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  • 1. Andrievsky, Alexander
    et al.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Department of Astronomy, Stockholm University, AlbaNova University Center, Stockholm, Sweden.
    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, 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.
    Bhat, P.
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Hydraulic effects in a radiative atmosphere with ionization2016In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 587, 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.

  • 3. Bhat, Pallavi
    et al.
    Subramanian, Kandaswamy
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    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, 240-247 p.Article 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.

  • 4. Bonanno, Alfio
    et al.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Del Sordo, Fabio
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    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, 016313- p.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.

  • 5.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Magnetic Prandtl number dependence of the kinetic-to-magnetic dissipation ratio2014In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 791, no 1, 12Article 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 Alfvén kinks.

  • 6.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Non-linear and chaotic dynamo regimes2012In: Proceedings of the International Astronomical Union: Vol. 8 Symposium S294, Cambridge University Press, 2012, no S294, 387-398 p.Conference paper (Refereed)
    Abstract [en]

    An update is given on the current status of solar and stellar dynamos. At present, it is still unclear why stellar cycle frequencies increase with rotation frequency in such a way that their ratio increases with stellar activity. The small-scale dynamo is expected to operate in spite of a small value of the magnetic Prandtl number in stars. Whether or not the global magnetic activity in stars is a shallow or deeply rooted phenomenon is another open question. Progress in demonstrating the presence and importance of magnetic helicity fluxes in dynamos is briefly reviewed, and finally the role of nonlocality is emphasized in modeling stellar dynamos using the mean-field approach. On the other hand, direct numerical simulations have now come to the point where the models show solar-like equatorward migration that can be compared with observations and that need to be understood theoretically.

  • 7.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    STELLAR MIXING LENGTH THEORY with ENTROPY RAIN2016In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 832, no 1, 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.

  • 8.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80303, USA; Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80303, USA; Department of Astronomy, AlbaNova University Center, Stockholm University, SE-10691 Stockholm, Sweden.
    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, 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.

  • 9.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Gressel, Oliver
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Jabbari, Sarah
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    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, A53- p.Article 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.

  • 10.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Gressel, Oliver
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Käpylä, Petri J.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mantere, M. J.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    New scaling for the alpha effect in slowly rotating turbulence2013In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 762, no 2, 127- p.Article 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.

  • 11.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Hubbard, Alexander
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Käpylä, Petri
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Dynamical quenching with non-local alpha and downward pumping2015In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 336, no 1, 91-96 p.Article 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.

  • 12.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kahniashvili, Tina
    Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay2017In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 118, no 5, 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)).

  • 13.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    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, 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.

  • 14.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    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 7, 075001Article 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.

  • 15.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Self-assembly of shallow magnetic spots through strongly stratified turbulence2013In: Astrophysical Journal Letters, ISSN 2041-8205, Vol. 776, no 2, L23- p.Article 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.

  • 16.
    Brandenburg, Axel
    et al.
    KTH, Centres, 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, 163-200 p.Article, 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.

  • 17.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    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, 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.

  • 18.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    Special Issue: From Mean-Field to Large-Scale Dynamos Introduction2013In: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 107, no 1-2, 1-2 p.Article in journal (Other academic)
  • 19.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan I.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Magnetic concentrations in stratified turbulence: The negative effective magnetic pressure instability2016In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 18, no 12, 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.

  • 20.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado; JILA and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, Colorado; Department of Astronomy, AlbaNova University Center, Stockholm University, Stockholm, Sweden.
    Schober, J.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, I.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado; Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, 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, 790-793 p.Article 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.

  • 21.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Laboratory for Atmospheric and Space Physics, University of Colorado; JILA and Department of Astrophysical and Planetary Sciences, University of Colorado Department of Mechanical Engineering, Ben-Gurion University of the Negev.
    Schober, Jennifer
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Laboratory for Atmospheric and Space Physics, University of Colorado, Department of Mechanical Engineering, Ben-Gurion University of the Negev.
    Kahniashvili, Tina
    Boyarsky, Alexey
    Frohlich, Jog
    Ruchayskiy, Oleg
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    The Turbulent Chiral Magnetic Cascade in the Early Universe2017In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 845, no 2, 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.

