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  • 1. Käpylä, Petri J.
    et al.
    Mantere, Maarit J.
    Cole, Elisabeth
    Warnecke, Jörn
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Effects of strong stratification on equatorward dynamo wave propagationManuscript (preprint) (Other academic)
    Abstract [en]

    We present results from simulations of rotating magnetized  turbulent convection in spherical wedge geometry representing parts  of the latitudinal and longitudinal extents of a star.  Here we consider a set of runs for which the density stratification is  varied, keeping the  Reynolds and Coriolis numbers at similar values. In the case of weak  stratification we find quasi-steady solutions for moderate rotation and oscillatory dynamos with poleward migration of activity belts  for more rapid rotation. For stronger stratification a similar transition as a function of the Coriolis number is found, but with an equatorward migrating branch near the equator. We test the domain size dependence of our results for a rapidly rotating run with equatorward migration by varying the longitudinal  extent of our wedge. The energy of the axisymmetric mean magnetic field decreases as the domain size increases and we find that an  m=1 mode is excited for a full 2π φ-extent, reminiscent of the  field configurations deduced from observations of rapidly rotating late-type stars.

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  • 2. Käpylä, Petri J.
    et al.
    Mantere, Maarit J.
    Cole, Elizabeth
    Warnecke, Jörn
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    EFFECTS OF ENHANCED STRATIFICATION ON EQUATORWARD DYNAMO WAVE PROPAGATION2013In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 778, no 1, article id 41Article in journal (Refereed)
    Abstract [en]

    We present results from simulations of rotating magnetized turbulent convection in spherical wedge geometry representing parts of the latitudinal and longitudinal extents of a star. Here we consider a set of runs for which the density stratification is varied, keeping the Reynolds and Coriolis numbers at similar values. In the case of weak stratification, we find quasi-steady dynamo solutions for moderate rotation and oscillatory ones with poleward migration of activity belts for more rapid rotation. For stronger stratification, the growth rate tends to become smaller. Furthermore, a transition from quasi-steady to oscillatory dynamos is found as the Coriolis number is increased, but now there is an equatorward migrating branch near the equator. The breakpoint where this happens corresponds to a rotation rate that is about three to seven times the solar value. The phase relation of the magnetic field is such that the toroidal field lags behind the radial field by about pi/2, which can be explained by an oscillatory alpha(2) dynamo caused by the sign change of the alpha-effect about the equator. We test the domain size dependence of our results for a rapidly rotating run with equatorward migration by varying the longitudinal extent of our wedge. The energy of the axisymmetric mean magnetic field decreases as the domain size increases and we find that an m = 1 mode is excited for a full 2 pi azimuthal extent, reminiscent of the field configurations deduced from observations of rapidly rotating late-type stars.

  • 3.
    Rivero Losada, Illa
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Nordic Optical Telescope, Spain.
    Warnecke, Jörn
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Max-Planck-Institut für Sonnensystemforschung, Germany.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, 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.
    Magnetic bipoles in rotating turbulence with coronal envelope2019In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 621, article id A61Article in journal (Refereed)
    Abstract [en]

    Context. The formation mechanism of sunspots and starspots is not yet fully understood. It is a major open problem in astrophysics.

    Aims. Magnetic flux concentrations can be produced by the negative effective magnetic pressure instability (NEMPI). This instability is strongly suppressed by rotation. However, the presence of an outer coronal envelope was previously found to strengthen the flux concentrations and make them more prominent. It also allows for the formation of bipolar regions (BRs). We aim to understand the important issue of whether the presence of an outer coronal envelope also changes the excitation conditions and the rotational dependence of NEMPI.

    Methods. We have used direct numerical simulations and mean-field simulations. We adopted a simple two-layer model of turbulence that mimics the jump between the convective turbulent and coronal layers below and above the surface of a star, respectively. The computational domain is Cartesian and located at a certain latitude of a rotating sphere. We investigated the effects of rotation on NEMPI by changing the Coriolis number, the latitude, the strengths of the imposed magnetic field, and the box resolution.

    Results. Rotation has a strong impact on the process of BR formation. Even rather slow rotation is found to suppress BR formation. However, increasing the imposed magnetic field strength also makes the structures stronger and alleviates the rotational suppression somewhat. The presence of a coronal layer itself does not significantly reduce the effects of rotational suppression.

