Ramesh Narayan

The University of Arizona, Tucson, Arizona, United States

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Publications (283)1422.34 Total impact

  • Lorenzo Sironi, Ramesh Narayan
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    ABSTRACT: In systems accreting well below the Eddington rate, the plasma in the innermost regions of the disk is collisionless and two-temperature, with the ions hotter than the electrons. Yet, whether a collisionless faster-than-Coulomb energy transfer mechanism exists in two-temperature accretion flows is still an open question. We study the physics of electron heating during the growth of ion velocity-space instabilities, by means of multi-dimensional particle-in-cell (PIC) simulations. A large-scale compression - embedded in a novel form of the PIC equations - continuously amplifies the field. This constantly drives a pressure anisotropy P_perp > P_parallel, due to the adiabatic invariance of the particle magnetic moments. We find that, for ion plasma beta values beta_i ~ 5-30 appropriate for the midplane of low-luminosity accretion flows, mirror modes dominate if the electron-to-proton temperature ratio is > 0.2, whereas if it is < 0.2 the ion cyclotron instability triggers the growth of strong Alfven-like waves, that pitch-angle scatter the ions to maintain marginal stability. We develop an analytical model of electron heating during the growth of the ion cyclotron instability, which we validate with PIC simulations. We find that for cold electrons (beta_e < m_e/m_i), the electron energy gain is controlled by the magnitude of the E-cross-B velocity induced by the ion cyclotron waves. This term is independent of the initial electron temperature, so it provides a solid energy floor even for electrons starting with extremely low temperatures. On the other hand, the electron energy gain for beta_e > m_e/m_i - governed by the conservation of the magnetic moment in the growing fields of the instability - is proportional to the initial electron temperature. Our results have implications for two-temperature accretion flows as well as the solar wind and intracluster plasmas. [abridged]
    11/2014;
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    ABSTRACT: Recent advances in general relativistic magnetohydrodynamic simulations have expanded and improved our understanding of the dynamics of black-hole accretion disks. However, current simulations do not capture the thermodynamics of electrons in the low density accreting plasma. This poses a significant challenge in predicting accretion flow images and spectra from first principles. Because of this, simplified emission models have often been used, with widely different configurations (e.g., disk- versus jet-dominated emission), and were able to account for the observed spectral properties of accreting black-holes. Exploring the large parameter space introduced by such models, however, requires significant computational power that exceeds conventional computational facilities. In this paper, we use GRay, a fast GPU-based ray-tracing algorithm, on the GPU cluster El Gato, to compute images and spectra for a set of six general relativistic magnetohydrodynamic simulations with different magnetic field configurations and black-hole spins. We also employ two different parametric models for the plasma thermodynamics in each of the simulations. We show that, if only the spectral properties of Sgr A* are used, all twelve models tested here can fit the spectra equally well. However, when combined with the measurement of the image size of the emission using the Event Horizon Telescope, current observations rule out all models with strong funnel emission, because the funnels are typically very extended. Our study shows that images of accretion flows with horizon-scale resolution offer a powerful tool in understanding accretion flows around black-holes and their thermodynamic properties.
