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  • 201. Rempel, Erico L.
    et al.
    Chian, Abraham C. -L.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Munoz, Pablo R.
    Shadden, Shawn C.
    Coherent structures and the saturation of a nonlinear dynamo2013Ingår i: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 729, s. 309-329Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Eulerian and Lagrangian tools are used to detect coherent structures in the velocity and magnetic fields of a mean-field dynamo, produced by direct numerical simulations of the three-dimensional compressible magnetohydrodynamic equations with an isotropic helical forcing and moderate Reynolds number. Two distinct stages of the dynamo are studied: the kinematic stage, where a seed magnetic field undergoes exponential growth; and the saturated regime. It is shown that the Lagrangian analysis detects structures with greater detail, in addition to providing information on the chaotic mixing properties of the flow and the magnetic fields. The traditional way of detecting Lagrangian coherent structures using finite-time Lyapunov exponents is compared with a recently developed method called function M. The latter is shown to produce clearer pictures which readily permit the identification of hyperbolic regions in the magnetic field, where chaotic transport/dispersion of magnetic field lines is highly enhanced.

  • 202. Rempel, Erico L.
    et al.
    Chian, Abraham C.-L.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Lagrangian chaos in an ABC-forced nonlinear dynamo2012Ingår i: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 86, nr 1, artikel-id 018405Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The Lagrangian properties of the velocity field in a magnetized fluid are studied using three-dimensional simulations of a helical magnetohydrodynamic dynamo. We compute the attracting and repelling Lagrangian coherent structures (LCS), which are dynamic lines and surfaces in the velocity field that delineate particle transport in flows with chaotic streamlines and act as transport barriers. Two dynamo regimes are explored, one with a robust coherent mean magnetic field and the other with intermittent bursts of magnetic energy. The LCS and the statistics of the finite-time Lyapunov exponents indicate that the stirring/mixing properties of the velocity field decay as a linear function of magnetic energy. The relevance of this study to the solar dynamo problem is also discussed.

  • 203. Rheinhardt, M.
    et al.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Modeling spatio temporal nonlocality in mean field dynamos2012Ingår i: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 333, nr 1, s. 71-77Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    When scale separation in space or time is poor, the mean-field alpha effect and turbulent diffusivity have to be replaced by integral kernels by which the dependence of the mean electromotive force on the mean magnetic field becomes nonlocal. Earlier work in computing these kernels using the test-field method is now generalized to the case in which both spatial and temporal scale separations are poor. The approximate form of the kernel for isotropic stationary turbulence is such that it can be treated in a straightforward manner by solving a partial differential equation for the mean electromotive force. The resulting mean-field equations are solved for oscillatory alpha-shear dynamos as well as alpha(2) dynamos with alpha linearly depending on position, which makes this dynamo oscillatory, too. In both cases, the critical values of the dynamo number is lowered due to spatio-temporal nonlocality.

  • 204.
    Rheinhardt, M.
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Test-field method for mean-field coefficients with MHD background2010Ingår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 520, s. A28-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Aims: The test-field method for computing turbulent transport coefficients from simulations of hydromagnetic flows is extended to the regime with a magnetohydrodynamic (MHD) background.

    Methods: A generalized set of test equations is derived using both the induction equation and a modified momentum equation. By employing an additional set of auxiliary equations, we obtain linear equations describing the response of the system to a set of prescribed test fields. Purely magnetic and MHD backgrounds are emulated by applying an electromotive force in the induction equation analogously to the ponderomotive force in the momentum equation. Both forces are chosen to have Roberts-flow like geometry.

    Results: Examples with purely magnetic as well as MHD backgrounds are studied where the previously used quasi-kinematic test-field method breaks down. In cases with homogeneous mean fields it is shown that the generalized test-field method produces the same results as the imposed-field method, where the field-aligned component of the actual electromotive force from the simulation is used. Furthermore, results for the turbulent diffusivity are given, which are inaccessible to the imposed-field method. For MHD backgrounds, new mean-field effects are found that depend on the occurrence of cross-correlations between magnetic and velocity fluctuations. In particular, there is a contribution to the mean Lorentz force that is linear in the mean field and hence reverses sign upon a reversal of the mean field. For strong mean fields, α is found to be quenched proportional to the fourth power of the field strength, regardless of the type of background studied.

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  • 205.
    Rheinhardt, Matthias
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Devlen, Ebru
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Ege, Turkey.
    Radler, Karl-Heinz
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Leibniz Institute for Astrophysics Potsdam, Germany.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Mean-field dynamo action from delayed transport2014Ingår i: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 441, nr 1, s. 116-126Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We analyse the nature of dynamo action that enables growing horizontally averaged magnetic fields in two particular flows that were studied by Roberts in 1972, namely his flows II and III. They have zero kinetic helicity either pointwise (flow II), or on average (flow III). Using direct numerical simulations, we determine the onset conditions for dynamo action at moderate values of the magnetic Reynolds number. Using the test-field method, we show that the turbulent magnetic diffusivity is then positive for both flows. However, we demonstrate that for both flows large-scale dynamo action occurs through delayed transport. Mathematically speaking, the magnetic field at earlier times contributes to the electromotive force through the off-diagonal components of the a tensor such that a zero mean magnetic field becomes unstable to dynamo action. This represents a qualitatively new mean-field dynamo mechanism not previously described.

  • 206. Rivero Losada, Illa
    et al.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Kleeorin, Nathan
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Mitra, Dhrubaditya
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Rotational effects on the negative magnetic pressure instability2012Ingår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 548, artikel-id A49Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Context. The surface layers of the Sun are strongly stratified. In the presence of turbulence with a weak mean magnetic field, a large-scale instability resulting in the formation of nonuniform magnetic structures, can be excited on the scale of many (more than ten) turbulent eddies (or convection cells). This instability is caused by a negative contribution of turbulence to the effective (mean-field) magnetic pressure and has previously been discussed in connection with the formation of active regions. Aims. We want to understand the effects of rotation on this instability in both two and three dimensions. Methods. We use mean-field magnetohydrodynamics in a parameter regime in which the properties of the negative effective magnetic pressure instability have previously been found to agree with properties of direct numerical simulations. Results. We find that the instability is already suppressed for relatively slow rotation with Coriolis numbers (i.e. inverse Rossby numbers) around 0.2. The suppression is strongest at the equator. In the nonlinear regime, we find traveling wave solutions with propagation in the prograde direction at the equator with additional poleward migration away from the equator. Conclusions. We speculate that the prograde rotation of the magnetic pattern near the equator might be a possible explanation for the faster rotation speed of magnetic tracers relative to the plasma velocity on the Sun. In the bulk of the domain, kinetic and current helicities are negative in the northern hemisphere and positive in the southern.

