Hostname: page-component-5db58dd55d-d6ndz Total loading time: 0 Render date: 2026-06-08T17:00:34.763Z Has data issue: false hasContentIssue false
  • English
  • Français

Advances in mean-field dynamo theory and applications to astrophysical turbulence

Part of: Focus on Plasma Astrophysics 50 years of Mean Field Electrodynamics

Published online by Cambridge University Press:  07 August 2018

Axel Brandenburg Open the ORCID record for Axel Brandenburg [Opens in a new window]
Axel Brandenburg*
Affiliation:
Laboratory for Atmospheric and Space Physics, JILA, and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80303, USA Nordita, KTH Royal Institute of Technology and Stockholm University, and Department of Astronomy, Stockholm University, SE-10691 Stockholm, Sweden
*
†Email address for correspondence: brandenb@nordita.org
Get access Rights & Permissions [Opens in a new window]

Abstract

Recent advances in mean-field theory are reviewed and applications to the Sun, late-type stars, accretion disks, galaxies and the early Universe are discussed. We focus particularly on aspects of spatio-temporal non-locality, which provided some of the main new qualitative and quantitative insights that emerged from applying the test-field method to magnetic fields of different length and time scales. We also review the status of nonlinear quenching and the relation to magnetic helicity, which is an important observational diagnostic of modern solar dynamo theory. Both solar and some stellar dynamos seem to operate in an intermediate regime that has not yet been possible to model successfully. This regime is bracketed by antisolar-like differential rotation on one end and stellar activity cycles belonging to the superactive stars on the other. The difficulty in modelling this regime may be related to shortcomings in simulating solar/stellar convection. On galactic and extragalactic length scales, the observational constraints on dynamo theory are still less stringent and more uncertain, but recent advances both in theory and observations suggest that more conclusive comparisons may soon be possible also here. The possibility of inversely cascading magnetic helicity in the early Universe is particularly exciting in explaining the recently observed lower limits of magnetic fields on cosmological length scales. Such magnetic fields may be helical with the same sign of magnetic helicity throughout the entire Universe. This would be a manifestation of parity breaking.

Keywords

astrophysical plasmas

Information

Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 4 , August 2018 , 735840404
Copyright
© Cambridge University Press 2018 

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.)

