2025ApJ...994..264X

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.