  • 207.
    Rivero Losada, Illa
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Kleeorin, Nathan
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Competition of rotation and stratification in flux concentrations2013Ingår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 556, artikel-id A83Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Context. In a strongly stratified turbulent layer, a uniform horizontal magnetic field can become unstable and spontaneously form local flux concentrations due to a negative contribution of turbulence to the large-scale (mean-field) magnetic pressure. This mechanism, which is called negative effective magnetic pressure instability (NEMPI), is of interest in connection with dynamo scenarios in which most of the magnetic field resides in the bulk of the convection zone and not at the bottom, as is often assumed. Recent work using mean-field hydromagnetic equations has shown that NEMPI becomes suppressed at rather low rotation rates with Coriolis numbers as low as 0.1. Aims. Here we extend these earlier investigations by studying the effects of rotation both on the development of NEMPI and on the effective magnetic pressure. We also quantify the kinetic helicity resulting from direct numerical simulations (DNS) with Coriolis numbers and strengths of stratification comparable to values near the solar surface and compare it with earlier work at smaller scale separation ratios. Further, we estimate the expected observable signals of magnetic helicity at the solar surface. Methods. To calculate the rotational effect on the effective magnetic pressure we consider both DNS and analytical studies using the tau approach. To study the effects of rotation on the development of NEMPI we use both DNS and mean-field calculations of the three-dimensional hydromagnetic equations in a Cartesian domain. Results. We find that the growth rates of NEMPI from earlier mean-field calculations are well reproduced with DNS, provided the Coriolis number is below 0.06. In that case, kinetic and magnetic helicities are found to be weak and the rotational effect on the effective magnetic pressure is negligible as long as the production of flux concentrations is not inhibited by rotation. For faster rotation, dynamo action becomes possible. However, there is an intermediate range of rotation rates where dynamo action on its own is not yet possible, but the rotational suppression of NEMPI is being alleviated. Conclusions. Production of magnetic flux concentrations through the suppression of turbulent pressure appears to be possible only in the uppermost layers of the Sun, where the convective turnover time is less than two hours.

  • 208.
    Rivero Losada, Illa
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Kleeorin, Nathan
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Magnetic flux concentrations in a polytropic atmosphere2014Ingår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 564, artikel-id A2Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Context. Strongly stratified hydromagnetic turbulence has recently been identified as a candidate for explaining the spontaneous formation of magnetic flux concentrations by the negative effective magnetic pressure instability (NEMPI). Much of this work has been done for isothermal layers, in which the density scale height is constant throughout. Aims. We now want to know whether earlier conclusions regarding the size of magnetic structures and their growth rates carry over to the case of polytropic layers, in which the scale height decreases sharply as one approaches the surface. Methods. To allow for a continuous transition from isothermal to poly tropic layers, we employ a generalization of the exponential function known as the q-exponential. This implies that the top of the polytropic layer shifts with changing polytropic index such that the scale height is always the same at some reference height. We used both mean-field simulations (MPS) and direct numerical simulations (DNS) of forced stratified turbulence to determine the resulting flux concentrations in polytropic layers. Cases of both horizontal and vertical applied magnetic fields were considered. Results. Magnetic structures begin to form at a depth where the magnetic field strength is a small fraction of the local equipartition field strength with respect to the turbulent kinetic energy. Unlike the isothermal case where stronger fields can give rise to magnetic flux concentrations at larger depths, in the polytropic case the growth rate of NEMPI decreases for structures deeper down. Moreover, the structures that form higher up have a smaller horizontal scale of about four times their local depth. For vertical fields, magnetic structures of super-equipartition strengths are formed, because such fields survive downward advection that causes NEMPI with horizontal magnetic fields to reach premature nonlinear saturation by what is called the potato-sack effect. The horizontal cross-section of such structures found in DNS is approximately circular, which is reproduced with MFS of NEMPI using a vertical magnetic field. Conclusions. Results based on isothermal models can be applied locally to polytropic layers. For vertical fields, magnetic flux concentrations of super-equipartition strengths form, which supports suggestions that sunspot formation might be a shallow phenomenon.

  • 209.
    Rivero Losada, Illa
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Nordic Optical Telescope, Spain.
    Warnecke, Jörn
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Max-Planck-Institut für Sonnensystemforschung, Germany.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA.
    Kleeorin, Nathan
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Magnetic bipoles in rotating turbulence with coronal envelope2019Ingår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 621, artikel-id A61Artikel i tidskrift (Refereegranskat)
    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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  • 210.
    Rogachevskii, Igor
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Kleeorin, Nathan
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA.
    Compressibility in turbulent magnetohydrodynamics and passive scalar transport: mean-field theory2018Ingår i: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 84, nr 5, artikel-id 735840502Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We develop a mean-field theory of compressibility effects in turbulent magnetohydrodynamics and passive scalar transport using the quasi-linear approximation and the spectral tau-approach. We find that compressibility decreases the a effect and the turbulent magnetic diffusivity both at small and large magnetic Reynolds numbers, Rm. Similarly, compressibility decreases the turbulent diffusivity for passive scalars both at small and large Peclet numbers, Pe. On the other hand, compressibility does not affect the effective pumping velocity of the magnetic field for large Rm, but it decreases it for small Rm. Density stratification causes turbulent pumping of passive scalars, but it is found to become weaker with increasing compressibility. No such pumping effect exists for magnetic fields. However, compressibility results in a new passive scalar pumping effect from regions of low to high turbulent intensity both for small and large Peclet numbers. It can be interpreted as compressible turbophoresis of non-inertial particles and gaseous admixtures, while the classical turbophoresis effect exists only for inertial particles and causes them to be pumped to regions with lower turbulent intensity.

  • 211.
    Rogachevskii, Igor
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Kleeorin, Nathan
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Eichler, David
    COSMIC-RAY CURRENT-DRIVEN TURBULENCE AND MEAN-FIELD DYNAMO EFFECT2012Ingår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 753, nr 1, artikel-id 6Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We show that an a effect is driven by the cosmic-ray (CR) Bell instability exciting left-right asymmetric turbulence. Alfven waves of a preferred polarization have maximally helical motion, because the transverse motion of each mode is parallel to its curl. We show how large-scale Alfven modes, when rendered unstable by CR streaming, can create new net flux over any finite region, in the direction of the original large-scale field. We perform direct numerical simulations (DNSs) of a magnetohydrodynamic fluid with a forced CR current and use the test-field method to determine the alpha effect and the turbulent magnetic diffusivity. As follows from DNS, the dynamics of the instability has the following stages: (1) in the early stage, the small-scale Bell instability that results in the production of small-scale turbulence is excited; (2) in the intermediate stage, there is formation of larger-scale magnetic structures; (3) finally, quasi-stationary large-scale turbulence is formed at a growth rate that is comparable to that expected from the dynamo instability, but its amplitude over much longer timescales remains unclear. The results of DNS are in good agreement with the theoretical estimates. It is suggested that this dynamo is what gives weakly magnetized relativistic shocks such as those from gamma-ray bursts (GRBs) a macroscopic correlation length. It may also be important for large-scale magnetic field amplification associated with CR production and diffusive shock acceleration in supernova remnants (SNRs) and blast waves from GRBs. Magnetic field amplification by Bell turbulence in SNRs is found to be significant, but it is limited owing to the finite time available to the super-Alfvenicly expanding remnant. The effectiveness of the mechanisms is shown to be dependent on the shock velocity. Limits on magnetic field growth in longer-lived systems, such as the Galaxy and unconfined intergalactic CRs, are also discussed.