Article purchase

Temporarily unavailable

References

Abramowicz, M. A., 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
Aharonian, F., Akhperjanian, A. G., Bazer-Bachi, A. R., Beilicke, M., Benbow, W., Berge, D., Bernlöhr, K., Boisson, C., Bolz, O., Borrel, V. et al. 2006 A low level of extragalactic background light as revealed by $\unicode[STIX]{x1D6FE}$ -rays from blazars. Nature 440, 1018–1021.Google Scholar
Allawala, A., Tobias, S. M. & Marston, J. B.2017 Dimensional reduction of direct statistical simulation. arXiv:1708.07805.Google Scholar
Andrievsky, A., Brandenburg, A., Noullez, A. & Zheligovsky, V. 2015 Negative magnetic eddy diffusivities from the test-field method and multiscale stability theory. Astrophys. J. 811, 135.Google Scholar
Arter, W. 1983 Magnetic flux transport by a convecting layer – topological, geometrical and compressible phenomena. J. Fluid Mech. 132, 25–48.Google Scholar
Augustson, K., Brun, A. S., Miesch, M. & Toomre, J. 2015 Grand minima and equatorward propagation in a cycling stellar convective dynamo. Astrophys. J. 809, 149.Google Scholar
Ayres, T. R. 2009 The cycles of $\unicode[STIX]{x1D6FC}$ Centauri. Astrophys. J. 696, 1931–1949.Google Scholar
Ayres, T. R. 2015 The far-ultraviolet ups and downs of alpha Centauri. Astron. J. 149, 58.Google Scholar
Babcock, H. W. 1961 The topology of the Sun’s magnetic field and the 22-year cycle. Astrophys. J. 133, 572–587.Google Scholar
Balbus, S. A. & Hawley, J. F. 1998 Instability, turbulence, and enhanced transport in accretion disks. Rev. Mod. Phys. 70, 1–53.Google Scholar
van Ballegooijen, A. A. 1984 The effect of Reynolds stress in the solar convective zone on the vertical structure of flux tubes, and on their convective instability. In Small-Scale Dynamical Processes in Quiet Stellar Atmospheres, Proceedings of the Conference held in Sunspot (ed. Keil, S. L.), pp. 260–264. Aura.Google Scholar
Balsara, D. S., Kim, J., Mac Low, M. M. & Mathews, G. J. 2004 Amplification of interstellar magnetic fields by supernova-driven turbulence. Astrophys. J. 617, 339–349.Google Scholar
Banerjee, R. & Jedamzik, K. 2004 Evolution of cosmic magnetic fields: from the very early Universe, to recombination, to the present. Phys. Rev. D 70, 123003.Google Scholar
Batchelor, G. K. 1950 On the spontaneous magnetic field in a conducting liquid in turbulent motion. Proc. R. Soc. Lond. A 201, 405–416.Google Scholar
Beaudoin, P., Simard, C., Cossette, J.-F. & Charbonneau, P. 2016 Double dynamo signatures in a global MHD simulation and mean-field dynamos. Astrophys. J. 826, 138.Google Scholar
Beck, R., Brandenburg, A., Moss, D., Shukurov, A. & Sokoloff, D. 1996 Galactic magnetism: recent developments and perspectives. Annu. Rev. Astron. Astrophys. 34, 155–206.Google Scholar
Beck, R., Poezd, A. D., Shukurov, A. & Sokoloff, D. D. 1994 Dynamos in evolving galaxies. Astron. Astrophys. 289, 94–100.Google Scholar
Bell, A. R. 2004 Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic rays. Mon. Not. R. Astron. Soc. 353, 550–558.Google Scholar
Bendre, A., Gressel, O. & Elstner, D. 2015 Dynamo saturation in direct simulations of the multi-phase turbulent interstellar medium. Astron. Nachr. 336, 991–1004.Google Scholar
Beresnyak, A. & Li, H. 2014 Basic Bell-MHD turbulence. Astrophys. J. 788, 107.Google Scholar
Berger, M. & Field, G. B. 1984 The topological properties of magnetic helicity. J. Fluid Mech. 147, 133–148.Google Scholar
Bhat, P., Ebrahimi, F. & Blackman, E. G. 2016b Large-scale dynamo action precedes turbulence in shearing box simulations of the magnetorotational instability. Mon. Not. R. Astron. Soc. 462, 818–829.Google Scholar
Bhat, P., Subramanian, K. & Brandenburg, A. 2016a A unified large/small-scale dynamo in helical turbulence. Mon. Not. R. Astron. Soc. 461, 240–247.Google Scholar
Biermann, L. & Schlüter, A. 1951 Cosmic radiation and cosmic magnetic fields. II. Origin of cosmic magnetic fields. Phys. Rev. 82, 863–868.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 $\unicode[STIX]{x1D6FC}$ in dynamo theory. Astrophys. J. 534, 984–988.Google Scholar
Blackman, E. G. & Field, G. B. 2002 New dynamical mean-field dynamo theory and closure approach. Phys. Rev. Lett. 89, 265007.Google Scholar
Blackman, E. G. & Field, G. B. 2003 A simple mean field approach to turbulent transport. Phys. Fluids 15, L73–L76.Google Scholar
Böhm-Vitense, E. 2007 Chromospheric activity in G and K main-sequence stars, and what it tells us about stellar dynamos. Astrophys. J. 657, 486–493.Google Scholar
Bonanno, A., Brandenburg, A., Del Sordo, F. & Mitra, D. 2012 Breakdown of chiral symmetry during saturation of the Tayler instability. Phys. Rev. E 86, 016313.Google Scholar
Boro Saikia, S., Marvin, C. J., Jeffers, S. V., Reiners, A., Cameron, R., Marsden, S. C., Petit, P., Warnecke, J. & Yadav, A. P. 2018 Chromospheric activity catalogue of 4454 cool stars. Questioning the active branch of stellar activity cycles. Astron. Astrophys, doi:10.1051/0004-6361/201629518.Google Scholar
Bourdin, Ph.-A., Bingert, S. & Peter, H. 2013 Observationally driven 3D magnetohydrodynamics model of the solar corona above an active region. Astron. Astrophys. 555, A123.Google Scholar
Bourdin, Ph.-A., Singh, N. K. & Brandenburg, A. 2018 Magnetic helicity reversal in the corona at small plasma beta. Astrophys. J. (submitted), arXiv:1804.04153.Google Scholar
Boyarsky, A., Fröhlich, J. & Ruchayskiy, O. 2012 Self-consistent evolution of magnetic fields and chiral asymmetry in the early Universe. Phys. Rev. Lett. 108, 031301.Google Scholar
Boyarsky, A., Fröhlich, J. & Ruchayskiy, O. 2015 Magnetohydrodynamics of chiral relativistic fluids. Phys. Rev. D 92, 043004.Google Scholar
Brandenburg, A. 1998a Disc turbulence and viscosity. In Theory of Black Hole Accretion Discs (ed. Abramowicz, M. A., Björnsson, G. & Pringle, J. E.), pp. 61–86. Cambridge University Press.Google Scholar
Brandenburg, A. 1998b Theoretical basis of stellar activity cycles. In Tenth Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun (ed. Donahue, R. & Bookbinder, J.), Astron. Soc. Pac. Conf. Ser., Col., vol. 154, pp. 173–191. Astronomical Society of the Pacific.Google Scholar
Brandenburg, A. 2001 The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence. Astrophys. J. 550, 824–840.Google Scholar
Brandenburg, A. 2005a The case for a distributed solar dynamo shaped by near-surface shear. Astrophys. J. 625, 539–547.Google Scholar
Brandenburg, A. 2005b Turbulence and its parameterization in accretion discs. Astron. Nachr. 326, 787–797.Google Scholar
Brandenburg, A. 2008 The dual role of shear in large-scale dynamos. Astron. Nachr. 329, 725–731.Google Scholar
Brandenburg, A. 2016 Stellar mixing length theory with entropy rain. Astrophys. J. 832, 6.Google Scholar
Brandenburg, A. 2017 Analytic solution of an oscillatory migratory $\unicode[STIX]{x1D6FC}^{2}$ stellar dynamo. Astron. Astrophys. 598, A117.Google Scholar
Brandenburg, A., Ashurova, M. B. & Jabbari, S. 2017a Compensating Faraday depolarization by magnetic helicity in the solar corona. Astrophys. J. Lett. 845, L15.Google Scholar
Brandenburg, A. & Campbell, C. G. 1997 Modelling magnetized accretion discs. In Accretion disks – New aspects (ed. Spruit, H. & Meyer-Hofmeister, E.), pp. 109–124. Springer.Google Scholar
Brandenburg, A. & Chatterjee, P. 2018 Strong nonlocality variations in a spherical mean-field dynamo. Astron. Nachr. 339, 118–126.Google Scholar
Brandenburg, A. & Dobler, W. 2001 Large scale dynamos with helicity loss through boundaries. Astron. Astrophys. 369, 329–338.Google Scholar
Brandenburg, A. & Giampapa, M. S. 2018 Enhanced stellar activity for slow antisolar differential rotation? Astrophys. J. Lett. 855, L22.Google Scholar
Brandenburg, A. & Kahniashvili, T. 2017 Classes of hydrodynamic and magnetohydrodynamic turbulent decay. Phys. Rev. Lett. 118, 055102.Google Scholar
Brandenburg, A. & Multamäki, T. 2004 How long can left and right handed life forms coexist? Intl J. Astrobiol. 3, 209–219.Google Scholar
Brandenburg, A. & Nordlund, Å. 2011 Astrophysical turbulence modeling. Rep. Prog. Phys. 74, 046901.Google Scholar
Brandenburg, A. & Rädler, K.-H. 2013 Yoshizawa’s cross-helicity effect and its quenching. Geophys. Astrophys. Fluid Dyn. 107, 207–217.Google Scholar
Brandenburg, A. & Schmitt, D. 1998 Simulations of an alpha-effect due to magnetic buoyancy. Astron. Astrophys. 338, L55–L58.Google Scholar
Brandenburg, A. & Sokoloff, D. 2002 Local and nonlocal magnetic diffusion and alpha-effect tensors in shear flow turbulence. Geophys. Astrophys. Fluid Dyn. 96, 319–344.Google Scholar
Brandenburg, A. & Stepanov, R. 2014 Faraday signature of magnetic helicity from reduced depolarization. Astrophys. J. 786, 91.Google Scholar
Brandenburg, A. & Subramanian, K. 2000 Large scale dynamos with ambipolar diffusion nonlinearity. Astron. Astrophys. 361, L33–L36.Google Scholar
Brandenburg, A. & Subramanian, K. 2005a Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417, 1–209.Google Scholar
Brandenburg, A. & Subramanian, K. 2005b Strong mean field dynamos require supercritical helicity fluxes. Astron. Nachr. 326, 400–408.Google Scholar
Brandenburg, A. & Tuominen, I. 1988 Variation of magnetic fields and flows during the solar cycle. Adv. Space Sci. 8, 185–189.Google Scholar
Brandenburg, A. & Tuominen, I. 1991 The solar dynamo. In The Sun and Cool Stars: Activity, Magnetism, Dynamos, IAU Coll. 130 (ed. Tuominen, I., Moss, D. & Rüdiger, G.), Lecture Notes in Physics, vol. 380, pp. 223–233. Springer.Google Scholar
Brandenburg, A. & Urpin, V. 1998 Magnetic fields in young galaxies due to the cross-helicity effect. Astron. Astrophys. 332, L41–L44.Google Scholar
Brandenburg, A. & von Rekowski, B. 2001 Astrophysical significance of the anisotropic kinetic alpha effect. Astron. Astrophys. 379, 1153–1160.Google Scholar
Brandenburg, A., Andersen, A. C., Höfner, S. & Nilsson, M. 2005 Homochiral growth through enantiomeric cross-inhibition. Orig. Life Evol. Biosph. 35, 225–241.Google Scholar
Brandenburg, A., Bigazzi, A. & Subramanian, K. 2001 The helicity constraint in turbulent dynamos with shear. Mon. Not. R. Astron. Soc. 325, 685–692.Google Scholar
Brandenburg, A., Candelaresi, S. & Chatterjee, P. 2009 Small-scale magnetic helicity losses from a mean-field dynamo. Mon. Not. R. Astron. Soc. 398, 1414–1422.Google Scholar
Brandenburg, A., Chatterjee, P., Del Sordo, F., Hubbard, A., Käpylä, P. J. & Rheinhardt, M. 2010 Turbulent transport in hydromagnetic flows. Phys. Scr. T142, 014028.Google Scholar
Brandenburg, A., Donner, K. J., Moss, D., Shukurov, A., Sokoloff, D. D. & Tuominen, I. 1992 Dynamos in discs and halos of galaxies. Astron. Astrophys. 259, 453–461.Google Scholar
