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  • 1. Andrievsky, Alexander
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Noullez, Alain
    Zheligovsky, Vladislav
    NEGATIVE MAGNETIC EDDY DIFFUSIVITIES FROM THE TEST-FIELD METHOD AND MULTISCALE STABILITY THEORY2015In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 811, no 2, article id 135Article in journal (Refereed)
    Abstract [en]

    The generation of a large-scale magnetic field in the kinematic regime in the absence of an alpha-effect is investigated by following two different approaches: the test-field method and the multiscale stability theory relying on the homogenization technique. Our computations of the magnetic eddy diffusivity tensor of the parity-invariant flow IV of G. O. Roberts and the modified Taylor-Green flow confirm the findings of previous studies. and also explain some of their apparent contradictions. The two flows have large symmetry groups; this is used to considerably simplify the eddy diffusivity tensor. Finally, a new analytic result is presented: upon expressing the eddy diffusivity tensor in terms of solutions to auxiliary problems for the adjoint operator, we derive relations between the magnetic eddy diffusivity tensors that arise for mutually reverse small-scale flows v(x) and - v(x).

  • 2.
    Barekat, A.
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. Max-Planck-Institut für Sonnensystemforschung, Germany.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Near-polytropic stellar simulations with a radiative surface2014In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 571, article id A68Article in journal (Refereed)
    Abstract [en]

    Context. Studies of solar and stellar convection often employ simple polytropic setups using the diffusion approximation instead of solving the proper radiative transfer equation. This allows one to control separately the polytropic index of the hydrostatic reference solution, the temperature contrast between top and bottom, and the Rayleigh and Peclet numbers. Aims. Here we extend such studies by including radiative transfer in the gray approximation using a Kramers-like opacity with freely adjustable coefficients. We study the properties of such models and compare them with results from the diffusion approximation. Methods. We use the Pencil code, which is a high-order finite difference code where radiation is treated using the method of long characteristics. The source function is given by the Planck function. The opacity is written as kappa = kappa(0)rho T-a(b), where a = 1 in most cases, b is varied from -3.5 to +5, and kappa(0) is varied by four orders of magnitude. We adopt a perfect monatomic gas. We consider sets of one-dimensional models and perform a comparison with the diffusion approximation in one-and two-dimensional models. Results. Except for the case where b = 5, we find one-dimensional hydrostatic equilibria with a nearly polytropic stratification and a polytropic index close to n = (3 -b)/(1 + a), covering both convectively stable (n > 3/2) and unstable (n < 3/2) cases. For b = 3 and a = -1, the value of n is undefined a priori and the actual value of n depends then on the depth of the domain. For large values of kappa(0), the thermal adjustment time becomes long, the Peclet and Rayleigh numbers become large, and the temperature contrast increases and is thus no longer an independent input parameter, unless the Stefan-Boltzmann constant is considered adjustable. Conclusions. Proper radiative transfer with Kramers-like opacities provides a useful tool for studying stratified layers with a radiative surface in ways that are more physical than what is possible with polytropic models using the diffusion approximation.

  • 3.
    Bhat, Pallavi
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Inter University Centre for Astronomy and Astrophysics, India; Princeton University, USA.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Hydraulic effects in a radiative atmosphere with ionization2016In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 587, article id A90Article in journal (Refereed)
    Abstract [en]

    Context. In his 1978 paper, Eugene Parker postulated the need for hydraulic downward motion to explain magnetic flux concentrations at the solar surface. A similar process has also recently been seen in simplified (e.g., isothermal) models of flux concentrations from the negative effective magnetic pressure instability (NEMPI).

    Aims. We study the effects of partial ionization near the radiative surface on the formation of these magnetic flux concentrations.

    Methods. We first obtain one-dimensional (1D) equilibrium solutions using either a Kramers-like opacity or the H-opacity. The resulting atmospheres are then used as initial conditions in two-dimensional (2D) models where flows are driven by an imposed gradient force that resembles a localized negative pressure in the form of a blob. To isolate the effects of partial ionization and radiation, we ignore turbulence and convection.

    Results. Because of partial ionization, an unstable stratification always forms near the surface. We show that the extrema in the specific entropy profiles correspond to the extrema in the degree of ionization. In the 2D models without partial ionization, strong flux concentrations form just above the height where the blob is placed. Interestingly, in models with partial ionization, such flux concentrations always form at the surface well above the blob. This is due to the corresponding negative gradient in specific entropy. Owing to the absence of turbulence, the downflows reach transonic speeds.

    Conclusions. We demonstrate that, together with density stratification, the imposed source of negative pressure drives the formation of flux concentrations. We find that the inclusion of partial ionization affects the entropy profile dramatically, causing strong flux concentrations to form closer to the surface. We speculate that turbulence effects are needed to limit the strength of flux concentrations and homogenize the specific entropy to a stratification that is close to marginal.

  • 4. Bhat, Pallavi
    et al.
    Subramanian, Kandaswamy
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    A unified large/small-scale dynamo in helical turbulence2016In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 461, no 1, p. 240-247Article in journal (Refereed)
    Abstract [en]

    We use high resolution direct numerical simulations (DNS) to show that helical turbulence can generate significant large-scale fields even in the presence of strong small-scale dynamo action. During the kinematic stage, the unified large/ small-scale dynamo grows fields with a shapeinvariant eigenfunction, with most power peaked at small scales or large k, as in Subramanian & Brandenburg. Nevertheless, the large-scale field can be clearly detected as an excess power at small k in the negatively polarized component of the energy spectrum for a forcing with positively polarized waves. Its strength (B) over bar, relative to the total rms field Brms, decreases with increasing magnetic Reynolds number, Re-M. However, as the Lorentz force becomes important, the field generated by the unified dynamo orders itself by saturating on successively larger scales. The magnetic integral scale for the positively polarized waves, characterizing the smallscale field, increases significantly from the kinematic stage to saturation. This implies that the small-scale field becomes as coherent as possible for a given forcing scale, which averts the Re-M-dependent quenching of (B) over bar /B-rms. These results are obtained for 1024(3) DNS with magnetic Prandtl numbers of PrM = 0.1 and 10. For PrM = 0.1, B/ Brms grows from about 0.04 to about 0.4 at saturation, aided in the final stages by helicity dissipation. For Pr-M = 10, (B) over bar /B-rms grows from much less than 0.01 to values of the order the 0.2. Our results confirm that there is a unified large/ small-scale dynamo in helical turbulence.

  • 5. Bonanno, Alfio
    et al.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Del Sordo, Fabio
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Mitra, Dhrubaditya
    Breakdown of chiral symmetry during saturation of the Tayler instability2012In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 86, no 1, p. 016313-Article in journal (Refereed)
    Abstract [en]

    We study spontaneous breakdown of chiral symmetry during the nonlinear evolution of the Tayler instability. We start with an initial steady state of zero helicity. Within linearized perturbation calculations, helical perturbations of this initial state have the same growth rate for either sign of helicity. Direct numerical simulations (DNS) of the fully nonlinear equations, however, show that an infinitesimal excess of one sign of helicity in the initial perturbation gives rise to a saturated helical state. We further show that this symmetry breaking can be described by weakly nonlinear finite-amplitude equations with undetermined coefficients which can be deduced solely from symmetry consideration. By fitting solutions of the amplitude equations to data from DNS, we further determine the coefficients of the amplitude equations.

  • 6.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Analytic solution of an oscillatory migratory alpha(2) stellar dynamo2017In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 598, article id A117Article in journal (Refereed)
    Abstract [en]

    Context. Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for homogeneous helical turbulence or constant alpha effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant alpha.

