High-energy Neutrino Signatures from Pulsar Remnants of Binary Neutron-Star Mergers: Coincident Detection Prospects with Gravitational Waves

Binary neutron-star (BNS) mergers are accompanied by multi-messenger emissions, including gravitational wave (GW), neutrino, and electromagnetic signals. Some fraction of BNS mergers may result in a rapidly spinning magnetar as a remnant, which can enhance both the EM and neutrino emissions. In this study, we model the neutrino emissions from such systems and discuss the prospects for detecting the neutrinos coincident with GW signatures. We consider a scenario where a magnetar remnant drives a pulsar wind using its spin energy. The wind interacts with the surrounding kilonova ejecta, forming a nebula filled with non-thermal photons. Ions and nuclei extracted from the magnetar's surface can be accelerated in the polar-cap and the termination-shock regions. We investigate the neutrino fluences resulting from photomeson interactions, where accelerated CR protons interact with the photons in the nebula. Our findings indicate that the peak neutrino fluence is $\sim 10^{-2}\rm GeV~cm^{-2}$ for a source at $40$ Mpc, which is reached approximately $\mathcal{O}( 1-10\ {\rm days})$ post merger. Finally, we examine the potential for GW-triggered stacking searches with IceCube-Gen2 using next-generation GW detectors such as the Cosmic Explorer (CE) and the Einstein Telescope (ET). We conclude that, assuming an optimistic neutrino emission model, a combination of CE+ET would offer a high probability of neutrino detection from these sources within an operational timescale of $\sim 20$ years. In case of non-detection, $2 \sigma$ level constraints on model parameters can be established within similar joint operation timescales.