Repeated Partial Disruptions in a White Dwarf-Neutron Star or White Dwarf-Black Hole Merger Modulate the Prompt Emission of Long-duration Merger-type GRBs

The progenitors of gamma-ray bursts (GRBs) have long been an unresolved issue. GRB 230307A stands out as an exceptionally bright event, belonging to the long-duration GRBs but also exhibiting a late-emission component reminiscent of a kilonova. Together with the similar events GRBs 060614 and 211211A, they make up a new subgroup of GRBs with intriguing progenitors. If such long-duration merger-type GRBs originated from the coalescence of a white dwarf (WD) with a neutron star (NS) or a black hole (BH), as proposed in the recent literature, then the larger tidal disruption radius of the WD, together with a nonnegligible residual orbital eccentricity, would make repeated partial tidal disruptions inevitable. This may modulate the mass accretion and jet launching process at the NS or BH, resulting in a quasiperiodic modulation (QPM) in the light curve of the GRB, with a period equal to the orbital period. The detection of potential QPMs during the early episode of prompt emission of these three GRBs supports this scenario, and the relatively slow QPM (> 1 s) suggests that the lighter object cannot be an NS. We propose that the progenitor system of GRBs 230307A, 060614, and 211211A consist of a WD of mass 1.3 M-circle dot, 0.9 M-circle dot, and 1.4 M-circle dot, respectively, and an NS (or BH). After several cycles of modulations, the WD is completely destroyed, and the accretion of the remaining debris dominates the extended emission episode.