    Aims. We present an analytic solution for a one-dimensional bounded domain resulting in oscillatory solutions for constant alpha, but different (Dirichlet and von Neumann or perfect conductor and vacuum) boundary conditions on the two boundaries.

    Methods. We solve a second order complex equation and superimpose two independent solutions to obey both boundary conditions.

    Results. The solution has time-independent energy density. On one end where the function value vanishes, the second derivative is finite, which would not be correctly reproduced with sine-like expansion functions where a node coincides with an inflection point. The field always migrates away from the perfect conductor boundary toward the vacuum boundary, independently of the sign of alpha.

    Conclusions. The obtained solution may serve as a benchmark for numerical dynamo experiments and as a pedagogical illustration that oscillatory migratory dynamos are possible with constant alpha.

  • 7.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Dissipation in dynamos at low and high magnetic Prandtl numbers2011In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 332, no 1, p. 51-56Article in journal (Refereed)
    Abstract [en]

    Using simulations of helically driven turbulence, it is shown that the ratio of kinetic to magnetic energy dissipation scales with the magnetic Prandtl number in power law fashion with an exponent of approximately 0.6. Over six orders of magnitude in the magnetic Prandtl number the magnetic field is found to be sustained by large-scale dynamo action of alpha-squared type. This work extends a similar finding for small magnetic Prandtl numbers to the regime of large magnetic Prandtl numbers. At large magnetic Prandtl numbers, most of the energy is dissipated viscously, lowering thus the amount of magnetic energy dissipation, which means that simulations can be performed at magnetic Reynolds numbers that are large compared to the usual limits imposed by a given resolution. This is analogous to an earlier finding that at small magnetic Prandtl numbers, most of the energy is dissipated resistively, lowering the amount of kinetic energy dissipation, so simulations can then be performed at much larger fluid Reynolds numbers than otherwise. The decrease in magnetic energy dissipation at large magnetic Prandtl numbers is discussed in the context of underluminous accretion found in some quasars.

  • 8.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Physics.
    MAGNETIC PRANDTL NUMBER DEPENDENCE OF THE KINETIC- TO- MAGNETIC DISSIPATION RATIO2014In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 791, no 1, p. 12-Article in journal (Refereed)
    Abstract [en]

    Using direct numerical simulations of three-dimensional hydromagnetic turbulence, either with helical or non-helical forcing, we show that the kinetic-to-magnetic energy dissipation ratio always increases with the magnetic Prandtl number, i.e., the ratio of kinematic viscosity to magnetic diffusivity. This dependence can always be approximated by a power law, but the exponent is not the same in all cases. For non-helical turbulence, the exponent is around 1/3, while for helical turbulence it is between 0.6 and 2/3. In the statistically steady state, the rate of energy conversion from kinetic into magnetic by the dynamo must be equal to the Joule dissipation rate. We emphasize that for both small-scale and large-scale dynamos, the efficiency of the energy conversion depends sensitively on the magnetic Prandtl number, and thus on the microphysical dissipation process. To understand this behavior, we also study shell models of turbulence and one-dimensional passive and active scalar models. We conclude that the magnetic Prandtl number dependence is qualitatively best reproduced in the one-dimensional model as a result of dissipation via localized Alfven kinks.

  • 9.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Simulations of Galactic Dynamos2015In: Magnetic Fields in Diffuse Media / [ed] Lazarian, A.; DalPino, E.M.D.; Melioli, C., Dordrecht: Springer, 2015, Vol. 407, p. 529-555Chapter in book (Refereed)
    Abstract [en]

    We review our current understanding of galactic dynamo theory, paying particular attention to numerical simulations both of the mean-field equations and the original three-dimensional equations relevant to describing the magnetic field evolution for a turbulent flow. We emphasize the theoretical difficulties in explaining non-axisymmetric magnetic fields in galaxies and discuss the observational basis for such results in terms of rotationmeasure analysis. Next, we discuss nonlinear theory, the role of magnetic helicity conservation and magnetic helicity fluxes. This leads to the possibility that galactic magnetic fields may be bi-helical, with opposite signs of helicity and large and small length scales. We discuss their observational signatures and close by discussing the possibilities of explaining the origin of primordial magnetic fields.

  • 10.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    STELLAR MIXING LENGTH THEORY WITH ENTROPY RAIN2016In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 832, no 1, article id 6Article in journal (Refereed)
    Abstract [en]

    The effects of a non-gradient flux term originating from the motion of convective elements with entropy perturbations of either sign are investigated and incorporated into a modified version of stellar mixing length theory (MLT). Such a term, first studied by Deardorff in the meteorological context, might represent the effects of cold intense downdrafts caused by the rapid cooling in the granulation layer at the top of the convection zone of late-type stars. These intense downdrafts were first seen in the strongly stratified simulations of Stein & Nordlund in the late 1980s. These downdrafts transport heat nonlocally, a phenomenon referred to as entropy rain. Moreover, the Deardorff term can cause upward enthalpy transport even in a weakly Schwarzschild-stably stratified layer. In that case, no giant cell convection would be excited. This is interesting in view of recent observations, which could be explained if the dominant flow structures were of small scale even at larger depths. To study this possibility, three distinct flow structures are examined: one in which convective structures have similar size and mutual separation at all depths, one in which the separation increases with depth, but their size is still unchanged, and one in which both size and separation increase with depth, which is the standard flow structure. It is concluded that the third possibility with fewer and thicker downdrafts in deeper layers remains the most plausible, but it may be unable to explain the suspected absence of large-scale flows with speeds and scales expected from MLT.

  • 11.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Ashurova, Mohira B.
    Jabbari, Sarah
    Compensating Faraday Depolarization by Magnetic Helicity in the Solar Corona2017In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 845, no 2, article id L15Article in journal (Refereed)
    Abstract [en]

    A turbulent dynamo in spherical geometry with an outer corona is simulated to study the sign of magnetic helicity in the outer parts. In agreement with earlier studies, the sign in the outer corona is found to be opposite to that inside the dynamo. Line-of-sight observations of polarized emission are synthesized to explore the feasibility of using the local reduction of Faraday depolarization to infer the sign of helicity of magnetic fields in the solar corona. This approach was previously identified as an observational diagnostic in the context of galactic magnetic fields. Based on our simulations, we show that this method can be successful in the solar context if sufficient statistics are gathered by using averages over ring segments in the corona separately for the regions north and south of the solar equator.

  • 12.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Chatterjee, P.
    Del Sordo, Fabio
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Hubbard, A.
    Käpylä, P. J.
    Rheinhardt, M.
    Turbulent transport in hydromagnetic flows2010In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T142, article id 14028Article in journal (Refereed)
    Abstract [en]

    The predictive power of mean-field theory is emphasized by comparing theory with simulations under controlled conditions. The recently developed test-field method is used to extract turbulent transport coefficients both in the kinematic and the nonlinear or quasi-kinematic cases. A striking example of the quasi-kinematic method is provided by magnetic buoyancy-driven flows that produce an alpha effect and turbulent diffusion.