  • 22.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Sokoloff, Dmitry
    Subramanian, Kandaswamy
    Current Status of Turbulent Dynamo Theory From Large Scale to Small-Scale Dynamos2012In: Space Science Reviews, ISSN 0038-6308, E-ISSN 1572-9672, Vol. 169, no 1-4, 123-157 p.Article, review/survey (Refereed)
    Abstract [en]

    Several recent advances in turbulent dynamo theory are reviewed. High resolution simulations of small-scale and large-scale dynamo action in periodic domains are compared with each other and contrasted with similar results at low magnetic Prandtl numbers. It is argued that all the different cases show similarities at intermediate length scales. On the other hand, in the presence of helicity of the turbulence, power develops on large scales, which is not present in non-helical small-scale turbulent dynamos. At small length scales, differences occur in connection with the dissipation cutoff scales associated with the respective value of the magnetic Prandtl number. These differences are found to be independent of whether or not there is large-scale dynamo action. However, large-scale dynamos in homogeneous systems are shown to suffer from resistive slow-down even at intermediate length scales. The results from simulations are connected to mean field theory and its applications. Recent work on magnetic helicity fluxes to alleviate large-scale dynamo quenching, shear dynamos, nonlocal effects and magnetic structures from strong density stratification are highlighted. Several insights which arise from analytic considerations of small-scale dynamos are discussed.

  • 23.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Stepanov, Rodion
    Faraday signature of magnetic helicity from reduced depolarization2014In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 786, no 2, 91- p.Article in journal (Refereed)
    Abstract [en]

    Using one-dimensional models, we show that a helical magnetic field with an appropriate sign of helicity can compensate the Faraday depolarization resulting from the superposition of Faraday-rotated polarization planes from a spatially extended source. For radio emission from a helical magnetic field, the polarization as a function of the square of the wavelength becomes asymmetric with respect to zero. Mathematically speaking, the resulting emission occurs then either at observable or at unobservable (imaginary) wavelengths. We demonstrate that rotation measure (RM) synthesis allows for the reconstruction of the underlying Faraday dispersion function in the former case, but not in the latter. The presence of positive magnetic helicity can thus be detected by observing positive RM in highly polarized regions in the sky and negative RM in weakly polarized regions. Conversely, negative magnetic helicity can be detected by observing negative RM in highly polarized regions and positive RM in weakly polarized regions. The simultaneous presence of two magnetic constituents with opposite signs of helicity is shown to possess signatures that can be quantified through polarization peaks at specific wavelengths and the gradient of the phase of the Faraday dispersion function. Similar polarization peaks can tentatively also be identified for the bi-helical magnetic fields that are generated self-consistently by a dynamo from helically forced turbulence, even though the magnetic energy spectrum is then continuous. Finally, we discuss the possibility of detecting magnetic fields with helical and non-helical properties in external galaxies using the Square Kilometre Array.

  • 24. Bykov, A. M.
    et al.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Department of Astronomy, Stockholm University, Sweden.
    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, 201-232 p.Article, 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.

  • 25. Cameron, R. H.
    et al.
    Dikpati, M.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    The Global Solar Dynamo2016In: Space Science Reviews, ISSN 0038-6308, E-ISSN 1572-9672, 1-29 p.Article in journal (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.

  • 26.
    Candelaresi, Simon
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kinetic helicity needed to drive large-scale dynamos2013In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 87, no 4, 043104- p.Article in journal (Refereed)
    Abstract [en]

    Magnetic field generation on scales that are large compared with the scale of the turbulent eddies is known to be possible via the so-called a effect when the turbulence is helical and if the domain is large enough for the a effect to dominate over turbulent diffusion. Using three-dimensional turbulence simulations, we show that the energy of the resulting mean magnetic field of the saturated state increases linearly with the product of normalized helicity and the ratio of domain scale to eddy scale, provided this product exceeds a critical value of around unity. This implies that large-scale dynamo action commences when the normalized helicity is larger than the inverse scale ratio. Our results show that the emergence of small-scale dynamo action does not have any noticeable effect on the large-scale dynamo. Recent findings by Pietarila Graham et al. [Phys. Rev. E 85, 066406 (2012)] of a smaller minimal helicity may be an artifact due to the onset of small-scale dynamo action at large magnetic Reynolds numbers. However, the onset of large-scale dynamo action is difficult to establish when the kinetic helicity is small. Instead of random forcing, they used an ABC flow with time-dependent phases. We show that such dynamos saturate prematurely in a way that is reminiscent of inhomogeneous dynamos with internal magnetic helicity fluxes. Furthermore, even for very low fractional helicities, such dynamos display large-scale fields that change direction, which is uncharacteristic of turbulent dynamos.

