Vortex generation in the early Universe

Abstract

Context. Accretion disks formed near primordial black holes can be sources of seed magnetic fields in the early Universe. In particular, the Biermann battery mechanism has been shown to generate primordial magnetic fields in an unmagnetized and turbulence-free accretion disk, but this depends on a delicate misalignment of density and pressure gradients in plasmas. Aims. We aim to reformulate the question of magnetogenesis in the context of plasma generalized vorticity and to search for a more robust mechanism of vorticity generation in the early Universe. Methods. We utilize the electro-vortical formalism in curved spacetime, which treats the plasma flow and electromagnetic field on an equal footing, and apply it to a thin accretion disk model near a rotating black hole. Results. We present a spacetime curvature-driven mechanism that persists even in the absence of the Biermann battery. We explore the vorticity and enstrophy generation rate dependencies on black hole masses and spin rates. Conclusions. Analysis indicates that the accretion disks around lower-mass, faster rotating black holes contribute the greatest amount to the enstrophy and vorticity generation rates from the spacetime curvature drive. The shorter turning radii at which the sign of the vorticity changes – corresponding with this region of phase space – may favor these length scales in vortical structure formation and subsequent evolution.