Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-23T13:35:47.414Z Has data issue: false hasContentIssue false
  • English
  • Français

Motivation and challenge to capture both large-scale and local transport in next generation accretion theory

Part of: Macroscopic Randomness Focus on Plasma Astrophysics

Published online by Cambridge University Press:  20 August 2015

Eric G. Blackman  and
Farrukh Nauman
Eric G. Blackman*
Affiliation:
Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA
Farrukh Nauman
Affiliation:
Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Accretion disc theory is less developed than stellar evolution theory although a similarly mature phenomenological picture is ultimately desired. While the interplay of theory and numerical simulations has amplified community awareness of the role of magnetic fields in angular momentum transport, there remains a long term challenge to incorporate the insights gained from simulations into improving practical models for comparison with observations. What has been learned from simulations that can lead to improvements beyond SS73 in practical models? Here, we emphasize the need to incorporate the role of non-local transport more precisely. To show where large-scale transport would fit into the theoretical framework and how it is currently missing, we review why the wonderfully practical approach of Shakura & Sunyaev (Astron. Astrophys., vol. 24, 1973, pp. 337–355, SS73) is necessarily a mean field theory, and one which does not include large-scale transport. Observations of coronae and jets, combined with the interpretation of results from shearing box simulations, of the magnetorotational instability (MRI) suggest that a significant fraction of disc transport is indeed non-local. We show that the Maxwell stresses in saturation are dominated by large-scale contributions and that the physics of MRI transport is not fully captured by a viscosity. We also clarify the standard physical interpretation of the MRI as it applies to shearing boxes. Computational limitations have so far focused most attention toward local simulations, but the next generation of global simulations should help to inform improved mean field theories. Mean field accretion theory and mean field dynamo theory should in fact be unified into a single theory that predicts the time evolution of spectra and luminosity from separate disc, corona and outflow contributions. Finally, we note that any mean field theory, including that of SS73, has a finite predictive precision that needs to be quantified when comparing the predictions to observations.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 5 , October 2015 , 395810505
Copyright
© Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowicz, M., Brandenburg, A. & Lasota, J.-P. 1996 The dependence of the viscosity in accretion discs on the shear/vorticity ratio. Mon. Not. R. Astron. Soc. 281, L21–L24.Google Scholar
Asada, K., Inoue, M., Nakamura, M., Kameno, S. & Nagai, H. 2008 Multifrequency polarimetry of the NRAO 140 jet: possible detection of a helical magnetic field and constraints on its pitch angle. Astrophys. J. 682, 798–802.Google Scholar
Balbus, S. A. 2003 Enhanced angular momentum transport in accretion disks. Ann. Rev. Astron. Astrophys. 41, 555–597.Google Scholar
Balbus, S. A. 2011 Fluid dynamics: a turbulent matter. Nature 470, 475–476.CrossRefGoogle ScholarPubMed
Balbus, S. A. & Hawley, J. F. 1991 A powerful local shear instability in weakly magnetized disks. I – Linear analysis. II – Nonlinear evolution. Astrophys. J. 376, 214–233.CrossRefGoogle Scholar