  • 27.
    Candelaresi, Simon
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Topological constraints on magnetic field relaxation2012In: Proc. Int. Astron. Union, 2012, no S294, 353-357 p.Conference paper (Refereed)
    Abstract [en]

    Magnetic field relaxation is determined by both the field's geometry and its topology. For relaxation processes, however, it turns out that its topology is a much more stringent constraint. As quantifier for the topology we use magnetic helicity and test whether it is a stronger condition than the linking of field lines. Further, we search for evidence of other topological invariants, which give rise to further restrictions in the field's relaxation. We find that magnetic helicity is the sole determinant in most cases. Nevertheless, we see evidence for restrictions not captured through magnetic helicity.

  • 28.
    Candelaresi, Simon
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden .
    Hillier, A.
    Maehara, H.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden .
    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, 67- p.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.

  • 29.
    Cole, Elizabeth
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Käpylä, P. J.
    Käpylä, M. J.
    Robustness of oscillatory α 2 dynamos in spherical wedges2016In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 593, 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 α2 and α2Ω mean-field dynamos with only latitudinal extent to examine the effects of varying the polar angle θ0 between the latitudinal boundaries and the poles in spherical coordinates. Results. In the case of constant α and ηt 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 α 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 θ0. When introducing radial shear, we again see oscillatory dynamos, and the direction of drift follows the Parker-Yoshimura rule. Conclusions. A reduced α 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.

  • 30. Cole, Elizabeth
    et al.
    Käpylä, Petri J.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mantere, Maarit J.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    An azimuthal dynamo wave in spherical shell convection2014In: Astrophysical Journal Letters, ISSN 2041-8205, Vol. 780, no 2, L22- p.Article 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.

  • 31.
    Del Sordo, Fabio
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Guerrero, Gustavo
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    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, 1686-1694 p.Article 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.

  • 32.
    Devlen, Ebru
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    A mean field dynamo from negative eddy diffusivity2013In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 432, no 2, 1651-1657 p.Article in journal (Refereed)
    Abstract [en]

    Using direct numerical simulations, we verify that Roberts-IV flow exhibits dynamo action dominated by horizontally averaged large-scale magnetic field. With the test-field method, we compute the turbulent magnetic diffusivity and find that it is negative and overcomes the molecular diffusivity, thus explaining quantitatively the large-scale dynamo for magnetic Reynolds numbers above approximate to 8. As expected for a dynamo of this type, but contrary to alpha-effect dynamos, the two horizontal field components grow independently of each other and have arbitrary amplitude ratios and phase differences. Small length-scales of the mean magnetic field are shown to be stabilized by the turbulent magnetic diffusivity becoming positive at larger wavenumbers. Oscillatory decaying or growing solutions have also been found in certain wavenumber intervals and sufficiently large values of the magnetic Reynolds number. For magnetic Reynolds numbers below approximate to 0.5, the turbulent magnetic diffusivity is confirmed to be positive, as expected for all incompressible flows. Earlier claims of a dynamo driven by a modified Taylor-Green flow through negative eddy diffusivity could not be confirmed.

  • 33. Haugen, Nils Erland L.
    et al.
    Kleeorin, Nathan
    Rogachevskii, Igor
    Brandenburg, Axel
    KTH, Centres, 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, 075106- p.Article 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.

  • 34.
    Jabbari, Sarah
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    BIPOLAR MAGNETIC SPOTS FROM DYNAMOS IN STRATIFIED SPHERICAL SHELL TURBULENCE2015In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 805, no 2, 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.

  • 35.
    Jabbari, Sarah
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Surface flux concentrations in a spherical alpha 2 dynamo2013In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 556, A106- p.Article in journal (Refereed)
    Abstract [en]

    Context. In the presence of strong density stratification, turbulence can lead to the large-scale instability of a horizontal magnetic field if its strength is in a suitable range (around a few percent of the turbulent equipartition value). This instability is related to a suppression of the turbulent pressure so that the turbulent contribution to the mean magnetic pressure becomes negative. This results in the excitation of a negative effective magnetic pressure instability (NEMPI). This instability has so far only been studied for an imposed magnetic field. Aims. We want to know how NEMPI works when the mean magnetic field is generated self-consistently by an alpha(2) dynamo, whether it is affected by global spherical geometry, and whether it can influence the properties of the dynamo itself. Methods. We adopt the mean-field approach, which has previously been shown to provide a realistic description of NEMPI in direct numerical simulations. We assume axisymmetry and solve the mean-field equations with the Pencil Code for an adiabatic stratification at a total density contrast in the radial direction of approximate to 4 orders of magnitude. Results. NEMPI is found to work when the dynamo-generated field is about 4% of the equipartition value, which is achieved through strong alpha quenching. This instability is excited in the top 5% of the outer radius, provided the density contrast across this top layer is at least 10. NEMPI is found to occur at lower latitudes when the mean magnetic field is stronger. For weaker fields, NEMPI can make the dynamo oscillatory with poleward migration. Conclusions. NEMPI is a viable mechanism for producing magnetic flux concentrations in a strongly stratified spherical shell in which a magnetic field is generated by a strongly quenched alpha effect dynamo.