  • 13.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, Colorado.
    Chatterjee, Piyali
    Strong nonlocality variations in a spherical mean-field dynamo2018In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 339, no 2-3, p. 118-126Article in journal (Refereed)
    Abstract [en]

    To explain the large-scale magnetic field of the sun and other bodies, the mean-field dynamo theory is commonly applied, where one solves the averaged equations for the mean magnetic field. However, the standard approach breaks down when the scale of the turbulent eddies becomes comparable to the scale of the variations of the mean magnetic field. Models showing sharp magnetic field structures have therefore been regarded as unreliable. Our aim is to look for new effects that occur when we relax the restrictions of the standard approach, which becomes particularly important at the bottom of the convection zone where the size of the turbulent eddies is comparable to the depth of the convection zone itself. We approximate the underlying integro-differential equation using a partial differential equation corresponding to a reaction-diffusion-type equation for the mean electromotive force, making an approach that is nonlocal in space and time feasible under conditions where spherical geometry and nonlinearity are included. In agreement with earlier findings, spatiotemporal nonlocality lowers the excitation conditions of the dynamo. Sharp structures are now found to be absent. However, in the surface layers, the field remains similar to before.

  • 14.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, U.S.A; Carnegie Mellon University, U.S.A..
    Durrer, Ruth
    Kahniashvili, Tina
    Mandalc, Sayan
    Yin, Weichen Winston
    Statistical properties of scale-invariant helical magnetic fields and applications to cosmology2018In: Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, E-ISSN 1475-7516, no 8, article id 034Article in journal (Refereed)
    Abstract [en]

    We investigate the statistical properties of isotropic, stochastic, Gaussian distributed, helical magnetic fields characterized by different shapes of the energy spectra at large length scales and study the associated realizability condition. We discuss smoothed magnetic fields that are commonly used when the primordial magnetic field is constrained by observational data. We are particularly interested in scale-invariant magnetic fields that can be generated during the inflationary stage by quantum fluctuations. We determine the correlation length of such magnetic fields and relate it to the infrared cutoff of perturbations produced during inflation. We show that this scale determines the observational signatures of the inflationary magnetic fields on the cosmic microwave background. At smaller scales, the scale-invariant spectrum changes with time. It becomes a steeper weak-turbulence spectrum at progressively larger scales. We show numerically that the critical length scale where this happens is the turbulent-diffusive scale, which increases with the square root of time.

  • 15.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Giampapa, Mark S.
    Enhanced Stellar Activity for Slow Antisolar Differential Rotation2018In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 855, no 2, article id L22Article in journal (Refereed)
    Abstract [en]

    High-precision photometry of solar-like members of the open cluster M67 with Kepler/K2 data has recently revealed enhanced activity for stars with a large Rossby number, which is the ratio of rotation period to the convective turnover time. Contrary to the well established behavior for shorter rotation periods and smaller Rossby numbers, the chromospheric activity of the more slowly rotating stars of M67 was found to increase with increasing Rossby number. Such behavior has never been reported before, although it was theoretically predicted to emerge as a consequence of antisolar differential rotation (DR) for stars with Rossby numbers larger than that of the Sun, because in those models the absolute value of the DR was found to exceed that for solar-like DR. Using gyrochronological relations and an approximate age of 4 Gyr for the members of M67, we compare with computed rotation rates using just the B - V color. The resulting rotation-activity relation is found to be compatible with that obtained by employing the measured rotation rate. This provides additional support for the unconventional enhancement of activity at comparatively low rotation rates and the possible presence of antisolar differential rotation.

  • 16.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Gressel, O.
    Jabbari, Sarah
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, N.
    Rogachevskii, I.
    Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field2014In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 562, article id A53Article in journal (Refereed)
    Abstract [en]

    Context. Strongly stratified hydromagnetic turbulence has previously been found to produce magnetic flux concentrations if the domain is large enough compared with the size of turbulent eddies. Mean-field simulations (MFS) using parameterizations of the Reynolds and Maxwell stresses show a large-scale negative effective magnetic pressure instability and have been able to reproduce many aspects of direct numerical simulations (DNS) regarding growth rate, shape of the resulting magnetic structures, and their height as a function of magnetic field strength. Unlike the case of an imposed horizontal field, for a vertical one, magnetic flux concentrations of equipartition strength with the turbulence can be reached, resulting in magnetic spots that are reminiscent of sunspots. Aims. We determine under what conditions magnetic flux concentrations with vertical field occur and what their internal structure is. Methods. We use a combination of MFS, DNS, and implicit large-eddy simulations (ILES) to characterize the resulting magnetic flux concentrations in forced isothermal turbulence with an imposed vertical magnetic field. Results. Using DNS, we confirm earlier results that in the kinematic stage of the large-scale instability the horizontal wavelength of structures is about 10 times the density scale height. At later times, even larger structures are being produced in a fashion similar to inverse spectral transfer in helically driven turbulence. Using ILES, we find that magnetic flux concentrations occur for Mach numbers between 0.1 and 0.7. They occur also for weaker stratification and larger turbulent eddies if the domain is wide enough. Using MFS, the size and aspect ratio of magnetic structures are determined as functions of two input parameters characterizing the parameterization of the effective magnetic pressure. DNS, ILES, and MFS show magnetic flux tubes with mean-field energies comparable to the turbulent kinetic energy. These tubes can reach a length of about eight density scale heights. Despite being <= 1% equipartition strength, it is important that their lower part is included within the computational domain to achieve the full strength of the instability. Conclusions. The resulting vertical magnetic flux tubes are being confined by downflows along the tubes and corresponding inflow from the sides, which keep the field concentrated. Application to sunspots remains a viable possibility.

  • 17.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Gressel, Oliver
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Käpylä, Petri J.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Helsinki, Finland.
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Mantere, M. J.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    NEW SCALING FOR THE ALPHA EFFECT IN SLOWLY ROTATING TURBULENCE2013In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 762, no 2, article id 127Article in journal (Refereed)
    Abstract [en]

    Using simulations of slowly rotating stratified turbulence, we show that the alpha effect responsible for the generation of astrophysical magnetic fields is proportional to the logarithmic gradient of kinetic energy density rather than that of momentum, as was previously thought. This result is in agreement with a new analytic theory developed in this paper for large Reynolds numbers and slow rotation. Thus, the contribution of density stratification is less important than that of turbulent velocity. The a effect and other turbulent transport coefficients are determined by means of the test-field method. In addition to forced turbulence, we also investigate supernova-driven turbulence and stellar convection. In some cases (intermediate rotation rate for forced turbulence, convection with intermediate temperature stratification, and supernova-driven turbulence), we find that the contribution of density stratification might be even less important than suggested by the analytic theory.

  • 18.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Haugen, N. E. L.
    Li, Xiang-Yu
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Meteorology . University of Colorado, USA.
    Subramanian, K.
    Varying the forcing scale in low Prandtl number dynamos2018In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 479, no 2, p. 2827-2833Article in journal (Refereed)
    Abstract [en]

    Small-scale dynamos are expected to operate in all astrophysical fluids that are turbulent and electrically conducting, for example the interstellar medium, stellar interiors, and accretion discs, where theymay also be affected by or competing with large-scale dynamos. However, the possibility of small-scale dynamos being excited at small and intermediate ratios of viscosity to magnetic diffusivity (the magnetic Prandtl number) has been debated, and the possibility of them depending on the large-scale forcing wavenumber has been raised. Here, we show, using four values of the forcing wavenumber, that the small-scale dynamo does not depend on the scale separation between the size of the simulation domain and the integral scale of the turbulence, i.e. the forcing scale. Moreover, the spectral bottleneck in turbulence, which has been implied as being responsible for raising the excitation conditions of small-scale dynamos, is found to be invariant under changing the forcing wavenumber. However, when forcing at the lowest few wavenumbers, the effective forcing wavenumber that enters in the definition of the magnetic Reynolds number is found to be about twice the minimum wavenumber of the domain. Our work is relevant to future studies of small-scale dynamos, of which several applications are being discussed.

