Tracing the Physical Lineage of GRB 211211A: Population Constraints on NS–WD Merger Gamma-Ray Bursts

Abstract The peculiar long gamma-ray burst (GRB) event, GRB 211211A, is known for its association with a kilonova feature. Whereas most long GRBs are thought to originate in the core collapse of massive stars, the presence of a kilonova suggests GRB 211211A was instead produced by a merger of a compact object binary. Building on the interpretation put forward by J. Yang et al.—who argue that GRB 211211A was powered by a massive white dwarf–neutron star (WD–NS) merger—we adopt this WD–NS scenario as our observationally supported starting point. If the burst truly originates from that channel, its rarity must mirror the formation and merger rate of WD–NS binaries—a rate still largely unexplored in conventional massive-binary population studies. In this work, we present a qualitative analysis based on binary evolution physics in order to understand the fraction of GRB 211211A in short GRBs (NS–WD/NS–NS fraction). Since the progenitors of massive WD–NS binaries occupy the initial mass function-preferred regime, where the zero-age main sequence mass range of the assumed WD mass range (1.2–1.4 M ⊙ ) is comparable to that of NSs, the NS–WD/NS–NS fraction emerging from our standard evolutionary path is expected to be ∼14%–37%, far higher than the observed fraction (∼5%). This discrepancy might imply a large, still-unidentified population of GRB 211211A-like events or an unusual origin of the NS—such as being hypernova-born or accretion-induced-collapse-born. Placing these results in a broader compact-binary context, implications for black-hole systems are also discussed.