Brandenburg, A., Donner, K. J., Moss, D., Shukurov, A., Sokoloff, D. D. & Tuominen, I. 1993 Vertical magnetic fields above the discs of spiral galaxies. Astron. Astrophys. 271, 36–50.Google Scholar
Brandenburg, A., Enqvist, K. & Olesen, P. 1996 Large-scale magnetic fields from hydromagnetic turbulence in the very early universe. Phys. Rev. D 54, 1291–1300.Google Scholar
Brandenburg, A., Gressel, O., Käpylä, P. J., Kleeorin, N., Mantere, M. J. & Rogachevskii, I. 2013 New scaling for the alpha effect in slowly rotating turbulence. Astrophys. J. 762, 127.Google Scholar
Brandenburg, A., Jennings, R. L., Nordlund, Å., Rieutord, M., Stein, R. F. & Tuominen, I. 1996 Magnetic structures in a dynamo simulation. J. Fluid Mech. 306, 325–352.Google Scholar
Brandenburg, A., Kahniashvili, T. & Tevzadze, A. G. 2015 Nonhelical inverse transfer of a decaying turbulent magnetic field. Phys. Rev. Lett. 114, 075001.Google Scholar
Brandenburg, A., Käpylä, P. J. & Mohammed, A. 2004 Non-Fickian diffusion and tau-approximation from numerical turbulence. Phys. Fluids 16, 1020–1027.Google Scholar
Brandenburg, A., Kemel, K., Kleeorin, N., Mitra, D. & Rogachevskii, I. 2011a Detection of negative effective magnetic pressure instability in turbulence simulations. Astrophys. J. Lett. 740, L50.Google Scholar
Brandenburg, A., Kemel, K., Kleeorin, N. & Rogachevskii, I. 2012a The negative effective magnetic pressure in stratified forced turbulence. Astrophys. J. 749, 179.Google Scholar
Brandenburg, A., Kleeorin, N. & Rogachevskii, I. 2010 Large-scale magnetic flux concentrations from turbulent stresses. Astron. Nachr. 331, 5–13.Google Scholar
Brandenburg, A., Krause, F., Meinel, R., Moss, D. & Tuominen, I. 1989 The stability of nonlinear dynamos and the limited role of kinematic growth rates. Astron. Astrophys. 213, 411–422.Google Scholar
Brandenburg, A., Mathur, S. & Metcalfe, T. S. 2017b Evolution of coexisting long and short period stellar activity cycles. Astrophys. J. 845, 79.Google Scholar
Brandenburg, A., Moss, D. & Shukurov, A. 1995 Galactic fountains as magnetic pumps. Mon. Not. R. Astron. Soc. 276, 651–662.Google Scholar
Brandenburg, A., Moss, D. & Tuominen, I. 1992a Stratification and thermodynamics in mean-field dynamos. Astron. Astrophys. 265, 328–344.Google Scholar
Brandenburg, A., Moss, D. & Tuominen, I. 1992b Turbulent pumping in the solar dynamo. In The Solar Cycle (ed. Harvey, K. L.), ASP Conference Series, vol. 27, pp. 536–542. Astronomical Society of the Pacific.Google Scholar
Brandenburg, A., Nordlund, Å., Pulkkinen, P., Stein, R. F. & Tuominen, I. 1990 3-D Simulation of turbulent cyclonic magneto-convection. Astron. Astrophys. 232, 277–291.Google Scholar
Brandenburg, A., Nordlund, Å., Stein, R. F. & Torkelsson, U. 1995 Dynamo generated turbulence and large scale magnetic fields in a Keplerian shear flow. Astrophys. J. 446, 741–754.Google Scholar
Brandenburg, A., Petrie, G. J. D. & Singh, N. K. 2017c Two-scale analysis of solar magnetic helicity. Astrophys. J. 836, 21.Google Scholar
Brandenburg, A., Procaccia, I. & Segel, D. 1995 The size and dynamics of magnetic flux structures in MHD turbulence. Phys. Plasmas 2, 1148–1156.Google Scholar
Brandenburg, A., Rädler, K.-H. & Kemel, K. 2012b Mean-field transport in stratified and/or rotating turbulence. Astron. Astrophys. 539, A35.Google Scholar
Brandenburg, A., Rädler, K.-H., Rheinhardt, M. & Käpylä, P. J. 2008a Magnetic diffusivity tensor and dynamo effects in rotating and shearing turbulence. Astrophys. J. 676, 740–751.Google Scholar
Brandenburg, A., Rädler, K.-H., Rheinhardt, M. & Subramanian, K. 2008b Magnetic quenching of alpha and diffusivity tensors in helical turbulence. Astrophys. J. Lett. 687, L49–L52.Google Scholar
Brandenburg, A., Rädler, K.-H. & Schrinner, M. 2008c Scale dependence of alpha effect and turbulent diffusivity. Astron. Astrophys. 482, 739–746.Google Scholar
Brandenburg, A., Rogachevskii, I. & Kleeorin, N. 2016 Magnetic concentrations in stratified turbulence: the negative effective magnetic pressure instability. New J. Phys. 18, 125011.Google Scholar
Brandenburg, A., Saar, S. H. & Turpin, C. R. 1998 Time evolution of the magnetic activity cycle period. Astrophys. J. Lett. 498, L51–L54.Google Scholar
Brandenburg, A., Schober, J. & Rogachevskii, I. 2017d The contribution of kinetic helicity to turbulent magnetic diffusivity. Astron. Nachr. 338, 790–793.Google Scholar
Brandenburg, A., Schober, J., Rogachevskii, I., Kahniashvili, T., Boyarsky, A., Fröhlich, J., Ruchayskiy, O. & Kleeorin, N. 2017e The turbulent chiral magnetic cascade in the early universe. Astrophys. J. Lett. 845, L21.Google Scholar
Brandenburg, A., Subramanian, K., Balogh, A. & Goldstein, M. L. 2011b Scale-dependence of magnetic helicity in the solar wind. Astrophys. J. 734, 9.Google Scholar
Brown, B. P., Miesch, M. S., Browning, M. K., Brun, A. S. & Toomre, J. 2011 Magnetic cycles in a convective dynamo simulation of a young solar-type star. Astrophys. J. 731, 69.Google Scholar
Browning, M. K. 2008 Simulations of dynamo action in fully convective stars. Astrophys. J. 676, 1262–1280.Google Scholar
Brun, A. S. 2004 On the interaction between differential rotation and magnetic fields in the Sun. Sol. Phys. 220, 307–316.Google Scholar
Brun, A. S., Miesch, M. S. & Toomre, J. 2004 Global-scale turbulent convection and magnetic dynamo action in the solar envelope. Astrophys. J. 614, 1073–1098.Google Scholar
Cameron, R. & Schüssler, M. 2015 The crucial role of surface magnetic fields for the solar dynamo. Science 347, 1333–1335.Google Scholar
Cameron, R. & Schüssler, M. 2017 An update of Leighton’s solar dynamo model. Astron. Astrophys. 599, A52.Google Scholar
Cameron, R. H., Duvall, T. L., Schüssler, M. & Schunker, H. 2018 Observing and modeling the poloidal and toroidal fields of the solar dynamo. Astron. Astrophys. 609, A56.Google Scholar
Campanelli, L. 2007 Evolution of magnetic fields in freely decaying magnetohydrodynamic turbulence. Phys. Rev. Lett. 98, 251302.Google Scholar
Candelaresi, S. & Brandenburg, A. 2013 How much helicity is needed to drive large-scale dynamos? Phys. Rev. E 87, 043104.Google Scholar
Candelaresi, S., Hubbard, A., Brandenburg, A. & Mitra, D. 2011 Magnetic helicity transport in the advective gauge family. Phys. Plasmas 18, 012903.Google Scholar
Cattaneo, F. & Hughes, D. W. 1996 Nonlinear saturation of the turbulent alpha effect. Phys. Rev. E 54, R4532–R4535.Google Scholar
Cattaneo, F. & Hughes, D. W. 2009 Problems with kinematic mean field electrodynamics at high magnetic Reynolds numbers. Mon. Not. R. Astron. Soc. 395, L48–L51.Google Scholar
Cattaneo, F. & Tobias, S. M. 2009 Dynamo properties of the turbulent velocity field of a saturated dynamo. J. Fluid Mech. 621, 205–214.Google Scholar
Chamandy, L., Subramanian, K. & Shukurov, A. 2013 Galactic spiral patterns and dynamo action – I. A new twist on magnetic arms. Mon. Not. R. Astron. Soc. 428, 3569–3589.Google Scholar
Charbonneau, P. 2010 Dynamo models of the solar cycle. Liv. Rev. Solar Phys. 7, 3.Google Scholar
Chatterjee, P., Nandy, D. & Choudhuri, A. R. 2004 Full-sphere simulations of a circulation-dominated solar dynamo: exploring the parity issue. Astron. Astrophys. 427, 1019–1030.Google Scholar
Chatterjee, P. & Choudhuri, A. R. 2006 On magnetic coupling between the two hemispheres in solar dynamo models. Sol. Phys. 239, 29–39.Google Scholar
Chatterjee, P., Mitra, D., Brandenburg, A. & Rheinhardt, M. 2011 Spontaneous chiral symmetry breaking by hydromagnetic buoyancy. Phys. Rev. E 84, 025403R.Google Scholar
Chatterjee, P., Mitra, D., Rheinhardt, M. & Brandenburg, A. 2011 Alpha effect due to buoyancy instability of a magnetic layer. Astron. Astrophys. 534, A46.Google Scholar
Choudhuri, A. R., Schüssler, M. & Dikpati, M. 1995 The solar dynamo with meridional circulation. Astron. Astrophys. 303, L29–L32.Google Scholar
Christensson, M., Hindmarsh, M. & Brandenburg, A. 2001 Inverse cascade in decaying 3D magnetohydrodynamic turbulence. Phys. Rev. E 64, 056405.Google Scholar
Cole, E., Brandenburg, A., Käpylä, P. J. & Käpylä, M. J. 2016 Robustness of oscillatory $\unicode[STIX]{x1D6FC}^{2}$ dynamos in spherical wedges. Astron. Astrophys. 593, A134.Google Scholar
Cooper, C. M., Wallace, J., Brookhart, M., Clark, M., Collins, C., Ding, W. X., Flanagan, K., Khalzov, I., Li, Y., Milhone, J. et al. 2014 The Madison plasma dynamo experiment: a facility for studying laboratory plasma astrophysics. Phys. Plasmas 21, 013505.Google Scholar
Courvoisier, A., Hughes, D. W. & Proctor, M. R. E. 2010 Self-consistent mean-field magnetohydrodynamics. Proc. R. Soc. Lond. 466, 583–601.Google Scholar
Cossette, J.-F. & Rast, M. P. 2016 Supergranulation as the largest buoyantly driven convective scale of the Sun. Astrophys. J. Lett. 829, L17.Google Scholar
Courvoisier, A., Hughes, D. W. & Tobias, S. M. 2006 $\unicode[STIX]{x1D6FC}$ -effect in a family of chaotic flows. Phys. Rev. Lett. 96, 034503.Google Scholar
Deardorff, J. W. 1966 The counter-gradient heat flux in the lower atmosphere and in the laboratory. J. Atmosph. Sci. 23, 503–506.Google Scholar
Deardorff, J. W. 1972 Theoretical expression for the countergradient vertical heat flux. J. Geophys. Res. 77, 5900–5904.Google Scholar
Del Sordo, F., Guerrero, G. & Brandenburg, A. 2013 Turbulent dynamo with advective magnetic helicity flux. Mon. Not. R. Astron. Soc. 429, 1686–1694.Google Scholar
Dermer, C. D., Cavadini, M., Razzaque, S., Finke, J. D., Chiang, J. & Lott, B. 2011 Time delay of cascade radiation for TeV blazars and the measurement of the intergalactic magnetic field. Astrophys. J. Lett. 733, L21.Google Scholar
Devlen, E., Brandenburg, A. & Mitra, D. 2013 A mean field dynamo from negative eddy diffusivity. Mon. Not. R. Astron. Soc. 432, 1651–1657.Google Scholar
Dikpati, M. & Charbonneau, P. 1999 A Babcock–Leighton flux transport dynamo with solar-like differential rotation. Astrophys. J. 518, 508–520.Google Scholar
Dikpati, M. & Gilman, P. A. 2001 Flux-Transport dynamos with $\unicode[STIX]{x1D6FC}$ -effect from global instability of tachocline differential rotation: a solution for magnetic parity selection in the sun. Astrophys. J. 559, 428–442.Google Scholar
Dikpati, M. & Gilman, P. A. 2006 Simulating and predicting solar cycles using a flux-transport dynamo. Astrophys. J. 649, 498–514.Google Scholar
Dikpati, M., de Toma, G., Gilman, P. A., Arge, C. N. & White, R. R. 2004 Diagnostics of polar field reversal in solar cycle 23 using a flux transport dynamo model. Astrophys. J. 601, 1136–1151.Google Scholar
Dikpati, M., de Toma, G. & Gilman, P. A. 2006 Predicting the strength of solar cycle 24 using a flux-transport dynamo-based tool. Geophys. Res. Lett. 33, L05102.Google Scholar
Dobler, W., Stix, M. & Brandenburg, A. 2006 Convection and magnetic field generation in fully convective spheres. Astrophys. J. 638, 336–347.Google Scholar