  • 19.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Hubbard, A.
    Käpylä, P. J.
    Dynamical quenching with non-local alpha and downward pumping2015In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 336, no 1, p. 91-96Article in journal (Refereed)
    Abstract [en]

    In light of new results, the one-dimensional mean-field dynamo model of Brandenburg & Kapyla (2007) with dynamical quenching and a nonlocal Babcock-Leighton a effect is re-examined for the solar dynamo. We extend the one-dimensional model to include the effects of turbulent downward pumping (Kitchatinov & Olemskoy 2011), and to combine dynamical quenching with shear. We use both the conventional dynamical quenching model of Kleeorin & Ruzmaikin (1982) and the alternate one of Hubbard & Brandenburg (2011), and confirm that with varying levels of non-locality in the a effect, and possibly shear as well, the saturation field strength can be independent of the magnetic Reynolds number.

  • 20.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Kahniashvili, Tina
    Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay2017In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 118, no 5, article id 055102Article in journal (Refereed)
    Abstract [en]

    We perform numerical simulations of decaying hydrodynamic and magnetohydrodynamic turbulence. We classify our time-dependent solutions by their evolutionary tracks in parametric plots between instantaneous scaling exponents. We find distinct classes of solutions evolving along specific trajectories toward points on a line of self-similar solutions. These trajectories are determined by the underlying physics governing individual cases, while the infrared slope of the initial conditions plays only a limited role. In the helical case, even for a scale-invariant initial spectrum (inversely proportional to wave number k), the solution evolves along the same trajectory as for a Batchelor spectrum (proportional to k(4)).

  • 21.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Kahniashvili, Tina
    Mandal, Sayan
    Pol, Alberto Roper
    Tevzadze, Alexander G.
    Vachaspati, Tanmay
    Evolution of hydromagnetic turbulence from the electroweak phase transition2017In: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 96, no 12, article id 123528Article in journal (Refereed)
    Abstract [en]

    We present new simulations of decaying hydromagnetic turbulence for a relativistic equation of state relevant to the early Universe. We compare helical and nonhelical cases either with kinetically or magnetically dominated initial fields. Both kinetic and magnetic initial helicities lead to maximally helical magnetic fields after some time, but with different temporal decay laws. Both are relevant to the early Universe, although no mechanisms have yet been identified that produce magnetic helicity with strengths comparable to the big bang nucleosynthesis limit at scales comparable to the Hubble horizon at the electroweak phase transition. Nonhelical magnetically dominated fields could still produce picoGauss magnetic fields under most optimistic conditions. Only helical magnetic fields can potentially have nanoGauss strengths at scales up to 30 kpc today.

  • 22.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kahniashvili, Tina
    Tevzadze, Alexander G.
    Nonhelical Inverse Transfer of a Decaying Turbulent Magnetic Field2015In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 114, no 7Article in journal (Refereed)
    Abstract [en]

    In the presence of magnetic helicity, inverse transfer from small to large scales is well known in magnetohydrodynamic (MHD) turbulence and has applications in astrophysics, cosmology, and fusion plasmas. Using high resolution direct numerical simulations of magnetically dominated self-similarly decaying MHD turbulence, we report a similar inverse transfer even in the absence of magnetic helicity. We compute for the first time spectral energy transfer rates to show that this inverse transfer is about half as strong as with helicity, but in both cases the magnetic gain at large scales results from velocity at similar scales interacting with smaller-scale magnetic fields. This suggests that both inverse transfers are a consequence of universal mechanisms for magnetically dominated turbulence. Possible explanations include inverse cascading of the mean squared vector potential associated with local near two dimensionality and the shallower k(2) subinertial range spectrum of kinetic energy forcing the magnetic field with a k(4) subinertial range to attain larger-scale coherence. The inertial range shows a clear k(-2) spectrum and is the first example of fully isotropic magnetically dominated MHD turbulence exhibiting weak turbulence scaling.

  • 23.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kemel, Koen
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, Nathan
    Mitra, Dhrubaditya
    Rogachevskii, Igor
    Detection of Negative Effective Magnetic Pressure Instability in Turbulence Simulations2011In: Astrophysical Journal, ISSN 0004-637X, EISSN 1538-4357, Vol. 740, no 2, p. L50-Article in journal (Refereed)
    Abstract [en]

    We present the first numerical demonstration of the negative effective magnetic pressure instability in direct numerical simulations of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma beta. By the action of this instability, initially uniform horizontal magnetic field forms flux concentrations whose scale is large compared to the turbulent scale. We further show that the magnetic energy of these large-scale structures is only weakly dependent on the magnetic Reynolds number. Our results support earlier mean-field calculations and analytic work that identified this instability. Applications to the formation of active regions in the Sun are discussed.

  • 24.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kemel, Koen
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    NEGATIVE EFFECTIVE MAGNETIC PRESSURE IN STRATIFIED FORCED TURBULENCE2012In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 749, no 2, article id 179Article in journal (Refereed)
    Abstract [en]

    To understand the basic mechanism of the formation of magnetic flux concentrations, we determine by direct numerical simulations the turbulence contributions to the mean magnetic pressure in a strongly stratified isothermal layer with large plasma beta, where a weak uniform horizontal mean magnetic field is applied. The negative contribution of turbulence to the effective mean magnetic pressure is determined for strongly stratified forced turbulence over a range of values of magnetic Reynolds and Prandtl numbers. Small-scale dynamo action is shown to reduce the negative effect of turbulence on the effective mean magnetic pressure. However, the turbulence coefficients describing the negative effective magnetic pressure phenomenon are found to converge for magnetic Reynolds numbers between 60 and 600, which is the largest value considered here. In all these models, the turbulent intensity is arranged to be nearly independent of height, so the kinetic energy density decreases with height due to the decrease in density. In a second series of numerical experiments, the turbulent intensity increases with height such that the turbulent kinetic energy density is nearly independent of height. Turbulent magnetic diffusivity and turbulent pumping velocity are determined with the test-field method for both cases. The vertical profile of the turbulent magnetic diffusivity is found to agree with what is expected based on simple mixing length expressions. Turbulent pumping is shown to be down the gradient of turbulent magnetic diffusivity, but it is twice as large as expected. Corresponding numerical mean-field models are used to show that a large-scale instability can occur in both cases, provided the degree of scale separation is large enough and hence the turbulent magnetic diffusivity small enough.

  • 25.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    SELF-ASSEMBLY OF SHALLOW MAGNETIC SPOTS THROUGH STRONGLY STRATIFIED TURBULENCE2013In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 776, no 2, article id L23Article in journal (Refereed)
    Abstract [en]

    Recent studies have demonstrated that in fully developed turbulence, the effective magnetic pressure of a large-scale field (non-turbulent plus turbulent contributions) can become negative. In the presence of strongly stratified turbulence, this was shown to lead to a large-scale instability that produces spontaneous magnetic flux concentrations. Furthermore, using a horizontal magnetic field, elongated flux concentrations with a strength of a few percent of the equipartition value were found. Here we show that a uniform vertical magnetic field leads to circular magnetic spots of equipartition field strengths. This could represent a minimalistic model of sunspot formation and highlights the importance of two critical ingredients: turbulence and strong stratification. Radiation, ionization, and supergranulation may be important for realistic simulations, but are not critical at the level of a minimalistic model of magnetic spot formation.