  • 36.
    Jabbari, Sarah
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Monash Univ, Australia; Stockholm Univ, Sweden.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Sweden; Univ Colorado, USA; Lab Atmospher & Space Phys, USA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Sweden; Ben Gurion Univ Negev, Israel.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Sweden; Ben Gurion Univ 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, 2753-2765 p.Article 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.

  • 37.
    Jabbari, Sarah
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Ben-Gurion University of the Negev, Israel.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Ben-Gurion University of the Negev, Israel.
    Turbulent reconnection of magnetic bipoles in stratified turbulence2016In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 459, no 4, 4046-4056 p.Article in journal (Refereed)
    Abstract [en]

    We consider strongly stratified forced turbulence in a plane-parallel layer with helicity and corresponding large-scale dynamo action in the lower part and non-helical turbulence in the upper. The magnetic field is found to develop strongly concentrated bipolar structures near the surface. They form elongated bands with a sharp interface between opposite polarities. Unlike earlier experiments with imposed magnetic field, the inclusion of rotation does not strongly suppress the formation of these structures. We perform a systematic numerical study of this phenomenon by varying magnetic Reynolds number, scale-separation ratio, and Coriolis number. We focus on the formation of a current sheet between bipolar regions where reconnection of oppositely oriented field lines occurs. We determine the reconnection rate by measuring either the inflow velocity in the vicinity of the current sheet or by measuring the electric field in the reconnection region. We demonstrate that for large Lundquist numbers, S > 10(3), the reconnection rate is nearly independent of S in agreement with results of recent numerical simulations performed by other groups in simpler settings.

  • 38.
    Jabbari, Sarah
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Rivero Losada, Illa
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Ben-Gurion University of the Negev, Israel .
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Ben-Gurion University of the Negev, Israel .
    Magnetic flux concentrations from dynamo-generated fields2014In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 568, A112- p.Article in journal (Refereed)
    Abstract [en]

    Context The mean field theory of magnetized stellar convection gives rise to two distinct instabilities; the large-scale dynamo instability, operating in the bulk of the convection zone and a negative effective magnetic pressure instability (NEMPI) operating in the strongly stratified surface layers. The latter might be important in connection with magnetic spot formation. However, as follows from theoretical analysis, the growth rate of NEMPI is suppressed with increasing rotation rates. On the other hand, recent direct numerical simulations (DNS) have shown a subsequent increase in the growth rate. Aims. We examine quantitatively whether this increase in the growth rate of NEMPI can be explained by an alpha(2) mean field dynamo, and whether both NEMPI and the dynamo instability can operate at the same time. Methods. We use both DNS and mean field simulations (MFS) to solve the underlying equations numerically either with or without an imposed horizontal held, We use the test-field method to compute relevant dynamo coefficients. Results. DNS show that magnetic flux concentrations are still possible up to rotation rates above which the large-scale dynamo effect produces mean magnetic fields. The resulting DNS growth rates are quantitatively reproduced with MPS. As expected for weak or vanishing rotation, the growth rate of NEMPI increases with increasing gravity, but there is a correction term for strong gravity and large turbulent magnetic diffusivity. Conclusions. Magnetic flux concentrations are still possible for rotation rates above which dynamo action takes over For the solar rotation rate, the corresponding turbulent turnover time is about 5 h, with dynamo action commencing in the layers beneath.

  • 39. Kaepylae, Petri J.
    et al.
    Rheinhardt, Matthias
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Department of Astronomy, AlbaNova University Center, Stockholm University; JILA and Department of Astrophysical and Planetary Sciences, University of Colorado; Laboratory for Atmospheric and Space Physics, 3665 Discovery Drive, Boulder, CO 80303, USA.
    Arlt, Rainer
    Kaepylae, Maarit J.
    Lagg, Andreas
    Olspert, Nigul
    Warnecke, Joern
    Extended Subadiabatic Layer in Simulations of Overshooting Convection2017In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 845, no 2, L23Article in journal (Refereed)
    Abstract [en]