Donner, K. J. & Brandenburg, A. 1990 Generation and interpretation of galactic magnetic fields. Astron. Astrophys. 240, 289–298.Google Scholar
Drobyshevskij, E. M. & Yuferev, V. S. 1974 Topological pumping of magnetic flux by three-dimensional convection. J. Fluid Mech. 65, 33–44.Google Scholar
Durrer, R. & Caprini, C. 2003 Primordial magnetic fields and causality. J. Cosmol. Astropart. Phys. 0311, 010.Google Scholar
Dvornikov, M. & Semikoz, V. B. 2017 Influence of the turbulent motion on the chiral magnetic effect in the early universe. Phys. Rev. D 95, 043538.Google Scholar
Eberhard, G. & Schwarzschild, K. 1913 On the reversal of the calcium lines H and K in stellar spectra. Astrophys. J. 38, 292–295.Google Scholar
Fan, Y. 2001 The emergence of a twisted $\unicode[STIX]{x1D6FA}$ -tube into the solar atmosphere. Astrophys. J. 554, L111–L114.Google Scholar
Fan, Y. 2008 The three-dimensional evolution of buoyant magnetic flux tubes in a model solar convective envelope. Astrophys. J. 676, 680–697.Google Scholar
Fan, Y. 2009 Magnetic fields in the solar convection zone. Liv. Rev. Sol. Phys. 6, 4.Google Scholar
Featherstone, N. A. & Hindman, B. W. 2016 The spectral amplitude of stellar convection and its scaling in the high-Rayleigh-number regime. Astrophys. J. 818, 32.Google Scholar
Ferrière, K. 1992a Effect of an ensemble of explosions on the galactic dynamo. I. General formulation. Astrophys. J. 389, 286–296.Google Scholar
Ferrière, K. 1992b Effect of the explosion of supernovae and superbubbles on the galactic dynamo. Astrophys. J. 391, 188–198.Google Scholar
Ferrière, K. 1993a The full alpha-tensor due to supernova explosions and superbubbles in the galactic disk. Astrophys. J. 404, 162–184.Google Scholar
Ferrière, K. 1993b Magnetic diffusion due to supernova explosions and superbubbles in the galactic disk. Astrophys. J. 409, 248–261.Google Scholar
Field, G. B. & Blackman, E. G. 2002 Dynamical quenching of the $\unicode[STIX]{x1D6FC}^{2}$ dynamo. Astrophys. J. 572, 685–692.Google Scholar
Field, G. B. & Carroll, S. M. 2000 Cosmological magnetic fields from primordial helicity. Phys. Rev. D 62, 103008.Google Scholar
Finn, J. M. & Antonsen, T. M. 1985 Magnetic helicity: what it is and what is it good for? Commun. Plasma Phys. Contr. Fusion 9, 111–123.Google Scholar
Forest, C. B., Bayliss, R. A., Kendrick, R. D., Nornberg, M. D., O’Donnell, R. & Spence, E. J. 2002 Hydrodynamic and numerical modeling of a spherical homogeneous dynamo experiment. Magnetohydrodynamics 38, 107–120.Google Scholar
Forest, C. B., Flanagan, K., Brookhart, M., Clark, M., Cooper, C. M., Désangles, V., Egedal, J., Endrizzi, D., Khalzov, I. V., Li, H. et al. 2015 The Wisconsin plasma astrophysics laboratory. J. Plasma Phys. 81, 345810501.Google Scholar
Frank, F. C. 1953 On spontaneous asymmetric synthesis. Biochim. Biophys. Acta 11, 459–464.Google Scholar
Frisch, U., She, Z. S. & Sulem, P. L. 1987 Large-scale flow driven by the anisotropic kinetic alpha effect. Physica 28D, 382–392.Google Scholar
Fromang, S. & Papaloizou, J. 2007 MHD simulations of the magnetorotational instability with zero net flux in a shearing box. I. The issue of convergence. Astron. Astrophys. 476, 1113–1122.Google Scholar
Fromang, S., Papaloizou, J., Lesur, G. & Heinemann, T. 2007 MHD simulations of the magnetorotational instability in a shearing box with zero net flux. II. The effect of transport coefficients. Astron. Astrophys. 476, 1123–1132.Google Scholar
Galloway, D. J. & Proctor, M. R. E. 1992 Numerical calculations of fast dynamos in smooth velocity fields with realistic diffusion. Nature 356, 691–693.Google Scholar
Gastine, T., Yadav, R. K., Morin, J., Reiners, A. & Wicht, J. 2014 From solar-like to antisolar differential rotation in cool stars. Mon. Not. R. Astron. Soc. 438, L76–L80.Google Scholar
Gellert, M., Rüdiger, G. & Hollerbach, R. 2011 Helicity and alpha-effect by current-driven instabilities of helical magnetic fields. Mon. Not. R. Astron. Soc. 414, 2696–2701.Google Scholar
Gent, F. A., Shukurov, A., Fletcher, A., Sarson, G. R. & Mantere, M. J. 2013a The supernova-regulated ISM – I. The multiphase structure. Mon. Not. R. Astron. Soc. 432, 1396–1423.Google Scholar
Gent, F. A., Shukurov, A., Sarson, G. R., Fletcher, A. & Mantere, M. J. 2013b The supernova-regulated ISM – II. The mean magnetic field. Mon. Not. R. Astron. Soc. 430, L40–L44.Google Scholar
Ghizaru, M., Charbonneau, P. & Smolarkiewicz, P. K. 2010 Magnetic cycles in global large-eddy simulations of solar convection. Astrophys. J. 715, L133–L137.Google Scholar
Giampapa, M. S., Brandenburg, A., Cody, A. M., Skiff, B. A. & Hall, J. C. 2017 The rotation and chromospheric activity of the solar-type stars in the open cluster M67. Astrophys. J. (submitted), https://www.nordita.org/preprints, no. 2017-121.Google Scholar
Gilman, P. A. 1977 Nonlinear dynamics of Boussinesq convection in a deep rotating shell. I. Geophys. Astrophys. Fluid Dyn. 8, 93–135.Google Scholar
Gilman, P. A. 1983 Dynamically consistent nonlinear dynamos driven by convection in a rotating spherical shell. II. Dynamos with cycles and strong feedbacks. Astrophys. J. Suppl. 53, 243–268.Google Scholar
Glatzmaier, G. A. 1985 Numerical simulations of stellar convective dynamos. II. Field propagation in the convection zone. Astrophys. J. 291, 300–307.Google Scholar
Goldreich, P. & Sridhar, S. 1995 Toward a theory of interstellar turbulence. 2: strong Alfvénic turbulence. Astrophys. J. 438, 763–775.Google Scholar
Greer, B. J., Hindman, B. W., Featherstone, N. A. & Toomre, J. 2015 Helioseismic imaging of fast convective flows throughout the near-surface shear layer. Astrophys. J. Lett. 803, L17.Google Scholar
Gressel, O. 2013 Dynamo effects in magnetorotational turbulence with finite thermal diffusivity. Astrophys. J. 770, 100.Google Scholar
Gressel, O., Elstner, D., Ziegler, U. & Rüdiger, G. 2008b Direct simulations of a supernova-driven galactic dynamo. Astron. Astrophys. 486, L35–L38.Google Scholar
Gressel, O., Elstner, D. & Ziegler, U. 2013 Towards a hybrid dynamo model for the Milky Way. Astron. Astrophys. 560, A93.Google Scholar
Gressel, O. & Pessah, M. E. 2015 Characterizing the mean-field dynamo in turbulent accretion disks. Astrophys. J. 810, 59.Google Scholar
Gressel, O., Ziegler, U., Elstner, D. & Rüdiger, G. 2008a Dynamo coefficients from local simulations of the turbulent ISM. Astron. Nachr. 329, 619–624.Google Scholar
Gruzinov, A. V. & Diamond, P. H. 1994 Self-consistent theory of mean-field electrodynamics. Phys. Rev. Lett. 72, 1651–1653.Google Scholar
Gruzinov, A. V. & Diamond, P. H. 1995 Self-consistent mean field electrodynamics of turbulent dynamos. Phys. Plasmas 2, 1941–1947.Google Scholar
Gruzinov, A. V. & Diamond, P. H. 1996 Nonlinear mean field electrodynamics of turbulent dynamos. Phys. Plasmas 3, 1853–1857.Google Scholar
Guerrero, G. & Käpylä, P. J. 2011 Dynamo action and magnetic buoyancy in convection simulations with vertical shear. Astron. Astrophys. 533, A40.Google Scholar
Hanasoge, S. M., Duvall, T. L. Jr & DeRosa, M. L. 2010 Seismic constraints on interior solar convection. Astrophys. J. Lett. 712, L98–L102.Google Scholar
Hanasoge, S. M., Duvall, T. L. & Sreenivasan, K. R. 2012 Anomalously weak solar convection. Proc. Natl. Acad. Sci. 109, 11928–11932.Google Scholar
Hanasoge, S., Gizon, L. & Sreenivasan, K. R. 2016 Seismic sounding of convection in the Sun. Ann. Rev. Fluid Dyn. 48, 191–217.Google Scholar
Hanasz, M., Kowal, G., Otmianowska-Mazur, K. & Lesch, H. 2004 Amplification of galactic magnetic fields by the cosmic-ray-driven dynamo. Astrophys. J. 605, L33–L36.Google Scholar
Hanasz, M., Otmianowska-Mazur, K., Kowal, G. & Lesch, H. 2009a Cosmic-ray-driven dynamo in galactic disks. A parameter study. Astron. Astrophys. 498, 335–346.Google Scholar
Hanasz, M., Wóltański, D. & Kowalik, K. 2009b Global galactic dynamo driven by cosmic rays and exploding magnetized stars. Astrophys. J. Lett. 706, L155–L159.Google Scholar
Harutyunyan, G., Strassmeier, K. G., Künstler, A., Carroll, T. A. & Weber, M. 2016 Anti-solar differential rotation on the active sub-giant HU Virginis. Astron. Astrophys. 592, A117.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, 690–703.Google Scholar
Hazra, G., Karak, B. B. & Choudhuri, A. R. 2014 Is a deep one-cell meridional circulation essential for the flux transport solar dynamo? Astrophys. J. 782, 93.Google Scholar
Heinemann, T., McWilliams, J. C. & Schekochihin, A. A. 2011 Magnetic-field generation by randomly forced shearing waves. Phys. Rev. Lett. 107, 255004.Google Scholar
Hickmann, K. S., Godinez, H. C., Henney, C. J. & Arge, C. N. 2015 Data assimilation in the ADAPT photospheric flux transport model. Sol. Phys. 290, 1105–1118.Google Scholar
Hood, A. W., Archontis, V., Galsgaard, K. & Moreno-Insertis, F. 2009 The emergence of toroidal flux tubes from beneath the solar photosphere. Astron. Astrophys. 503, 999–1011.Google Scholar
Hotta, H., Rempel, M. & Yokoyama, T. 2014 High-resolution calculations of the solar global convection with the reduced speed of sound technique. I. The structure of the convection and the magnetic field without the rotation. Astrophys. J. 786, 24.Google Scholar
Hotta, H., Rempel, M. & Yokoyama, T. 2015 Efficient small-scale dynamo in the solar convection zone. Astrophys. J. 803, 42.Google Scholar
Hotta, H., Rempel, M. & Yokoyama, T. 2016 Large-scale magnetic fields at high Reynolds numbers in magnetohydrodynamic simulations. Science 351, 1427–1430.Google Scholar
Hoyng, P. 1988 Turbulent transport of magnetic fields. III. Stochastic excitation of global magnetic field modes. Astrophys. J. 332, 857–871.Google Scholar
Hoyng, P. 1993 Helicity fluctuations in mean field theory: an explanation for the variability of the solar cycle? Astron. Astrophys. 272, 321–339.Google Scholar
Hoyng, P. 2003 The field, the mean and the meaning. In Advances in nonlinear dynamos (The Fluid Mechanics of Astrophysics and Geophysics, Vol. 9) (ed. Ferriz-Mas, A. & Núñez, M.), pp. 1–36. Taylor & Francis.Google Scholar
Hubbard, A. & Brandenburg, A. 2009 Memory effects in turbulent transport. Astrophys. J. 706, 712–726.Google Scholar
Hubbard, A. & Brandenburg, A. 2010 Magnetic helicity fluxes in an $\unicode[STIX]{x1D6FC}^{2}$ dynamo embedded in a halo. Geophys. Astrophys. Fluid Dyn. 104, 577–590.Google Scholar
Hubbard, A. & Brandenburg, A. 2011 Magnetic helicity flux in the presence of shear. Astrophys. J. 727, 11.Google Scholar
Hubbard, A. & Brandenburg, A. 2012 Catastrophic quenching in $\unicode[STIX]{x1D6FC}\unicode[STIX]{x1D6FA}$ dynamos revisited. Astrophys. J. 748, 51.Google Scholar
Hubbard, A., Del Sordo, F., Käpylä, P. J. & Brandenburg, A. 2009 The $\unicode[STIX]{x1D6FC}$ effect with imposed and dynamo-generated magnetic fields. Mon. Not. R. Astron. Soc. 398, 1891–1899.Google Scholar