  • 212. Rogachevskii, Igor
    et al.
    Kleeorin, Nathan
    Käpylä, Petri J.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Pumping velocity in homogeneous helical turbulence with shear2011Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 84, artikel-id 56314Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Using different analytical methods (the quasilinear approach, the path-integral technique, and the tau-relaxation approximation) we develop a comprehensive mean-field theory for a pumping effect of the mean magnetic field in homogeneous nonrotating helical turbulence with imposed large-scale shear. The effective pumping velocity is proportional to the product of α effect and large-scale vorticity associated with the shear, and causes a separation of the toroidal and poloidal components of the mean magnetic field along the direction of the mean vorticity. We also perform direct numerical simulations of sheared turbulence in different ranges of hydrodynamic and magnetic Reynolds numbers and use a kinematic test-field method to determine the effective pumping velocity. The results of the numerical simulations are in agreement with the theoretical predictions.

  • 213.
    Rogachevskii, Igor
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel; University of Colorado, USA.
    Ruchayskiy, Oleg
    Boyarsky, Alexey
    Fröhlich, Jürg
    Kleeorin, Nathan
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA.
    Schober, Jennifer
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. I. Theory2017Ingår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 846, nr 2, artikel-id 153Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The magnetohydrodynamic (MHD) description of plasmas with relativistic particles necessarily includes an additional new field, the chiral chemical potential associated with the axial charge (i.e., the number difference between right-and left-handed relativistic fermions). This chiral chemical potential gives rise to a contribution to the electric current density of the plasma (chiral magnetic effect). We present a self-consistent treatment of the chiral MHD equations, which include the back-reaction of the magnetic field on a chiral chemical potential and its interaction with the plasma velocity field. A number of novel phenomena are exhibited. First, we show that the chiral magnetic effect decreases the frequency of the Alfven wave for incompressible flows, increases the frequencies of the Alfven wave and of the fast magnetosonic wave for compressible flows, and decreases the frequency of the slow magnetosonic wave. Second, we show that, in addition to the well-known laminar chiral dynamo effect, which is not related to fluid motions, there is a dynamo caused by the joint action of velocity shear and chiral magnetic effect. In the presence of turbulence with vanishing mean kinetic helicity, the derived mean-field chiral MHD equations describe turbulent large-scale dynamos caused by the chiral alpha effect, which is dominant for large fluid and magnetic Reynolds numbers. The chiral alpha effect is due to an interaction of the chiral magnetic effect and fluctuations of the small-scale current produced by tangling magnetic fluctuations (which are generated by tangling of the large-scale magnetic field by sheared velocity fluctuations). These dynamo effects may have interesting consequences in the dynamics of the early universe, neutron stars, and the quark-gluon plasma.

  • 214. Roper Pol, Alberto
    et al.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA; Carnegie Mellon Universiy, USA.
    Kahniashvili, Tina
    Kosowsky, Arthur
    Mandal, Sayan
    The timestep constraint in solving the gravitational wave equations sourced by hydromagnetic turbulence2020Ingår i: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 114, nr 1-2, s. 130-161Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Hydromagnetic turbulence produced during phase transitions in the early universe can be a powerful source of stochastic gravitational waves (GWs). GWs can be modelled by the linearised spatial part of the Einstein equations sourced by the Reynolds and Maxwell stresses. We have implemented two different GW solvers into the Pencil Code - a code which uses a third order timestep and sixth order finite differences. Using direct numerical integration of the GW equations, we study the appearance of a numerical degradation of the GW amplitude at the highest wavenumbers, which depends on the length of the timestep - even when the Courant-Friedrichs-Lewy condition is ten times below the stability limit. This degradation leads to a numerical error, which is found to scale with the third power of the timestep. A similar degradation is not seen in the magnetic and velocity fields. To mitigate numerical degradation effects, we alternatively use the exact solution of the GW equations under the assumption that the source is constant between subsequent timesteps. This allows us to use a much longer timestep, which cuts the computational cost by a factor of about ten.

  • 215. Roper Pol, Alberto
    et al.
    Mandal, Sayan
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA; Ilia State University, Georgia; Carnegie Mellon University, USA.
    Kahniashvili, Tina
    Kosowsky, Arthur
    Numerical simulations of gravitational waves from early-universe turbulence2020Ingår i: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 102, nr 8, artikel-id 083512Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We perform direct numerical simulations of magnetohydrodynamic turbulence in the early universe and numerically compute the resulting stochastic background of gravitational waves and relic magnetic fields. These simulations do not make the simplifying assumptions of earlier analytic work. If the turbulence is assumed to have an energy-carrying scale that is about a hundredth of the Hubble radius at the time of generation, as expected in a first-order phase transition, the peak of gravitational wave power will be in the mHz frequency range for a signal produced at the electroweak scale. The efficiency of gravitational wave (GW) production varies significantly with how the turbulence is driven. Detectability of turbulence at the electroweak scale by the planned Laser Interferometer Space Antenna (LISA) requires anywhere from 0.1% to 10% of the thermal plasma energy density to be in plasma motions or magnetic fields, depending on the model of the driving process. Our results predict a new universal form below the spectral peak frequency that is shallower than previously thought. This implies larger values of the GWenergy spectra in the low-frequency range. This extends the range where turbulence is detectable with LISA to lower frequencies, corresponding to higher energy scales than the assumed energy-carrying scale.