    We present numerical simulations of hydrodynamic overshooting convection in local Cartesian domains. We find that a substantial fraction of the lower part of the convection zone (CZ) is stably stratified according to the Schwarzschild criterion while the enthalpy flux is outward directed. This occurs when the heat conduction profile at the bottom of the CZ is smoothly varying, based either on a Kramers-like opacity prescription as a function of temperature and density or a static profile of a similar shape. We show that the subadiabatic layer arises due to nonlocal energy transport by buoyantly driven downflows in the upper parts of the CZ. Analysis of the force balance of the upflows and downflows confirms that convection is driven by cooling at the surface. We find that the commonly used prescription for the convective enthalpy flux being proportional to the negative entropy gradient does not hold in the stably stratified layers where the flux is positive. We demonstrate the existence of a non-gradient contribution to the enthalpy flux, which is estimated to be important throughout the convective layer. A quantitative analysis of downflows indicates a transition from a tree-like structure where smaller downdrafts merge into larger ones in the upper parts to a structure in the deeper parts where a height-independent number of strong downdrafts persist. This change of flow topology occurs when a substantial subadiabatic layer is present in the lower part of the CZ.

  • 40. Kahniashvili, Tina
    et al.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Campanelli, Leonardo
    Ratra, Bharat
    Tevzadze, Alexander G.
    Evolution of inflation-generated magnetic field through phase transitions2012In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 86, no 10, 103005- p.Article in journal (Refereed)
    Abstract [en]

    We study the evolution of an inflation-generated magnetic field, due to its coupling to fluid motions, during cosmological phase transitions. We find that the magnetic field stays almost unchanged on large scales, while on small scales, the spectrum is modified in such a way that power at small scales becomes progressively suppressed. We also show that the magnetic field generates turbulent motions in the initially turbulence-free plasma. On large scales, the slope of the resulting kinetic energy spectrum is consistent with that of white noise.

  • 41. Kahniashvili, Tina
    et al.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Durrer, Ruth
    Tevzadze, Alexander G.
    Yin, Winston
    Scale-invariant helical magnetic field evolution and the duration of inflation2017In: Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, E-ISSN 1475-7516, no 11, 002Article in journal (Refereed)
    Abstract [en]

    We consider a scale-invariant helical magnetic field generated during inflation. We show that, if the mean magnetic helicity density of such a field is measured, it can be used to determine a lower bound on the duration of inflation. Even if we just have upper bounds on the helicity, these can be used to derive constraints on the minimal duration if one assumes that the magnetic field generated during inflation is helical. Using three-dimensional simulations, we show that an initially scale-invariant field develops, which is similar both with and without magnetic helicity. In the fully helical case, however, the magnetic field appears to have a more pronounced folded structure.

  • 42. Kahniashvili, Tina
    et al.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Tevzadze, Alexander G.
    The evolution of primordial magnetic fields since their generation2016In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 91, no 10, 104008Article in journal (Refereed)
    Abstract [en]

    We study the evolution of primordial magnetic fields in an expanding cosmic plasma. For this purpose we present a comprehensive theoretical model to consider the evolution of MHD turbulence that can be used over a wide range of physical conditions, including cosmological and astrophysical applications. We model different types of decaying cosmic MHD turbulence in the expanding Universe and characterize the large-scale magnetic fields in such a medium. Direct numerical simulations of freely decaying MHD turbulence are performed for different magnetogenesis scenarios: magnetic fields generated during cosmic inflation as well as electroweak and QCD phase transitions in the early Universe. Magnetic fields and fluid motions are strongly coupled due to the high Reynolds number in the early Universe. Hence, we abandon the simple adiabatic dilution model to estimate magnetic field amplitudes in the expanding Universe and include turbulent mixing effects on the large-scale magnetic field evolution. Numerical simulations have been carried out for non-helical and helical magnetic field configurations. The numerical results show the possibility of inverse transfer of energy in magnetically dominated non-helical MHD turbulence. On the other hand, decay properties of helical turbulence depend on whether the turbulent magnetic field is in a weakly or a fully helical state. Our results show that primordial magnetic fields can be considered as a seed for the observed large-scale magnetic fields in galaxies and clusters. Bounds on the magnetic field strength are obtained and are consistent with the upper and lower limits set by observations of extragalactic magnetic fields.