Hughes, D. W. & Proctor, M. R. E. 1988 Magnetic fields in the solar convection zone: magnetoconvection and magnetic buoyancy. Ann. Rev. Fluid Dyn. 20, 187–223.Google Scholar
Hughes, D. W. & Proctor, M. R. E. 2009 Large-scale dynamo action driven by velocity shear and rotating convection. Phys. Rev. Lett. 102, 044501.Google Scholar
Jabbari, S., Brandenburg, A., Kleeorin, N. & Rogachevskii, I. 2017 Sharp magnetic structures from dynamos with density stratification. Mon. Not. R. Astron. Soc. 467, 2753–2765.Google Scholar
Jing, J., Park, S.-H., Liu, C., Lee, J., Wiegelmann, T., Xu, Y., Deng, N. & Wang, H. 2012 Evolution of relative magnetic helicity and current helicity in NOAA active region 11158. Astrophys. J. 752, L9.Google Scholar
Jouve, L., Brown, B. P. & Brun, A. S. 2010 Exploring the $P_{\text{cyc}}$ versus $P_{\text{rot}}$ relation with flux transport dynamo models of solar-like stars. Astron. Astrophys. 509, A32.Google Scholar
Joyce, M. & Shaposhnikov, M. 1997 Primordial magnetic fields, right electrons, and the Abelian anomaly. Phys. Rev. Lett. 79, 1193–1196.Google Scholar
Kahniashvili, T., Tevzadze, A. G., Brandenburg, A. & Neronov, A. 2013 Evolution of primordial magnetic fields from phase transitions. Phys. Rev. D 87, 083007.Google Scholar
Käpylä, M. J., Gent, F. A., Väisälä, M. S. & Sarson, G. R. 2018a The supernova-regulated ISM. III. Generation of vorticity, helicity, and mean flows. Astron. Astrophys. 611, A15.Google Scholar
Käpylä, M. J., Käpylä, P. J., Olspert, N., Brandenburg, A., Warnecke, J., Karak, B. B. & Pelt, J. 2016 Multiple dynamo modes as a mechanism for long-term solar activity variations. Astron. Astrophys. 589, A56.Google Scholar
Käpylä, P. J. 2018 Magnetic and rotational quenching of the $\unicode[STIX]{x1D6EC}$ effect. Astron. Astrophys. (submitted), arXiv:1712.08045.Google Scholar
Käpylä, P. J. & Brandenburg, A. 2009 Turbulent dynamos with shear and fractional helicity. Astrophys. J. 699, 1059–1166.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
Käpylä, P. J., Brandenburg, A., Kleeorin, N., Käpylä, M. J. & Rogachevskii, I. 2016 Magnetic flux concentrations from turbulent stratified convection. Astron. Astrophys. 588, A150.Google Scholar
Käpylä, P. J., Käpylä, M. J. & Brandenburg, A. 2014 Confirmation of bistable stellar differential rotation profiles. Astron. Astrophys. 570, A43.Google Scholar
Käpylä, P. J., Käpylä, M. J., Olspert, N., Warnecke, J. & Brandenburg, A. 2017a Convection-driven spherical shell dynamos at varying Prandtl numbers. Astron. Astrophys. 599, A4.Google Scholar
Käpylä, P. J., Korpi, M. J. & Brandenburg, A. 2008 Large-scale dynamos in turbulent convection with shear. Astron. Astrophys. 491, 353–362.Google Scholar
Käpylä, P. J., Korpi, M. J., Brandenburg, A., Mitra, D. & Tavakol, R. 2010 Convective dynamos in spherical wedge geometry. Astron. Nachr. 331, 73–81.Google Scholar
Käpylä, P. J., Mantere, M. J. & Brandenburg, A. 2012 Cyclic magnetic activity due to turbulent convection in spherical wedge geometry. Astrophys. J. Lett. 755, L22.Google Scholar
Käpylä, P. J., Mantere, M. J., Cole, E., Warnecke, J. & Brandenburg, A. 2013 Effects of strong stratification on equatorward dynamo wave propagation. Astrophys. J. 778, 41.Google Scholar
Käpylä, P. J., Rheinhardt, M., Brandenburg, A., Arlt, R., Käpylä, M. J., Lagg, A., Olspert, N. & Warnecke, J. 2017b Extended subadiabatic layer in simulations of overshooting convection. Astrophys. J. Lett. 845, L23.Google Scholar
Käpylä, P. J., Viviani, M., Käpylä, M. J. & Brandenburg, A. 2018b Effects of a subadiabatic layer on convection and dynamos in spherical wedge simulations. Geophys. Astrophys. Fluid Dyn. (submitted), arXiv:1803.05898.Google Scholar
Karak, B. B., Käpylä, M. J., Käpylä, P. J., Brandenburg, A., Olspert, N. & Pelt, J. 2015 Magnetically controlled stellar differential rotation near the transition from solar to anti-solar profiles. Astron. Astrophys. 576, A26.Google Scholar
Karak, B. B., Kitchatinov, L. L. & Choudhuri, A. R. 2014 A dynamo model of magnetic activity in solar-like stars with different rotational velocities. Astrophys. J. 791, 59.Google Scholar
Karak, B. B., Rheinhardt, M., Brandenburg, A., Käpylä, P. J. & Käpylä, M. J. 2014 Quenching and anisotropy of hydromagnetic turbulent transport. Astrophys. J. 795, 16.Google Scholar
Kazantsev, A. P. 1968 Enhancement of a magnetic field by a conducting fluid. Sov. Phys. JETP 26, 1031–1034.Google Scholar
Kemel, K., Brandenburg, A., Kleeorin, N. & Rogachevskii, I. 2012 Properties of the negative effective magnetic pressure instability. Astron. Nachr. 333, 95–100.Google Scholar
Kemel, K., Brandenburg, A., Kleeorin, N., Mitra, D. & Rogachevskii, I. 2012 Spontaneous formation of magnetic flux concentrations in stratified turbulence. Sol. Phys. 280, 321–333.Google Scholar
Kemel, K., Brandenburg, A., Kleeorin, N., Mitra, D. & Rogachevskii, I. 2013 Active region formation through the negative effective magnetic pressure instability. Sol. Phys. 287, 293–313.Google Scholar
Kitchatinov, L. L. 1991 Turbulent transport of magnetic fields in a highly conducting rotating fluid and the solar cycle. Astron. Astrophys. 243, 483–491.Google Scholar
Kitchatinov, L. L. & Mazur, M. V. 2000 Stability and equilibrium of emerged magnetic flux. Sol. Phys. 191, 325–340.Google Scholar
Kitchatinov, L. L. & Rüdiger, G. 2004 Anti-solar differential rotation. Astron. Nachr. 325, 496–500.Google Scholar
Kleeorin, N., Mond, M. & Rogachevskii, I. 1993 Magnetohydrodynamic instabilities in developed small-scale turbulence. Phys. Fluids 5, 4128–4134.Google Scholar
Kleeorin, N., Mond, M. & Rogachevskii, I. 1996 Magnetohydrodynamic turbulence in the solar convective zone as a source of oscillations and sunspots formation. Astron. Astrophys. 307, 293–309.Google Scholar
Kleeorin, N., Moss, D., Rogachevskii, I. & Sokoloff, D. 2000 Helicity balance and steady-state strength of the dynamo generated galactic magnetic field. Astron. Astrophys. 361, L5–L8.Google Scholar
Kleeorin, N., Moss, D., Rogachevskii, I. & Sokoloff, D. 2002 The role of magnetic helicity transport in nonlinear galactic dynamos. Astron. Astrophys. 387, 453–462.Google Scholar
Kleeorin, N., Moss, D., Rogachevskii, I. & Sokoloff, D. 2003 Nonlinear magnetic diffusion and magnetic helicity transport in galactic dynamos. Astron. Astrophys. 400, 9–18.Google Scholar
Kleeorin, N. & Rogachevskii, I. 1994 Effective Ampère force in developed magnetohydrodynamic turbulence. Phys. Rev. E 50, 2716–2730.Google Scholar
Kleeorin, N. I., Rogachevskii, I. V. & Ruzmaikin, A. A. 1989 Negative magnetic pressure as a trigger of large-scale magnetic instability in the solar convective zone. Pis. Astron. Zh. 15, 639–645.Google Scholar
Kleeorin, N. I., Rogachevskii, I. V. & Ruzmaikin, A. A. 1990 Magnetic force reversal and instability in a plasma with advanced magnetohydrodynamic turbulence. Sov. Phys. JETP 70, 878–883.Google Scholar
Kleeorin, N., Rogachevskii, I. & Ruzmaikin, A. 1995 Magnitude of the dynamo-generated magnetic field in solar-type convective zones. Astron. Astrophys. 297, 159–167.Google Scholar
Kleeorin, N. I. & Ruzmaikin, A. A. 1982 Dynamics of the average turbulent helicity in a magnetic field. Magnetohydrodynamics 18, 116–122; Translation from Magnitnaya Gidrodinamika, 2, pp. 17–24, 1982.Google Scholar
Kleeorin, N. I., Ruzmaikin, A. A. & Sokoloff, D. D. 1983 Activity cycle periods in late-type stars. Astrophys. Space Sci. 95, 131–136.Google Scholar
Kochukhov, O., Makaganiuk, V., Piskunov, N., Snik, F., Jeffers, S. V., Johns-Krull, C. M., Keller, C. U., Rodenhuis, M. & Valenti, J. A. 2011 First detection of linear polarization in the line profiles of active cool stars. Astrophys. J. Lett. 732, L19.Google Scholar
Korpi, M. J., Brandenburg, A., Shukurov, A., Tuominen, I. & Nordlund, Å. 1999 A supernova regulated interstellar medium: simulations of the turbulent multiphase medium. Astrophys. J. Lett. 514, L99–L102.Google Scholar
Korpi, M. J., Käpylä, P. J. & Väisälä, M. S. 2010 Influence of Ohmic diffusion on the excitation and dynamics of MRI. Astron. Nachr. 331, 34–45.Google Scholar
Kővári, Z., Kriskovics, L., Künstler, A., Carroll, T. A., Strassmeier, K. G., Vida, K., Oláh, K., Bartus, J. & Weber, M. 2015 Antisolar differential rotation of the K1-giant $\unicode[STIX]{x1D70E}$ Geminorum revisited. Astron. Astrophys. 573, A98.Google Scholar
Kővári, Z., Strassmeier, K. G., Carroll, T. A., Oláh, K., Kriskovics, L., Kővári, E., Kovács, O., Vida, K., Granzer, T. & Weber, M. 2017 Antisolar differential rotation with surface lithium enrichment on the single K-giant V1192 Orionis. Astron. Astrophys. 606, A42.Google Scholar
Kowal, G., Otmianowska-Mazur, K. & Hanasz, M. 2006 Dynamo coefficients in Parker unstable disks with cosmic rays and shear. The new methods of estimation. Astron. Astrophys. 445, 915–929.Google Scholar
Krause, F. & Rädler, K.-H. 1980 Mean-field Magnetohydrodynamics and Dynamo Theory. Pergamon Press.Google Scholar
Krivodubskii, V. N. 1984 Magnetic field transfer in the turbulent solar envelope. Sov. Astron. 28, 205–211.Google Scholar
Küker, M., Rüdiger, G. & Schultz, M. 2001 Circulation-dominated solar shell dynamo models with positive alpha-effect. Astron. Astrophys. 374, 301–308.Google Scholar
Lanotte, A., Noullez, A., Vergassola, M. & Wirth, A. 1999 Large-scale dynamo produced by negative magnetic eddy diffusivities. Geophys. Astrophys. Fluid Dyn. 91, 131–146.Google Scholar
Lehtinen, J., Jetsu, L., Hackman, T., Kajatkari, P. & Henry, G. W. 2016 Activity trends in young solar-type stars. Astron. Astrophys. 588, A38.Google Scholar
Leighton, R. B. 1969 A magneto-kinematic model of the solar cycle. Astrophys. J. 156, 1–26.Google Scholar
Lim, E.-K., Yurchyshyn, V. & Goode, P. 2012 First simultaneous detection of moving magnetic features in photospheric intensity and magnetic field data. Astrophys. J. 753, 89.Google Scholar
Liu, Y. & Schuck, P. W. 2012 Magnetic energy and helicity in two emerging active regions in the sun. Astrophys. J. 761, 105.Google Scholar
Lord, J. W., Cameron, R. H., Rast, M. P., Rempel, M. & Roudier, T. 2014 The role of subsurface flows in solar surface convection: modeling the spectrum of supergranular and larger scale flows. Astrophys. J. 793, 24.Google Scholar
Losada, I. R., Brandenburg, A., Kleeorin, N., Mitra, D. & Rogachevskii, I. 2012 Rotational effects on the negative magnetic pressure instability. Astron. Astrophys. 548, A49.Google Scholar
Losada, I. R., Brandenburg, A., Kleeorin, N. & Rogachevskii, I. 2013 Competition of rotation and stratification in flux concentrations. Astron. Astrophys. 556, A83.Google Scholar
