detuning frequency of the interferometer). The control laser is detuned away from the optomechanical cavity resonant frequency by ${\omega }_m$; the resonance profile of the cavity is illustrated by the Lorentzian shape.

Figure 7

A schematic showing the relevant fields, noises, GW signal, and the propagation transfer matrices involved in obtaining the input-output relation for calculating the sensitivity curve.

Figure 8

The realization of frequency-dependent squeezing angle with 3 or 4 filter cavities. The 4-cavity realization matches the optimal one at all frequencies of interest, while the 3-cavity realization matches the optimal one above 100 Hz.

Figure 9

The corresponding sensitivity curves (quantum noise only) for the two realizations with 3 and 4 squeezing filter cavities.

Figure 10

Plot illustrating the effect of the signal-recycling detuning frequency ${\mathrm{\Delta }}_{\mathrm{SR}}$ on the quantum-limited sensitivity.

Figure 11

Plot showing how different values of the mechanical resonant frequency ${\omega }_m$ influence the sensitivity.

Figure 12

Plot showing how choices of the readout quadrature affect the sensitivity.

Figure 13

BNS postmerger waveforms for different EOS extracted from Refs. [52, 53, 54], assuming a $1.35M_{\odot }+1.35M_{\odot }$ NS binary located at 100 Mpc away. The magenta dashed line represents the target sensitivity of the high-frequency detector design.

Figure 14

Expected SNRs for detecting the entire postmerger waveform of the loudest event, i.e., the maximum SNR (top panel), and the number of events with $\mathrm{SNR}\ge 5$ (bottom panel) within a one-year observation for different detectors. Each EOS has a bar corresponding to the 90% confidence interval of the merger rate obtained in Ref. [1]. The selected EOSs cover a range of stiffness with the corresponding NS mass above $2M_{\odot }$.

Figure 15

SGWB from postmerger oscillations of BNS. The component masses are sampled according to Eq. (c2) and the mode frequencies are scaled according to Eq. (c7). The scattered points come from the finite size of the Monte Carlo sample.