Inherent Self-consistency of the Electron Fraction between Neutrino-dominated Accretion Flows and Their Progenitors

Stellar-mass black holes (BHs) surrounded by neutrino-dominated accretion flows (NDAFs) are a leading central engine of gamma-ray bursts (GRBs). In this work, we investigate the electron fraction distribution in NDAFs with or without disk outflows for different accretion rates, BH spins, and outflow rates. Our results show that, for the cases of the massive disks at relatively low accretion rates, the outer boundaries of the disks are predominantly advection cooled, yielding electron fractions of Y _e ∼ 0.5, as expected for massive collapsar progenitors. By contrast, in the cases of lower-mass disks at high accretion rates, neutrino cooling becomes highly efficient, and mildly electron-degenerate disks emerge, characterized by Y _e ≲ 0.38 at the outer boundary of the disk, even for the strong outflows, which is consistent with materials from compact object merger scenarios. Moreover, we find that these trends remain robust across different BH spins. Consequently, the self-consistent agreement between the electron fraction properties at the outer boundaries of NDAFs and those expected from GRB progenitors provides effective support for NDAFs serving as the GRB central engines.