White dwarf-neutron star binaries: a plausible pathway for long-duration gamma-ray bursts from compact object mergers?

Abstract: Two long-duration gamma-ray bursts were recently discovered with kilonovae, the signature of r-process element production in a compact binary merger, rather than supernovae. This has forced a re-evaluation of the long-established dichotomy between short bursts (< 2s, arising from compact binary mergers) and long bursts (> 2s, a class of massive star core-collapse event). We aim to determine whether white dwarf-neutron star (WDNS) and white dwarf-black hole (WDBH) mergers are plausible explanations for long-duration compact merger GRBs, in terms of their galactocentric merger offsets and cosmological rates. We model the host galaxies of GRBs 211211A and 230307A, and employ binary population synthesis, to predict the offset distributions of compact mergers. We compare with the observed offsets, investigate evolutionary pathways, predict their cosmological rates, and compare with volumetric GRB rates. We find that WDNS mergers occur at lower host offsets than binary NS mergers, but that in the specific cases of GRBs 211211A and 230307A, the observed offsets are consistent with either scenario. We predict that WDNS mergers occur at a similar rate to binary NS mergers and long GRBs, and that WDBH mergers are a factor of ten rarer, with the caveat that these rates currently carry uncertainties at the order of magnitude level. We have demonstrated, solely in terms of galactocentric offsets and event rates, that WDNS mergers are a plausible explanation for GRBs 211211A and 230307A, and long GRBs from compact object mergers more generally. WDNS binaries have lower systemic velocities than binary neutron stars, but longer delay times, and ultimately merge with an offset distribution that is not measurably different without large samples. Therefore, offsets and rates alone cannot currently distinguish between compact binary progenitor models for supernova-less long duration GRBs.