    10/2014;
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    ABSTRACT: The transient Swift J1644+57 is believed to have been produced by an unlucky star wandering too close to a supermassive black hole (BH) leading to a tidal disruption event. This unusual flare displayed highly super-Eddington X-ray emission which likely originated in a relativistic, collimated jet. This presents challenges to modern accretion and jet theory as upper limits of prior BH activity, which we obtain from the radio afterglow of this event, imply that both the pre-disruption BH and stellar magnetic fluxes fall many orders of magnitude short of what is required to power the observed X-ray luminosity. We argue that a pre-existing, "fossil" accretion disc can contain a sufficient reservoir of magnetic flux and that the stellar debris stream is capable of dragging this flux into the BH. To demonstrate this, we perform local, 3D magnetohydrodynamic simulations of the disc--stream interaction and demonstrate that the interface between the two is unstable to mixing. This mixing entrains a sufficient amount of fossil disc magnetic flux into the infalling stellar debris to power the jet. We argue that the interaction with the fossil disc can have a pronounced effect on the structure and dynamics of mass fallback and likely the resulting transient. Finally, we describe possible ramifications of these interactions on unresolved problems in tidal disruption dynamics, in particular, the efficiency of debris circularization, and effects of the disruption on the preexisting black hole system. Animations online: http://goo.gl/T84tLs
    10/2014;
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    Xinyi Guo, Lorenzo Sironi, Ramesh Narayan
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    ABSTRACT: Electron acceleration to non-thermal energies is known to occur in low Mach number (M<5) shocks in galaxy clusters and solar flares, but the electron acceleration mechanism remains poorly understood. Using two-dimensional (2D) particle-in-cell (PIC) plasma simulations, we showed in Paper I that electrons are efficiently accelerated in low Mach number (M=3) quasi-perpendicular shocks via a Fermi-like process. The electrons bounce between the upstream region and the shock front, with each reflection at the shock resulting in energy gain via shock drift acceleration. The upstream scattering is provided by oblique magnetic waves, that are self-generated by the electrons escaping ahead of the shock. In the present work, we employ additional 2D PIC simulations to address the nature of the upstream oblique waves. We find that the waves are generated by the shock-reflected electrons via the firehose instability, which is driven by an anisotropy in the electron velocity distribution. We systematically explore how the efficiency of wave generation and of electron acceleration depend on the magnetic field obliquity, the flow magnetization (or equivalently, the plasma beta), and the upstream electron temperature. We find that the mechanism works for shocks with high plasma beta (>20) at nearly all magnetic field obliquities, and for electron temperatures in the range relevant for galaxy clusters. Our findings offer a natural solution to the conflict between the bright radio synchrotron emission observed from the outskirts of galaxy clusters and the low electron acceleration efficiency usually expected in low Mach number shocks.
    09/2014;
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    ABSTRACT: Observations of the black hole in the center of the Milky Way with the Event Horizon Telescope at 1.3 mm have revealed a size of the emitting region that is smaller than the size of the black-hole shadow. This can be reconciled with the spectral properties of the source, if the accretion flow is seen at a relatively high inclination (50-60 degrees). Such an inclination makes the angular momentum of the flow, and perhaps of the black hole, nearly aligned with the angular momenta of the orbits of stars that lie within 3 arcsec from the black hole. We discuss the implications of such an alignment for the properties of the black hole and of its accretion flow. We argue that future Event-Horizon-Telescope observations will not only refine the inclination of Sgr A* but also measure precisely its orientation on the plane of the sky.
    09/2014;
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    ABSTRACT: The image of the emission surrounding the black hole in the center of the Milky Way is predicted to exhibit the imprint of general relativistic (GR) effects, including the existence of a shadow feature and a photon ring of diameter ~50 microarcseconds. Structure on these scales can be resolved by millimeter-wavelength very long baseline interferometry (VLBI). However, strong-field GR features of interest will be blurred at lambda >= 1.3 mm due to scattering by interstellar electrons. The scattering properties are well understood over most of the relevant range of baseline lengths, suggesting that the scattering may be (mostly) invertible. We simulate observations of a model image of Sgr A* and demonstrate that the effects of scattering can indeed be mitigated by correcting the visibilities before reconstructing the image. This technique is also applicable to Sgr A* at longer wavelengths.
