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Flows and dynamos in a model of stellar radiative zones

Part of: 50 years of Mean Field Electrodynamics

Published online by Cambridge University Press:  25 June 2018

Radostin D. Simitev Open the ORCID record for Radostin D. Simitev [Opens in a new window]  and
Friedrich H. Busse
Radostin D. Simitev*
Affiliation:
School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QQ, UK
Friedrich H. Busse
Affiliation:
Institute of Physics, University of Bayreuth, Bayreuth 95440, Germany
*
†Email address for correspondence: [email protected]
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Abstract

Stellar radiative zones are typically assumed to be motionless in standard models of stellar structure but there is sound theoretical and observational evidence that this cannot be the case. We investigate by direct numerical simulations a three-dimensional and time-dependent model of stellar radiation zones consisting of an electrically conductive and stably stratified anelastic fluid confined to a rotating spherical shell and driven by a baroclinic torque. As the baroclinic driving is gradually increased a sequence of transitions from an axisymmetric and equatorially symmetric time-independent flow to flows with a strong poloidal component and lesser symmetry are found. It is shown that all flow regimes characterised by significant non-axisymmetric components are capable of generating a self-sustained magnetic field. As the value of the Prandtl number is decreased and the value of the Ekman number is decreased, flows become strongly time dependent with progressively complex spatial structure and dynamos can be generated at lower values of the magnetic Prandtl number.

Keywords

astrophysical plasmasplasma flows
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 3 , June 2018 , 735840308
Copyright
© Cambridge University Press 2018 