Balbus, S. A. & Hawley, J. F. 1998 Instability, turbulence, and enhanced transport in accretion disks. Rev. Mod. Phys. 70, 1–53.Google Scholar
Barranco, J. A. & Marcus, P. S. 2005 Three-dimensional vortices in stratified protoplanetary disks. Astrophys. J. 623, 1157–1170.CrossRefGoogle Scholar
Beckwith, K., Armitage, P. J. & Simon, J. B. 2011 Turbulence in global simulations of magnetized thin accretion discs. Mon. Not. R. Astron. Soc. 416, 361–382.Google Scholar
Bhattacharjee, A. & Hameiri, E. 1986 Self-consistent dynamolike activity in turbulent plasmas. Phys. Rev. Lett. 57, 206–209.Google Scholar
Blackman, E. G. 1998 Variability associated with alpha accretion disc theory for standard and advection-dominated discs. Mon. Not. R. Astron. Soc. 299, L48–L52.Google Scholar
Blackman, E. G. 1999 On particle energization in accretion flows. Mon. Not. R. Astron. Soc. 302, 723–730.CrossRefGoogle Scholar
Blackman, E. G. 2004 How spectral shapes of magnetic energy and magnetic helicity influence their respective decay timescales. Plasma Phys. Control. Fusion 46, 423–430.CrossRefGoogle Scholar
Blackman, E. G. 2015 Magnetic helicity and large scale magnetic fields: a primer. Space Sci. Rev. 188 (1–4), 59–91.Google Scholar
Blackman, E. G. & Brandenburg, A. 2002 Dynamic nonlinearity in large-scale dynamos with shear. Astrophys. J. 579, 359–373.Google Scholar
Blackman, E. G. & Brandenburg, A. 2003 Doubly helical coronal ejections from dynamos and their role in sustaining the solar cycle. Astrophys. J. Lett. 584, L99–L102.Google Scholar
Blackman, E. G. & Field, G. B. 2000a Constraints on the magnitude of ${\it\alpha}$ in dynamo theory. Astrophys. J. 534, 984–988.Google Scholar
Blackman, E. G. & Field, G. B. 2000b Coronal activity from dynamos in astrophysical rotators. Mon. Not. R. Astron. Soc. 318, 724–732.CrossRefGoogle Scholar
Blackman, E. G. & Field, G. B. 2002 New dynamical mean-field dynamo theory and closure approach. Phys. Rev. Lett. 89 (26), 265007.Google Scholar
Blackman, E. G., Frank, A. & Welch, C. 2001 Magnetohydrodynamic stellar and disk winds: application to planetary nebulae. Astrophys. J. 546, 288–298.CrossRefGoogle Scholar
Blackman, E. G. & Lucchini, S. 2014 Using kinematic properties of pre-planetary nebulae to constrain engine paradigms. Mon. Not. R. Astron. Soc. 440, L16–L20.Google Scholar
Blackman, E. G., Nauman, F. & Edgar, R. G.2010. Quantifying the imprecision of accretion theory and implications for multi-epoch observations of protoplanetary discs, arXiv: e-prints.Google Scholar
Blackman, E. G., Penna, R. F. & Varnière, P. 2008 Empirical relation between angular momentum transport and thermal-to-magnetic pressure ratio in shearing box simulations. New Astronomy 13, 244–251.CrossRefGoogle Scholar
Blackman, E. G. & Pessah, M. E. 2009 Coronae as a consequence of large-scale magnetic fields in turbulent accretion disks. Astrophys. J. Lett. 704, L113–L117.Google Scholar
Blandford, R. D. & Begelman, M. C. 1999 On the fate of gas accreting at a low rate on to a black hole. Mon. Not. R. Astron. Soc. 303, L1–L5.CrossRefGoogle Scholar
Blandford, R. D. & Payne, D. G. 1982 Hydromagnetic flows from accretion discs and the production of radio jets. Mon. Not. R. Astron. Soc. 199, 883–903.Google Scholar
Bodo, G., Cattaneo, F., Mignone, A. & Rossi, P. 2014 On the convergence of magnetorotational turbulence in stratified isothermal shearing boxes. Astrophys. J. Lett. 787, L13.Google Scholar
Bondi, H. 1952 On spherically symmetrical accretion. Mon. Not. R. Astron. Soc. 112, 195.CrossRefGoogle Scholar
