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Title: GRAND MINIMA AND EQUATORWARD PROPAGATION IN A CYCLING STELLAR CONVECTIVE DYNAMO

Abstract

The 3D MHD Anelastic Spherical Harmonic code, using slope-limited diffusion, is employed to capture convective and dynamo processes achieved in a global-scale stellar convection simulation for a model solar-mass star rotating at three times the solar rate. The dynamo-generated magnetic fields possesses many timescales, with a prominent polarity cycle occurring roughly every 6.2 years. The magnetic field forms large-scale toroidal wreaths, whose formation is tied to the low Rossby number of the convection in this simulation. The polarity reversals are linked to the weakened differential rotation and a resistive collapse of the large-scale magnetic field. An equatorial migration of the magnetic field is seen, which is due to the strong modulation of the differential rotation rather than a dynamo wave. A poleward migration of magnetic flux from the equator eventually leads to the reversal of the polarity of the high-latitude magnetic field. This simulation also enters an interval with reduced magnetic energy at low latitudes lasting roughly 16 years (about 2.5 polarity cycles), during which the polarity cycles are disrupted and after which the dynamo recovers its regular polarity cycles. An analysis of this grand minimum reveals that it likely arises through the interplay of symmetric and antisymmetric dynamo families.more » This intermittent dynamo state potentially results from the simulation’s relatively low magnetic Prandtl number. A mean-field-based analysis of this dynamo simulation demonstrates that it is of the α-Ω type. The timescales that appear to be relevant to the magnetic polarity reversal are also identified.« less

Authors:
;  [1];  [2];  [3]
  1. High Altitude Observatory, Center Green 1, Boulder, CO 80301 (United States)
  2. Laboratoire AIM Paris-Saclay, CEA/DSM–CNRS–Université Paris Diderot, IRFU/SAp, Gif-sur-Yvette (France)
  3. JILA and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309 (United States)
Publication Date:
OSTI Identifier:
22525557
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 809; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COMPUTERIZED SIMULATION; CONVECTION; DIFFUSION; MAGNETIC FIELDS; MAGNETIC FLUX; MAGNETOHYDRODYNAMICS; MAIN SEQUENCE STARS; MEAN-FIELD THEORY; MODULATION; PRANDTL NUMBER; ROTATION; SPHERICAL CONFIGURATION; STAR MODELS; TURBULENCE