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References

Aerts, C., Christensen-Dalsgaard, J. & Kurtz, D. 2010 Asteroseismology. Springer.Google Scholar
Braginsky, S. & Roberts, P. 1995 Equations governing convection in earth’s core and the geodynamo. Geophys. Astrophys. Fluid Dyn. 79 (1–4), 1–97.Google Scholar
Braithwaite, J. 2006 A differential rotation driven dynamo in a stably stratified star. Astron. Astrophys. 449, 451–460.Google Scholar
Brandenburg, A. & Subramanian, K. 2005 Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417 (1-4), 1–209.Google Scholar
Bullard, E. & Gellman, H. 1954 Homogeneous dynamos and terrestrial magnetism. Phil. Trans. R. Soc. A 247 (928), 213–278.Google Scholar
Busse, F. H. 1982 On the problem of stellar rotation. Astrophys. J. 259, 759–766.CrossRefGoogle Scholar
Busse, F. H. 2003 The sequence-of-bifurcations approach towards understanding turbulent fluid flow. Surv. Geophys. 24 (3), 269–288.Google Scholar
Busse, F. H., Grote, E. & Simitev, R. D. 2003 Convection in rotating spherical shells and its dynamo action. In Earth’s Core and Lower Mantle (ed. Jones, C., Soward, A. & Zhang, K.), pp. 130–152. Taylor & Francis.Google Scholar
Busse, F. H. & Simitev, R. D. 2005a Convection in rotating spherical fluid shells and its dynamo states. In The Fluid Mechanics of Astrophysics and Geophysics. CRC Press.Google Scholar
Busse, F. H. & Simitev, R. D. 2005b Dynamos driven by convection in rotating spherical shells. Astron. Nachr. 326 (3–4), 231–240.Google Scholar
Busse, F. H. & Simitev, R. D. 2011 Remarks on some typical assumptions in dynamo theory. Geophys. Astrophys. Fluid Dyn. 105, 234.Google Scholar
Chaplin, W. & Miglio, A. 2013 Asteroseismology of solar-type and red-giant stars. Annu. Rev. Astron. Astrophys. 51 (1), 353–392.CrossRefGoogle Scholar
Donati, J.-F. & Landstreet, J. 2009 Magnetic fields of nondegenerate stars. Annu. Rev. Astron. Astrophys. 47 (1), 333–370.Google Scholar
Dudley, M. L. & James, R. W. 1989 Time-dependent kinematic dynamos with stationary flows. Proc. R. Soc. Lond. A 425 (1869), 407–429.Google Scholar
Espinosa, L. & Rieutord, M. 2013 Self-consistent 2d models of fast-rotating early-type stars. Astron. Astrophys. 552, A35.Google Scholar
Fan, Y. & Fang, F. 2014 A simulation of convective dynamo in the solar convective envelope: maintenance of the solar-like differential rotation and emerging flux. Astrophys. J. 789 (1), 35.Google Scholar
Gastine, T., Yadav, R. K., Morin, J., Reiners, A. & Wicht, J. 2013 From solar-like to antisolar differential rotation in cool stars. Mon. Not. R. Astron. Soc. 438 (1), L76–L80.Google Scholar
Gizon, L., Birch, A. & Spruit, H. 2010 Local helioseismology: three-dimensional imaging of the solar interior. Annu. Rev. Astron. Astrophys. 48 (1), 289–338.Google Scholar
Gough, D. 1969 The anelastic approximation for thermal convection. J. Atmos. Sci. 26, 448.Google Scholar
Grote, E., Busse, F. H. & Simitev, R. D. 2002 Buoyancy driven convection in rotating spherical shells and its dynamo action. In High Performance Computing in Science and Engineering’01, pp. 12–34. Springer.Google Scholar
Gubbins, D. & Zhang, K. 1993 Symmetry properties of the dynamo equations for palaeomagnetism and geomagnetism. Phys. Earth Planet. Inter. 75 (4), 225–241.Google Scholar
Hypolite, D. & Rieutord, M. 2014 Dynamics of the envelope of a rapidly rotating star or giant planet in gravitational contraction. Astron. Astrophys. 572, A15.Google Scholar
Jones, C. A., Boronski, P., Brun, A. S., Glatzmaier, G. A., Gastine, T., Miesch, M. S. & Wicht, J. 2011 Anelastic convection-driven dynamo benchmarks. Icarus 216 (1), 120–135.Google Scholar
Kaiser, R. & Busse, F. H. 2017 On the robustness of the toroidal velocity theorem. Geophys. Astrophys. Fluid Dyn. 111 (5), 355–368.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. 2017 Convection-driven spherical shell dynamos at varying Prandtl numbers. Astron. Astrophys. 599, A4.Google Scholar
Karak, B. B., Käpylä, P. J., Käpylä, M. 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
Kerswell, R. R. 1993 Elliptical instabilities of stratified, hydromagnetic waves. Geophys. Astrophys. Fluid Dyn. 71 (1–4), 105–143.CrossRefGoogle Scholar
Lantz, S. & Fan, Y. 1999 Anelastic magnetohydrodynamic equations for modeling solar and stellar convection zones. Astrophys. J. Suppl. Ser. 121 (1), 247.Google Scholar