Brandenburg, A. 1998 Disc turbulence and viscosity. In Theory of Black Hole Accretion Disks (ed. Abramowicz, M. A., Björnsson, G. & Pringle, J. E.), pp. 61–90. Cambridge University Press.Google Scholar
Brandenburg, A. & Donner, K. J. 1997 The dependence of the dynamo alpha on vorticity. Mon. Not. R. Astron. Soc. 288, L29–L33.Google Scholar
Brandenburg, A., Nordlund, A., Stein, R. F. & Torkelsson, U. 1995 Dynamo-generated turbulence and large-scale magnetic fields in a Keplerian shear flow. Astrophys. J. 446, 741.CrossRefGoogle Scholar
Brandenburg, A. & Subramanian, K. 2005 Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417, 1–209.CrossRefGoogle Scholar
Calvet, N., D’Alessio, P., Watson, D. M., Franco-Hernández, R., Furlan, E., Green, J., Sutter, P. M., Forrest, W. J., Hartmann, L., Uchida, K. I., Keller, L. D., Sargent, B., Najita, J., Herter, T. L., Barry, D. J. & Hall, P. 2005 Disks in transition in the taurus population: spitzer IRS spectra of GM aurigae and DM tauri. Astrophys. J. Lett. 630, L185–L188.CrossRefGoogle Scholar
Campbell, C. G. 2000 An accretion disc model with a magnetic wind and turbulent viscosity. Mon. Not. R. Astron. Soc. 317, 501–527.Google Scholar
Campbell, C. G. 2003 A semi-analytic solution for the radial and vertical structure of accretion discs with a magnetic wind. Mon. Not. R. Astron. Soc. 345, 123–143.Google Scholar
Campbell, C. G. & Caunt, S. E. 1999 An analytic model for magneto-viscous accretion discs. Mon. Not. R. Astron. Soc. 306, 122–136.Google Scholar
Charbonneau, P. 2014 Solar dynamo theory. Ann. Rev. Astron. Astrophys. 52, 251–290.Google Scholar
Colgate, S. A., Cen, R., Li, H., Currier, N. & Warren, M. S. 2003 Cosmological mestel disks and the Rossby vortex instability: the origin of supermassive black holes. Astrophys. J. Lett. 598, L7–L10.Google Scholar
Davis, S. W., Stone, J. M. & Pessah, M. E. 2010 Sustained magnetorotational turbulence in local simulations of stratified disks with zero net magnetic flux. Astrophys. J. 713, 52–65.Google Scholar
De Villiers, J.-P. & Hawley, J. F. 2003 Global general relativistic magnetohydrodynamic simulations of accretion tori. Astrophys. J. 592, 1060–1077.Google Scholar
Ebrahimi, F. & Bhattacharjee, A. 2014 Helicity-flux-driven ${\it\alpha}$ effect in laboratory and astrophysical plasmas. Phys. Rev. Lett. 112 (12), 125003.Google Scholar
Ebrahimi, F. & Blackman, E. G. 2015 Large scale magnetohydrodynamic dynamos in cylinders. Phys. Rev. Lett. (submitted).Google Scholar
Field, G. B. & Rogers, R. D. 1993 Radiation from magnetized accretion disks in active galactic nuclei. Astrophys. J. 403, 94–109.CrossRefGoogle Scholar
Flock, M., Dzyurkevich, N., Klahr, H., Turner, N. & Henning, T. 2012 Large-scale azimuthal structures of turbulence in accretion disks: dynamo triggered variability of accretion. Astrophys. J. 744, 144.Google Scholar
Fromang, S. 2010 MHD simulations of the magnetorotational instability in a shearing box with zero net flux: the case $Pm=4$ . Astron. Astrophys. 514, L5.Google Scholar
Fromang, S. & Nelson, R. P. 2006 Global MHD simulations of stratified and turbulent protoplanetary discs. I. Model properties. Astron. Astrophys. 457, 343–358.Google Scholar
Gabuzda, D. C., Christodoulou, D. M., Contopoulos, I. & Kazanas, D. 2012 Evidence for helical magnetic fields in kiloparsec-scale AGN jets and the action of a cosmic battery. J. Phys.: Conf. Ser. 355 (1), 012019.Google Scholar
Gammie, C. F. 1996 Linear theory of magnetized, viscous, self-gravitating gas disks. Astrophys. J. 462, 725.Google Scholar