Machida, M., Nakamura, K. E., Kudoh, T., Akahori, T., Sofue, Y. & Matsumoto, R. 2013 Dynamo activities driven by magnetorotational instability and the Parker instability in galactic gaseous disks. Astrophys. J. 764, 81.Google Scholar
Masada, Y. & Sano, T. 2014 Mean-field modeling of an $\unicode[STIX]{x1D6FC}^{2}$ dynamo coupled with direct numerical simulations of rigidly rotating convection. Astrophys. J. Lett. 794, L6.Google Scholar
Matthaeus, W. H. & Goldstein, M. L. 1982 Measurement of the rugged invariants of magnetohydrodynamics in the solar wind. J. Geophys. Res. 87, 6011–6028.Google Scholar
Mestel, L. & Subramanian, K. 1991 Galactic dynamos and density wave theory. Mon. Not. R. Astron. Soc. 248, 677–687.Google Scholar
Miesch, M., Matthaeus, W., Brandenburg, A., Petrosyan, A., Pouquet, A., Cambon, C., Jenko, F., Uzdensky, D., Stone, J., Tobias, S. et al. 2015 Large-eddy simulations of magnetohydrodynamic turbulence in space and astrophysics. Space Sci. Rev. 194, 97–137.Google Scholar
Miesch, M. S., Brun, A. S., De Rosa, M. L. & Toomre, J. 2008 Structure and evolution of giant cells in global models of solar convection. Astrophys. J. 673, 557–575.Google Scholar
Miesch, M. S. & Toomre, J. 2009 Turbulence, magnetism, and shear in stellar interiors. Ann. Rev. Fluid Dyn. 41, 317–345.Google Scholar
Mitra, D. & Brandenburg, A. 2012 Scaling and intermittency in incoherent $\unicode[STIX]{x1D6FC}$ –shear dynamo. Mon. Not. R. Astron. Soc. 420, 2170–2177.Google Scholar
Mitra, D., Candelaresi, S., Chatterjee, P., Tavakol, R. & Brandenburg, A. 2010b Equatorial magnetic helicity flux in simulations with different gauges. Astron. Nachr. 331, 130–135.Google Scholar
Mitra, D., Tavakol, R., Brandenburg, A. & Moss, D. 2009 Turbulent dynamos in spherical shell segments of varying geometrical extent. Astrophys. J. 697, 923–933.Google Scholar
Mitra, D., Tavakol, R., Käpylä, P. J. & Brandenburg, A. 2010a Oscillatory migrating magnetic fields in helical turbulence in spherical domains. Astrophys. J. Lett. 719, L1–L4.Google Scholar
Moffatt, H. K. 1970 Turbulent dynamo action at low magnetic Reynolds number. J. Fluid Mech. 41, 435–452.Google Scholar
Moffatt, H. K. 1972 An approach to a dynamic theory of dynamo action in a rotating conducting fluid. J. Fluid Mech. 53, 385–399.Google Scholar
Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.Google Scholar
Morgenthaler, A., Petit, P., Morin, J., Aurière, M., Dintrans, B., Konstantinova-Antova, R. & Marsden, S. 2011 Direct observation of magnetic cycles in Sun-like stars. Astron. Nachr. 332, 866–871.Google Scholar
Moss, D., Barker, D. M., Brandenburg, A. & Tuominen, I. 1995 Nonaxisymmetric dynamo solutions and extended starspots on late type stars. Astron. Astrophys. 294, 155–164.Google Scholar
Moss, D. & Brandenburg, A. 1995 The generation of nonaxisymmetric magnetic fields in the giant planets. Geophys. Astrophys. Fluid Dyn. 80, 229–240.Google Scholar
Moss, D., Brandenburg, A. & Tuominen, I. 1991 Properties of mean field dynamos with nonaxisymmetric $\unicode[STIX]{x1D6FC}$ -effect. Astron. Astrophys. 247, 576–579.Google Scholar
Moss, D., Tuominen, I. & Brandenburg, A. 1990 Nonlinear dynamos with magnetic buoyancy in spherical geometry. Astron. Astrophys. 228, 284–294.Google Scholar
Nandy, D. & Choudhuri, A. R. 2002 Explaining the latitudinal distribution of sunspots with deep meridional. Science 296, 1671–1673.Google Scholar
Nandy, D., Muñoz-Jaramillo, A. & Martens, P. C. H. 2011 The unusual minimum of sunspot cycle 23 caused by meridional plasma flow variations. Nature 471, 80–82.Google Scholar
Nelson, N. J., Brown, B. P., Brun, A. S., Miesch, M. S. & Toomre, J. 2013 Magnetic wreaths and cycles in convective dynamos. Astrophys. J. 762, 73.Google Scholar
Nelson, N. J., Brown, B. P., Brun, A. S., Miesch, M. S. & Toomre, J. 2014 Buoyant magnetic loops generated by global convective dynamo action. Sol. Phys. 289, 441–458.Google Scholar
Nelson, N. J. & Miesch, M. S. 2014 Generating buoyant magnetic flux ropes in solar-like convective dynamos. Plasma Phys. Control. Fusion 56, 064004.Google Scholar
Nordlund, Å., Brandenburg, A., Jennings, R. L., Rieutord, M., Ruokolainen, J., Stein, R. F. & Tuominen, I. 1992 Dynamo action in stratified convection with overshoot. Astrophys. J. 392, 647–652.Google Scholar
Noyes, R. W., Hartmann, L., Baliunas, S. L., Duncan, D. K. & Vaughan, A. H. 1984a Rotation, convection, and magnetic activity in lower main-sequence stars. Astrophys. J. 279, 763–777.Google Scholar
Noyes, R. W., Weiss, N. O. & Vaughan, A. H. 1984b The relation between stellar rotation rate and activity cycle periods. Astrophys. J. 287, 769–773.Google Scholar
Olesen, P. 1997 Inverse cascades and primordial magnetic fields. Phys. Lett. B 398, 321–325.Google Scholar
Olspert, N., Lehtinen, J. J., Käpylä, M. J., Pelt, J. & Grigorievskiy, A. 2018 Estimating activity cycles with probabilistic methods II. The Mount Wilson Ca H&K data. Astron. Astrophys. (submitted), arXiv:1712.08240.Google Scholar
O’Mara, B., Miesch, M. S., Featherstone, N. A. & Augustson, K. C. 2016 Velocity amplitudes in global convection simulations: the role of the Prandtl number and near-surface driving. Adv. Space Res. 58, 1475–1489.Google Scholar
Ossendrijver, M., Stix, M. & Brandenburg, A. 2001 Magnetoconvection and dynamo coefficients: dependence of the $\unicode[STIX]{x1D6FC}$ -effect on rotation and magnetic field. Astron. Astrophys. 376, 713–726.Google Scholar
Park, K. & Blackman, E. G. 2012a Comparison between turbulent helical dynamo simulations and a non-linear three-scale theory. Mon. Not. R. Astron. Soc. 419, 913–924.Google Scholar
Park, K. & Blackman, E. G. 2012b Simulations of a magnetic fluctuation driven large-scale dynamo and comparison with a two-scale model. Mon. Not. R. Astron. Soc. 423, 2120–2131.Google Scholar
Parker, E. N. 1955a Hydromagnetic dynamo models. Astrophys. J. 122, 293–314.Google Scholar
Parker, E. N. 1955b The formation of sunspots from the solar toroidal field. Astrophys. J. 121, 491–507.Google Scholar
Parker, E. N. 1971a The generation of magnetic fields in astrophysical bodies. II. The galactic field. Astrophys. J. 163, 255–278.Google Scholar
Parker, E. N. 1971b The generation of magnetic fields in astrophysical bodies. IV. The solar and terrestrial dynamos. Astrophys. J. 164, 491–509.Google Scholar
Parker, E. N. 1975 The generation of magnetic fields in astrophysical bodies. X. Magnetic buoyancy and the solar dynamo. Astrophys. J. 198, 205–209.Google Scholar
Parker, E. N. 1979 Cosmical Magnetic Fields. Clarendon Press.Google Scholar
Parker, E. N. 1987 The dynamo dilemma. Sol. Phys. 110, 11–21.Google Scholar
Parker, E. N. 1992 Fast dynamos, cosmic rays, and the galactic magnetic field. Astrophys. J. 401, 137–145.Google Scholar
Pavlović, P., Leite, N. & Sigl, G. 2017 Chiral magnetohydrodynamic turbulence. Phys. Rev. D 96, 023504.Google Scholar
Perri, B. & Brandenburg, A. 2018 Spontaneous flux concentrations from the negative effective magnetic pressure instability beneath a radiative stellar surface. Astron. Astrophys. 609, A99.Google Scholar
Piontek, R. A. & Ostriker, E. C. 2007 Models of vertically stratified two-phase ISM disks with MRI-driven turbulence. Astrophys. J. 663, 183–203.Google Scholar
Pipin, V. V. 2008 The mean electro-motive force and current helicity under the influence of rotation, magnetic field and shear. Geophys. Astrophys. Fluid Dyn. 102, 21–49.Google Scholar
Pipin, V. V. 2015 Dependence of magnetic cycle parameters on period of rotation in non-linear solar-type dynamos. Mon. Not. R. Astron. Soc. 451, 1528–1539.Google Scholar
Pipin, V. V. 2017 Non-linear regimes in mean-field full-sphere dynamo. Mon. Not. R. Astron. Soc. 466, 3007–3020.Google Scholar
Pipin, V. V. & Kosovichev, A. G. 2011 The subsurface-shear-shaped solar $\unicode[STIX]{x1D6FC}\unicode[STIX]{x1D6FA}$ dynamo. Astrophys. J. 727, L45.Google Scholar
Pipin, V. V. & Kosovichev, A. G. 2013 The mean-field solar dynamo with a double cell meridional circulation pattern. Astrophys. J. 776, 36.Google Scholar
Pipin, V. V. & Kosovichev, A. G. 2016 Dependence of stellar magnetic activity cycles on rotational period in a nonlinear solar-type dynamo. Astrophys. J. 823, 133.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
Pipin, V. V., Kuzanyan, K. M., Zhang, H. & Kosovichev, A. G. 2011 Turbulent cross-helicity in the mean-field solar dynamo problem. Astrophys. J. 743, 160.Google Scholar
Pipin, V. V., Sokoloff, D. D., Zhang, H. & Kuzanyan, K. M. 2013a Helicity conservation in nonlinear mean-field solar dynamo. Astrophys. J. 768, 46.Google Scholar
Pipin, V. V., Zhang, H., Sokoloff, D. D., Kuzanyan, K. M. & Gao, Y. 2013b The origin of the helicity hemispheric sign rule reversals in the mean-field solar-type dynamo. Mon. Not. R. Astron. Soc. 435, 2581–2588.Google Scholar
Pouquet, A., Frisch, U. & Léorat, J. 1976 Strong MHD helical turbulence and the nonlinear dynamo effect. J. Fluid Mech. 77, 321–354.Google Scholar
Proctor, M. R. E. 2007 Effects of fluctuation on alpha-omega dynamo models. Mon. Not. R. Astron. Soc. 382, L39–L42.Google Scholar
Pulkkinen, P., Tuominen, I., Brandenburg, A., Nordlund, Å. & Stein, R. F. 1993 Rotational effects on convection simulated at different latitudes. Astron. Astrophys. 267, 265–275.Google Scholar
Racine, É., Charbonneau, P., Ghizaru, M., Bouchat, A. & Smolarkiewicz, P. K. 2011 On the mode of dynamo action in a global large-eddy simulation of solar convection. Astrophys. J. 735, 46.Google Scholar
Rädler, K.-H. 1969 On some electromagnetic phenomena in electrically conducting turbulently moving matter, especially in the presence of Coriolis forces. Geodyn. Geophys. Veröff., Reihe II 13, 131–135.Google Scholar
Rädler, K.-H. 1973 Zur Dynamotheorie kosmischer Magnetfelder. I. Gleichungen für sphärische Dynamomodelle. Astron. Nachr. 294, 213–223.Google Scholar
Rädler, K.-H. 1976 Mean-field magnetohydrodynamics as a basis of solar dynamo theory. In Basic Mechanisms of Solar Activity, Proceedings from IAU Symposium No. 71 held in Prague, Czechoslovakia (ed. Bumba, V. & Kleczek, J.), pp. 323–344. D. Reidel Publishing Company Dordrecht.Google Scholar
Rädler, K.-H. 1980 Mean field approach to spherical dynamo models. Astron. Astrophys. 301, 101–129.Google Scholar
Rädler, K.-H. 1986a Investigations of spherical kinematic mean-field dynamo models. Astron. Nachr. 307, 89–113.Google Scholar
Rädler, K.-H. 1986b On the effect of differential rotation on axisymmetric and non-axisymmetric magnetic fields of cosmical bodies. Plasma Phys. ESA SP‐251, 569–574.Google Scholar
Rädler, K.-H. 1990 The solar dynamo. In Inside the Sun (ed. Berthomieu, G. & Cribier, M.), pp. 385–402. Kluwer.Google Scholar
Rädler, K.-H. 1995 Cosmic dynamos. Rev. Mod. Astr. 8, 295–322.Google Scholar
Rädler, K.-H. 2014 Mean-field dynamos: the old concept and some recent developments. Karl Schwarzschild Award Lecture 2013. Astron. Nachr. 335, 459–469.Google Scholar