    The Astrophysical Journal 09/2014; 795(2). · 6.73 Impact Factor
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    ABSTRACT: Using the Very Long Baseline Array, we have measured a trigonometric parallax for the micro quasar GRS 1915+105, which contains a black hole and a K-giant companion. This yields a direct distance estimate of 8.6 (+2.0,-1.6) kpc and a revised estimate for the mass of the black hole of 12.4 (+2.0,-1.8) Msun. GRS 1915+105 is at about the same distance as some HII regions and water masers associated with high-mass star formation in the Sagittarius spiral arm of the Galaxy. The absolute proper motion of GRS 1915+105 is -3.19 +/- 0.03 mas/y and -6.24 +/- 0.05 mas/y toward the east and north, respectively, which corresponds to a modest peculiar speed of 22 +/-24 km/s at the parallax distance, suggesting that the binary did not receive a large velocity kick when the black hole formed. On one observational epoch, GRS 1915+105 displayed superluminal motion along the direction of its approaching jet. Considering previous observations of jet motions, the jet in GRS 1915+105 can be modeled with a jet inclination to the line of sight of 60 +/- 5 deg and a variable flow speed between 0.65c and 0.81c, which possibly indicates deceleration of the jet at distances from the black hole >2000 AU. Finally, using our measurements of distance and estimates of black hole mass and inclination, we provisionally confirm our earlier result that the black hole is spinning very rapidly.
    The Astrophysical Journal 09/2014; 796(1). · 6.73 Impact Factor
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    ABSTRACT: We present a sub-grid model that emulates the magnetic dynamo operating in magnetized accretion disks. We have implemented this model in the general relativisic radiation magnetohydrodynamic (GRRMHD) code \koral, using results from local shearing sheet simulations of the magnetorotational instability to fix the parameters of the dynamo. With the inclusion of this dynamo, we are able to run 2D axisymmetric GRRMHD simulations of accretion disks for arbitrarily long times. The simulated disks exhibit sustained turbulence, with the poloidal and toroidal magnetic field components driven towards a state similar to that seen in 3D studies. Using this dynamo code, we present a set of long-duration global simulations of super-Eddington, optically-thick disks around non-spinning and spinning black holes. Super-Eddington disks around non-rotating black holes exhibit a surprisingly large efficiency, $\eta\approx0.04$, independent of the accretion rate, where we measure efficiency in terms of the total energy output, both radiation and mechanical, flowing out to infinity. Super-Eddington disks around spinning black holes are even more efficient, and appear to extract black hole rotational energy through a process similar to the Blandford-Znajek mechanism. All the simulated models are characterized by highly super-Eddington radiative fluxes collimated along the rotation axis. We also present a set of simulations that were designed to have Eddington or slightly sub-Eddington accretion rates ($\dot{M} \lesssim 2\dot M_{\rm Edd}$). None of these models reached a steady state. Instead, the disks collapsed as a result of runaway cooling, presumably because of a thermal instability.
    07/2014;
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    Xinyi Guo, Lorenzo Sironi, Ramesh Narayan
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    ABSTRACT: Electron acceleration to non-thermal energies in low Mach number (M<5) shocks is revealed by radio and X-ray observations of galaxy clusters and solar flares, but the electron acceleration mechanism remains poorly understood. Diffusive shock acceleration, also known as first-order Fermi acceleration, cannot be directly invoked to explain the acceleration of electrons. Rather, an additional mechanism is required to pre-accelerate the electrons from thermal to supra-thermal energies, so they can then participate in the Fermi process. In this work, we use two- and three-dimensional particle-in-cell plasma simulations to study electron acceleration in low Mach number shocks. We focus on the particle energy spectra and the acceleration mechanism in a reference run with M=3. We find that about 15 percent of the electrons can be efficiently accelerated, forming a non-thermal power-law tail in the energy spectrum with a slope of p~2.4. Initially, thermal electrons are energized at the shock front via shock drift acceleration. The accelerated electrons are then reflected back upstream, where their interaction with the incoming flow generates magnetic waves. In turn, the waves scatter the electrons propagating upstream back toward the shock, for further energization via shock drift acceleration. In summary, the self-generated waves allow for repeated cycles of shock drift acceleration, similarly to a sustained Fermi-like process. This mechanism offers a natural solution to the conflict between the bright radio synchrotron emission observed from the outskirts of galaxy clusters and the low electron acceleration efficiency usually expected in low Mach number shocks.
