Implications of Magnetic Flux-Disk Mass Correlation in Black Hole-Neutron Star Mergers for GRB sub-populations

We perform numerical relativity simulations of black hole-neutron star (BH-NS) mergers with a fixed mass ratio of $q = 3$, varying the BH spin to produce a wide range of post-merger accretion disk masses. Our high-order numerical scheme, fine resolution, and Large Eddy Simulation techniques enable us to achieve likely the most resolved BH-NS merger simulations to date, capturing the post-merger magnetic field amplification driven by turbulent dynamo processes. Following tidal disruption and during disk formation, the Kelvin-Helmholtz instability in the spiral arm drives a turbulent state in which the magnetic field, initialized to a realistic average value of $10^{11}\, \rm{G}$, grows to an average of approximately $10^{14}\, \rm{G}$ in the first $\approx 20\, \mathrm{ms}$ post-merger. Notably, the dimensionless magnetic flux on the BH, $ \phi $, evolves similarly across nearly two orders of magnitude in disk mass. This similarity, along with estimates from longer numerical simulations of the decay of the mass accretion rate, suggests a universal timescale at which the dimensionless flux saturates at a magnetically arrested state (MAD) such that $ \phi \approx 50 $ at $t_{\rm MAD} \gtrsim 10\,{\rm s}$. The unified framework of Gottlieb et al. (2023) established that the MAD timescale sets the duration of the resulting compact binary gamma-ray burst (cbGRB), implying that all BH-NS mergers contribute to the recently detected new class of long-duration cbGRBs.