  • 43. Kahniashvili, Tina
    et al.
    Tevzadze, Alexander G.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Neronov, Andrii
    Evolution of primordial magnetic fields from phase transitions2013In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 87, no 8, 083007- p.Article in journal (Refereed)
    Abstract [en]

    We consider the evolution of primordial magnetic fields generated during cosmological, electroweak, or QCD phase transitions. We assume that the magnetic field generation can be described as an injection of magnetic energy to cosmological plasma at a given scale determined by the moment of magnetic field generation. A high Reynolds number ensures strong coupling between the magnetic field and fluid motions. The subsequent evolution of the magnetic field is governed by decaying hydromagnetic turbulence. Both our numerical simulations and a phenomenological description allow us to recover "universal'' laws for the decay of magnetic energy and the growth of magnetic correlation length in the turbulent (low-viscosity) regime. In particular, we show that during the radiation-dominated epoch, the energy and correlation length of nonhelical magnetic fields scale as conformal time to the powers -1/2 and +1/2, respectively. For helical magnetic fields, the energy and correlation length scale as conformal time to the powers -1/3 and +2/3, respectively. The universal decay law of the magnetic field implies that the strength of the magnetic field generated during the QCD phase transition could reach similar to 10(-9) G with the present-day correlation length similar to 50 kpc. The fields generated at the electroweak phase transition could be as strong as similar to 10(-10) G with correlation lengths reaching similar to 0.3 kpc. These values of the magnetic fields are consistent with the lower bounds of the extragalactic magnetic fields.

  • 44. Kapyla, M. J.
    et al.
    Kapyla, P. J.
    Olspert, N.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Warnecke, J.
    Karak, Bidya Binay
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Pelt, J.
    Multiple dynamo modes as a mechanism for long-term solar activity variations2016In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 589, A56Article in journal (Refereed)
    Abstract [en]

    Context. Solar magnetic activity shows both smooth secular changes, such as the modern Grand Maximum, and quite abrupt drops that are denoted as grand minima, such as the Maunder Minimum. Direct numerical simulations (DNS) of convection-driven dynamos off er one way of examining the mechanisms behind these events. Aims. In this work, we analyze a solution of a solar-like DNS that was evolved for roughly 80 magnetic cycles of 4.9 years and where epochs of irregular behavior are detected. The emphasis of our analysis is to find physical causes for such behavior. Methods. The DNS employed is a semi-global (wedge-shaped) magnetoconvection model. For the data analysis tasks we use Ensemble Empirical Mode Decomposition and phase dispersion methods, as they are well suited for analyzing cyclic (non-periodic) signals. Results. A special property of the DNS is the existence of multiple dynamo modes at different depths and latitudes. The dominant mode is solar-like (equatorward migration at low latitudes and poleward at high latitudes). This mode is accompanied by a higher frequency mode near the surface and at low latitudes, showing poleward migration, and a low-frequency mode at the bottom of the convection zone. The low-frequency mode is almost purely antisymmetric with respect to the equator, while the dominant mode has strongly fluctuating mixed parity. The overall behavior of the dynamo solution is extremely complex, exhibiting variable cycle lengths, epochs of disturbed and even ceased surface activity, and strong short-term hemispherical asymmetries. Surprisingly, the most prominent suppressed surface activity epoch is actually a global magnetic energy maximum; during this epoch the bottom toroidal magnetic field obtains a maximum, demonstrating that the interpretation of grand minima-type events is non-trivial. The hemispherical asymmetries are seen only in the magnetic field, while the velocity field exhibits considerably weaker asymmetry. Conclusions. We interpret the overall irregular behavior as being due to the interplay of the different dynamo modes showing different equatorial symmetries, especially the smoother part of the irregular variations being related to the variations of the mode strengths, evolving with different and variable cycle lengths. The abrupt low-activity epoch in the dominant dynamo mode near the surface is related to a strong maximum of the bottom toroidal field strength, which causes abrupt disturbances especially in the differential rotation profile via the suppression of the Reynolds stresses.

  • 45.
    Kapyla, Petri
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Univ Helsinki, Dept Phys, Finland.
    Kapyla, M. J.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Department of Astronomy, Stockholm University, Sweden .
    Confirmation of bistable stellar differential rotation profiles2014In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 570, A43- p.Article in journal (Refereed)
    Abstract [en]