  • 216. Ruediger, G.
    et al.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    alpha effect in a turbulent liquid-metal plane Couette flow2014Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 89, nr 3, s. 033009-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We calculate the mean electromotive force in plane Couette flows of a nonrotating conducting fluid under the influence of a large-scale magnetic field for driven turbulence. A vertical stratification of the turbulence intensity results in an alpha effect owing to the presence of horizontal shear. Here we discuss the possibility of an experimental determination of the components of the alpha tensor using both quasilinear theory and nonlinear numerical simulations. For magnetic Prandtl numbers of the order of unity, we find that in the high-conductivity limit the alpha effect in the direction of the flow clearly exceeds the component in spanwise direction. In this limit, alpha runs linearly with the magnetic Reynolds number Rm, while in the low-conductivity limit it runs with the product Rm . Re, where Re is the kinetic Reynolds number, so that for a given Rm the alpha effect grows with decreasing magnetic Prandtl number. For the small magnetic Prandtl numbers of liquid metals, a common value for the horizontal elements of the alpha tensor appears, which makes it unimportant whether the alpha effect is measured in the spanwise or the streamwise directions. The resulting effect should lead to an observable voltage of about 0.5 mV in both directions for magnetic fields of 1 kG and velocity fluctuations of about 1 m/s in a channel of 50-cm height (independent of its width).

  • 217. Ruediger, G.
    et al.
    Kitchatinov, L. L.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Cross Helicity and Turbulent Magnetic Diffusivity in the Solar Convection Zone2011Ingår i: Solar Physics, ISSN 0038-0938, E-ISSN 1573-093X, Vol. 269, nr 1, s. 3-12Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In a density-stratified turbulent medium, the cross helicity (u' . B') is considered as a result of the interaction of the velocity fluctuations and a large-scale magnetic field. By means of a quasilinear theory and by numerical simulations, we find the cross helicity and the mean vertical magnetic field to be anti-correlated. In the high-conductivity limit the ratio of the helicity and the mean magnetic field equals the ratio of the magnetic eddy diffusivity and the (known) density scale height. The result can be used to predict that the cross helicity at the solar surface will exceed the value of 1 gauss km s(-1). Its sign is anti-correlated to that of the radial mean magnetic field. Alternatively, we can use our result to determine the value of the turbulent magnetic diffusivity from observations of the cross helicity.

  • 218. Rädler, Karl-Heinz
    et al.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Del Sordo, Fabio
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Rheinhardt, Matthias
    Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows2011Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 84, nr 4, s. 46321-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the Péclet or magnetic Reynolds number is not too large, and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic cases several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented, as well as numerical results obtained by the test-field method, which applies independently of this approximation. Particular attention is paid to nonlocal and noninstantaneous connections between the turbulence-caused terms and the mean fields. Two examples of irrotational flows, in which interesting phenomena in the above sense occur, are investigated in detail. In particular, it is demonstrated that the decay of a mean scalar in a compressible fluid under the influence of these flows can be much slower than without any flow, and can be strongly influenced by the so-called memory effect, that is, the fact that the relevant mean-field coefficients depend on the decay rates themselves.

  • 219. Rädler, K.-H.
    et al.
    Brandenburg, A.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Mean electromotive force proportional to mean flow in MHD turbulence2010Ingår i: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 331, nr 1, s. 14-21Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In mean-field magnetohydrodynamics the mean electromotive force due to velocity and magnetic-field fluctuations plays a crucial role. In general it consists of two parts, one independent of and another one proportional to the mean magnetic field. The first part may be nonzero only in the presence of mhd turbulence, maintained, e.g., by small-scale dynamo action. It corresponds to a battery, which lets a mean magnetic field grow from zero to a finite value. The second part, which covers, e.g., the \alpha effect, is important for large-scale dynamos. Only a few examples of the aforementioned first part of the mean electromotive force have been discussed so far. It is shown that a mean electromotive force proportional to the mean fluid velocity, but independent of the mean magnetic field, may occur in an originally homogeneous isotropic mhd turbulence if there are nonzero correlations of velocity and electric current fluctuations or, what is equivalent, of vorticity and magnetic field fluctuations. This goes beyond the Yoshizawa effect, which consists in the occurrence of mean electromotive forces proportional to the mean vorticity or to the angular velocity defining the Coriolis force in a rotating frame and depends on the cross-helicity defined by the velocity and magnetic field fluctuations. Contributions to the mean electromotive force due to inhomogeneity of the turbulence are also considered. Possible consequences of the above findings for the generation of magnetic fields in cosmic bodies are discussed.

  • 220.
    Sarin, Nikhil
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC).
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC).
    Haskell, Brynmor
    Confronting the Neutron Star Population with Inverse Cascades2023Ingår i: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 952, nr 1, artikel-id L21Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The origin and evolution of magnetic fields of neutron stars from birth have long been a source of debate. Here, motivated by recent simulations of the Hall cascade with magnetic helicity, we invoke a model where the large-scale magnetic field of neutron stars grows as a product of small-scale turbulence through an inverse cascade. We apply this model to a simulated population of neutron stars at birth and show how this model can account for the evolution of such objects across the  diagram, explaining both pulsar and magnetar observations. Under the assumption that small-scale turbulence is responsible for large-scale magnetic fields, we place a lower limit on the spherical harmonic degree of the energy-carrying magnetic eddies of ≈40. Our results favor the presence of a highly resistive pasta layer at the base of the neutron star crust. We further discuss the implications of this paradigm on direct observables, such as the nominal age and braking index of pulsars.

  • 221. Schober, J.
    et al.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA.
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Chiral fermion asymmetry in high-energy plasma simulations2020Ingår i: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 114, nr 1-2, s. 106-129Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The chiral magnetic effect (CME) is a quantum relativistic effect that describes the appearance of an additional electric current along a magnetic field. It is caused by an asymmetry between the number densities of left- and right-handed fermions, which can be maintained at high energies when the chirality flipping rate can be neglected, for example in the early Universe. The inclusion of the CME in the Maxwell equations leads to a modified set of magnetohydrodynamical (MHD) equations. The CME is studied here in numerical simulations with the Pencil Code. We discuss how the CME is implemented in the code and how the time step and the spatial resolution of a simulation need to be adjusted in presence of a chiral asymmetry. The CME plays a key role in the evolution of magnetic fields, since it results in a dynamo effect associated with an additional term in the induction equation. This term is formally similar to the α effect in classical mean-field MHD. However, the chiral dynamo can operate without turbulence and is associated with small spatial scales that can be, in the case of the early Universe, orders of magnitude below the Hubble radius. A chiral αμ effect has also been identified in mean-field theory. It occurs in the presence of turbulence, but is not related to kinetic helicity. Depending on the plasma parameters, chiral dynamo instabilities can amplify magnetic fields over many orders of magnitude. These instabilities can potentially affect the propagation of MHD waves. Our numerical simulations demonstrate strong modifications of the dispersion relation for MHD waves for large chiral asymmetry. We also study the coupling between the evolution of the chiral chemical potential and the ordinary chemical potential, which is proportional to the sum of the number densities of left- and right-handed fermions. An important consequence of this coupling is the emergence of chiral magnetic waves (CMWs). We confirm numerically that linear CMWs and MHD waves are not interacting. Our simulations suggest that the chemical potential has only a minor effect on the non-linear evolution of the chiral dynamo.