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  • 4.
    Warnecke, Jörn
    Stockholm University, Faculty of Science, Department of Astronomy.
    Combining Models of Coronal Mass Ejections and Solar Dynamos2013Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Observations show that Coronal Mass Ejections (CMEs) are associated with twisted magnetic flux configurations. Conventionally, CMEs are modeled by shearing and twisting the footpoints of a certain distribution of magnetic flux at the solar surface and letting it evolve at the surface. Of course, the surface velocities and magnetic field patterns should ultimately be obtained from realistic simulations of the solar convection zone where the field is generated by dynamo action. Therefore, a unified treatment of the convection zone and the CMEs is needed. Numerical simulations of turbulent dynamos show that the amplification of magnetic fields can be catastrophically quenched at magnetic Reynolds numbers typical of the interior of the Sun. A strong flux of magnetic helicity leaving the dynamo domain can alleviate this quenching. In this sense, a realistic (magnetic) boundary condition is an important ingredient of a successful solar dynamo model. Using a two-layer model developed in this thesis, we combine a dynamo-active region with a magnetically inert but highly conducting upper layer which models the solar corona. In four steps we improve this setup from a forced to a convectively driven dynamo and from an isothermal to a polytropic stratified corona. The simulations show magnetic fields that emerge at the surface of the dynamo region and are ejected into the coronal part of the domain. Their morphological form allows us to associate these events with CMEs. Magnetic helicity is found to change sign in the corona to become consistent with recent helicity measurements in the solar wind. Our convection-driven dynamo model with a coronal envelope has a solar-like differential rotation with radial (spoke-like) contours of constant rotation rate, together with a solar-like meridional circulation and a near-surface shear layer. The spoke-like rotation profile is due to latitudinal entropy gradient which violates the Taylor--Proudman balance through the baroclinic term. We find mean magnetic fields that migrate equatorward in models both with and without the coronal layer. One remarkable result is that the dynamo action benefits substantially from the presence of a corona becoming stronger and more realistic. The two-layer model represents a new approach to describe the generation of coronal mass ejections in a self-consistent manner. On the other hand, it has important implications for solar dynamo models as it admits many magnetic features observed in the Sun.

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    Comprehensive Summary
  • 5.
    Warnecke, Jörn
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Flux emergence: flares and coronal mass ejections driven by dynamo action underneath the solar surface2011Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Helically shaped magnetic field structuresknown as coronal mass ejections (CMEs) are closely related to so-called eruptive flares. On the one hand, these events are broadly believed to be due tothe buoyant rise of magnetic flux tubes from the bottom of the convection zone to the photosphere where they form structures such as sunspots. On the other hand, models of eruptive flares and CMEs have no connection to the convection zone and the magnetic field generated bydynamo action. It is well known that a dynamo can produce helical structures and twisted magnetic fields as observed in the Sun. In this work we ask, how a dynamo-generated magnetic field appears above the surface without buoyancy force and how this field evolves inthe outer atmosphere of the Sun.

    We apply a new approach of a two layer model, where the lower one represents the convection zone and the upper one the solar corona. The two layers are included in one single simulation domain. In the lower layer, we use a helical forcing function added to the momentum equation to create a turbulent dynamo. Due to dynamo action, a large-scale field is formed. As a first step we use a Cartesian cube. We solve the equations of the so-called force-free model in the upper layer to create nearly force-free coronal magnetic fields. In a second step we use a spherical wedge, which extends radially from 0.7 to 2 solar radii. We include density stratification due to gravity in anisothermal domain. The wedge includes both hemispheres of the Sun and we apply a helicalforcing with different signs in each hemisphere.

    As a result, a large-scale field is generated by a turbulent dynamo acting underneath the surface. Due to the latitudinal variation of the helicity produced by the helical forcing, the dynamo is oscillating in the spherical wedge. Twisted magnetic fields emerge above the surface and form arch-like structures with strong current sheets. Plasmoids and CME-like structures are ejected recurrently into the outerlayers. In the spherical simulations we find that the magnetic helicity changes sign in the exterior, which is in agreement with recent analysis of the solar wind data.