    The Astrophysical Journal 06/2014; 794(2). · 6.73 Impact Factor
  • Pankaj S. Joshi, Ramesh Narayan
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    ABSTRACT: One of the most spectacular predictions of the general theory of relativity is the black hole, an object that plays a central role in modern physics [1,2,3] and astrophysics [4,5]. Black holes are, however, plagued by fundamental paradoxes that remain unresolved to this day. First, the black hole event horizon is teleological in nature [6], which means that we need to know the entire future space-time of the universe to determine the current location of the horizon. This is essentially impossible. Second, any information carried by infalling matter is lost once the material falls through the event horizon. Even though the black hole may later evaporate by emitting Hawking radiation [7], the lost information does not reappear, which has the rather serious and disturbing consequence that quantum unitarity is violated [8]. Here we propose that the above paradoxes are restricted to a particular idealized model of collapse first studied in the 1930s [9, 10] in which the event horizon, which defines the boundary of the black hole, forms initially, and the singularity in the interior of the black hole forms at a later time. In contrast, gravitational collapse from more reasonable and/or physically more realistic initial conditions often leads to models in which the event horizon and the singularity form simultaneously. We show that this apparently simple modification mitigates the causality and teleological paradoxes and at the same time lends support to two recently proposed solutions to the information paradox, namely, the "firewall" [11] and "classical chaos" [12].
    02/2014;
  • David Abarca, A. Sadowski, R. Narayan
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    ABSTRACT: Recent observations have shown a 3 Earth Mass cloud of ionized gas en route towards Sgr A*, the black hole at the center of the Galaxy. In the event that G2 or a similar cloud deposits some of its mass in the accretion disk around Sgr A*, we expect this mass to accrete onto the black hole over the course of several years, with observable consequences. We have investigated the process by which excess mass is propagated through a radiatively inefficient accretion flow. We attempt to derive a prescription for the accretion timescale as a function of the initial conditions of the excess mass. We also attempt to predict the fraction of the deposited mass that is accreted and the fraction that is lost to an outflow, as well as the change in the radio luminosity of Sgr A* as a function of time. To derive these estimates, we adopt a toy model in which gas from the cloud is placed in a torus on top of a previously run numerical MHD simulation of a radiatively inefficient accretion disk, and then continue the simulation to monitor the fate of the torus gas. For various scenarios, we track the accretion rate and surface density of the excess matter.
    01/2014;
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    Ramesh Narayan, Jeffrey E. McClintock
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    ABSTRACT: Astronomers have discovered two populations of black holes: (i) stellar-mass black holes with masses in the range 5 to 30 solar masses, millions of which are present in each galaxy in the universe, and (ii) supermassive black holes with masses in the range $10^6$ to $10^{10}$ solar masses, one each in the nucleus of every galaxy. There is strong circumstantial evidence that all these objects are true black holes with event horizons. The measured masses of supermassive black hole are strongly correlated with properties of their host galaxies, suggesting that these black holes, although extremely small in size, have a strong influence on the formation and evolution of entire galaxies. Spin parameters have recently been measured for a handful of black holes. Based on the data, there is an indication that the kinetic power of at least one class of relativistic jet ejected from accreting black holes may be correlated with black hole spin. If verified, it would suggest that these jets are powered by a generalized Penrose process mediated by magnetic fields.