Gammie, C. F. & Menou, K. 1998 On the origin of episodic accretion in dwarf novae. Astrophys. J. Lett. 492, L75–L78.Google Scholar
Ghisellini, G., Tavecchio, F., Maraschi, L., Celotti, A. & Sbarrato, T. 2014 The power of relativistic jets is larger than the luminosity of their accretion disks. Nature 515, 376–378.Google Scholar
Ghosh, P. & Lamb, F. K. 1978 Disk accretion by magnetic neutron stars. Astrophys. J. Lett. 223, L83–L87.Google Scholar
Gierliński, M. & Zdziarski, A. A. 1999 Accretion disk in CYG X-1 in the soft state. In High Energy Processes in Accreting Black Holes (ed. Poutanen, J. & Svensson, R.), Astronomical Society of the Pacific Conference Series, vol. 161, p. 64.Google Scholar
Gressel, O. 2010 A mean-field approach to the propagation of field patterns in stratified magnetorotational turbulence. Mon. Not. R. Astron. Soc. 405, 41–48.Google Scholar
Guan, X. & Gammie, C. F. 2011 Radially extended, stratified, local models of isothermal disks. Astrophys. J. 728, 130.Google Scholar
Hartnoll, S. A. & Blackman, E. G. 2000 Reprocessed emission from warped accretion discs with application to X-ray iron line profiles. Mon. Not. R. Astron. Soc. 317, 880–892.Google Scholar
Hawley, J. F., Gammie, C. F. & Balbus, S. A. 1996 Local three-dimensional simulations of an accretion disk hydromagnetic dynamo. Astrophys. J. 464, 690.Google Scholar
Hawley, J. F., Guan, X. & Krolik, J. H. 2011 Assessing quantitative results in accretion simulations: from local to global. Astrophys. J. 738, 84.Google Scholar
Heinemann, T., McWilliams, J. C. & Schekochihin, A. A. 2011 Large-scale magnetic field generation by randomly forced shearing waves. Phys. Rev. Lett. 107 (25), 255004.CrossRefGoogle ScholarPubMed
Hoyle, F. & Lyttleton, R. A. 1939 The evolution of the stars. Proc. Camb. Phil. Soc. 35, 592.Google Scholar
Hubbard, A. & Brandenburg, A. 2011 Magnetic helicity flux in the presence of shear. Astrophys. J. 727, 11.Google Scholar
Hubbard, A., McNally, C. P., Oishi, J. S., Lyra, W. & Mac Low, M.-M.2014. Radial stresses and energy transport in accretion disks, arXiv: e-prints.Google Scholar
Ji, H. 2011 Current status and future prospects for laboratory study of angular momentum transport relevant to astrophysical disks. In IAU Symposium (ed. Bonanno, A., de Gouveia Dal Pino, E. & Kosovichev, A. G.), IAU Symposium, vol. 274, pp. 18–25. Cambridge University Press.Google Scholar
Kant, I.1755 Universal Natural History and Theories of the Heaven. (1755a) Allgemeine Naturgeschichte und Theorie des Himmels oder Versuch von der Verfassung und dem mechanischen Ursprunge des ganzen Weltgebäudes, nach Newtonischen Grundsätzen abgehandelt (AK 1: 215–368). Engl. translation (1968) Universal Natural History and Theory of the Heavens, in W. Ley (ed.) Kant’s Cosmogony (New York: Greenwood Publishing).Google Scholar
Käpylä, P. J. & Korpi, M. J. 2011 Magnetorotational instability driven dynamos at low magnetic Prandtl numbers. Mon. Not. R. Astron. Soc. 413, 901–907.Google Scholar
Kim, K. H., Watson, D. M., Manoj, P., Forrest, W. J., Najita, J., Furlan, E., Sargent, B., Espaillat, C., Muzerolle, J., Megeath, S. T., Calvet, N., Green, J. D. & Arnold, L. 2013 Transitional disks and their origins: an infrared spectroscopic survey of orion A. Astrophys. J. 769, 149.CrossRefGoogle Scholar
King, A. R., Pringle, J. E. & Livio, M. 2007 Accretion disc viscosity: How big is alpha? Mon. Not. R. Astron. Soc. 376, 1740–1746.Google Scholar