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    Thesis
  • 6.
    Warnecke, Jörn
    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).
    Surface appearance of dynamo-generated large-scale fields2010In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 523, p. A19-Article in journal (Refereed)
    Abstract [en]

    Aims: Twisted magnetic fields are frequently seen to emerge above the visible surface of the Sun. This emergence is usually associated with the rise of buoyant magnetic flux structures. Here we ask how magnetic fields from a turbulent large-scale dynamo appear above the surface if there is no magnetic buoyancy. Methods: The computational domain is split into two parts. In the lower part, which we refer to as the turbulence zone, the flow is driven by an assumed helical forcing function leading to dynamo action. Above this region, which we refer to as the exterior, a nearly force-free magnetic field is computed at each time step using the stress-and-relax method. Results: Twisted arcade-like field structures are found to emerge in the exterior above the turbulence zone. Strong current sheets tend to form above the neutral line, where the vertical field component vanishes. Time series of the magnetic field structure show recurrent plasmoid ejections. The degree to which the exterior field is force free is estimated as the ratio of the dot product of current density and magnetic field strength to their respective rms values. This ratio reaches values of up to 95% in the exterior. A weak outward flow is driven by the residual Lorentz force.

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  • 7.
    Warnecke, Jörn
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    Mitra, D.
    Dynamo-driven plasmoid ejections above a spherical surface2011In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 534, p. A 11-Article in journal (Refereed)
    Abstract [en]

    Aims: We extend earlier models of turbulent dynamos with an upper, nearly force-free exterior to spherical geometry, and study how flux emerges from lower layers to the upper ones without being driven by magnetic buoyancy. We also study how this affects the possibility of plasmoid ejection. Methods: A spherical wedge is used that includes northern and southern hemispheres up to mid-latitudes and a certain range in longitude of the Sun. In radius, we cover both the region that corresponds to the convection zone in the Sun and the immediate exterior up to twice the radius of the Sun. Turbulence is driven with a helical forcing function in the interior, where the sign changes at the equator between the two hemispheres. Results: An oscillatory large-scale dynamo with equatorward migration is found to operate in the turbulence zone. Plasmoid ejections occur in regular intervals, similar to what is seen in earlier Cartesian models. These plasmoid ejections are tentatively associated with coronal mass ejections (CMEs). The magnetic helicity is found to change sign outside the turbulence zone, which is in agreement with recent findings for the solar wind. Movie is available in electronic form at http://www.aanda.org

  • 8.
    Warnecke, Jörn
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Mitra, Dhrubaditya
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Magnetic twist: a source and property of space weather2012In: Journal of Space Weather and Space Climate, E-ISSN 2115-7251, Vol. 2, p. A11-Article in journal (Refereed)
    Abstract [en]

    Aim: We present evidence for finite magnetic helicity density in the heliosphere and numerical models thereof, and relate it to the magnetic field properties of the dynamo in the solar convection zone.

    Methods: We use simulations and solar wind data to compute magnetic helicity either directly from the simulations or indirectly using time series of the skew-symmetric components of the magnetic correlation tensor.

    Results: We find that the solar dynamo produces negative magnetic helicity at small scales and positive at large scales. However, in the heliosphere these properties are reversed and the magnetic helicity is now positive at small scales and negative at large scales. We explain this by the fact that a negative diffusive magnetic helicity flux corresponds to a positive gradient of magnetic helicity, which leads to a change of sign from negative to positive values at some radius in the northern hemisphere.

  • 9.
    Warnecke, Jörn
    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).
    Mitra, Dhrubaditya
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Plasmoid ejections driven by dynamo action underneath a spherical surface2010In: Proceedings of the International Astronomical Union, ISSN 1743-9213, E-ISSN 1743-9221, Vol. 6, no Symposium S274, p. 306-309Article in journal (Refereed)
    Abstract [en]

    We present a unified three-dimensional model of the convection zone and upper atmosphere of the Sun in spherical geometry. In this model, magnetic fields, generated by a helically forced dynamo in the convection zone, emerge without the assistance of magnetic buoyancy. We use an isothermal equation of state with gravity and density stratification. Recurrent plasmoid ejections, which rise through the outer atmosphere, is observed. In addition, the current helicity of the small-scale field is transported outwards and form large structures like magnetic clouds.