    12/2013;
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    ABSTRACT: Black hole (BH) accretion flows and jets are dynamic hot relativistic magnetized plasma flows whose radiative opacity can significantly affect flow structure and behavior. We describe a numerical scheme, tests, and an astrophysically relevant application using the M1 radiation closure within a new three-dimensional (3D) general relativistic (GR) radiation (R) magnetohydrodynamics (MHD) massively parallel code called HARMRAD. Our 3D GRRMHD simulation of super-Eddington accretion (about $20$ times Eddington) onto a rapidly rotating BH (dimensionless spin $j=0.9375$) shows sustained non-axisymmemtric disk turbulence, a persistent electromagnetic jet driven by the Blandford-Znajek effect, and a total radiative output consistently near the Eddington rate. The total accretion efficiency is of order $20\%$, the large-scale electromagnetic jet efficiency is of order $10\%$, and the total radiative efficiency that reaches large distances remains low at only order $1\%$. However, the radiation jet and the electromagnetic jet both emerge from a geometrically beamed polar region, with super-Eddington isotropic equivalent luminosities. Such simulations with HARMRAD can enlighten the role of BH spin vs.\ disks in launching jets, help determine the origin of spectral and temporal states in x-ray binaries, help understand how tidal disruption events (TDEs) work, provide an accurate horizon-scale flow structure for M87 and other active galactic nuclei (AGN), and isolate whether AGN feedback is driven by radiation or by an electromagnetic, thermal, or kinetic wind/jet. For example, the low radiative efficiency and weak BH spin-down rate from our simulation suggest that BH growth over cosmological times to billions of solar masses by redshifts of $z\sim 6-8$ is achievable even with rapidly rotating BHs and ten solar mass BH seeds.
    Monthly Notices of the Royal Astronomical Society 12/2013; 441(4). · 5.52 Impact Factor
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    ABSTRACT: Black hole binaries exhibit a wide range of variability phenomena, from large-scale state changes to broadband noise and quasi-periodic oscillations, but the physical nature of much of this variability is poorly understood. We examine the variability properties of three GRMHD simulations of thin accretion disks around black holes of varying spin, producing light curves and power spectra as would be seen by observers. We find that the simulated power spectra show a broad feature at high frequency, which increases in amplitude with the inclination of the observer. We show that this high-frequency feature is a product of the Doppler effect and that its location is a function of the mass and spin of the black hole. This Doppler feature demonstrates that power spectral properties of the accretion disk can be tied to, and potentially used to determine, physical properties of the black hole.
    12/2013; 785(2).
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    ABSTRACT: A new general relativistic radiation magnetohydrodynamical code KORAL, is described, which employs the M1 scheme to close the radiation moment equations. The code has been successfully verified against a number of tests. Axisymmetric simulations of super-critical magnetized accretion on a non-rotating black hole (a=0.0) and a spinning black hole (a=0.9) are presented. The accretion rates in the two models are \dot M = 100-200 \dot M_Edd. These first general relativistic simulations of super-critical black hole accretion are potentially relevant to tidal disruption events and hyper-accreting supermassive black holes in the early universe. Both simulated models are optically and geometrically thick, and have funnels through which energy escapes in the form of relativistic gas, Poynting flux and radiative flux. The jet is significantly more powerful in the a=0.9 run. The net energy outflow rate in the two runs correspond to efficiencies of 5% (a=0) and 33% (a=0.9), as measured with respect to the mass accretion rate at the black hole. These efficiencies agree well with those measured in previous simulations of non-radiative geometrically thick disks. Furthermore, in the a=0.9 run, the outflow power appears to originate in the spinning black hole, suggesting that the associated physics is again similar in non-radiative and super-critical accretion flows. While the two simulations are efficient in terms of total energy outflow, both runs are radiatively inefficient. Their luminosities are only \sim 1-10 L_Edd, which corresponds to a radiative efficiency \sim 0.1%. Interestingly, most of the radiative luminosity emerges through the funnels, which subtend a very small solid angle. Therefore, measured in terms of a local radiative flux, the emitted radiation is highly super-Eddington.
    11/2013; 439(1).