Klahr, H. H. & Bodenheimer, P. 2003 Turbulence in accretion disks: vorticity generation and angular momentum transport via the global baroclinic instability. Astrophys. J. 582, 869–892.Google Scholar
Kleeorin, N. I. & Ruzmaikin, A. A. 1981 Dynamics of the mean turbulent helicity in magnetic field. Magnetohydrodynamics. Magnetohydrodynamics 18, 116–122.Google Scholar
Königl, A. 1989 Self-similar models of magnetized accretion disks. Astrophys. J. 342, 208–223.Google Scholar
Kotko, I. & Lasota, J.-P. 2012 The viscosity parameter ${\it\alpha}$ and the properties of accretion disc outbursts in close binaries. Astron. Astrophys. 545, A115.Google Scholar
Küker, M., Henning, T. & Rüdiger, G. 2003 Magnetic star-disk coupling in classical $T$ tauri systems. Astrophys. J. 589, 397–409.CrossRefGoogle Scholar
Kuncic, Z. & Bicknell, G. V. 2004 Dynamics and energetics of turbulent, magnetized disk accretion around black holes: a first-principles approach to disk-corona-outflow coupling. Astrophys. J. 616, 669–687.Google Scholar
Kuncic, Z. & Bicknell, G. V. 2007 Towards a new standard model for black hole accretion. Astrophys. Space Suppl. 311, 127–135.Google Scholar
Kylafis, N. D. & Belloni, T. M. 2015 Accretion and ejection in black-hole x-ray transients. In Astrophysics and Space Science Library (ed. Contopoulos, I., Gabuzda, D. & Kylafis, N.), Astrophysics and Space Science Library, vol. 414, p. 245. EDP Sciences.Google Scholar
Lai, D. 2014 Theory of disk accretion onto magnetic stars. In European Physical Journal Web of Conferences, vol. 64, p. 1001. EDP Sciences.Google Scholar
Laplace, P.1796 Exposition du Sytéme du Monde, Reprinted in the Cambridge Library Collection; 2009, Cambridge University Press, ISBN-13: 978-1108002097.Google Scholar
Lesur, G. & Longaretti, P.-Y. 2005 On the relevance of subcritical hydrodynamic turbulence to accretion disk transport. Astron. Astrophys. 444, 25–44.Google Scholar
Lesur, G. & Ogilvie, G. I. 2010 On the angular momentum transport due to vertical convection in accretion discs. Mon. Not. R. Astron. Soc. 404, L64–L68.Google Scholar
Li, H., Finn, J. M., Lovelace, R. V. E. & Colgate, S. A. 2000 Rossby wave instability of thin accretion disks. II. detailed linear theory. Astrophys. J. 533, 1023–1034.Google Scholar
Lii, P. S., Romanova, M. M., Ustyugova, G. V., Koldoba, A. V. & Lovelace, R. V. E. 2014 Propeller-driven outflows from an MRI disc. Mon. Not. R. Astron. Soc. 441, 86–100.Google Scholar
Longaretti, P.-Y. 2002 On the phenomenology of hydrodynamic shear turbulence. Astrophys. J. 576, 587–598.CrossRefGoogle Scholar
Lovelace, R. V. E., Li, H., Colgate, S. A. & Nelson, A. F. 1999 Rossby wave instability of Keplerian accretion disks. Astrophys. J. 513, 805–810.Google Scholar
Lynden-Bell, D. 1969 Galactic nuclei as collapsed old quasars. Nature 223, 690–694.Google Scholar
Lynden-Bell, D. 2006 Magnetic jets from swirling discs. Mon. Not. R. Astron. Soc. 369, 1167–1188.Google Scholar
Lynden-Bell, D. & Pringle, J. E. 1974 The evolution of viscous discs and the origin of the nebular variables. Mon. Not. R. Astron. Soc. 168, 603–637.Google Scholar
van der Marel, N., van Dishoeck, E. F., Bruderer, S., Birnstiel, T., Pinilla, P., Dullemond, C. P., van Kempen, T. A., Schmalzl, M., Brown, J. M., Herczeg, G. J., Mathews, G. S. & Geers, V. 2013 A major asymmetric dust trap in a transition disk. Science 340, 1199–1202.Google Scholar
Matt, S. & Pudritz, R. E. 2005 The spin of accreting stars: dependence on magnetic coupling to the disc. Mon. Not. R. Astron. Soc. 356, 167–182.CrossRefGoogle Scholar
McNally, C. P. & Pessah, M. E.2014. On vertically global, horizontally local models for astrophysical disks, arXiv: e-prints.Google Scholar