Latter, H. & Ivers, D. 2010 Spherical single-roll dynamos at large magnetic Reynolds numbers. Phys. Fluids 22 (6), 066601.Google Scholar
Le Bars, M. & Le Dizès, S. 2006 Thermo-elliptical instability in a rotating cylindrical shell. J. Fluid Mech. 563, 189.Google Scholar
Marti, P., Schaeffer, N., Hollerbach, R., Cébron, D., Nore, C., Luddens, F., Guermond, J.-L., Aubert, J., Takehiro, S., Sasaki, Y. et al. 2014 Full sphere hydrodynamic and dynamo benchmarks. Geophys. J. Int. 197 (1), 119–134.Google Scholar
Mathis, S. 2013 Transport processes in stellar interiors. In Studying Stellar Rotation and Convection: Theoretical Background and Seismic Diagnostics (ed. Goupil, M., Belkacem, K., Neiner, C., Lignières, F. & Green, J. J.), pp. 23–47. Springer.Google Scholar
Matsui, H., Heien, E., Aubert, J., Aurnou, J. M., Avery, M., Brown, B., Buffett, B. A., Busse, F. H., Christensen, U. R., Davies, C. J. et al. 2016 Performance benchmarks for a next generation numerical dynamo model. Geochem. Geophys. Geosyst. 17 (5), 1586–1607.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 heliophysics and astrophysics. Space Sci. Rev. 194 (1), 97–137.Google Scholar
Miesch, M. & Toomre, J. 2009 Turbulence, magnetism, and shear in stellar interiors. Annu. Rev. Fluid Mech. 41 (1), 317–345.Google Scholar
Rieutord, M. 2006 The dynamics of the radiative envelope of rapidly rotating stars. Astron. Astrophys. 451 (3), 1025–1036.Google Scholar
Rieutord, M. & Beth, A. 2014 Dynamics of the radiative envelope of rapidly rotating stars: effects of spin-down driven by mass loss. Astron. Astrophys. 570, A42.CrossRefGoogle Scholar
Rieutord, M. & Rincon, F. 2010 The Sun’s supergranulation. Living Rev. Solar Phys. 7:2.CrossRefGoogle Scholar
van Saders, J. L. & Pinsonneault, M. H. 2013 Fast star, slow star; old star, young star: subgiant rotation as a population and stellar physics diagnostic. Astrophys. J. 776 (2), 67.CrossRefGoogle Scholar
Schekochihin, A. A., Cowley, S. C., Maron, J. L. & McWilliams, J. C. 2004 Critical magnetic Prandtl number for small-scale dynamo. Phys. Rev. Lett. 9 (5), 054502.Google Scholar
Schekochihin, A. A., Haugen, N. E. L., Brandenburg, A., Cowley, S. C., Maron, J. L. & McWilliams, J. C. 2005 The onset of a small-scale turbulent dynamo at low magnetic Prandtl numbers. Astrophys. J. 625 (2), L115–L118.Google Scholar
Schwarzschild, M. 1947 On stellar rotation. Astrophys. J. 106, 427.Google Scholar
Simitev, R. D. & Busse, F. H. 2003 Patterns of convection in rotating spherical shells. New J. Phys. 5, 97.Google Scholar
Simitev, R. D. & Busse, F. H. 2012 Bistable attractors in a model of convection-driven spherical dynamos. Phys. Scr. 86 (1), 018409.Google Scholar
Simitev, R. D. & Busse, F. H. 2017 Baroclinically-driven flows and dynamo action in rotating spherical fluid shells. Geophys. Astrophys. Fluid Dyn. 111 (5), 369–379.Google Scholar
Simitev, R. D., Kosovichev, A. & Busse, F. H. 2015 Dynamo effects near the transition from solar to anti-solar differential rotation. Astrophys. J. 810 (1), 80.Google Scholar
Spruit, H. & Knobloch, E. 1984 Baroclinic instability in stars. Astron. Astrophys. 132, 89–96.Google Scholar
Sun, Z., Schubert, G. & Glatzmaier, G. 1993 Transitions to chaotic thermal convection in a rapidly rotating spherical fluid shell. Geophys. Astrophys. Fluid Dyn. 69 (1), 95–131.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 (1), 599–643.CrossRefGoogle Scholar
Tilgner, A. 1999 Spectral methods for the simulation of incompressible flows in spherical shells. Intl J. Numer. Meth. Fluids 30 (6), 713–724.Google Scholar
Turck-Chièze, S. & Talon, S. 2008 The dynamics of the solar radiative zone. Adv. Space Res. 41 (6), 855–860.Google Scholar
Vidal, J., Cébron, D., Schaeffer, N. & Hollerbach, R. 2018 Magnetic fields driven by tidal mixing in radiative stars. Mon. Not. R. Astron. Soc. 475 (4), 4579–4594.Google Scholar
Willis, A. P. & Barenghi, C. F. 2002 A Taylor–Couette dynamo. Astron. Astrophys. 393 (1), 339–343.Google Scholar
Zahn, J.-P. 1992 Circulation and turbulence in rotating stars. Astron. Astrophys. 265 (1), 115–132.Google Scholar
von Zeipel, H. 1924 The radiative equilibrium of a rotating system of gaseous masses. Mon. Not. R. Astron. Soc. 84, 665–683.CrossRefGoogle Scholar