  • 222. Schober, J.
    et al.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA.
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Kleeorin, Nathan
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Energetics of turbulence generated by chiral MHD dynamos2019Ingår i: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 113, nr 1-2, s. 107-130Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    An asymmetry in the number density of left- and right-handed fermions is known to give rise to a new term in the induction equation that can result in a dynamo instability. At high temperatures, when a chiral asymmetry can survive for long enough, this chiral dynamo instability can amplify magnetic fields efficiently, which in turn drive turbulence via the Lorentz force. While it has been demonstrated in numerical simulations that this chiral magnetically driven turbulence exists and strongly affects the dynamics of the magnetic field, the details of this process remain unclear. The goal of this paper is to analyse the energetics of chiral magnetically driven turbulence and its effect on the generation and dynamics of the magnetic field using direct numerical simulations. We study these effects for different initial conditions, including a variation of the initial chiral chemical potential and the magnetic Prandtl number, . In particular, we determine the ratio of kinetic to magnetic energy, , in chiral magnetically driven turbulence. Within the parameter space explored in this study, reaches a value of approximately 0.064-0.074-independently of the initial chiral asymmetry and for . Our simulations suggest, that decreases as a power law when increasing by decreasing the viscosity. While the exact scaling depends on the details of the fitting criteria and the Reynolds number regime, an approximate result of is reported. Using the findings from our numerical simulations, we analyse the energetics of chiral magnetically driven turbulence in the early Universe.

  • 223. Schober, Jennifer
    et al.
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). Ilia State University, Georgia; Carnegie Mellon University, USA.
    Dynamo instabilities in plasmas with inhomogeneous chiral chemical potential2022Ingår i: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 105, nr 4, artikel-id 043507Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the dynamics of magnetic fields in chiral magnetohydrodynamics, which takes into account the effects of an additional electric current related to the chiral magnetic effect in high-energy plasmas. We perform direct numerical simulations, considering weak seed magnetic fields and inhomogeneities of the chiral chemical potential μ5 with a zero mean. We demonstrate that a small-scale chiral dynamo can occur in such plasmas if fluctuations of μ5 are correlated on length scales that are much larger than the scale on which the dynamo growth rate reaches its maximum. Magnetic fluctuations grow by many orders of magnitude due to the small-scale chiral dynamo instability. Once the nonlinear backreaction of the generated magnetic field on fluctuations of μ5 sets in, the ratio of these scales decreases and the dynamo saturates. When magnetic fluctuations grow sufficiently to drive turbulence via the Lorentz force before reaching maximum field strength, an additional mean-field dynamo phase is identified. The mean magnetic field grows on a scale that is larger than the integral scale of turbulence after the amplification of the fluctuating component saturates. The growth rate of the mean magnetic field is caused by a magnetic α effect that is proportional to the current helicity. With the onset of turbulence, the power spectrum of μ5 develops a universal k−1 scaling independently of its initial shape, while the magnetic energy spectrum approaches a k−3 scaling.

  • 224. Schober, Jennifer
    et al.
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Ilia State University, Georgia; Carnegie Mellon University, USA.
    Production of a Chiral Magnetic Anomaly with Emerging Turbulence and Mean-Field Dynamo Action2022Ingår i: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 128, nr 6, artikel-id 065002Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In relativistic magnetized plasmas, asymmetry in the number densities of left- and right-handed fermions, i.e., a nonzero chiral chemical potential μ5, leads to an electric current along the magnetic field. This causes a chiral dynamo instability for a uniform μ5, but our simulations reveal a dynamo even for fluctuating μ5 with zero mean. It produces magnetically dominated turbulence and generates mean magnetic fields via the magnetic α effect. Eventually, a universal scale-invariant k−1 spectrum of μ5 and a k−3 magnetic spectrum are formed independently of the initial condition.

  • 225.
    Schober, Jennifer
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Laboratoire d ’ Astrophysique, EPFL, Switzerland.
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel; University of Colorado, USA.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA.
    Boyarsky, Alexey
    Fröhlich, Jürg
    Ruchayskiy, Oleg
    Kleeorin, Nathan
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. II. Simulations2018Ingår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 858, nr 2, artikel-id 124Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Using direct numerical simulations (DNS), we study laminar and turbulent dynamos in chiral magnetohydrodynamics with an extended set of equations that accounts for an additional contribution to the electric current due to the chiral magnetic effect (CME). This quantum phenomenon originates from an asymmetry between left-and right-handed relativistic fermions in the presence of a magnetic field and gives rise to a chiral dynamo. We show that the magnetic field evolution proceeds in three stages: (1) a small-scale chiral dynamo instability, (2) production of chiral magnetically driven turbulence and excitation of a large-scale dynamo instability due to a new chiral effect (alpha(mu) effect), and (3) saturation of magnetic helicity and magnetic field growth controlled by a conservation law for the total chirality. The alpha(mu) effect becomes dominant at large fluid and magnetic Reynolds numbers and is not related to kinetic helicity. The growth rate of the large-scale magnetic field and its characteristic scale measured in the numerical simulations agree well with theoretical predictions based on mean-field theory. The previously discussed two-stage chiral magnetic scenario did not include stage (2), during which the characteristic scale of magnetic field variations can increase by many orders of magnitude. Based on the findings from numerical simulations, the relevance of the CME and the chiral effects revealed in the relativistic plasma of the early universe and of protoneutron stars are discussed.

  • 226.
    Sharma, Ramkishor
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC).
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). Carnegie Mellon University, USA; Ilia State University, Georgia.
    Low frequency tail of gravitational wave spectra from hydromagnetic turbulence2022Ingår i: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 106, nr 10, artikel-id 103536Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Hydrodynamic and magnetohydrodynamic turbulence in the early Universe can drive gravitational waves (GWs) and imprint their spectrum onto that of GWs, which might still be observable today. We study the production of the GW background from freely decaying magnetohydrodynamic turbulence from helical and nonhelical initial magnetic fields. To understand the produced GW spectra, we develop a simple model on the basis of the evolution of the magnetic stress tensor. We find that the GW spectra obtained in this model reproduce those obtained in numerical simulations if we consider the detailed time evolution of the low frequency tail of the stress spectrum from numerical simulations. We also show that the shapes of the produced GW frequency spectra are different for helical and nonhelical cases for the same initial magnetic energy spectra. Such differences can help distinguish helical and nonhelical initial magnetic fields from a polarized background of GWs—especially when the expected circular polarization cannot be detected directly.