    Context. Solar-like differential rotation is characterized by a rapidly rotating equator and slower poles. However, theoretical models and numerical simulations can also result in a slower equator and faster poles when the overall rotation is slow. Aims. We study the critical rotational influence under which differential rotation flips from solar-like (fast equator, slow poles) to an anti-solar one (slow equator, fast poles). We also estimate the non-diffusive (A effect) and diffusive (turbulent viscosity) contributions to the Reynolds stress. Methods. We present the results of three-dimensional numerical simulations of mildly turbulent convection in spherical wedge geometry. Here we apply a fully compressible setup which would suffer from a prohibitive time step constraint if the real solar luminosity was used. To avoid this problem while still representing the same rotational influence on the flow as in the Sun, we increase the luminosity by a factor of roughly 106 and the rotation rate by a factor of 10(2). We regulate the convective velocities by varying the amount of heat transported by thermal conduction, turbulent diffusion, and resolved convection. Results. Increasing the efficiency of resolved convection leads to a reduction of the rotational influence on the flow and a sharp transition from solar-like to anti-solar differential rotation for Coriolis numbers around 1.3. We confirm the recent finding of a large-scale flow bistability: contrasted with running the models from an initial condition with unprescribed differential rotation, the initialization of the model with certain kind of rotation profile sustains the solution over a wider parameter range. The anti-solar profiles are found to be more stable against perturbations in the level of convective turbulent velocity than the solar-type solutions. Conclusions. Our results may have implications for real stars that start their lives as rapid rotators implying solar-like rotation in the early main-sequence evolution. As they slow down, they might be able to retain solar-like rotation for lower Coriolis numbers, and thus longer in time, before switching to anti-solar rotation. This could partially explain the puzzling findings of anti-solar rotation profiles for models in the solar parameter regime.

  • 46.
    Karak, Bidya Binay
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Max-Planck-Institut für Sonnensystemforschung, Germany.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. AlbaNova University Center, Stockholm University, Sweden; University of Colorado, United States.
    Is the small-scale magnetic field correlated with the dynamo cycle?2016In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 816, no 1Article in journal (Refereed)
    Abstract [en]

    The small-scale magnetic field is ubiquitous at the solar surface - even at high latitudes. From observations we know that this field is uncorrelated (or perhaps even weakly anticorrelated) with the global sunspot cycle. Our aim is to explore the origin, and particularly the cycle dependence, of such a phenomenon using three-dimensional dynamo simulations. We adopt a simple model of a turbulent dynamo in a shearing box driven by helically forced turbulence. Depending on the dynamo parameters, large-scale (global) and small-scale (local) dynamos can be excited independently in this model. Based on simulations in different parameter regimes, we find that, when only the large-scale dynamo is operating in the system, the small-scale magnetic field generated through shredding and tangling of the large-scale magnetic field is positively correlated with the global magnetic cycle. However, when both dynamos are operating, the small-scale field is produced from both the small-scale dynamo and the tangling of the large-scale field. In this situation, when the large-scale field is weaker than the equipartition value of the turbulence, the small-scale field is almost uncorrelated with the large-scale magnetic cycle. On the other hand, when the large-scale field is stronger than the equipartition value, we observe an anticorrelation between the small-scale field and the large-scale magnetic cycle. This anticorrelation can be interpreted as a suppression of the small-scale dynamo. Based on our studies we conclude that the observed small-scale magnetic field in the Sun is generated by the combined mechanisms of a small-scale dynamo and tangling of the large-scale field.

  • 47.
    Karak, Bidya Binay
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kapyla, P. J.
    Kapyla, M. J.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Olspert, N.
    Pelt, J.
    Magnetically controlled stellar differential rotation near the transition from solar to anti-solar profiles2015In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 576, A26Article in journal (Refereed)
    Abstract [en]

    Context. Late-type stars rotate differentially owing to anisotropic turbulence in their outer convection zones. The rotation is called solar-like (SL) when the equator rotates fastest and anti-solar (AS) otherwise. Hydrodynamic simulations show a transition from SL to AS rotation as the influence of rotation on convection is reduced, but the opposite transition occurs at a different point in the parameter space. The system is bistable, i.e., SL and AS rotation profiles can both be stable. Aims. We study the effect of a dynamo-generated magnetic field on the large-scale flows, particularly on the possibility of bistable behaviour of differential rotation. Methods. We solve the hydromagnetic equations numerically in a rotating spherical shell that typically covers +/- 75 degrees latitude (wedge geometry) for a set of different radiative conductivities controlling the relative importance of convection. We analyse the resulting differential rotation, meridional circulation, and magnetic field and compare the corresponding modifications of the Reynolds and Maxwell stresses. Results. In agreement with earlier findings, our models display SL rotation profiles when the rotational influence on convection is strong and a transition to AS when the rotational influence decreases. We find that dynamo-generated magnetic fields help to produce SL differential rotation compared to the hydrodynamic simulations. We do not observe any bistable states of differential rotation. In the AS cases we find coherent single-cell meridional circulation, whereas in SL cases we find multi-cellular patterns. In both cases, we obtain poleward circulation near the surface with a magnitude close to that observed in the Sun. In the slowly rotating cases, we find activity cycles, but no clear polarity reversals, whereas in the more rapidly rotating cases irregular variations are obtained. Moreover, both differential rotation and meridional circulation have significant temporal variations that are similar in strength to those of the Sun. Conclusions. Purely hydrodynamic simulations of differential rotation and meridional circulation are shown to be of limited relevance as magnetic fields, self-consistently generated by dynamo action, significantly affect the flows.

