Efficient Generation of Jets from Magnetically Arrested Accretion on a Rapidly Spinning Black Hole

We describe global, 3D, time-dependent, non-radiative, general-relativistic, magnetohydrodynamic simulations of accreting black holes (BHs). The simulations are designed to transport a large amount of magnetic flux to the center, more than the accreting gas can force into the BH. The excess magnetic flux remains outside the BH, impedes accretion, and leads to a magnetically arrested disc. We find powerful outflows. For a BH with spin parameter a = 0.5, the efficiency with which the accretion system generates outflowing energy in jets and winds is eta ~ 30%. For a = 0.99, we find eta ~ 140%, which means that more energy flows out of the BH than flows in. The only way this can happen is by extracting spin energy from the BH. Thus the a = 0.99 simulation represents an unambiguous demonstration, within an astrophysically plausible scenario, of the extraction of net energy from a spinning BH via the Penrose-Blandford-Znajek mechanism. We suggest that magnetically arrested accretion might explain observations of active galactic nuclei with apparent eta ~ few x 100%.Comment: 5 pages, 2 figures, MNRAS, accepte

Equation of State in Relativistic Magnetohydrodynamics: variable versus constant adiabatic index

The role of the equation of state for a perfectly conducting, relativistic magnetized fluid is the main subject of this work. The ideal constant $\Gamma$-law equation of state, commonly adopted in a wide range of astrophysical applications, is compared with a more realistic equation of state that better approximates the single-specie relativistic gas. The paper focus on three different topics. First, the influence of a more realistic equation of state on the propagation of fast magneto-sonic shocks is investigated. This calls into question the validity of the constant $\Gamma$-law equation of state in problems where the temperature of the gas substantially changes across hydromagnetic waves. Second, we present a new inversion scheme to recover primitive variables (such as rest-mass density and pressure) from conservative ones that allows for a general equation of state and avoids catastrophic numerical cancellations in the non-relativistic and ultrarelativistic limits. Finally, selected numerical tests of astrophysical relevance (including magnetized accretion flows around Kerr black holes) are compared using different equations of state. Our main conclusion is that the choice of a realistic equation of state can considerably bear upon the solution when transitions from cold to hot gas (or viceversa) are present. Under these circumstances, a polytropic equation of state can significantly endanger the solution.Comment: 14 pages, 14 figure

Prograde and Retrograde Black Holes: Whose Jet is More Powerful?

The outflow efficiency (eta) from black hole (BH) accretion disc systems is known to depend upon both the BH spin (a) and the amount of large-scale magnetic flux threading the BH and disc. Semi-analytical flux-trapping models suggest retrograde BHs should trap much more large-scale magnetic flux near the BH leading to much higher eta than for prograde BHs. We self-consistently determine the amount of large-scale magnetic flux trapped by rapidly spinning (a = -0.9 and 0.9) BHs using global 3D time-dependent non-radiative general relativistic magnetohydrodynamic simulations of thick (h/r ~ 0.3-0.6) discs. We find that BH-trapped flux builds up until it is strong enough to disrupt the inner accretion disc. Contrary to prior flux-trapping models, which do not include the back-reaction of magnetic flux on the disc, our simulations show prograde BHs trap more magnetic flux, leading to about 3 times higher eta than retrograde BHs for |a| = 0.9. Both spin orientations can produce highly efficient jets, eta ~ 100%, with increasing eta for increasing disc thickness. The similarity of eta for prograde and retrograde BHs makes it challenging to infer the sign of BH spin based on jet energetics alone.Comment: 5 pages, 3 figures. Accepted to MNRAS. For associated movies see http://youtu.be/yNZLjsrz0Wo and http://youtu.be/bQE69wti3a

On the efficiency of the Blandford-Znajek mechanism for low angular momentum relativistic accretion