Rädler, K.-H. & Brandenburg, A. 2009 Mean-field effects in the Galloway–Proctor flow. Mon. Not. R. Astron. Soc. 393, 113–125.Google Scholar
Rädler, K.-H., Brandenburg, A., Del Sordo, F. & Rheinhardt, M. 2011 Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows. Phys. Rev. E 84, 4.Google Scholar
Rädler, K.-H., Kleeorin, N. & Rogachevskii, I. 2003 The mean electromotive force for MHD turbulence: the case of a weak mean magnetic field and slow rotation. Geophys. Astrophys. Fluid Dyn. 97, 249–274.Google Scholar
Rädler, K.-H. & Ness, N. F. 1990 The symmetry properties of planetary magnetic fields. J. Geophys. Res. 95, 2311–2318.Google Scholar
Rädler, K.-H. & Rheinhardt, M. 2007 Mean-field electrodynamics: critical analysis of various analytical approaches to the mean electromotive force. Geophys. Astrophys. Fluid Dyn. 101, 11–48.Google Scholar
Rädler, K.-H., Rheinhardt, M., Apstein, E. & Fuchs, H. 2002a On the mean-field theory of the Karlsruhe dynamo experiment I. Kinematic theory. Magnetohydrodynamics 38, 41–71.Google Scholar
Rädler, K.-H., Rheinhardt, M., Apstein, E. & Fuchs, H. 2002b On the mean-field theory of the Karlsruhe dynamo experiment II. Back-reaction of the magnetic field on the fluid flow. Magnetohydrodynamics 38, 73–94.Google Scholar
Rädler, K.-H., Rheinhardt, M., Apstein, E. & Fuchs, H. 2002c On the mean-field theory of the Karlsruhe dynamo experiment. Nonlinear Process. Geophys. 38, 171–187.Google Scholar
Rädler, K.-H. & Stepanov, R. 2006 Mean electromotive force due to turbulence of a conducting fluid in the presence of mean flow. Phys. Rev. E 73, 056311.Google Scholar
Rädler, K.-H. & Wiedemann, E. 1989 Numerical experiments with a simple nonlinear mean-field dynamo model. Geophys. Astrophys. Fluid Dyn. 49, 71–80.Google Scholar
Rädler, K.-H., Wiedemann, E., Brandenburg, A., Meinel, R. & Tuominen, I. 1990 Nonlinear mean-field dynamo models: stability and evolution of three-dimensional magnetic field configurations. Astron. Astrophys. 239, 413–423.Google Scholar
Reinhold, T. & Arlt, R. 2015 Discriminating solar and antisolar differential rotation in high-precision light curves. Astron. Astrophys. 576, A15.Google Scholar
Rempel, M. 2005 Solar differential rotation and meridional flow: the role of a subadiabatic tachocline for the Taylor–Proudman balance. Astrophys. J. 622, 1320–1332.Google Scholar
Rempel, M. 2017 Extension of the MURaM radiative MHD code for coronal simulations. Astrophys. J. 834, 10.Google Scholar
Rempel, M. & Cheung, M. C. M. 2014 Numerical simulations of active region scale flux emergence: from spot formation to decay. Astrophys. J. 785, 90.Google Scholar
Rheinhardt, M. & Brandenburg, A. 2010 Test-field method for mean-field coefficients with MHD background. Astron. Astrophys. 520, A28.Google Scholar
Rheinhardt, M. & Brandenburg, A. 2012 Modeling spatio-temporal nonlocality in mean-field dynamos. Astron. Nachr. 333, 71–77.Google Scholar
Rheinhardt, M., Devlen, E., Rädler, K.-H. & Brandenburg, A. 2014 Mean-field dynamo action from delayed transport. Mon. Not. R. Astron. Soc. 441, 116–126.Google Scholar
Rieutord, M., Brandenburg, A., Mangeney, A. & Drossart, P. 1994 Reynolds stress and differential rotation in Boussinesq convection in a rotating spherical shell. Astron. Astrophys. 286, 471–480.Google Scholar
Roberts, G. O. 1972 Dynamo action of fluid motions with two-dimensional periodicity. Phil. Trans. R. Soc. Lond. A A 271, 411–454; doi:10.1098/rsta.1972.0015.Google Scholar
Roberts, P. H. 1972 Kinematic dynamo models. Phil. Trans. R. Soc. Lond. A A272, 663–698; doi:10.1098/rsta.1972.0074.Google Scholar
Roberts, P. H. & Soward, A. M. 1975 A unified approach to mean field electrodynamics. Astron. Nachr. 296, 49–64.Google Scholar
Roberts, P. H. & Soward, A. M. 1992 Dynamo theory. Ann. Rev. Fluid Dyn. 24, 459–512.Google Scholar
Roberts, P. H. 1993 Dynamo theory. In Astrophysical Fluid Dynamics (ed. Zahn, J.-P. & Zinn-Justin, J.), pp. 229–323. North-Holland.Google Scholar
Rogachevskii, I. & Kleeorin, N. 1997 Intermittency and anomalous scaling for magnetic fluctuations. Phys. Rev. E 56, 417–426.Google Scholar
Rogachevskii, I. & Kleeorin, N. 2003 Electromotive force and large-scale magnetic dynamo in a turbulent flow with a mean shear. Phys. Rev. E 68, 036301.Google Scholar
Rogachevskii, I. & Kleeorin, N. 2004 Nonlinear theory of a ‘shear–current’ effect and mean-field magnetic dynamos. Phys. Rev. E 70, 046310.Google Scholar
Rogachevskii, I. & Kleeorin, N. 2007 Magnetic fluctuations and formation of large-scale inhomogeneous magnetic structures in a turbulent convection. Phys. Rev. E 76, 056307.Google Scholar
Rogachevskii, I., Kleeorin, N., Brandenburg, A. & Eichler, D. 2012 Cosmic-ray current-driven turbulence and mean-field dynamo effect. Astrophys. J. 753, 6.Google Scholar
Rogachevskii, I., Ruchayskiy, O., Boyarsky, A., Fröhlich, J., Kleeorin, N., Brandenburg, A. & Schober, J. 2017 Laminar and turbulent dynamos in chiral magnetohydrodynamics. I. Theory. Astrophys. J. 846, 153.Google Scholar
Rosén, L., Kochukhov, O., Hackman, T. & Lehtinen, J. 2016 Magnetic fields of young solar twins. Astron. Astrophys. 593, A35.Google Scholar
Rüdiger, G. 1978 On the $\unicode[STIX]{x1D6FC}$ -effect for slow and fast rotation. Astron. Nachr. 299, 217–222.Google Scholar
Rüdiger, G. 1980 Reynolds stresses and differential rotation I. On recent calculations of zonal fluxes in slowly rotating stars. Geophys. Astrophys. Fluid Dyn. 16, 239–261.Google Scholar
Rüdiger, G. 1989 Differential Rotation and Stellar Convection: Sun and Solar-type Stars. Gordon & Breach.Google Scholar
Rüdiger, G. & Hollerbach, R. 2004 The Magnetic Universe. Wiley-VCH.Google Scholar
Rüdiger, G. & Kitchatinov, L. L. 1993 Alpha-effect and alpha-quenching. Astron. Astrophys. 269, 581–588.Google Scholar
Rüdiger, G. & Kitchatinov, L. L. 2006 Do mean-field dynamos in nonrotating turbulent shear-flows exist? Astron. Nachr. 327, 298–303.Google Scholar
Rüdiger, G. & Pipin, V. V. 2000 Viscosity-alpha and dynamo-alpha for magnetically driven compressible turbulence in Kepler disks. Astron. Astrophys. 362, 756–761.Google Scholar
Rüdiger, G. & Spahn, F. 1992 On the stability of mean-field models of the solar convection zone. Sol. Phys. 138, 1–9.Google Scholar
Rüdiger, G., Kitchatinov, L. L. & Brandenburg, A. 2011 Cross helicity and turbulent magnetic diffusivity in the solar convection zone. Sol. Phys. 269, 3–12.Google Scholar
Rüdiger, G., Pipin, V. V. & Belvedère, G. 2001 Alpha-effect, helicity and angular momentum transport for a magnetically driven turbulence in the solar convection zone. Sol. Phys. 198, 241–251.Google Scholar
Ruzmaikin, A. A., Sokoloff, D. D. & Shukurov, A. M. 1988 Magnetic Fields of Galaxies. Kluwer.Google Scholar
Salvesen, G., Simon, J. B., Armitage, P. J. & Begelman, M. C. 2016 Accretion disc dynamo activity in local simulations spanning weak-to-strong net vertical magnetic flux regimes. Mon. Not. R. Astron. Soc. 457, 857–874.Google Scholar
Sandars, P. G. H. 2003 A toy model for the generation of homochirality during polymerization. Orig. Life Evol. Biosph. 33, 575–587.Google Scholar
Schekochihin, A. A., Haugen, N. E. L., Brandenburg, A., Cowley, S. C., Maron, J. L. & McWilliams, J. C. 2005 Onset of small scale dynamo at small magnetic Prandtl numbers. Astrophys. J. 625, L115–L118.Google Scholar
Schmitt, D. & Schüssler, M. 1989 Non-linear dynamos. I. One-dimensional model of a thin layer dynamo. Astron. Astrophys. 223, 343–351.Google Scholar
Schober, J., Rogachevskii, I., Brandenburg, A., Boyarsky, A., Fröhlich, J., Ruchayskiy, O. & Kleeorin, N. 2018 Laminar and turbulent dynamos in chiral magnetohydrodynamics. II. Simulations. Astrophys. J. 858, 124.Google Scholar
Schou, J., Antia, H. M., Basu, S., Bogart, R. S., Bush, R. I., Chitre, S. M., Christensen-Dalsgaard, J., di Mauro, M. P., Dziembowski, W. A., Eff-Darwich, A. et al. 1998 Helioseismic studies of differential rotation in the solar envelope by the solar oscillations investigation using the Michelson Doppler Imager. Astrophys. J. 505, 390–417.Google Scholar
Schrijver, C. J. 1983 Coronal activity in F-, G-, and K-type stars. I – Relations between parameters characterizing stellar structure and activity. Astron. Astrophys. 127, 289–296.Google Scholar
Schrijver, C. J., Cote, J., Zwaan, C. & Saar, S. H. 1989 Relations between the photospheric magnetic field and the emission from the outer atmospheres of cool stars. I. The solar Ca II K line core emission. Astrophys. J. 337, 964–976.Google Scholar
Schrinner, M., Rädler, K.-H., Schmitt, D., Rheinhardt, M. & Christensen, U. 2005 Mean-field view on rotating magnetoconvection and a geodynamo model. Astron. Nachr. 326, 245–249.Google Scholar
Schrinner, M., Rädler, K.-H., Schmitt, D., Rheinhardt, M. & Christensen, U. R. 2007 Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo. Geophys. Astrophys. Fluid Dyn. 101, 81–116.Google Scholar
See, V., Jardine, M., Vidotto, A. A., Donati, J.-F., Boro Saikia, S., Bouvier, J., Fares, R., Folsom, C. P., Gregory, S. G., Hussain, G. et al. 2016 The connection between stellar activity cycles and magnetic field topology. Mon. Not. R. Astron. Soc. 462, 4442–4450.Google Scholar
Sellwood, J. A. & Balbus, S. A. 1999 Differential rotation and turbulence in extended HI disks. Astrophys. J. 511, 660–665.Google Scholar
She, Z.-S., Jackson, E. & Orszag, S. A. 1990 Intermittent vortex structures in homogeneous isotropic turbulence. Nature 344, 226–228.Google Scholar
Shi, J.-M., Stone, J. M. & Huang, C. X. 2016 Saturation of the magnetorotational instability in the unstratified shearing box with zero net flux: convergence in taller boxes. Mon. Not. R. Astron. Soc. 456, 2273–2289.Google Scholar
Shukurov, A. 1998 Magnetic spiral arms in galaxies. Mon. Not. R. Astron. Soc. 299, L21–L24.Google Scholar
Simard, C., Charbonneau, P. & Dubé, C. 2016 Characterization of the turbulent electromotive force and its magnetically-mediated quenching in a global EULAG-MHD simulation of solar convection. Astrophys. Space Sci. 58, 1522–1537.Google Scholar
Singh, N. K., Käpylä, M. J., Brandenburg, A., Käpylä, P. J., Lagg, A. & Virtanen, I. 2018 Bihelical spectrum of solar magnetic helicity and its evolution. Astrophys. J. (in press), arXiv:1804.04994.Google Scholar
Sokoloff, D. D. & Shukurov, A. M. 1990 Regular magnetic fields in coronae of spiral galaxies. Nature 347, 51–53.Google Scholar
Solanki, S. K., Inhester, B. & Schüssler, M. 2006 The solar magnetic field. Rep. Prog. Phys. 69, 563–668.Google Scholar
Snellman, J. E., Käpylä, P. J., Korpi, M. J. & Liljeström, A. J. 2009 Reynolds stresses from hydrodynamic turbulence with shear and rotation. Astron. Astrophys. 505, 955–968.Google Scholar
