Impact of a mean field dynamo on neutron star mergers leading to magnetar remnants

We investigate the impact of a mean field model for the $\alpha\Omega$-dynamo potentially active in the post-merger phase of a binary neutron star coalescence. We do so by deriving equations for ideal general relativistic magnetohydrodynamics (GRMHD) with an additional $\alpha-$term, which closely resemble their Newtonian counterpart, but remain compatible with standard numerical relativity simulations. We propose a heuristic dynamo closure relation for the magnetorotational instability-driven turbulent dynamo in the outer layers of a differentially rotating magnetar remnant and its accretion disk. As a first demonstration, we apply this framework to the early stages of post-merger evolution ($\lesssim 50\, \rm ms$). We demonstrate that depending on the efficacy of the dynamo action, magnetically driven outflows can be present with their amount of baryon loading correlating with the magnetic field amplification. These outflows can also contain precursor flaring episodes before settling into a quasi-steady state. For the dynamo parameters explored in this work, we observe electromagnetic energy fluxes of up to $10^{50}\, \rm erg/s$, although larger amplification parameters will likely lead to stronger fluxes. Our results are consistent with the expectation that substantial dynamo amplification (either during or after the merger) may be necessary for neutron-star remnants to power short gamma-ray bursts or precursors thereof.