  • 48.
    Karak, Bidya Binay
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kitchatinov, L. L.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Hysteresis between distinct modes of turbulent dynamos2015In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 803, no 2, 95Article in journal (Refereed)
    Abstract [en]

    Nonlinear mean-field models of the solar dynamo show long-term variability, which may be relevant to different states of activity inferred from long-term radiocarbon data. This paper is aimed at probing the dynamo hysteresis predicted by the recent mean-field models of Kitchatinov & Olemskoy with direct numerical simulations. We perform three-dimensional (3D) simulations of large-scale dynamos in a shearing box with helically forced turbulence. As an initial condition, we either take a weak random magnetic field or we start from a snapshot of an earlier simulation. Two quasi-stable states are found to coexist in a certain range of parameters close to the onset of the large-scale dynamo. The simulations converge to one of these states depending on the initial conditions. When either the fractional helicity or the magnetic Prandtl number is increased between successive runs above the critical value for onset of the dynamo, the field strength jumps to a finite value. However, when the fractional helicity or the magnetic Prandtl number is then decreased again, the field strength stays at a similar value (strong field branch) even below the original onset. We also observe intermittent decaying phases away from the strong field branch close to the point where large-scale dynamo action is just possible. The dynamo hysteresis seen previously in mean-field models is thus reproduced by 3D simulations. Its possible relation to distinct modes of solar activity such as grand minima is discussed.

  • 49.
    Karak, Bidya Binay
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rheinhardt, Matthias
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden .
    Kapyla, Petri J.
    Kapyla, Maarit J.
    QUENCHING AND ANISOTROPY OF HYDROMAGNETIC TURBULENT TRANSPORT2014In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 795, no 1, 16- p.Article in journal (Refereed)
    Abstract [en]

    Hydromagnetic turbulence affects the evolution of large-scale magnetic fields through mean-field effects like turbulent diffusion and the alpha effect. For stronger fields, these effects are usually suppressed or quenched, and additional anisotropies are introduced. Using different variants of the test-fieldmethod, we determine the quenching of the turbulent transport coefficients for the forced Roberts flow, isotropically forced non-helical turbulence, and rotating thermal convection. We see significant quenching only when the mean magnetic field is larger than the equipartition value of the turbulence. Expressing the magnetic field in terms of the equipartition value of the quenched flows, we obtain for the quenching exponents of the turbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts flow, forced turbulence, and convection, respectively. However, when the magnetic field is expressed in terms of the equipartition value of the unquenched flows, these quenching exponents become about 4, 1.5, and 2.3, respectively. For the alpha effect, the exponent is about 1.3 for the Roberts flow and 2 for convection in the first case, but 4 and 3, respectively, in the second. In convection, the quenching of turbulent pumping follows the same power law as turbulent diffusion, while for the coefficient describing the Omega x J effect nearly the same quenching exponent is obtained as for alpha. For forced turbulence, turbulent diffusion proportional to the second derivative along the mean magnetic field is quenched much less, especially for larger values of the magnetic Reynolds number. However, we find that in corresponding axisymmetric mean-field dynamos with dominant toroidal field the quenched diffusion coefficients are the same for the poloidal and toroidal field constituents.

  • 50.
    Kemel, Koen
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Kleeorin, N.
    Mitra, D.
    Rogachevskii, I.
    Active region formation through the negative effective magnetic pressure instability2014In: Solar Dynamics and Magnetism from the Interior to the Atmosphere, Springer-Verlag New York, 2014, 293-313 p.Chapter in book (Other academic)
    Abstract [en]

    The negative effective magnetic-pressure instability operates on scales encompassing many turbulent eddies, which correspond to convection cells in the Sun. This instability is discussed here in connection with the formation of active regions near the surface layers of the Sun. This instability is related to the negative contribution of turbulence to the mean magnetic pressure that causes the formation of large-scale magnetic structures. For an isothermal layer, direct numerical simulations and mean-field simulations of this phenomenon are shown to agree in many details, for example the onset of the instability occurs at the same depth. This depth increases with increasing field strength, such that the growth rate of this instability is independent of the field strength, provided the magnetic structures are fully contained within the domain. A linear stability analysis is shown to support this finding. The instability also leads to a redistribution of turbulent intensity and gas pressure that could provide direct observational signatures.

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