Maximum Spin of Black Holes Driving Jets

TL;DR

This paper models the maximum spin of black holes driven by jet production, showing that jets exert a braking torque that limits black hole spin to about 93-96% of the maximum, aligning with simulation results.

Contribution

It introduces a new spin-up function accounting for jet braking torque, providing a simple model that matches numerical simulations for black hole spin evolution.

Findings

Black holes reach an equilibrium spin of about 93% of maximum due to jet braking.

The model's jet efficiency-spin relationship agrees with simulation data.

Maximum achievable black hole spin is limited by jet-induced torque.

Abstract

Unbounded outflows in the form of highly collimated jets and broad winds appear to be a ubiquitous feature of accreting black hole systems. The most powerful jets are thought to derive a significant fraction, if not the majority, of their power from the rotational energy of the black hole. Whatever the precise mechanism that causes them, these jets must therefore exert a braking torque on the black hole. We calculate the spin-up function for an accreting black hole, accounting for this braking torque. We find that the predicted black hole spin-up function depends only on the black hole spin and dimensionless parameters describing the accretion flow. Using recent relativistic magnetohydrodynamical numerical simulation results to calibrate the efficiency of angular momentum transfer in the flow, we find that an ADAF flow will spin a black hole up (or down) to an equilibrium value of about 96% of the maximal spin value in the absence of jets. Combining our ADAF system with a simple model for jet power, we demonstrate that an equilibrium is reached at approximately 93% of the maximal spin value, as found in the numerical simulation studies of the spin-up of accreting black holes, at which point the spin-up of the hole by accreted material is balanced by the braking torque arising from jet production. Our model also yields a relationship between jet efficiency and black hole spin that is in surprisingly good agreement with that seen in the simulation studies, indicating that our simple model is a useful and convenient description of ADAF inflow - jet outflow about a spinning black hole for incorporation in models of the formation and evolution of galaxies, groups and clusters of galaxies.