  • 10.
    Warnecke, Jörn
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Käpylä, Petri J.
    Mantere, Maarit J.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Ejections of Magnetic Structures Above a Spherical Wedge Driven by a Convective Dynamo with Differential Rotation2012In: Solar Physics, ISSN 0038-0938, E-ISSN 1573-093X, Vol. 280, no 2, p. 299-319Article in journal (Refereed)
    Abstract [en]

    We combine a convectively driven dynamo in a spherical shell with a nearly isothermal density-stratified cooling layer that mimics some aspects of a stellar corona to study the emergence and ejections of magnetic field structures. This approach is an extension of earlier models, where forced turbulence simulations were employed to generate magnetic fields. A spherical wedge is used which consists of a convection zone and an extended coronal region to a parts per thousand aEuro parts per thousand 1.5 times the radius of the sphere. The wedge contains a quarter of the azimuthal extent of the sphere and 150(a similar to) in latitude. The magnetic field is self-consistently generated by the turbulent motions due to convection beneath the surface. Magnetic fields are found to emerge at the surface and are ejected to the coronal part of the domain. These ejections occur at irregular intervals and are weaker than in earlier work. We tentatively associate these events with coronal mass ejections on the Sun, even though our model of the solar atmosphere is rather simplistic.

  • 11.
    Warnecke, Jörn
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Käpylä, Petri J.
    Mantere, Maarit J.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Solar-like differential rotation in a convective dynamo with a coronal envelopeManuscript (preprint) (Other academic)
    Abstract [en]

    We report on the results of four convective dynamo simulations with an souter coronal layer. The magnetic field is self-consistently generated by the convectivemotions beneath the surface. Above the convection zone we include a polytropic layerthat extends to 1.6 solar radii. The temperature increases in this regionto ≈8 times the value at the surface, corresponding to ≈1.2 times the value at the bottom of the spherical shell. We associate this region with the solar corona. We find a solar-like differential rotation with radial contours of constant rotation rate, together with a solar-like meridionalcirculation and a near-surface shear layer. This spoke-like rotation profile is caused by a non-zero latitudinalentropy gradient which violates the Taylor-Proudman balance via thebaroclinic term. The lower density stratification compared with the Sun leads to anequatorward return flow above the surface. The mean magnetic field is in most of the casesoscillatory with equatorward migration in one case. In other cases the equatorward migration is overlaid by stationary oreven poleward migrating mean fields.

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  • 12.
    Warnecke, Jörn
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Käpylä, Petri J.
    Mantere, Maarit J.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    SPOKE-LIKE DIFFERENTIAL ROTATION IN A CONVECTIVE DYNAMO WITH A CORONAL ENVELOPE2013In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 778, no 2Article in journal (Refereed)
    Abstract [en]

    We report on the results of four convective dynamo simulations with an outer coronal layer. The magnetic field is self-consistently generated by the convective motions beneath the surface. Above the convection zone, we include a polytropic layer that extends to 1.6 solar radii. The temperature increases in this region to approximate to 8 times the value at the surface, corresponding to approximate to 1.2 times the value at the bottom of the spherical shell. We associate this region with the solar corona. We find solar-like differential rotation with radial contours of constant rotation rate, together with a near-surface shear layer. This non-cylindrical rotation profile is caused by a non-zero latitudinal entropy gradient that offsets the Taylor-Proudman balance through the baroclinic term. The meridional circulation is multi-cellular with a solar-like poleward flow near the surface at low latitudes. In most of the cases, the mean magnetic field is oscillatory with equatorward migration in two cases. In other cases, the equatorward migration is overlaid by stationary or even poleward migrating mean fields.

  • 13.
    Warnecke, Jörn
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Rivero Losada, Illa
    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; 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.
    Bipolar Magnetic Structures Driven by Stratified Turbulence with a Coronal Envelope2013In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 777, no 2, article id L37Article in journal (Refereed)
    Abstract [en]

    We report the spontaneous formation of bipolar magnetic structures in direct numerical simulations of stratified forced turbulence with an outer coronal envelope. The turbulence is forced with transverse random waves only in the lower (turbulent) part of the domain. Our initial magnetic field is either uniform in the entire domain or confined to the turbulent layer. After about 1-2 turbulent diffusion times, a bipolar magnetic region of vertical field develops with two coherent circular structures that live during one turbulent diffusion time, and then decay during 0.5 turbulent diffusion times. The resulting magnetic field strengths inside the bipolar region are comparable to the equipartition value with respect to the turbulent kinetic energy. The bipolar magnetic region forms a loop-like structure in the upper coronal layer. We associate the magnetic structure formation with the negative effective magnetic pressure instability in the two-layer model.

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