  • 26.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Lazarian, A.
    Astrophysical Hydromagnetic Turbulence2014In: Microphysics of Cosmic Plasmas / [ed] Balogh, A.; Bykov, A.; Cargill, P.; Dendy, R.; DeWit, T. D.; Raymond, J., Dordrecht: Springer, 2014, p. 87-124Chapter in book (Refereed)
    Abstract [en]

    Recent progress in astrophysical hydromagnetic turbulence is being reviewed. The physical ideas behind the now widely accepted Goldreich-Sridhar model and its extension to compressible magnetohydrodynamic turbulence are introduced. Implications for cosmic ray diffusion and acceleration is being discussed. Dynamo-generated magnetic fields with and without helicity are contrasted against each other. Certain turbulent transport processes are being modified and often suppressed by anisotropy and inhomogeneities of the turbulence, while others are being produced by such properties, which can lead to new large-scale instabilities of the turbulent medium. Applications of various such processes to astrophysical systems are being considered.

  • 27.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Lazarian, A.
    Astrophysical Hydromagnetic Turbulence2013In: Space Science Reviews, ISSN 0038-6308, E-ISSN 1572-9672, Vol. 178, no 2-4, p. 163-200Article, review/survey (Refereed)
    Abstract [en]

    Recent progress in astrophysical hydromagnetic turbulence is being reviewed. The physical ideas behind the now widely accepted Goldreich-Sridhar model and its extension to compressible magnetohydrodynamic turbulence are introduced. Implications for cosmic ray diffusion and acceleration is being discussed. Dynamo-generated magnetic fields with and without helicity are contrasted against each other. Certain turbulent transport processes are being modified and often suppressed by anisotropy and inhomogeneities of the turbulence, while others are being produced by such properties, which can lead to new large-scale instabilities of the turbulent medium. Applications of various such processes to astrophysical systems are being considered.

  • 28.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Mathur, Savita
    Metcalfe, Travis S.
    Evolution of Co-existing Long and Short Period Stellar Activity Cycles2017In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 845, no 1, article id 79Article in journal (Refereed)
    Abstract [en]

    The magnetic activity of the Sun becomes stronger and weaker over roughly an 11 year cycle, modulating the radiation and charged particle environment experienced by the Earth as space weather. Decades of observations from the Mount Wilson Observatory have revealed that other stars also show regular activity cycles in their Ca II H+K line emission, and identified two different relationships between the length of the cycle and the rotation rate of the star. Recent observations at higher cadence have allowed the discovery of shorter cycles with periods between 1-3 years. Some of these shorter cycles coexist with longer cycle periods, suggesting that two underlying dynamos can operate simultaneously. We combine these new observations with previous data, and show that the longer and shorter cycle periods agree remarkably well with those expected from an earlier analysis based on the mean activity level and the rotation period. The relative turbulent length scales associated with the two branches of cyclic behavior suggest that a near-surface dynamo may be the dominant mechanism that drives cycles in more active stars, whereas a dynamo operating in deeper layers may dominate in less active stars. However, several examples of equally prominent long and short cycles have been found at all levels of activity of stars younger than 2.3 Gyr. Deviations from the expected cycle periods show no dependence on the depth of the convection zone or on the metallicity. For some stars that exhibit longer cycles, we compute the periods of shorter cycles that might be detected with future high-cadence observations.

  • 29.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Petrie, Gordon J. D.
    Singh, Nishant K.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Two-scale Analysis of Solar Magnetic Helicity2017In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 836, no 1, article id 21Article in journal (Refereed)
    Abstract [en]

    We develop a two-scale formalism to determine global magnetic helicity spectra in systems where the local magnetic helicity has opposite signs on both sides of the equator, giving rise to cancellation with conventional methods. We verify this approach using first a synthetic one-dimensional magnetic field and then two-dimensional slices from a three dimensional a effect-type dynamo-generated magnetic field, with forced turbulence of opposite helicity above and below the midplane of the domain. We then apply this formalism to global solar synoptic vector magnetograms. To improve the statistics, data from three consecutive Carrington rotations (2161-2163) are combined into a single map. We find that the spectral magnetic helicity representative of the northern hemisphere is negative at all wavenumbers and peaks at approximate to 0.06 Mm(-1) (scales around 100 Mm). There is no evidence of bihelical magnetic fields that are found in three-dimensional turbulence simulations of helicity-driven a effect-type dynamos.

  • 30.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Petrosyan, A.
    Kinetic helicity decay in linearly forced turbulence2012In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 333, no 3, p. 195-201Article in journal (Refereed)
    Abstract [en]

    The decay of kinetic helicity is studied in numerical models of forced turbulence using either an externally imposed forcing function as an inhomogeneous term in the equations or, alternatively, a term linear in the velocity giving rise to a linear instability. The externally imposed forcing function injects energy at the largest scales, giving rise to a turbulent inertial range with nearly constant energy flux while for linearly forced turbulence the spectral energy is maximum near the dissipation wavenumber. Kinetic helicity is injected once a statistically steady state is reached, but it is found to decay on a turbulent time scale regardless of the nature of the forcing and the value of the Reynolds number

  • 31.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Raedler, K-H
    Kemel, Koen
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Mean field transport in stratified and/or rotating turbulence2012In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 539, p. A35-Article in journal (Refereed)
    Abstract [en]

    Context. The large-scale magnetic fields of stars and galaxies are often described in the framework of mean-field dynamo theory. At moderate magnetic Reynolds numbers, the transport coefficients defining the mean electromotive force can be determined from simulations. This applies analogously also to passive scalar transport. Aims. We investigate the mean electromotive force in the kinematic framework, that is, ignoring the back-reaction of the magnetic field on the fluid velocity, under the assumption of axisymmetric turbulence determined by the presence of either rotation, density stratification, or both. We use an analogous approach for the mean passive scalar flux. As an alternative to convection, we consider forced turbulence in an isothermal layer. When using standard ansatzes, the mean magnetic transport is then determined by nine, and the mean passive scalar transport by four coefficients. We give results for all these transport coefficients. Methods. We use the test-field method and the test-scalar method, where transport coefficients are determined by solving sets of equations with properly chosen mean magnetic fields or mean scalars. These methods are adapted to mean fields which may depend on all three space coordinates. Results. We find the anisotropy of turbulent diffusion to be moderate in spite of rapid rotation or strong density stratification. Contributions to the mean electromotive force determined by the symmetric part of the gradient tensor of the mean magnetic field, which were ignored in several earlier investigations, turn out to be important. In stratified rotating turbulence, the a effect is strongly anisotropic, suppressed along the rotation axis on large length scales, but strongly enhanced at intermediate length scales. Also the Omega x (J) over bar effect is enhanced at intermediate length scales. The turbulent passive scalar diffusivity is typically almost twice as large as the turbulent magnetic diffusivity. Both magnetic and passive scalar diffusion are slightly enhanced along the rotation axis, but decreased if there is gravity. Conclusions. The test-field and test-scalar methods provide powerful tools for analyzing transport properties of axisymmetric turbulence. Future applications are proposed ranging from anisotropic turbulence due to the presence of a uniform magnetic field to inhomogeneous turbulence where the specific entropy is nonuniform, for example. Some of the contributions to the mean electromotive force which have been ignored in several earlier investigations, in particular those given by the symmetric part of the gradient tensor of the mean magnetic field, turn out to be of significant magnitude.

  • 32.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Magnetic concentrations in stratified turbulence: the negative effective magnetic pressure instability2016In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 18, article id 125011Article in journal (Refereed)
    Abstract [en]

    In the presence of strong density stratification, hydromagnetic turbulence attains qualitatively new properties: the formation of magnetic flux concentrations. We review here the theoretical foundations of this mechanism in terms of what is now called the negative effective magnetic pressure instability. We also present direct numerical simulations of forced turbulence in strongly stratified layers and discuss the qualitative and quantitative similarities with corresponding mean-field simulations. Finally, the relevance to sunspot formation is discussed.