Citation Formats

Augustson, Kyle, Miesch, Mark, Brun, Allan Sacha, and Toomre, Juri. GRAND MINIMA AND EQUATORWARD PROPAGATION IN A CYCLING STELLAR CONVECTIVE DYNAMO. United States: N. p., 2015. Web. doi:10.1088/0004-637X/809/2/149.
Augustson, Kyle, Miesch, Mark, Brun, Allan Sacha, & Toomre, Juri. GRAND MINIMA AND EQUATORWARD PROPAGATION IN A CYCLING STELLAR CONVECTIVE DYNAMO. United States. doi:10.1088/0004-637X/809/2/149.
Augustson, Kyle, Miesch, Mark, Brun, Allan Sacha, and Toomre, Juri. 2015. "GRAND MINIMA AND EQUATORWARD PROPAGATION IN A CYCLING STELLAR CONVECTIVE DYNAMO". United States. doi:10.1088/0004-637X/809/2/149.
@article{osti_22525557,
title = {GRAND MINIMA AND EQUATORWARD PROPAGATION IN A CYCLING STELLAR CONVECTIVE DYNAMO},
author = {Augustson, Kyle and Miesch, Mark and Brun, Allan Sacha and Toomre, Juri},
abstractNote = {The 3D MHD Anelastic Spherical Harmonic code, using slope-limited diffusion, is employed to capture convective and dynamo processes achieved in a global-scale stellar convection simulation for a model solar-mass star rotating at three times the solar rate. The dynamo-generated magnetic fields possesses many timescales, with a prominent polarity cycle occurring roughly every 6.2 years. The magnetic field forms large-scale toroidal wreaths, whose formation is tied to the low Rossby number of the convection in this simulation. The polarity reversals are linked to the weakened differential rotation and a resistive collapse of the large-scale magnetic field. An equatorial migration of the magnetic field is seen, which is due to the strong modulation of the differential rotation rather than a dynamo wave. A poleward migration of magnetic flux from the equator eventually leads to the reversal of the polarity of the high-latitude magnetic field. This simulation also enters an interval with reduced magnetic energy at low latitudes lasting roughly 16 years (about 2.5 polarity cycles), during which the polarity cycles are disrupted and after which the dynamo recovers its regular polarity cycles. An analysis of this grand minimum reveals that it likely arises through the interplay of symmetric and antisymmetric dynamo families. This intermittent dynamo state potentially results from the simulation’s relatively low magnetic Prandtl number. A mean-field-based analysis of this dynamo simulation demonstrates that it is of the α-Ω type. The timescales that appear to be relevant to the magnetic polarity reversal are also identified.},
doi = {10.1088/0004-637X/809/2/149},
journal = {Astrophysical Journal},
number = 2,
volume = 809,
place = {United States},
year = 2015,
month = 8
}
  • We present results from four convectively driven stellar dynamo simulations in spherical wedge geometry. All of these simulations produce cyclic and migrating mean magnetic fields. Through detailed comparisons, we show that the migration direction can be explained by an αΩ dynamo wave following the Parker-Yoshimura rule. We conclude that the equatorward migration in this and previous work is due to a positive (negative) α effect in the northern (southern) hemisphere and a negative radial gradient of Ω outside the inner tangent cylinder of these models. This idea is supported by a strong correlation between negative radial shear and toroidal fieldmore » strength in the region of equatorward propagation.« less
  • We present results from simulations of rotating magnetized turbulent convection in spherical wedge geometry representing parts of the latitudinal and longitudinal extents of a star. Here we consider a set of runs for which the density stratification is varied, keeping the Reynolds and Coriolis numbers at similar values. In the case of weak stratification, we find quasi-steady dynamo solutions for moderate rotation and oscillatory ones with poleward migration of activity belts for more rapid rotation. For stronger stratification, the growth rate tends to become smaller. Furthermore, a transition from quasi-steady to oscillatory dynamos is found as the Coriolis number ismore » increased, but now there is an equatorward migrating branch near the equator. The breakpoint where this happens corresponds to a rotation rate that is about three to seven times the solar value. The phase relation of the magnetic field is such that the toroidal field lags behind the radial field by about π/2, which can be explained by an oscillatory α{sup 2} dynamo caused by the sign change of the α-effect about the equator. We test the domain size dependence of our results for a rapidly rotating run with equatorward migration by varying the longitudinal extent of our wedge. The energy of the axisymmetric mean magnetic field decreases as the domain size increases and we find that an m = 1 mode is excited for a full 2π azimuthal extent, reminiscent of the field configurations deduced from observations of rapidly rotating late-type stars.« less
  • We present a method to characterize the spectral transfers of magnetic energy between scales in simulations of stellar convective dynamos. The full triadic transfer functions are computed thanks to analytical coupling relations of spherical harmonics based on the Clebsch-Gordan coefficients. The method is applied to mean field {alpha}{Omega} dynamo models as benchmark tests. From a physical standpoint, the decomposition of the dynamo field into primary and secondary dynamo families proves very instructive in the {alpha}{Omega} case. The same method is then applied to a fully turbulent dynamo in a solar convection zone, modeled with the three-dimensional MHD Anelastic Spherical Harmonicsmore » code. The initial growth of the magnetic energy spectrum is shown to be non-local. It mainly reproduces the kinetic energy spectrum of convection at intermediate scales. During the saturation phase, two kinds of direct magnetic energy cascades are observed in regions encompassing the smallest scales involved in the simulation. The first cascade is obtained through the shearing of the magnetic field by the large-scale differential rotation that effectively cascades magnetic energy. The second is a generalized cascade that involves a range of local magnetic and velocity scales. Non-local transfers appear to be significant, such that the net transfers cannot be reduced to the dynamics of a small set of modes. The saturation of the large-scale axisymmetric dipole and quadrupole is detailed. In particular, the dipole is saturated by a non-local interaction involving the most energetic scale of the magnetic energy spectrum, which points to the importance of the magnetic Prandtl number for large-scale dynamos.« less
  • Numerical simulations of stellar dynamos are reviewed. Dynamic dynamo models solve the nonlinear, three-dimensional, time-dependent, magnetohydrodynamic equations for the convective velocity, the thermodynamic variables, and the generated magnetic field in a rotating, spherical shell of ionized gas. When the dynamo operates in the convection zone, the simulated magnetic fields propagate away from the equator in the opposite direction inferred from the solar butterfly diagram. When simulated at the base of the convection zone, the fields propagate in the right direction at roughly the right speed. However, owing to the numerical difficulty, a full magnetic cycle has not been simulated inmore » this region. As a result, it is still uncertain where and how the solar dynamo operates.« less
  • We present numerical simulations of nonlinear, three-dimensional, time-dependent, giant-cell stellar convection and magnetic field generation. The velocity, magnetic field, and thermodynamic variables satisfy the anelastic magnetohydrodynamic equations for a stratified, rotating, spherical shell of ionized gas. The interaction of rotation and convection produces a nonlinear transport of angular momentum that maintains a differential rotation in radius and latitude. At the surface, our simulated angular velocity peaks in the equatorial region in agreement with Doppler measurements of the solar surface rotation rate; below the surface, it decreases with depth in agreement with what is inferred from the rotational frequency splitting ofmore » solar oscillations. The interaction of rotation and convection also maintains left-handed helical fluid motions in the northern hemisphere and right-handed motions in the southern hemisphere. Magnetic fields are generated by the shearing and twisting effects of the differential rotation and helical motions and are destroyed by eddy diffusion. They in turn feedback onto the velocity and thermodynamic fields via the Lorentz force and Joule heating. Although we have not continued the computation long enough to simulate a complete magnetic cycle, our solutions demonstrate how the induced magnetic fields propagate away from the equator in the opposite direction inferred from the solar butterfly diagram. We suggest that, instead of operating in the turbulent convective region, the solar dynamo may be operating at the base of the convection zone where our simulated helicity has the opposite sign and a smaller amplitude.« less