Miller, K. A. & Stone, J. M. 2000 The formation and structure of a strongly magnetized corona above a weakly magnetized accretion disk. Astrophys. J. 534, 398–419.CrossRefGoogle Scholar
Moss, D. & Shukurov, A. 2004 Accretion disc dynamos opened up by external magnetic fields. Astron. Astrophys. 413, 403–414.Google Scholar
Moss, D., Shukurov, A. & Sokoloff, D. 2000 Accretion and galactic dynamos. Astron. Astrophys. 358, 1142–1150.Google Scholar
Mushotzky, R. F., Done, C. & Pounds, K. A. 1993 X-ray spectra and time variability of active galactic nuclei. Ann. Rev. Astron. Astrophys. 31, 717–761.Google Scholar
Nauman, F. & Blackman, E. G. 2014 On characterizing non-locality and anisotropy for the magnetorotational instability. Mon. Not. R. Astron. Soc. 441, 1855–1860.Google Scholar
Nauman, F. & Blackman, E. G. 2015 Sensitivity of the magnetorotational instability to the shear parameter in stratified simulations. Mon. Not. R. Astron. Soc. 446, 2102–2109.CrossRefGoogle Scholar
Nelson, N. J., Brown, B. P., Brun, A. S., Miesch, M. S. & Toomre, J. 2011 Buoyant magnetic loops in a global dynamo simulation of a Young Sun. Astrophys. J. Lett. 739, L38.Google Scholar
Nelson, N. J. & Miesch, M. S. 2014 Generating buoyant magnetic flux ropes in solar-like convective dynamos. Plasma Phys. Control. Fusion 56 (6), 064004.Google Scholar
Ogilvie, G. I. 2003 On the dynamics of magnetorotational turbulent stresses. Mon. Not. R. Astron. Soc. 340, 969–982.Google Scholar
Paoletti, M. S. & Lathrop, D. P. 2011 Angular momentum transport in turbulent flow between independently rotating cylinders. Phys. Rev. Lett. 106 (2), 024501.Google Scholar
Parkin, E. R. & Bicknell, G. V. 2013 Global simulations of magnetorotational turbulence – I. Convergence and the quasi-steady state. Mon. Not. R. Astron. Soc. 435, 2281–2298.Google Scholar
Penna, R. F., Narayan, R. & Sa̧dowski, A. 2013 General relativistic magnetohydrodynamic simulations of Blandford-Znajek jets and the membrane paradigm. Mon. Not. R. Astron. Soc. 436, 3741–3758.Google Scholar
Penna, R. F., Sa̧owski, A. & McKinney, J. C. 2012 Thin-disc theory with a non-zero-torque boundary condition and comparisons with simulations. Mon. Not. R. Astron. Soc. 420, 684–698.Google Scholar
Pérez, L. M., Isella, A., Carpenter, J. M. & Chandler, C. J. 2014 Large-scale asymmetries in the transitional disks of SAO 206462 and SR 21. Astrophys. J. Lett. 783, L13.Google Scholar
Perna, R., Bozzo, E. & Stella, L. 2006 On the spin-up/spin-down transitions in accreting x-ray binaries. Astrophys. J. 639, 363–376.Google Scholar
Pessah, M. E., Chan, C.-K. & Psaltis, D. 2006 Local model for angular-momentum transport in accretion disks driven by the magnetorotational instability. Phys. Rev. Lett. 97 (22), 221103.Google Scholar
Pessah, M. E., Chan, C.-K. & Psaltis, D. 2007 Angular momentum transport in accretion disks: scaling laws in MRI-driven turbulence. Astrophys. J. Lett. 668, L51–L54.Google Scholar
Pessah, M. E., Chan, C.-K. & Psaltis, D. 2008 The fundamental difference between shear alpha viscosity and turbulent magnetorotational stresses. Mon. Not. R. Astron. Soc. 383, 683–690.Google Scholar
Pipin, V. V. & Pevtsov, A. A. 2014 Magnetic helicity of the global field in solar cycles 23 and 24. Astrophys. J. 789, 21.Google Scholar
Pouquet, A., Frisch, U. & Leorat, J. 1976 Strong MHD helical turbulence and the nonlinear dynamo effect. J. Fluid Mech. 77, 321–354.Google Scholar