  • 227.
    Sharma, Ramkishor
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC).
    Dahl, Jani
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). Carnegie Mellon University, USA; Ilia State University, Georgia.
    Hindmarsh, Mark
    Shallow relic gravitational wave spectrum with acoustic peak2023Ingår i: Journal of Cosmology and Astroparticle Physics, E-ISSN 1475-7516, nr 12, artikel-id 042Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the gravitational wave (GW) spectrum produced by acoustic waves in the early universe, such as would be produced by a first order phase transition, focusing on the low-frequency side of the peak. We confirm with numerical simulations the Sound Shell model prediction of a steep rise with wave number k of k9  to a peak whose magnitude grows at a rate (H/kp)H, where H is the Hubble rate and kp the peak wave number, set by the peak wave number of the fluid velocity power spectrum. We also show that hitherto neglected terms give a shallower part with amplitude (H/kp)2  in the range H ≲ k ≲ kp, which in the limit of small H/k rises as k. This linear rise has been seen in other modelling and also in direct numerical simulations. The relative amplitude between the linearly rising part and the peak therefore depends on the peak wave number of the velocity spectrum and the lifetime of the source, which in an expanding background is bounded above by the Hubble time H-1. For slow phase transitions, which have the lowest peak wave number and the loudest signals, the acoustic GW peak appears as a localized enhancement of the spectrum, with a rise to the peak less steep than k9. The shape of the peak, absent in vortical turbulence, may help to lift degeneracies in phase transition parameter estimation at future GW observatories.

  • 228.
    Singh, Nishant K.
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Chitre, S. M.
    Rheinhardt, Matthias
    Properties of p and f modes in hydromagnetic turbulence2015Ingår i: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 447, nr 4, s. 3708-3722Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    With the ultimate aim of using the fundamental or f mode to study helioseismic aspects of turbulence-generated magnetic flux concentrations, we use randomly forced hydromagnetic simulations of a piecewise isothermal layer in two dimensions with reflecting boundaries at top and bottom. We compute numerically diagnostic wavenumber-frequency diagrams of the vertical velocity at the interface between the denser gas below and the less dense gas above. For an Alfven-to-sound speed ratio of about 0.1, a 5 per cent frequency increase of the f mode can be measured when k(x)H(p) = 3-4, where k(x) is the horizontal wavenumber and H-p is the pressure scaleheight at the surface. Since the solar radius is about 2000 times larger than H-p, the corresponding spherical harmonic degree would be 6000-8000. For weaker fields, a k(x)-dependent frequency decrease by the turbulent motions becomes dominant. For vertical magnetic fields, the frequency is enhanced for k(x)H(p) approximate to 4, but decreased relative to its nonmagnetic value for k(x)H(p) approximate to 9.

  • 229.
    Singh, Nishant K.
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Rheinhardt, Matthias
    FANNING OUT OF THE SOLAR f-MODE IN THE PRESENCE OF NON-UNIFORM MAGNETIC FIELDS?2014Ingår i: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 795, nr 1, s. L8-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We show that in the presence of a magnetic field that is varying harmonically in space, the fundamental mode, or f-mode, in a stratified layer is altered in such a way that it fans out in the diagnostic k omega diagram, with mode power also within the fan. In our simulations, the surface is defined by a temperature and density jump in a piecewise isothermal layer. Unlike our previous work (Singh et al. 2014), where a uniform magnetic field was considered, here we employ a non-uniform magnetic field together with hydromagnetic turbulence at length scales much smaller than those of the magnetic field. The expansion of the f-mode is stronger for fields confined to the layer below the surface. In some of those cases, the k omega diagram also reveals a new class of low-frequency vertical stripes at multiples of twice the horizontal wavenumber of the background magnetic field. We argue that the study of the f-mode expansion might be a new and sensitive tool to determine subsurface magnetic fields with azimuthal or other horizontal periodicity.

  • 230. Singh, Nishant K.
    et al.
    Käpylä, Maarit J.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Käpylä, Petri J.
    Lagg, Andreas
    Virtanen, Ilpo
    Bihelical Spectrum of Solar Magnetic Helicity and Its Evolution2018Ingår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 863, nr 2, artikel-id 182Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Using a recently developed two-scale formalism to determine the magnetic helicity spectrum, we analyze synoptic vector magnetograms built with data from the Vector Spectromagnetograph instrument on the Synoptic Optical Long-term Investigations of the Sun telescope during 2010 January-2016 July. In contrast to an earlier study using only three Carrington rotations (CRs), our analysis includes 74 synoptic CR maps. We recover here bihelical spectra at different phases of solar cycle. 24, where the net magnetic helicity in the majority of the data is consistent with a large-scale dynamo with helical turbulence operating in the Sun. More than 20% of the analyzed maps, however, show violations of the expected sign rule.

  • 231.
    Singh, Nishant K.
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Raichur, Harsha
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA.
    HIGH-WAVENUMBER SOLAR f-MODE STRENGTHENING PRIOR TO ACTIVE REGION FORMATION2016Ingår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 832, nr 2, artikel-id 120Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We report a systematic strengthening of the local solar surface or fundamental f- mode one to two days prior to the emergence of an active region (AR) in the same (corotating) location. Except for a possibly related increase in the kurtosis of the magnetic field, no indication can be seen in the magnetograms at that time. Our study is motivated by earlier numerical findings of Singh et al., which showed that, in the presence of a nonuniform magnetic field that is concentrated a few scale heights below the surface, the f- mode fans out in the diagnostic kw diagram at high wavenumbers. Here we explore this possibility using data from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory and show for six isolated ARs, 11130, 11158, 11242, 11105, 11072, and 11768, that at large latitudinal wavenumbers (corresponding to horizontal scales of around 3000 km), the f- mode displays strengthening about two days prior to AR formation and thus provides a new precursor for AR formation. Furthermore, we study two ARs, 12051 and 11678, apart from a magnetically quiet patch lying next to AR. 12529, to demonstrate the challenges in extracting such a precursor signal when a newly forming AR emerges in a patch that lies in close proximity to. one or several already existing ARs, which are expected to pollute neighboring patches. We then discuss plausible procedures for extracting precursor signals from regions with crowded environments. The idea that the f- mode is perturbed days before any visible magnetic activity occurs at the surface can be important in constraining dynamo models aimed at understanding the global magnetic activity of the Sun.

