The stochastic gravitational-wave background (SGWB) generated by the inspiral and merger of binary neutron stars is traditionally modeled assuming that the inspiral is promptly followed by the collapse of the merger remnant to a rotating black hole. While this is reasonable for the most massive binaries, it is not what is expected in general, as the remnant may survive for up to hundreds of milliseconds and radiate an amount of energy that is significantly larger than that lost during the whole inspiral. To account for this additional contribution to the SGWB, we consider a waveform model that includes both the inspiral and the postmerger emission. We show for the first time that for a large set of parametrized equations of state (EOSs) compatible with observational constraints, there is considerable spectral power in the 1–2 kHz range, distinct from that associated with the inspiral and leading to a dimensionless GW energy density ${\mathrm{\Omega }}_{\mathrm{GW}}\simeq {10}^{-10}–{10}^{-9}$. We discuss the enhanced detectability of the SGWB by third-generation detectors such as the Einstein Telescope and Cosmic Explorer, and show how it depends on the signal-to-noise ratio of foreground binaries and on the remnant lifetime. Interestingly, even a nondetection of the high-frequency part of the SGWB could provide valuable constraints on the remnant lifetime, offering novel insights into the postmerger dynamics and the EOS of nuclear matter.

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• Gravitational wave sources
• Gravitational waves
• Neutron stars & pulsars
• Gravitational wave detectors