Prendergast, K. H. & Burbidge, G. R. 1968 On the nature of some galactic x-ray sources. Astrophys. J. Lett. 151, L83.Google Scholar
Pudritz, R. E., Hardcastle, M. J. & Gabuzda, D. C. 2012 Magnetic fields in astrophysical jets: from launch to termination. Space Sci. Rev. 169, 27–72.Google Scholar
Quataert, E., Heinemann, T. & Spitkovsky, A.2014. Linear instabilities driven by differential rotation in very weakly magnetized plasmas, arXiv: e-prints.Google Scholar
Quataert, E. & Narayan, R. 1999 Spectral models of advection-dominated accretion flows with winds. Astrophys. J. 520, 298–315.Google Scholar
Regev, O. & Umurhan, O. M. 2008 On the viability of the shearing box approximation for numerical studies of MHD turbulence in accretion disks. Astron. Astrophys. 481, 21–32.CrossRefGoogle Scholar
Rekowski, M. v., Rüdiger, G. & Elstner, D. 2000 Structure and magnetic configurations of accretion disk-dynamo models. Astron. Astrophys. 353, 813–822.Google Scholar
Reynolds, C. S. 2014 Measuring black hole spin using x-ray reflection spectroscopy. Space Sci. Rev. 183, 277–294.Google Scholar
Risaliti, G., Harrison, F. A., Madsen, K. K., Walton, D. J., Boggs, S. E., Christensen, F. E., Craig, W. W., Grefenstette, B. W., Hailey, C. J., Nardini, E., Stern, D. & Zhang, W. W. 2013 A rapidly spinning supermassive black hole at the centre of NGC 1365. Nature 494, 449–451.Google Scholar
Romanova, M. M., Ustyugova, G. V., Koldoba, A. V. & Lovelace, R. V. E. 2012 MRI-driven accretion on to magnetized stars: global 3D MHD simulations of magnetospheric and boundary layer regimes. Mon. Not. R. Astron. Soc. 421, 63–77.Google Scholar
Rüdiger, G. 1987 Turbulence theory and the frictional energy source in accretion disk models. Acta Astronomica 37, 223.Google Scholar
Rüdiger, G., Elstner, D. & Schultz, M. 1993 Dynamo-driven accretion in galaxies. Astron. Astrophys. 270, 53–59.Google Scholar
Rüdiger, G. & Kichatinov, L. L. 1993 Alpha-effect and alpha-quenching. Astron. Astrophys. 269, 581–588.Google Scholar
Salpeter, E. E. 1964 Accretion of interstellar matter by massive objects. Astrophys. J. 140, 796–800.Google Scholar
Sa̧dowski, A., Narayan, R., Tchekhovskoy, A., Abarca, D., Zhu, Y. & McKinney, J. C. 2015 Global simulations of axisymmetric radiative black hole accretion discs in general relativity with a mean-field magnetic dynamo. Mon. Not. R. Astron. Soc. 447, 49–71.Google Scholar
Schartman, E., Ji, H., Burin, M. J. & Goodman, J. 2012 Stability of quasi-Keplerian shear flow in a laboratory experiment. Astron. Astrophys. 543, A94.Google Scholar
Seehafer, N. 1990 Electric current helicity in the solar atmosphere. Solar Phys. 125, 219–232.Google Scholar
Shakura, N. I. & Postnov, K. A.2014. On properties of Velikhov-Chandrasekhar MRI in ideal and non-ideal plasma, arXiv: e-prints.Google Scholar
Shakura, N. I. & Sunyaev, R. A. 1973 Black holes in binary systems. Observational appearance. Astron. Astrophys. 24, 337–355.Google Scholar
Shklovskii, I. S. 1963 On the nature of radio galaxies. Sov. Astron. 6, 465.Google Scholar
Shukurov, A., Sokoloff, D., Subramanian, K. & Brandenburg, A. 2006 Galactic dynamo and helicity losses through fountain flow. Astron. Astrophys. 448, L33–L36.Google Scholar
Simon, J. B., Hawley, J. F. & Beckwith, K. 2011 Resistivity-driven state changes in vertically stratified accretion disks. Astrophys. J. 730, 94.Google Scholar
Sorathia, K. A., Reynolds, C. S., Stone, J. M. & Beckwith, K. 2012 Global simulations of accretion disks. I. convergence and comparisons with local models. Astrophys. J. 749, 189.Google Scholar