  • 232. Singh, Nishant K.
    et al.
    Raichur, Harsha
    Käpylä, Maarit J.
    Rheinhardt, Matthias
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Käpylä, Petri J.
    f-mode strengthening from a localised bipolar subsurface magnetic field2020Ingår i: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 114, nr 1-2, s. 196-212Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Recent numerical work in helioseismology has shown that a periodically varying subsurface magnetic field leads to a fanning of the f-mode, which emerges from a density jump at the surface. In an attempt to model a more realistic situation, we now modulate this periodic variation with an envelope, giving thus more emphasis on localised bipolar magnetic structures in the middle of the domain. Some notable findings are: (i) compared to the purely hydrodynamic case, the strength of the f-mode is significantly larger at high horizontal wavenumbers k, but the fanning is weaker for the localised subsurface magnetic field concentrations investigated here than the periodic ones studied earlier; (ii) when the strength of the magnetic field is enhanced at a fixed depth below the surface, the fanning of the f-mode in the diagram increases proportionally in such a way that the normalised f-mode strengths remain nearly the same in different such cases; (iii) the unstable Bloch modes reported previously in case of harmonically varying magnetic fields are now completely absent when more realistic localised magnetic field concentrations are imposed beneath the surface, thus suggesting that the Bloch modes are unlikely to be supported during most phases of the solar cycle; (iv) the f-mode strength appears to depend also on the depth of magnetic field concentrations such that it shows a relative decrement when the maximum of the magnetic field is moved to a deeper layer. We argue that detections of f-mode perturbations such as those being explored here could be effective tracers of solar magnetic fields below the photosphere before these are directly detectable as visible manifestations in terms of active regions or sunspots.

  • 233.
    Singh, Nishant K.
    et al.
    Stockholm Univ, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden.
    Rogachevskii, Igor
    Stockholm Univ, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA.
    Enhancement of Small-scale Turbulent Dynamo by Large-scale Shear2017Ingår i: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 850, nr 1, artikel-id L8Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Small-scale dynamos (SSDs) are ubiquitous in a broad range of turbulent flows with large-scale shear, ranging from solar and galactic magnetism to accretion disks, cosmology, and structure formation. Using high-resolution direct numerical simulations, we show that in non-helically forced turbulence with zero mean magnetic field, large-scale shear supports SSD action, i.e., the dynamo growth rate increases with shear and shear enhances or even produces turbulence, which, in turn, further increases the growth rate. When the production rates of turbulent kinetic energy due to shear and forcing are comparable, we find scalings for the growth rate gamma of the SSD and the turbulent rms velocity u(rms) with shear rate S that are independent of the magnetic Prandtl number: gamma proportional to vertical bar S vertical bar and u(rms) proportional to vertical bar S vertical bar(2/3). For large fluid and magnetic Reynolds numbers, gamma, normalized by its shear-free value, depends only on shear. Having compensated for shear-induced effects on turbulent velocity, we find that the normalized growth rate of the SSD exhibits the scaling, (gamma) over tilde proportional to vertical bar S vertical bar(2/3), arising solely from the induction equation for a given velocity field.

  • 234. Sinha, Suvadip
    et al.
    Gupta, Om
    Singh, Vishal
    Lekshmi, B.
    Nandy, Dibyendu
    Mitra, Dhrubaditya
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Chatterjee, Saikat
    Bhattacharya, Sourangshu
    Chatterjee, Saptarshi
    Srivastava, Nandita
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC).
    Pal, Sanchita
    A Comparative Analysis of Machine-learning Models for Solar Flare Forecasting: Identifying High-performing Active Region Flare Indicators2022Ingår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 935, nr 1, artikel-id 45Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Solar flares create adverse space weather impacting space- and Earth-based technologies. However, the difficulty of forecasting flares, and by extension severe space weather, is accentuated by the lack of any unique flare trigger or a single physical pathway. Studies indicate that multiple physical properties contribute to active region flare potential, compounding the challenge. Recent developments in machine learning (ML) have enabled analysis of higher-dimensional data leading to increasingly better flare forecasting techniques. However, consensus on high-performing flare predictors remains elusive. In the most comprehensive study to date, we conduct a comparative analysis of four popular ML techniques (k nearest neighbors, logistic regression, random forest classifier, and support vector machine) by training these on magnetic parameters obtained from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory for the entirety of solar cycle 24. We demonstrate that the logistic regression and support vector machine algorithms perform extremely well in forecasting active region flaring potential. The logistic regression algorithm returns the highest true skill score of 0.967 ± 0.018, possibly the highest classification performance achieved with any strictly parametric study. From a comparative assessment, we establish that magnetic properties like total current helicity, total vertical current density, total unsigned flux, R_VALUE, and total absolute twist are the top-performing flare indicators. We also introduce and analyze two new performance metrics, namely, severe and clear space weather indicators. Our analysis constrains the most successful ML algorithms and identifies physical parameters that contribute most to active region flare productivity.

  • 235. Snellman, J. E.
    et al.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Käpylä, P. J.
    Mantere, M. J.
    Verification of Reynolds stress parameterizations from simulations2012Ingår i: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 333, nr 1, s. 78-83Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We determine the timescales associated with turbulent decay and isotropization in closure models using anisotropically forced and freely decaying turbulence simulations and study the applicability of these models. We compare the results from anisotropically forced three-dimensional numerical simulations with the predictions of the closure models and obtain the turbulent timescales mentioned above as functions of the Reynolds number. In a second set of simulations, turning the forcing off enables us to study the validity of the closures in freely decaying turbulence. Both types of experiments suggest that the timescale of turbulent decay converges to a constant value at higher Reynolds numbers. Furthermore, the relative importance of isotropization is found to be about 2.5 times larger at higher Reynolds numbers than in the more viscous regime.

  • 236. Snellman, J. E.
    et al.
    Rheinhardt, M.
    Käpylä, P. J.
    Mantere, M. J.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Mean-field closure parameters for passive scalar turbulence2012Ingår i: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 86, nr 1, artikel-id 018406Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Direct numerical simulations (DNSs) of isotropically forced homogeneous stationary turbulence with an imposed passive scalar concentration gradient are compared with an analytical closure model which provides evolution equations for the mean passive scalar flux and variance. Triple correlations of fluctuations appearing in these equations are described in terms of relaxation terms proportional to the quadratic correlations. Three methods are used to extract the relaxation timescales tau(i) from DNSs. Firstly, we insert the closure ansatz into our equations, assume stationarity and solve for tau(i). Secondly, we use only the closure ansatz itself and obtain tau(i) from the ratio of quadratic and triple correlations. Thirdly, we remove the imposed passive scalar gradient and fit an exponential law to the decaying solution. We vary the Reynolds (Re) and Peclet numbers (while fixing their ratio at unity) and the degree of scale separation and find for large Re a fair correspondence between the different methods. The ratio of the turbulent relaxation time of the passive scalar flux to the turnover time of the turbulent eddies is of the order of 3, which is in remarkable agreement with earlier work. Finally, we make an effort to extract the relaxation timescales relevant for the viscous and diffusive effects. We find two regimes that are valid for small and large Re, respectively, but the dependence of the parameters on scale separation suggests that they are not universal.

