Exploring the sensitivity of gravitational wave detectors to neutron star physics

The physics of neutron stars can be studied with gravitational waves emitted from coalescing binary systems. Tidal effects become significant during the last few orbits and can be visible in the gravitational wave spectrum above 500 Hz. After the merger, the neutron star remnant oscillates at frequencies above 1 kHz and can collapse into a black hole. Gravitational wave detectors with a sensitivity of $\ensuremath{\simeq}{10}^{\ensuremath{-}24}\text{ }\text{ }\mathrm{strain}/\sqrt{\mathrm{Hz}}$ at 2--4 kHz can observe these oscillations from a source which is approximately 100 Mpc away. The current observatories, such as LIGO and Virgo, are limited by shot noise at high frequencies and have a sensitivity of greater than or equal to $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}\text{ }\text{ }\mathrm{strain}/\sqrt{\mathrm{Hz}}$ at 3 kHz. In this paper, we propose an optical configuration of gravitational wave detectors, which can be set up in present facilities using the current interferometer topology. This scheme has the potential to reach $7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}25}\text{ }\text{ }\mathrm{strain}/\sqrt{\mathrm{Hz}}$ at 2.5 kHz without compromising the detector sensitivity to black hole binaries. We argue that the proposed instruments have the potential to detect similar amount of postmerger neutron star oscillations as the next generation detectors, such as Cosmic Explorer and Einstein Telescope. We also optimize the arm length of the future detectors for neutron star physics and find that the optimal arm length is $\ensuremath{\approx}20\text{ }\text{ }\mathrm{km}$. These instruments have the potential to observe neutron star postmerger oscillations at a rate of approximately 30 events per year with a signal-to-noise ratio of 5 or more.