Squire, J. & Bhattacharjee, A.2015a Coherent nonhelical shear dynamos driven by magnetic fluctuations at low Reynolds numbers, arXiv:1507.03154.Google Scholar
Squire, J. & Bhattacharjee, A.2015b Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence, arXiv:1508.01566.Google Scholar
Stapelfeldt, K. R., Duchêne, G., Perrin, M., Wolff, S., Krist, J. E., Padgett, D. L., Ménard, F. & Pinte, C. 2014 HST imaging of new edge-on circumstellar disks in nearby star-forming regions. In IAU Symposium (ed. Booth, M., Matthews, B. C. & Graham, J. R.), vol. 299, pp. 99–103. Cambridge University Press.Google Scholar
Stepanovs, D., Fendt, C. & Sheikhnezami, S. 2014 Modeling MHD accretion–ejection: episodic ejections of jets triggered by a mean-field disk dynamo. Astrophys. J. 796, 29.Google Scholar
Strauss, H. R. 1985 The dynamo effect in fusion plasmas. Phys. Fluids 28, 2786–2792.Google Scholar
Suzuki, T. K. & Inutsuka, S.-i. 2014 Magnetohydrodynamic simulations of global accretion disks with vertical magnetic fields. Astrophys. J. 784, 121.Google Scholar
Swedenborg, E.1734. (Principia) Latin: Opera Philosophica et Mineralia (English: Philosophical and Mineralogical Works) I.Google Scholar
Tagger, M. & Pellat, R. 1999 An accretion–ejection instability in magnetized disks. Astron. Astrophys. 349, 1003–1016.Google Scholar
Taylor, G. B. & Perley, R. A. 1993 Magnetic fields in the hydra a cluster. Astrophys. J. 416, 554.Google Scholar
Trefethen, L. N., Trefethen, A. E., Reddy, S. C. & Driscoll, T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578–584.Google Scholar
Tremaine, S. & Davis, S. W. 2014 Dynamics of warped accretion discs. Mon. Not. R. Astron. Soc. 441, 1408–1434.Google Scholar
Van Eck, C. L., Brown, J. C., Shukurov, A. & Fletcher, A. 2015 Magnetic fields in a sample of nearby spiral galaxies. Astrophys. J. 799, 35.Google Scholar
Varnière, P. & Tagger, M. 2002 Accretion-ejection instability in magnetized disks: feeding the corona with Alfvén waves. Astron. Astrophys. 394, 329–338.Google Scholar
Velikhov, E. P. 1959 Stability of an ideally conducting liquid flowing between cylinders rotating in a magnetic field. Sov. J. Exp. Theoret. Phys. 36, 1398–1404.Google Scholar
Vishniac, E. T. 2009 The saturation limit of the magnetorotational instability. Astrophys. J. 696, 1021–1028.Google Scholar
Vishniac, E. T. & Cho, J. 2001 Magnetic helicity conservation and astrophysical dynamos. Astrophys. J. 550, 752–760.Google Scholar
Vorobyov, E. I. & Basu, S. 2007 Self-regulated gravitational accretion in protostellar discs. Mon. Not. R. Astron. Soc. 381, 1009–1017.Google Scholar
Yousef, T. A., Heinemann, T., Schekochihin, A. A., Kleeorin, N., Rogachevskii, I., Iskakov, A. B., Cowley, S. C. & McWilliams, J. C. 2008 Generation of magnetic field by combined action of turbulence and shear. Phys. Rev. Lett. 100 (18), 184501.CrossRefGoogle ScholarPubMed
Yuan, F. & Narayan, R. 2014 Hot accretion flows around black holes. Ann. Rev. Astron. Astrophys. 52, 529–588.Google Scholar
Zel’dovich, Y. B. 1964 The fate of a star and the evolution of gravitational energy upon accretion. Sov. Phys. Dokl. 9, 195.Google Scholar
Zhang, H., Moss, D., Kleeorin, N., Kuzanyan, K., Rogachevskii, I., Sokoloff, D., Gao, Y. & Xu, H. 2012 Current helicity of active regions as a tracer of large-scale solar magnetic helicity. Astrophys. J. 751, 47.Google Scholar
Zhang, S.-N. 2013 Black hole binaries and microquasars. Frontiers Phys. 8, 630–660.Google Scholar
Zhu, Z., Hartmann, L., Gammie, C. & McKinney, J. C. 2009 Two-dimensional simulations of FU orionis disk outbursts. Astrophys. J. 701, 620–634.Google Scholar