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    ABSTRACT: In the case involving particles the necessary and sufficient condition for the Penrose process to extract energy from a rotating black hole is absorption of particles with negative energies and angular momenta. No torque at the black hole horizon occurs. In this article we consider the case of arbitrary fields or matter described by an unspecified, general energy-momentum tensor and show that the necessary and sufficient condition for extraction of black-hole's rotational energy is analogous to that in mechanical Penrose process: absorption of negative energy and negative angular momentum. We also show that a necessary condition for the Penrose process to occur is for the Noether current (the conserved energy-momentum density vector) to be spacelike or past-directed (timelike or null) on some part of the horizon. In the particle case our general criterion for the occurrence of a Penrose process reproduces the standard result. In the case of relativistic jet-producing "magnetically arrested disks" we show that the negative energy and angular momentum absorption condition is obeyed when the Blandford-Znajek mechanism is at work and hence the high energy extraction efficiency up to $\sim 300%$ found in recent numerical simulations of such accretion flows results from tapping of the black hole's rotational energy through the Penrose process. We show how black-hole rotational energy extraction works in this case by describing the Penrose process in terms of the Noether current.
    10/2013; 89(2).
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    Robert F. Penna, Akshay Kulkarni, Ramesh Narayan
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    ABSTRACT: General relativistic magnetohydrodynamic (GRMHD) simulations are providing influential models for black hole spin measurements, gamma ray bursts, and supermassive black hole feedback. Many of these simulations use the same initial condition: a rotating torus of fluid in hydrostatic equilibrium. A persistent concern is that simulation results sometimes depend on arbitrary features of the initial torus. For example, the Bernoulli parameter (which is related to outflows), appears to be controlled by the Bernoulli parameter of the initial torus. In this paper, we give a new equilibrium torus solution and describe two applications for the future. First, it can be used as a more physical initial condition for GRMHD simulations than earlier torus solutions. Second, it can be used in conjunction with earlier torus solutions to isolate the simulation results that depend on initial conditions. We assume axisymmetry, an ideal gas equation of state, constant entropy, and ignore self-gravity. We fix an angular momentum distribution and solve the relativistic Euler equations in the Kerr metric. The Bernoulli parameter, rotation rate, and geometrical thickness of the torus can be adjusted independently. Our torus tends to be more bound and have a larger radial extent than earlier torus solutions. While this paper was in preparation, several GRMHD simulations appeared based on our equilibrium torus. We believe it will continue to provide a more realistic starting point for future simulations.
    Astronomy and Astrophysics 09/2013; · 5.08 Impact Factor
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    ABSTRACT: In Gou et al. (2011), we reported that the black hole primary in the X-ray binary Cygnus X-1 is a near-extreme Kerr black hole with a spin parameter a*>0.95(3{\sigma}). We confirm this result while setting a new and more stringent limit: a*>0.983 at the 3{\sigma}(99.7%) level of confidence. The earlier work, which was based on an analysis of all three useful spectra that were then available, was possibly biased by the presence in these spectra of a relatively strong Compton power-law component: The fraction of the thermal seed photons scattered into the power law was f_s=23-31%, while the upper limit for reliable application of the continuum-fitting method is f_s<25%. We have subsequently obtained six additional spectra of Cygnus X-1 suitable for the measurement of spin. Five of these spectra are of high quality with f_s in the range 10% to 19%, a regime where the continuum-fitting method has been shown to deliver very reliable results. Individually, the six spectra give lower limits on the spin parameter that range from a*>0.95 to a*>0.98, allowing us to conservatively conclude that the spin of the black hole is a*>0.983 (3{\sigma}).