  • 33.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Schober, Jennifer
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA; University of the Negev, Israel.
    The contribution of kinetic helicity to turbulent magnetic diffusivity2017In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 338, no 7, p. 790-793Article in journal (Refereed)
    Abstract [en]

    Using numerical simulations of forced turbulence, we show that for magnetic Reynolds numbers larger than unity, that is, beyond the regime of quasilinear theory, the turbulent magnetic diffusivity attains an additional negative contribution that is quadratic in the kinetic helicity. In particular, for large magnetic Reynolds numbers, the turbulent magnetic diffusivity without helicity is about twice the value with helicity. Such a contribution was not previously anticipated, but, as we discuss, it turns out to be important when accurate estimates of the turbulent magnetic diffusivity are needed.

  • 34.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Schober, Jennifer
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA; Ben-Gurion University of the Negev, Israel.
    Kahniashvili, Tina
    Boyarsky, Alexey
    Fröhlich, Jürg
    Ruchayskiy, Oleg
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    The Turbulent Chiral Magnetic Cascade in the Early Universe2017In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 845, no 2, article id L21Article in journal (Refereed)
    Abstract [en]

    The presence of asymmetry between fermions of opposite handedness in plasmas of relativistic particles can lead to exponential growth of a helical magnetic field via a small-scale chiral dynamo instability known as the chiral magnetic effect. Here, we show, using dimensional arguments and numerical simulations, that this process produces through the Lorentz force chiral magnetically driven turbulence. A k(-2) magnetic energy spectrum emerges via inverse transfer over a certain range of wavenumbers k. The total chirality (magnetic helicity plus normalized chiral chemical potential) is conserved in this system. Therefore, as the helical magnetic field grows, most of the total chirality gets transferred into magnetic helicity until the chiral magnetic effect terminates. Quantitative results for height, slope, and extent of the spectrum are obtained. Consequences of this effect for cosmic magnetic fields are discussed.

  • 35. Bushby, P. J.
    et al.
    Käpylä, P. J.
    Masada, Y.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Favier, B.
    Guervilly, C.
    Käpylä, M. J.
    Large-scale dynamos in rapidly rotating plane layer convection2018In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 612, article id A97Article in journal (Refereed)
    Abstract [en]

    Context. Convectively driven flows play a crucial role in the dynamo processes that are responsible for producing magnetic activity in stars and planets. It is still not fully understood why many astrophysical magnetic fields have a significant large-scale component. Aims. Our aim is to investigate the dynamo properties of compressible convection in a rapidly rotating Cartesian domain, focusing upon a parameter regime in which the underlying hydrodynamic flow is known to be unstable to a large-scale vortex instability. Methods. The governing equations of three-dimensional non-linear magnetohydrodynamics (MHD) are solved numerically. Different numerical schemes are compared and we propose a possible benchmark case for other similar codes. Results. In keeping with previous related studies, we find that convection in this parameter regime can drive a large-scale dynamo. The components of the mean horizontal magnetic field oscillate, leading to a continuous overall rotation of the mean field. Whilst the large-scale vortex instability dominates the early evolution of the system, the large-scale vortex is suppressed by the magnetic field and makes a negligible contribution to the mean electromotive force that is responsible for driving the large-scale dynamo. The cycle period of the dynamo is comparable to the ohmic decay time, with longer cycles for dynamos in convective systems that are closer to onset. In these particular simulations, large-scale dynamo action is found only when vertical magnetic field boundary conditions are adopted at the upper and lower boundaries. Strongly modulated large-scale dynamos are found at higher Rayleigh numbers, with periods of reduced activity (grand minima-like events) occurring during transient phases in which the large-scale vortex temporarily re-establishes itself, before being suppressed again by the magnetic field.

  • 36. Bykov, A. M.
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Malkov, M. A.
    Osipov, S. M.
    Microphysics of Cosmic Ray Driven Plasma Instabilities2014In: Microphysics of Cosmic Plasmas / [ed] Balogh, A.; Bykov, A.; Cargill, P.; Dendy, R.; DeWit, T. D.; Raymond, J., Dordrcht: Springer, 2014, p. 125-156Chapter in book (Refereed)
    Abstract [en]

    Energetic nonthermal particles (cosmic rays, CRs) are accelerated in supernova remnants, relativistic jets and other astrophysical objects. The CR energy density is typically comparable with that of the thermal components and magnetic fields. In this review we discuss mechanisms of magnetic field amplification due to instabilities induced by CRs. We derive CR kinetic and magnetohydrodynamic equations that govern cosmic plasma systems comprising the thermal background plasma, comic rays and fluctuating magnetic fields to study CR-driven instabilities. Both resonant and non-resonant instabilities are reviewed, including the Bell short-wavelength instability, and the firehose instability. Special attention is paid to the longwavelength instabilities driven by the CR current and pressure gradient. The helicity production by the CR current-driven instabilities is discussed in connection with the dynamo mechanisms of cosmic magnetic field amplification.

  • 37. Bykov, A. M.
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Malkov, M. A.
    Osipov, S. M.
    Microphysics of Cosmic Ray Driven Plasma Instabilities2013In: Space Science Reviews, ISSN 0038-6308, E-ISSN 1572-9672, Vol. 178, no 2-4, p. 201-232Article, review/survey (Refereed)
    Abstract [en]

    Energetic nonthermal particles (cosmic rays, CRs) are accelerated in supernova remnants, relativistic jets and other astrophysical objects. The CR energy density is typically comparable with that of the thermal components and magnetic fields. In this review we discuss mechanisms of magnetic field amplification due to instabilities induced by CRs. We derive CR kinetic and magnetohydrodynamic equations that govern cosmic plasma systems comprising the thermal background plasma, comic rays and fluctuating magnetic fields to study CR-driven instabilities. Both resonant and non-resonant instabilities are reviewed, including the Bell short-wavelength instability, and the firehose instability. Special attention is paid to the longwavelength instabilities driven by the CR current and pressure gradient. The helicity production by the CR current-driven instabilities is discussed in connection with the dynamo mechanisms of cosmic magnetic field amplification.

  • 38. Cameron, R. H.
    et al.
    Dikpati, M.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    The Global Solar Dynamo2017In: Space Science Reviews, ISSN 0038-6308, E-ISSN 1572-9672, Vol. 210, no 1-4, p. 367-395Article, review/survey (Refereed)
    Abstract [en]

    A brief summary of the various observations and constraints that underlie solar dynamo research are presented. The arguments that indicate that the solar dynamo is an alpha-omega dynamo of the Babcock-Leighton type are then shortly reviewed. The main open questions that remain are concerned with the subsurface dynamics, including why sunspots emerge at preferred latitudes as seen in the familiar butterfly wings, why the cycle is about 11 years long, and why the sunspot groups emerge tilted with respect to the equator (Joy's law). Next, we turn to magnetic helicity, whose conservation property has been identified with the decline of large-scale magnetic fields found in direct numerical simulations at large magnetic Reynolds numbers. However, magnetic helicity fluxes through the solar surface can alleviate this problem and connect theory with observations, as will be discussed.

