Toward observing neutron star collapse with gravitational wave detectors

Gravitational waves from binary neutron star inspirals have been detected along with the electromagnetic transients coming from the aftermath of the merger in GW170817. However, much is still unknown about the postmerger dynamics that connects these two sets of observables. This includes if, and when, the postmerger remnant star collapses to a black hole, and what are the necessary conditions to power a short gamma-ray burst and other observed electromagnetic counterparts. Observing the collapse of the postmerger neutron star would shed light on these questions, constraining models for the short gamma-ray burst engine and the hot neutron star equation of state. In this work, we explore the scope of using gravitational wave detectors to measure the timing of the collapse either indirectly, by establishing the shutoff of the postmerger gravitational emission, or—more challengingly—directly, by detecting the collapse signal. For the indirect approach, we consider a kilohertz high-frequency detector design that utilizes a previously studied coupled arm cavity and signal recycling cavity resonance. This design would give a signal-to-noise ratio of 0.5–8.6 (depending on the variation of waveform parameters) for a collapse gravitational wave signal occurring at 10 ms postmerger of a binary at 50 Mpc and with total mass 2.7  𝑀⊙. This detector design is limited by quantum shot noise and the signal-to-noise ratio largely depends on the detector power, which is adopted as 4 MW in this work. For the direct approach, we propose a narrow band detector design, utilizing the sensitivity around the frequency of the arm cavity free spectral range. To attain the maximal achievable quantum sensitivity, which is fundamentally limited by optical loss, we suggest the application of an optomechanical filter cavity that converts the signal recycling cavity into a signal amplifier. The proposed detector achieves a signal-to-noise ratio of 0.3–1.9, independent of the collapse time. This detector is limited by both the fundamental classical and quantum noise with the arm cavity power chosen as 10 MW.