    The Astrophysical Journal 08/2013; 790(1). · 6.73 Impact Factor
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    ABSTRACT: Recently it has been observed that the scaling of jet power with black hole spin in galactic X-ray binaries is consistent with the predictions of the Blandford-Znajek (BZ) jet model. These observations motivate us to revisit the BZ model using general relativistic magnetohydrodynamic simulations of magnetized jets from accreting (h/r ~ 0.3), spinning (0 < a_* < 0.98) black holes. We have three main results. First, we quantify the discrepancies between the BZ jet power and our simulations: assuming maximum efficiency and uniform fields on the horizon leads to a ~10% overestimate of jet power, while ignoring the accretion disk leads to a further ~50% overestimate. Simply reducing the standard BZ jet power prediction by 60% gives a good fit to our simulation data. Our second result is to show that the membrane formulation of the BZ model correctly describes the physics underlying simulated jets: torques, dissipation, and electromagnetic fields on the horizon. This provides intuitive yet rigorous pictures for the black hole energy extraction process. Third, we compute the effective resistance of the load region and show that the load and the black hole achieve near perfect impedance matching. Taken together, these results increase our confidence in the BZ model as the correct description of jets observed from astrophysical black holes.
    Monthly Notices of the Royal Astronomical Society 07/2013; 436(4). · 5.52 Impact Factor
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    A. Sadowski, R. Narayan, R. Penna, Y. Zhu
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    ABSTRACT: A set of long-duration general relativistic magnetohydrodynamic simulations of radiatively inefficient accretion discs around rotating black holes are presented, and are used to estimate the energy, mass and momentum outflow rates from such systems. Outflows occur via two fairly distinct modes: a relativistic jet and a sub-relativistic wind. The jet power depends strongly on the black hole spin and on the magnetic flux at the horizon. Unless these are very small, the energy output in the jet dominates over that in the wind. In the limit of a rapidly spinning black hole accreting in the magnetically arrested limit, when the magnetic flux at the black hole is maximum, the jet power exceeds the total rate of accretion of rest mass energy. However, because of strong collimation, the jet probably does not have a significant effect on its surrounding. In the case of an accreting supermassive black hole, external feedback via a jet is likely important only on the largest galaxy cluster scales. The power in the wind is more modest and shows a weaker dependence on the black spin and magnetic flux. Nevertheless, because the wind subtends a large solid angle, it is expected to provide efficient feedback on a wide range of scales inside the host galaxy. Using the simulation results as a guide, empirical formulae are obtained for the energy outflow rates in the jet and the wind, and also for the respective momentum outflow rates. The mass outflow rates are more uncertain, especially in the case of the wind.
    Monthly Notices of the Royal Astronomical Society 07/2013; · 5.52 Impact Factor

Publication Stats

11k Citations
1,422.34 Total Impact Points

Institutions

  • 2014
    • The University of Arizona
      Tucson, Arizona, United States
  • 1992–2014
    • Harvard-Smithsonian Center for Astrophysics
      • • Institute for Theory and Computation
      • • Smithsonian Astrophysical Observatory
      Cambridge, Massachusetts, United States
  • 2013
    • San Diego State University
      • Department of Astronomy
      San Diego, California, United States
  • 2010
    • Stanford University
      • Kavli Institute for Particle Physics and Cosmology (KIPAC)
      Stanford, CA, United States
  • 1996–2010
    • Harvard University
      • Department of Astronomy
      Cambridge, Massachusetts, United States
  • 2002
    • Princeton University
      • Department of Astrophysical Sciences
      Princeton, New Jersey, United States
  • 2001
    • University of Rochester
      • Laboratory for Laser Energetics (LLE)
      Rochester, New York, United States
  • 2000
    • University of Toronto
      • Canadian Institute for Theoretical Astrophysics
      Toronto, Ontario, Canada
    • Chalmers University of Technology
      Goeteborg, Västra Götaland, Sweden
  • 1999
    • Kurchatov Institute
      Moskva, Moscow, Russia
  • 1991
    • Tel Aviv University
      • Department of Physics and Astronomy
      Tell Afif, Tel Aviv, Israel
  • 1986–1989
    • California Institute of Technology
      • Jet Propulsion Laboratory
      Pasadena, California, United States
  • 1981–1985
    • Raman Research Institute
      Bengalūru, Karnātaka, India