Equilibrium models of Weyssenhoff spin fluid accretion tori around Kerr black holes

Abstract: The construction of equilibrium models of accretion disks around compact objects has become a highly relevant topic in the recent times, thanks to the current understanding that indicates a direct relationship between these objects with the electromagnetic emission of supermassive compact objects residing at center of the galaxies M87 and Milky Way, both observed by the Event Horizon Telescope Collaboration. As the physical properties of the compact sources are estimated using the results of computer simulations of the system comprising of the disk plus the compact object, adding new physical ingredients to the initial data of the simulation is pertinent to enhance our knowledge about these objects. In this work, we thus present equilibrium solutions of geometrically thick, non-self-gravitating, constant orbital specific angular momentum, neutral Weyssenhoff spin fluid accretion tori in the Kerr spacetime, building upon a previous work that was restricted to the Schwarzschild geometry. Our models are obtained under the assumptions of stationarity and axisymmetry in the fluid quantities, circularity of the flow and a polytropic equation of state. We study how the deviations from an ideal no-spin fluid depend on both the magnitude of the macroscopic spin of the fluid and on the spin parameter of the Kerr black hole, carefully encompassing both the co-rotating and the counter-rotating cases. Our results demonstrate that the characterstic radii, the thickness and the radial extent of such a torus can change importantly in the presence of the macroscopic spin of the ideal fluid. We also find some limitations of our approach that constraint the amount of spin the fluid can have in the rotating Kerr background. Finally, we present a parameter space exploration that gives us additional constraints on the possible values of the fluid spin denoted by the parameter $s_0$.