Multi-wavelength analysis of the progenitor of GRB 230307A via Bayesian model comparison

GRB 230307A is one of the brightest long-duration gamma-ray bursts (GRBs) ever detected, yet its progenitor remains uncertain due to the variety of plausible astrophysical scenarios. In this work, we investigate four possible progenitors for GRB 230307A: a binary neutron star (BNS), a neutron star--white dwarf (NS--WD) system, a neutron star--black hole (NS--BH) merger, and a tidal disruption event (TDE) involving a white dwarf and a supermassive black hole. Additionally, we explore three distinct central engine models powering the kilonova associated with the BNS: radioactive decay of $r$-process nuclei in a two-component ejecta model, a magnetar-driven model including magnetic dipole spin-down, and a combined model of magnetar spin-down with ${}^{56}$Ni radioactive decay. We perform Bayesian multi-wavelength light-curve analyses using physically motivated models and priors, and evaluate model performance through Bayes factors and leave-one-out cross-validation (LOO) scores. Our results show a statistical preference for a BNS or NS--WD progenitor producing a kilonova powered by a magnetar and ${}^{56}$Ni decay, characterized by a ${}^{56}$Ni mass of $\sim4\times10^{-4}\,M_{\odot}$ and an ejecta mass of $0.06\,M_{\odot}$. Furthermore, under the assumption of a BNS origin within this model, we infer binary component masses of $m_{1} = 1.81^{+0.46}_{-0.61}\,M_{\odot}$ and $m_{2} = 1.61^{+0.65}_{-0.41}\,M_{\odot}$, with a dimensionless tidal deformability of $\tilde{\Lambda} = 471^{+318}_{-395}$. From the component mass posteriors, we infer that the observed offset can be explained by a natal kick as long as the systemic velocity is nearly aligned with the pre-kick orbital motion. In this case, the required kick velocity (co-moving frame) and binary separation range within $v'_{\mathrm{k}}\sim100$--$150~\mathrm{km\,s^{-1}}$, and $a_0\sim2$--$3~R_{\odot}$, respectively.