Snodin, A. P., Brandenburg, A., Mee, A. J. & Shukurov, A. 2006 Simulating field-aligned diffusion of a cosmic ray gas. Mon. Not. R. Astron. Soc. 373, 643–652.Google Scholar
Squire, J. & Bhattacharjee, A. 2015 Electromotive force due to magnetic fluctuations in sheared rotating turbulence. Phys. Rev. E 92, 053101.Google Scholar
Squire, J. & Bhattacharjee, A. 2016 The magnetic shear-current effect: generation of large-scale magnetic fields by the small-scale dynamo. J. Plasma Phys. 82, 535820201.Google Scholar
Spruit, H. 1997 Convection in stellar envelopes: a changing paradigm. Mem. Soc. Astron. Ital. 68, 397–413.Google Scholar
Sridhar, S. & Subramanian, K. 2009 Nonperturbative quasilinear approach to the shear dynamo problem. Phys. Rev. E 80, 066315.Google Scholar
Steenbeck, M. & Krause, F. 1969a Zur Dynamotheorie stellarer und planetarer Magnetfelder I. Berechnung sonnenähnlicher Wechselfeldgeneratoren. Astron. Nachr. 291, 49–84.Google Scholar
Steenbeck, M. & Krause, F. 1969b Zur Dynamotheorie stellarer und planetarer Magnetfelder II. Berechnung planetenähnlicher Gleichfeldgeneratoren. Astron. Nachr. 291, 271–286.Google Scholar
Steenbeck, M., Krause, F. & Rädler, K.-H. 1966 Berechnung der mittleren Lorentz-Feldstärke $\overline{\boldsymbol{v}\times \boldsymbol{B}}$ für ein elektrisch leitendes Medium in turbulenter, durch Coriolis–Kräfte beeinflußter Bewegung. Z. Naturforsch. 21a, 369–376; see also the translation in Roberts & Stix, The turbulent dynamo, Tech. Note 60, NCAR, Boulder, Colorado, 1971.Google Scholar
Stefani, F. & Gerbeth, G. 2003 Oscillatory mean-field dynamos with a spherically symmetric, isotropic helical turbulence parameter $\unicode[STIX]{x1D6FC}$ . Phys. Rev. E 67, 027302.Google Scholar
Stix, M. 1974 Comments on the solar dynamo. Astron. Astrophys. 37, 121–133.Google Scholar
Stone, J. M., Hawley, J. F., Gammie, C. F. & Balbus, S. A. 1996 Three dimensional magnetohydrodynamical simulations of vertically stratified accretion disks. Astrophys. J. 463 656–673.Google Scholar
Strassmeier, K. G., Kratzwald, L. & Weber, M. 2003 Doppler imaging of stellar surface structure. XX. The rapidly-rotating single K2-giant HD 31 993 $=$ V1192 Orionis. Astron. Astrophys. 408, 1103–1113.Google Scholar
Strugarek, A., Beaudoin, P., Charbonneau, P., Brun, A. S. & do Nascimento, J.-D. 2017 Reconciling solar and stellar magnetic cycles with nonlinear dynamo simulations. Science 357, 185–187.Google Scholar
Subramanian, K. 1999 Unified treatment of small- and large-scale dynamos in helical turbulence. Phys. Rev. Lett. 83, 2957–2960.Google Scholar
Subramanian, K. 2002 Magnetic helicity in galactic dynamos. Bull. Austral. Soc. India 30, 715–721.Google Scholar
Subramanian, K. & Brandenburg, A. 2006 Magnetic helicity density and its flux in weakly inhomogeneous turbulence. Astrophys. J. 648, L71–L74.Google Scholar
Subramanian, K. & Brandenburg, A. 2014 Traces of large-scale dynamo action in the kinematic stage. Mon. Not. R. Astron. Soc. 445, 2930–2940.Google Scholar
Sur, S., Brandenburg, A. & Subramanian, K. 2008 Kinematic alpha effect in isotropic turbulence simulations. Mon. Not. R. Astron. Soc. 385, L15–L19.Google Scholar
Syntelis, P., Archontis, V., Gontikakis, C. & Tsinganos, K. 2015 Emergence of non-twisted magnetic fields in the sun: jets and atmospheric response. Astron. Astrophys. 584, A10.Google Scholar
Taylor, A. M., Vovk, I. & Neronov, A. 2011 Extragalactic magnetic fields constraints from simultaneous GeV-TeV observations of blazars. Astron. Astrophys. 529, A144.Google Scholar
Thompson, M. J., Christensen-Dalsgaard, J., Miesch, M. S. & Toomre, J. 2003 The internal rotation of the sun. Annu. Rev. Astron. Astrophys. 41, 599–643.Google Scholar
Tilgner, A. & Brandenburg, A. 2008 A growing dynamo from a saturated Roberts flow dynamo. Mon. Not. R. Astron. Soc. 391, 1477–1481.Google Scholar
Tobias, S. M. & Marston, J. B. 2013 Direct statistical simulation of out-of-equilibrium jets. Phys. Rev. Lett. 110, 104502.Google Scholar
Tobias, S. M. & Marston, J. B. 2017 Direct statistical simulation of jets and vortices in 2D flows. Phys. Fluids 29, 111111.Google Scholar
Tobias, S. M., Brummell, N. H., Clune, T. L. & Toomre, J. 1998b Pumping of magnetic fields by turbulent penetrative convection. Astrophys. J. Lett. 502, L177–L177.Google Scholar
Tobias, S. M., Brummell, N. H., Clune, T. L. & Toomre, J. 2001 Transport and storage of magnetic field by overshooting turbulent compressible convection. Astrophys. J. 549, 1183–1203.Google Scholar
Tobias, S. M., Proctor, M. R. E. & Knobloch, E. 1997 The role of absolute instability in the solar dynamo. Astron. Astrophys. 318, L55–L58.Google Scholar
Tobias, S. M., Proctor, M. R. E. & Knobloch, E. 1998a Convective and absolute instabilities of fluid flows in finite geometry. Physica D 113, 43–72.Google Scholar
Tuominen, I. & Rüdiger, G. 1989 Solar differential rotation as a multiparameter turbulence problem. Astron. Astrophys. 217, 217–228.Google Scholar
Tuominen, I., Brandenburg, A., Moss, D. & Rieutord, M. 1994 Does solar differential rotation arise from a large scale instability? Astron. Astrophys. 284, 259–264.Google Scholar
Tziotziou, K., Georgoulis, M. K. & Liu, Y. 2013 Interpreting eruptive behavior in NOAA AR 11158 via the region’s magnetic energy and relative-helicity budgets. Astrophys. J. 772, 115.Google Scholar
Vainshtein, S. I. & Cattaneo, F. 1992 Nonlinear restrictions on dynamo action. Astrophys. J. 393, 165–171.Google Scholar
Vainshtein, S. I. & Ruzmaikin, A. A. 1971 Generation of the large-scale Galactic magnetic field. Astron. Zh. 48, 902–909.Google Scholar
Vemareddy, P., Ambastha, A., Maurya, R. A. & Chae, J. 2012 On the injection of helicity by the shearing motion of fluxes in relation to flares and coronal mass ejections. Astrophys. J. 761, 86.Google Scholar
Vilhu, O. 1984 The nature of magnetic activity in lower main sequence stars. Astron. Astrophys. 133, 117–126.Google Scholar
Vishniac, E. T. & Brandenburg, A. 1997 An incoherent $\unicode[STIX]{x1D6FC}$ – $\unicode[STIX]{x1D6FA}$ dynamo in accretion disks. Astrophys. J. 475, 263–274.Google Scholar
Vitense, E. 1953 Die Wasserstoffkonvektionszone der Sonne. Z. Astrophys. 32, 135–164.Google Scholar
Viviani, M., Warnecke, J., Käpylä, M. J., Käpylä, P. J., Olspert, N., Cole-Kodikara, E. M., Lehtinen, J. J. & Brandenburg, A. 2018 Transition from axi- to nonaxisymmetric dynamo modes in spherical convection models of solar-like stars. Astron. Astrophys, doi:10.1051/0004-6361/201732191.Google Scholar
Wang, H., Liu, C., Deng, N., Zeng, Z., Xu, Y., Jing, J. & Cao, W. 2014 Study of two successive three-ribbon solar flares on 2012 July 6. Astrophys. J. Lett. 781, L23.Google Scholar
Warnecke, J. 2018 Dynamo cycles in global convection simulations of solar-like stars. Astron. Astrophys, doi:10.1051/0004-6361/201732413.Google Scholar
Warnecke, J., Brandenburg, A. & Mitra, D. 2011 Dynamo-driven plasmoid ejections above a spherical surface. Astron. Astrophys. 534, A11.Google Scholar
Warnecke, J., Brandenburg, A. & Mitra, D. 2012 Magnetic twist: a source and property of space weather. J. Space Weather Space Clim. 2, A11.Google Scholar
Warnecke, J., Käpylä, P. J., Käpylä, M. J. & Brandenburg, A. 2014 On the cause of solar-like equatorward migration in global convective dynamo simulations. Astrophys. J. Lett. 796, L12.Google Scholar
Warnecke, J., Losada, I. R., Brandenburg, A., Kleeorin, N. & Rogachevskii, I. 2013 Bipolar magnetic structures driven by stratified turbulence with a coronal envelope. Astrophys. J. Lett. 777, L37.Google Scholar
Warnecke, J., Losada, I. R., Brandenburg, A., Kleeorin, N. & Rogachevskii, I. 2016 Bipolar region formation in stratified two-layer turbulence. Astron. Astrophys. 589, A125.Google Scholar
Warnecke, J., Rheinhardt, M., Käpylä, P. J., Käpylä, M. J. & Brandenburg, A. 2018 Turbulent transport coefficients in spherical wedge dynamo simulations of solar-like stars. Astron. Astrophys. 609, A51.Google Scholar
Weber, M., Strassmeier, K. G. & Washuettl, A. 2005 Indications for anti-solar differential rotation of giant stars. Astron. Nachr. 326, 287–291.Google Scholar
Wilson, O. C. 1978 Chromospheric variations in main-sequence stars. Astrophys. J. 266, 379–396.Google Scholar
Worledge, D., Knobloch, E., Tobias, S. & Proctor, M. 1997 Dynamo waves in semi-infinite and finite domains. Proc. R. Soc. Lond. A 453, 119–143.Google Scholar
Yokoi, N. 2013 Cross helicity and related dynamo. Geophys. Astrophys. Fluid Dyn. 107, 114–184.Google Scholar
Yokoi, N., Schmitt, D., Pipin, V. & Hamba, F. 2016 A new simple dynamo model for stellar activity cycle. Astrophys. J. 824, 67.Google Scholar
Yoshizawa, A. & Yokoi, N. 1993 Turbulent magnetohydrodynamic dynamo effect for accretion disks using the cross-helicity effect. Astrophys. J. 407, 540–548.Google Scholar
Yoshimura, H. 1975 A model of the solar cycle driven by the dynamo action of the global convection in the solar convection zone. Astrophys. J. Suppl. 29, 467–494.Google Scholar
Yousef, T. A., Brandenburg, A. & Rüdiger, G. 2003 Turbulent magnetic Prandtl number and magnetic diffusivity quenching from simulations. Astron. Astrophys. 411, 321–327.Google Scholar
Yousef, T. A., Heinemann, T., Schekochihin, A. A., Kleeorin, N., Rogachevskii, I., Iskakov, A. B., Cowley, S. C. & McWilliams, J. C. 2008a Generation of magnetic field by combined action of turbulence and shear. Phys. Rev. Lett. 100, 184501.Google Scholar
Yousef, T. A., Heinemann, T., Rincon, F., Schekochihin, A. A., Kleeorin, N., Rogachevskii, I., Cowley, S. C. & McWilliams, J. C. 2008b Numerical experiments on dynamo action in sheared and rotating turbulence. Astron. Nachr. 329, 737–749.Google Scholar
Zeldovich, Ya. B. 1957 The magnetic field in the two-dimensional motion of a conducting turbulent liquid. Sov. Phys. JETP 4, 460–462.Google Scholar
Zeldovich, Ya. B., Ruzmaikin, A. A. & Sokoloff, D. D. 1983 Magnetic Fields in Astrophysics. Gordon & Breach.Google Scholar
Zhao, J., Bogart, R. S., Kosovichev, A. G., Duvall, T. L. Jr & Hartlep, T. 2013 Detection of equatorward meridional flow and evidence of double-cell meridional circulation inside the sun. Astrophys. J. 774, L29.Google Scholar
Zhang, H., Brandenburg, A. & Sokoloff, D. D. 2014 Magnetic helicity and energy spectra of a solar active region. Astrophys. J. Lett. 784, L45.Google Scholar
Zhang, H., Brandenburg, A. & Sokoloff, D. D. 2016 Evolution of magnetic helicity and energy spectra of solar active regions. Astrophys. J. 819, 146.Google Scholar
Ziegler, U. & Rüdiger, G. 2000 Angular momentum transport and dynamo-effect in stratified, weakly magnetic disks. Astron. Astrophys. 356, 1141–1148.Google Scholar
Zrake, J. 2014 Inverse cascade of nonhelical magnetic turbulence in a relativistic fluid. Astrophys. J. 794, L26.Google Scholar