Inter-disks inversion surfaces

Abstract

We consider a counter-rotating torus orbiting a central Kerr black hole (BH) with dimensionless spin a, and its accretion flow into the BH, in an agglomerate of an outer counter-rotating torus and an inner co-rotating torus. This work focus is the analysis of the inter-disks inversion surfaces. Inversion surfaces are spacetime surfaces, defined by the condition \(u^{\phi }=0\) on the flow torodial velocity, located out of the BH ergoregion, and totally embedding the BH. They emerge as a necessary condition, related to the spacetime frame-dragging, for the counter-rotating flows into the central Kerr BH. In our analysis we study the inversion surfaces of the Kerr spacetimes for the counter-rotating flow from the outer torus, impacting on the inner co-rotating disk. Being totally or partially embedded in (internal to) the inversion surfaces, the inner co-rotating torus (or jet) could be totally or in part “shielded”, respectively, from the impact with flow with \(a u^{\phi }<0\). We prove that, in general, in the spacetimes with \(a<0.551\) the co-rotating toroids are always external to the accretion flows inversion surfaces. For \(0.551<a<0.886\), co-rotating toroids could be partially internal (with the disk inner region, including the inner edge) in the flow inversion surface. For BHs with \(a>0.886\), a co-rotating torus could be entirely embedded in the inversion surface and, for larger spins, it is internal to the inversion surfaces. Tori orbiting in the BH outer ergoregion are a particular case. Further constraints on the BHs spins are discussed in the article.