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Register a new userMaximum Spin of Black Holes Driving Jets
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Authors
Andrew J. Benson
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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.
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It has for long been an article of faith among astrophysicists that black hole spin energy is responsible for powering the relativistic jets seen in accreting black holes. Two recent advances have strengthened the case. First, numerical general relativistic magnetohydrodynamic simulations of accreting spinning black holes show that relativistic jets form spontaneously. In at least some cases, there is unambiguous evidence that much of the jet energy comes from the black hole, not the disk. Second, spin parameters of a number of accreting stellar-mass black holes have been measured. For ballistic jets from these systems, it is found that the radio luminosity of the jet correlates with the spin of the black hole. This suggests a causal relationship between black hole spin and jet power, presumably due to a generalized Penrose process.
Under the assumption that jets in active galactic nuclei are powered by accretion and the spin of the central supermassive black hole, we are able to reproduce the radio luminosity functions of high- and low-excitation galaxies. High-excitation galaxies are explained as high-accretion rate but very low spin objects, while low-excitation galaxies have low accretion rates and bimodal spin distributions, with approximately half of the population having maximal spins. At higher redshifts (z~1), the prevalence of high accretion rate objects means the typical spin was lower, while in the present day Universe is dominated by low accretion rate objects, with bimodal spin distributions.
We build an evolution model of the central black hole that depends on the processes of gas accretion, the capture of stars, mergers as well as electromagnetic torque. In case of gas accretion in the presence of cooling sources, the flow is momentum-driven, after which the black hole reaches a saturated mass; subsequently, it grows only by stellar capture and mergers. We model the evolution of the mass and spin with the initial seed mass and spin in $Lambda$CDM cosmology. For stellar capture, we have assumed a power-law density profile for the stellar cusp in a framework of relativistic loss cone theory that include the effects of black hole spin, Carters constant, loss cone angular momentum, and capture radius. Based on this, the predicted capture rates of $10^{-5}$--$10^{-6}$ yr$^{-1}$ are closer to the observed range. We have considered the merger activity to be effective for $z lesssim 4$, and we self-consistently include the Blandford-Znajek torque. We calculate these effects on the black hole growth individually and in combination, for deriving the evolution. Before saturation, accretion dominates the black hole growth ($sim 95%$ of the final mass), and subsequently, stellar capture and mergers take over with roughly equal contribution. The simulations of the evolution of the $M_{bullet} - sigma$ relation using these effects are consistent with available observations. We run our model backward in time and retrodict the parameters at formation. Our model will provide useful inputs for building demographics of the black holes and in formation scenarios involving stellar capture.
We use results from simulations of the production of magnetohydrodynamic jets around black holes to derive the cosmic spin history of the most massive black holes. We assume that the efficiency of jet production is a monotonic function of spin a, as given by the simulations, and that the accretion flow geometry is similarly thick for quasars accreting close to the Eddington ratio and for low-excitation radio galaxies accreting at very small Eddington rates. We use the ratio of the comoving densities of the jet power and the radiated accretion power associated with supermassive black holes with Mbh>~10^8 Msol to estimate the cosmic history of the characteristic spin a. The evolution of this ratio, which increases with decreasing z, is consistent with a picture where the z~0 active galactic nuclei have typically higher spins than those at z~2 (with typical values a~0.35-0.95 and a~0.0-0.25 respectively). We discuss the implications in terms of the relative importance of accretion and mergers in the growth of supermassive black holes with Mbh>~10^8 Msol.
The current understanding of the formation of powerful bi-directional jets in systems such as radio galaxies and quasars is that the process involves a supermassive black hole that is being fed with magnetized gas through an orbiting accretion disc. In this paper we discuss the dynamics of the jet powered by rotating black holes, in the presence of a magnetic field, including the scaling of the jet length and their typical time scales. We consider a unified picture covering all phenomena involving jets and rotating black holes ranging from gamma ray bursts to extragalactic jets and discuss the relevant scaling laws. We have also discussed the acceleration of the particles in jets and consequent synchrotron and inverse Compton radiations. Accelerated protons from jets as possible sources of high energy cosmic rays are also discussed.
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