Blandford-Znajek (BZ) mechanism has usually been studied in the literature for accretion with considerably high angular momentum leading either to the formation of a cold Keplerian disc, or a hot and geometrically thick sub-Keplerian flow as described within the framework of ADAF/RIAF. However, in nearby elliptical galaxies, as well as for our own Galactic centre, accretion with very low angular momentum is prevalent. Such quasi-spherical strongly sub-Keplerian accretion has complex dynamical features and can accommodate stationary shocks. In this letter, we present our calculation for the maximum efficiency obtainable through the BZ mechanism for complete general relativistic weakly rotating axisymmetric flow in the Kerr metric. Both shocked and shock free flow has been studied in detail for rotating and counter rotating accretion. Such study has never been done in the literature before. We find that the energy extraction efficiency is low, about 0.1%, and increases by a factor 15 if the ram pressure is included. Such an efficiency is still much higher than the radiative efficiency of such optically thin flows. For BZ mechanism, shocked flow produces higher efficiency than the shock free solutions and retrograde flow provides a slightly larger value of the efficiency than that for the prograde flow.Comment: Substantially revised final version to appear in MNRAS Letters. Three colour figure

Transport of Large Scale Poloidal Flux in Black Hole Accretion

We report on a global, three-dimensional GRMHD simulation of an accretion torus embedded in a large scale vertical magnetic field orbiting a Schwarzschild black hole. This simulation investigates how a large scale vertical field evolves within a turbulent accretion disk and whether global magnetic field configurations suitable for launching jets and winds can develop. We find that a "coronal mechanism" of magnetic flux motion, which operates largely outside the disk body, dominates global flux evolution. In this mechanism, magnetic stresses driven by orbital shear create large-scale half-loops of magnetic field that stretch radially inward and then reconnect, leading to discontinuous jumps in the location of magnetic flux. In contrast, little or no flux is brought in directly by accretion within the disk itself. The coronal mechanism establishes a dipole magnetic field in the evacuated funnel around the orbital axis with a field intensity regulated by a combination of the magnetic and gas pressures in the inner disk. These results prompt a reevaluation of previous descriptions of magnetic flux motion associated with accretion. Local pictures are undercut by the intrinsically global character of magnetic flux. Formulations in terms of an "effective viscosity" competing with an "effective resistivity" are undermined by the nonlinearity of of the magnetic dynamics and the fact that the same turbulence driving mass motion (traditionally identified as "viscosity") can alter magnetic topology.Comment: 45 pages, 17 figures, 1 movie; ApJ accepted; updated version contains several new figures and a movie detailing the operation of the coronal mechanism. The movie and a version of the paper with high resolution figures can be found at http://www.astro.virginia.edu/~krb3u/0906.2784

Maximum Spin of Black Holes Driving Jets

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.Comment: 15 pages, 5 figures, accepted for publication in MNRAS. Corrected errors in jet efficiency formula in text and some equations in Appendices. Errors affected text only, results are unchange

Protecting privacy of users in brain-computer interface applications

Machine learning (ML) is revolutionizing research and industry. Many ML applications rely on the use of large amounts of personal data for training and inference. Among the most intimate exploited data sources is electroencephalogram (EEG) data, a kind of data that is so rich with information that application developers can easily gain knowledge beyond the professed scope from unprotected EEG signals, including passwords, ATM PINs, and other intimate data. The challenge we address is how to engage in meaningful ML with EEG data while protecting the privacy of users. Hence, we propose cryptographic protocols based on secure multiparty computation (SMC) to perform linear regression over EEG signals from many users in a fully privacy-preserving(PP) fashion, i.e., such that each individual's EEG signals are not revealed to anyone else. To illustrate the potential of our secure framework, we show how it allows estimating the drowsiness of drivers from their EEG signals as would be possible in the unencrypted case, and at a very reasonable computational cost. Our solution is the first application of commodity-based SMC to EEG data, as well as the largest documented experiment of secret sharing-based SMC in general, namely, with 15 players involved in all the computations

Three-Dimensional Simulations of Magnetized Thin Accretion Disks around Black Holes: Stress in the Plunging Region

We describe three-dimensional general relativistic magnetohydrodynamic simulations of a geometrically thin accretion disk around a non-spinning black hole. The disk has a thickness $h/r\sim0.05-0.1$ over the radial range $(2-20)GM/c^2$. In steady state, the specific angular momentum profile of the inflowing magnetized gas deviates by less than 2% from that of the standard thin disk model of Novikov & Thorne (1973). Also, the magnetic torque at the radius of the innermost stable circular orbit (ISCO) is only $\sim2$ of the inward flux of angular momentum at this radius. Both results indicate that magnetic coupling across the ISCO is relatively unimportant for geometrically thin disks.Comment: 4 pages, 4 figures, ApJL accepte

Modeling Subsurface Biodegradation of Non-Aqueous Phase Liquids: A Literature Review

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