  • 39.
    Candelaresi, Simon
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Dundee, UK.
    Hillier, A.
    Maehara, H.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Shibata, K.
    SUPERFLARE OCCURRENCE AND ENERGIES ON G-, K-, AND M-TYPE DWARFS2014In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 792, no 1, p. 67-Article in journal (Refereed)
    Abstract [en]

    Kepler data from G-, K-, and M-type stars are used to study conditions that lead to superflares with energies above 10(34) erg. From the 117,661 stars included, 380 show superflares with a total of 1690 such events. We study whether parameters, like effective temperature or rotation rate, have any effect on the superflare occurrence rate or energy. With increasing effective temperature we observe a decrease in the superflare rate, which is analogous to the previous findings of a decrease in dynamo activity with increasing effective temperature. For slowly rotating stars, we find a quadratic increase of the mean occurrence rate with the rotation rate up to a critical point, after which the rate decreases linearly. Motivated by standard dynamo theory, we study the behavior of the relative starspot coverage, approximated as the relative brightness variation. For faster rotating stars, an increased fraction of stars shows higher spot coverage, which leads to higher superflare rates. A turbulent dynamo is used to study the dependence of the Ohmic dissipation as a proxy of the flare energy on the differential rotation or shear rate. The resulting statistics of the dissipation energy as a function of dynamo number is similar to the observed flare statistics as a function of the inverse Rossby number and shows similarly strong fluctuations. This supports the idea that superflares might well be possible for solar-type G stars.

  • 40. Chan, Chi-kwan
    et al.
    Mitra, Dhrubaditya
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    Dynamics of saturated energy condensation in two-dimensional turbulence2012In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 85, no 3, p. 036315-Article in journal (Refereed)
    Abstract [en]

    In two-dimensional forced Navier-Stokes turbulence, energy cascades to the largest scales in the system to form a pair of coherent vortices known as the Bose condensate. We show, both numerically and analytically, that the energy condensation saturates and the system reaches a statistically stationary state. The time scale of saturation is inversely proportional to the viscosity and the saturation energy level is determined by both the viscosity and the force. We further show that, without sufficient resolution to resolve the small-scale enstrophy spectrum, numerical simulations can give a spurious result for the saturation energy level. We also find that the movement of the condensate is similar to the motion of an inertial particle with an effective drag force. Furthermore, we show that the profile of the saturated coherent vortices can be described by a Gaussian core with exponential wings.

  • 41. Chatterjee, P.
    et al.
    Mitra, D.
    Rheinhardt, M.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Alpha effect due to buoyancy instability of a magnetic layer2011In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 534, p. A 46-Article in journal (Refereed)
    Abstract [en]

    Context. A strong toroidal field can exist in form of a magnetic layer in the overshoot region below the solar convection zone. This motivates a more detailed study of the magnetic buoyancy instability with rotation. Aims: We calculate the α effect due to helical motions caused by an unstable magnetic layer in a rotating density-stratified system with angular velocity Ω making an angle θ with the vertical. We also study the dependence of the α effect on θ and the strength of the initial magnetic field. Methods: We carry out three-dimensional hydromagnetic simulations in Cartesian geometry. A turbulent electromotive force (EMF) due to the correlations of the small scale velocity and magnetic field is generated. We use the test-field method to calculate the transport coefficients of the inhomogeneous turbulence produced by the layer. Results: We show that the growth rate of the instability and the twist of the magnetic field vary monotonically with the ratio of thermal conductivity to magnetic diffusivity. The resulting α effect is non-uniform and increases with the strength of the initial magnetic field. It is thus an example of an "anti-quenched" α effect. The α effect is also nonlocal, i.e. scale dependent, requiring around 8-16 Fourier modes to reconstruct the actual mean EMF based on the actual mean field.

  • 42. Cole, E.
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Käpylä, P. J.
    Käpylä, M. J.
    Robustness of oscillatory alpha(2) dynamos in spherical wedges2016In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 593, article id A134Article in journal (Refereed)
    Abstract [en]

    Context. Large-scale dynamo simulations are sometimes confined to spherical wedge geometries by imposing artificial boundary conditions at high latitudes. This may lead to spatio-temporal behaviours that are not representative of those in full spherical shells. Aims. We study the connection between spherical wedge and full spherical shell geometries using simple mean-field dynamos. Methods. We solve the equations for one-dimensional time-dependent alpha(2) and alpha(2)Omega mean-field dynamos with only latitudinal extent to examine the effects of varying the polar angle theta(0) between the latitudinal boundaries and the poles in spherical coordinates. Results. In the case of constant alpha and eta(t) profiles, we find oscillatory solutions only with the commonly used perfect conductor boundary condition in a wedge geometry, while for full spheres all boundary conditions produce stationary solutions, indicating that perfect conductor conditions lead to unphysical solutions in such a wedge setup. To search for configurations in which this problem can be alleviated we choose a profile of the turbulent magnetic diffusivity that decreases toward the poles, corresponding to high conductivity there. Oscillatory solutions are now achieved with models extending to the poles, but the magnetic field is strongly concentrated near the poles and the oscillation period is very long. By changing both the turbulent magnetic diffusivity and alpha profiles so that both effects are more concentrated toward the equator, we see oscillatory dynamos with equatorward drift, shorter cycles, and magnetic fields distributed over a wider range of latitudes. Those profiles thus remove the sensitive and unphysical dependence on theta(0). When introducing radial shear, we again see oscillatory dynamos, and the direction of drift follows the Parker-Yoshimura rule. Conclusions. A reduced alpha effect near the poles with a turbulent diffusivity concentrated toward the equator yields oscillatory dynamos with equatorward migration and reproduces best the solutions in spherical wedges. For weak shear, oscillatory solutions are obtained only for perfect conductor field conditions and negative shear. Oscillatory solutions become preferred at sufficiently strong shear. Recent three-dimensional dynamo simulations producing solar-like magnetic activity are expected to lie in this range.

  • 43. Cole, Elizabeth
    et al.
    Käpylä, Petri J.
    Mantere, Maarit J.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    AN AZIMUTHAL DYNAMO WAVE IN SPHERICAL SHELL CONVECTION2014In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 780, no 2, article id L22Article in journal (Refereed)
    Abstract [en]

    We report the discovery of an azimuthal dynamo wave of a low-order (m = 1) mode in direct numerical simulations (DNS) of turbulent convection in spherical shells. Such waves are predicted by mean-field dynamo theory and have been obtained previously in mean-field models. An azimuthal dynamo wave has been proposed as a possible explanation for the persistent drifts of spots observed on several rapidly rotating stars, as revealed through photometry and Doppler imaging. However, this has been judged unlikely because evidence for such waves from DNS has been lacking. Here we present DNS of large-scale magnetic fields showing a retrograde m = 1 mode. Its pattern speed is nearly independent of latitude and does not reflect the speed of the differential rotation at any depth. The extrema of magnetic m = 1 structures coincide reasonably well with the maxima of m = 2 structures of the temperature. These results provide direct support for the observed drifts being due to an azimuthal dynamo wave.

  • 44.
    Del Sordo, Fabio
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Guerrero, G.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Turbulent dynamos with advective magnetic helicity flux2013In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 429, no 2, p. 1686-1694Article in journal (Refereed)
    Abstract [en]

    Many astrophysical bodies harbour magnetic fields that are thought to be sustained by a dynamo process. However, it has been argued that the production of large-scale magnetic fields by mean-field dynamo action is strongly suppressed at large magnetic Reynolds numbers owing to the conservation of magnetic helicity. This phenomenon is known as catastrophic quenching. Advection of magnetic fields by stellar and galactic winds towards the outer boundaries and away from the dynamo is expected to alleviate such quenching. Here we explore the relative roles played by advective and turbulent-diffusive fluxes of magnetic helicity in the dynamo. In particular, we study how the dynamo is affected by advection. We do this by performing direct numerical simulations of a turbulent dynamo of alpha(2) type driven by forced turbulence in a Cartesian domain in the presence of a flow away from the equator where helicity changes sign. Our results indicate that in the presence of advection, the dynamo, otherwise stationary, becomes oscillatory. We confirm an earlier result for turbulent-diffusive magnetic helicity fluxes that for small magnetic Reynolds numbers (Rm less than or similar to 100 ... 200, based on the wavenumber of the energy-carrying eddies) the magnetic helicity flux scales less strongly with magnetic Reynolds number (Rm(-1/2)) than the term describing magnetic helicity destruction by resistivity (Rm(-1)). Our new results now suggest that for larger Rm the former becomes approximately independent of Rm, while the latter falls off more slowly. We show for the first time that both for weak and stronger winds, the magnetic helicity flux term becomes comparable to the resistive term for Rm greater than or similar to 1000, which is necessary for alleviating catastrophic quenching.

