Slingshot on compact binaries in the nuclear region of galaxies as the origin of large offset gamma-ray bursts

A growing number of gamma-ray bursts (GRBs) have been observed at large projected offsets from the centres of their putative host galaxies, sometimes extending to several tens of kiloparsecs. When the GRB is associated with a kilonova, a compact binary with at least one neutron star is expected to be involved, and the cause of the offset can be attributed to the neutron star natal kick. In this work, we explore an alternative mechanism: the gravitational scattering of compact binaries populating the nuclear region of the host galaxy, by an intermediate-mass black hole or secondary supermassive black hole. We specifically consider populations of neutron star-neutron star (NS-NS), neutron star-black hole (NS-BH), and neutron star-white dwarf (NS-WD) binaries, and analyse the ejection of bound systems from the nuclear region through a gravitational-slingshot effect. We proceed analytically to derive the conditions for binary survival and to parametrise the post-encounter velocity. To quantify the associated merger offsets, we numerically integrate the post-slingshot trajectory of the binary centre-of-mass in host-galaxy potentials that include the primary SMBH, the stellar component, and the dark-matter halo, considering both elliptical-like and spiral-like galaxy profiles. Our parameter sampling shows that NS-NS and NS-WD binaries typically merge farther from the galactic centre than NS-BH systems, with approximately 30-45% of successful ejections merging at three-dimensional distances exceeding 100 kpc; these extreme-offset mergers occur within about 0.1-10 Gyr after ejection. These results motivate the analysed mechanism as a candidate channel for observed extreme-offset transients.