  • 45. Dosopoulou, F.
    et al.
    Del Sordo, Fabio
    Stockholm University, Faculty of Science, Department of Astronomy.
    Tsagas, C. G.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    Vorticity production and survival in viscous and magnetized cosmologies2012In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 85, no 6, p. 063514-Article in journal (Refereed)
    Abstract [en]

    We study the role of viscosity and the effects of a magnetic field on a rotating, self-gravitating fluid, using Newtonian theory and adopting the ideal magnetohydrodynamic approximation. Our results confirm that viscosity can generate vorticity in inhomogeneous environments, while the magnetic tension can produce vorticity even in the absence of fluid pressure and density gradients. Linearizing our equations around an Einstein-de Sitter cosmology, we find that viscosity adds to the diluting effect of the universal expansion. Typically, however, the dissipative viscous effects are confined to relatively small scales. We also identify the characteristic length below which the viscous dissipation is strong and beyond which viscosity is essentially negligible. In contrast, magnetism seems to favor cosmic rotation. The magnetic presence is found to slow down the standard decay rate of linear vortices, thus leading to universes with more residual rotation than generally anticipated.

  • 46. Haugen, Nils Erland L.
    et al.
    Kleeorin, Nathan
    Rogachevskii, Igor
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Detection of turbulent thermal diffusion of particles in numerical simulations2012In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 24, no 7, article id 075106Article in journal (Refereed)
    Abstract [en]

    The phenomenon of turbulent thermal diffusion in temperature-stratified turbulence causing a non-diffusive turbulent flux (i.e., non-counter-gradient transport) of inertial and non-inertial particles in the direction of the turbulent heat flux is found using direct numerical simulations (DNS). In simulations with and without gravity, this phenomenon is found to cause a peak in the particle number density around the minimum of the mean fluid temperature for Stokes numbers less than 1, where the Stokes number is the ratio of particle Stokes time to turbulent Kolmogorov time at the viscous scale. Turbulent thermal diffusion causes the formation of inhomogeneities in the spatial distribution of inertial particles whose scale is large in comparison with the integral scale of the turbulence. The strength of this effect is maximum for Stokes numbers around unity, and decreases again for larger values. The dynamics of inertial particles is studied using Lagrangian modelling in forced temperature-stratified turbulence, whereas non-inertial particles and the fluid are described using DNS in an Eulerian framework.

  • 47. Hubbard, A.
    et al.
    Del Sordo, Fabio
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Käpylä, P. J.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    The α effect with imposed and dynamo-generated magnetic fields2009In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 398, no 4, p. 1891-1899Article in journal (Refereed)
    Abstract [en]

    Estimates for the non-linear α effect in helical turbulence with an applied magnetic field are presented using two different approaches: the imposed-field method where the electromotive force owing to the applied field is used, and the test-field method where separate evolution equations are solved for a set of different test fields. Both approaches agree for stronger fields, but there are apparent discrepancies for weaker fields that can be explained by the influence of dynamo-generated magnetic fields on the scale of the domain that are referred to as meso-scale magnetic fields. Examples are discussed where these meso-scale fields can lead to both drastically overestimated and underestimated values of α compared with the kinematic case. It is demonstrated that the kinematic value can be recovered by resetting the fluctuating magnetic field to zero in regular time intervals. It is concluded that this is the preferred technique both for the imposed-field and the test-field methods.

  • 48. Hubbard, Alexander
    et al.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    CATASTROPHIC QUENCHING IN alpha Omega DYNAMOS REVISITED2012In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 748, no 1, p. 51-Article in journal (Refereed)
    Abstract [en]

    At large magnetic Reynolds numbers, magnetic helicity evolution plays an important role in astrophysical large-scale dynamos. The recognition of this fact led to the development of the dynamical alpha quenching formalism, which predicts catastrophically low mean fields in open systems. Here, we show that in oscillatory alpha Omega dynamos this formalism predicts an unphysical magnetic helicity transfer between scales. An alternative technique is proposed where this artifact is removed by using the evolution equation for the magnetic helicity of the total field in the shearing advective gauge. In the traditional dynamical alpha quenching formalism, this can be described by an additional magnetic helicity flux of small-scale fields that does not appear in homogeneous alpha(2) dynamos. In alpha Omega dynamos, the alternative formalism is shown to lead to larger saturation fields than what has been obtained in some earlier models with the traditional formalism. We have compared the predictions of the two formalisms to results of direct numerical simulations, finding that the alternative formulation provides a better fit. This suggests that worries about catastrophic dynamo behavior in the limit of large magnetic Reynolds number are unfounded.

  • 49.
    Jabbari, Sarah
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Mitra, Dhrubaditya
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    BIPOLAR MAGNETIC SPOTS FROM DYNAMOS IN STRATIFIED SPHERICAL SHELL TURBULENCE2015In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 805, no 2, article id 166Article in journal (Refereed)
    Abstract [en]

    Recent work by Mitra et al. (2014) has shown that in strongly stratified forced two-layer turbulence with helicity and corresponding large-scale dynamo action in the lower layer, and nonhelical turbulence in the upper, a magnetic field occurs in the upper layer in the form of sharply bounded bipolar magnetic spots. Here we extend this model to spherical wedge geometry covering the northern hemisphere up to 75 degrees latitude and an azimuthal extent of 180 degrees. The kinetic helicity and therefore also the large-scale magnetic field are strongest at low latitudes. For moderately strong stratification, several bipolar spots form that eventually fill the full longitudinal extent. At early times, the polarity of spots reflects the orientation of the underlying azimuthal field, as expected from Parker's Omega-shaped flux loops. At late times their tilt changes such that there is a radial field of opposite orientation at different latitudes separated by about 10 degrees. Our model demonstrates the spontaneous formation of spots of sizes much larger than the pressure scale height. Their tendency to produce filling factors close to unity is argued to be reminiscent of highly active stars. We confirm that strong stratification and strong scale separation are essential ingredients behind magnetic spot formation, which appears to be associated with downflows at larger depths.

  • 50.
    Jabbari, Sarah
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. Monash University, Australia.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Sharp magnetic structures from dynamos with density stratification2017In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 467, no 3, p. 2753-2765Article in journal (Refereed)
    Abstract [en]

    Recent direct numerical simulations (DNS) of large-scale turbulent dynamos in strongly stratified layers have resulted in surprisingly sharp bipolar structures at the surface. Here, we present new DNS of helically and non-helically forced turbulence with and without rotation and compare with corresponding mean-field simulations (MFS) to show that these structures are a generic outcome of a broader class of dynamos in density-stratified layers. The MFS agree qualitatively with the DNS, but the period of oscillations tends to be longer in the DNS. In both DNS and MFS, the sharp structures are produced by converging flows at the surface and might be driven in non-linear stage of evolution by the Lorentz force associated with the large-scale dynamo-driven magnetic field if the dynamo number is at least 2.5 times supercritical.

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