  • 237.
    Sordo, Fabio Del
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    How can vorticity be produced in irrotationally forced flows?2010Ingår i: Proceedings of the International Astronomical Union, ISSN 1743-9213, E-ISSN 1743-9221, Vol. 6, s. 373-375Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A spherical hydrodynamical expansion flow can be described as the gradient of a potential. In that case no vorticity should be produced, but several additional mechanisms can drive its production. Here we analyze the effects of baroclinicity, rotation and shear in the case of a viscous fluid. Those flows resemble what happens in the interstellar medium. In fact in this astrophysical environment supernovae explosion are the dominant flows and, in a first approximation, they can be seen as spherical. One of the main difference is that in our numerical study we examine only weakly supersonic flows, while supernovae explosions are strongly supersonic.

  • 238. Subramanian, Kandaswamy
    et al.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Traces of large-scale dynamo action in the kinematic stage2014Ingår i: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 445, nr 3, s. 2930-2940Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Using direct numerical simulations (DNS), we verify that in the kinematic regime, a turbulent helical dynamo grows in such a way that the magnetic energy spectrum remains to high-precision shape-invariant, i.e. at each wavenumber k the spectrum grows with the same growth rate. Signatures of large-scale dynamo action can be identified through the excess of magnetic energy at small k, of one of the two oppositely polarized constituents. Also a suitably defined planar average of the magnetic field can be chosen such that its rms value isolates the strength of the mean field. However, these different means of analysis suggest that the strength of the large-scale field diminishes with increasing magnetic Reynolds number Re-M like Re(M)(-1/2)for intermediate values and like Re-M(-3/4) for larger ones. Both an analysis from the Kazantsev model including helicity and the DNS show that this arises due to the magnetic energy spectrum still peaking at resistive scales, even when helicity is present. As expected, the amplitude of the large-scale field increases with increasing fractional helicity, enabling us to determine the onset of large-scale dynamo action and distinguishing it from that of the small-scale dynamo. Our DNS show that, contrary to earlier results for smaller scale separation (only 1.5 instead of now 4), the small-scale dynamo can still be excited at magnetic Prandtl numbers of 0.1 and only moderate values of the magnetic Reynolds numbers (similar to 160).

  • 239. Sur, Sharanya
    et al.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    The role of the Yoshizawa effect in the Archontis dynamo2009Ingår i: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 399, nr 1, s. 273-280Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The generation of mean magnetic fields is studied for a simple non-helical flow where a net cross-helicity of either sign can emerge. This flow, which is also known as the Archontis flow, is a generalization of the Arnold-Beltrami-Childress flow, but with the cosine terms omitted. The presence of cross-helicity leads to a mean-field dynamo effect that is known as the Yoshizawa effect. Direct numerical simulations of such flows demonstrate the presence of magnetic fields on scales larger than the scale of the flow. Contrary to earlier expectations, the Yoshizawa effect is found to be proportional to the mean magnetic field and can therefore lead to its exponential instead of just linear amplification for magnetic Reynolds numbers that exceed a certain critical value. Unlike α effect dynamos, it is found that the Yoshizawa effect is not notably constrained by the presence of a conservation law. It is argued that this is due to the presence of a forcing term in the momentum equation, which leads to a non-zero correlation with the magnetic field. Finally, the application to energy convergence in solar wind turbulence is discussed.

  • 240. Svedin, Andreas
    et al.
    Cuellar, Milena C.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Data assimilation for stratified convection2013Ingår i: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 433, nr 3, s. 2278-2285Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We show how the 3DVAR data assimilation methodology can be used in the astrophysical context of a two-dimensional convection flow. We study the way in which this variational approach finds best estimates of the current state of the flow from a weighted average of model states and observations. We use numerical simulations to generate synthetic observations of a vertical two-dimensional slice of the outer part of the solar convection zone for varying noise levels, and implement 3DVAR when the covariance matrices are diagonal and proportional to the identity matrix. Our simulation results demonstrate the capability of 3DVAR to produce error estimates of system states that can be more than two orders of magnitude below the original noise level present in the observations. This work illustrates the importance of applying data to obtain accurate model estimates given a set of observations. It also exemplifies how data assimilation techniques can be applied to simulations of stratified convection.

  • 241. Tevzadze, Alexander G.
    et al.
    Kisslinger, Leonard
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Kahniashvili, Tina
    MAGNETIC FIELDS FROM QCD PHASE TRANSITIONS2012Ingår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 759, nr 1, s. 54-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the evolution of QCD phase transition-generated magnetic fields (MFs) in freely decaying MHD turbulence of the expanding universe. We consider an MF generation model that starts from basic non-perturbative QCD theory and predicts stochastic MFs with an amplitude of the order of 0.02 mu G and small magnetic helicity. We employ direct numerical simulations to model the MHD turbulence decay and identify two different regimes: a weakly helical turbulence regime, when magnetic helicity increases during decay, and fully helical turbulence, when maximal magnetic helicity is reached and an inverse cascade develops. The results of our analysis show that in the most optimistic scenario themagnetic correlation length in the comoving frame can reach 10 kpc with the amplitude of the effective MF being 0.007 nG. We demonstrate that the considered model of magnetogenesis can provide the seed MF for galaxies and clusters.

  • 242. Vaisala, M. S.
    et al.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Mitra, D.
    Käpylä, P. J.
    Mantere, M. J.
    Quantifying the effect of turbulent magnetic diffusion on the growth rate of the magneto-rotational instability2014Ingår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 567, artikel-id A139Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Context. In astrophysics, turbulent diffusion is often used in place of microphysical diffusion to avoid resolving the small scales. However, we expect this approach to break down when time and length scales of the turbulence become comparable with other relevant time and length scales in the system. Turbulent diffusion has previously been applied to the magneto-rotational instability (MRI), but no quantitative comparison of growth rates at different turbulent intensities has been performed. Aims. We investigate to what extent turbulent diffusion can be used to model the effects of small-scale turbulence on the kinematic growth rates of the MRI, and how this depends on angular velocity and magnetic field strength. Methods. We use direct numerical simulations in three-dimensional shearing boxes with periodic boundary conditions in the spanwise direction and additional random plane-wave volume forcing to drive a turbulent flow at a given length scale. We estimate the turbulent diffusivity using a mixing length formula and compare with results obtained with the test-field method. Results. It turns out that the concept of turbulent diffusion is remarkably accurate in describing the effect of turbulence on the growth rate of the MRI. No noticeable breakdown of turbulent diffusion has been found, even when time and length scales of the turbulence become comparable with those imposed by the MRI itself. On the other hand, quenching of turbulent magnetic diffusivity by the magnetic field is found to be absent. Conclusions. Turbulence reduces the growth rate of the MRI in the same way as microphysical magnetic diffusion does.

  • 243. Vermersch, V.
    et al.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Shear-driven magnetic buoyancy oscillations2009Ingår i: Astronomische Nachrichten, ISSN 0004-6337, Vol. 330, nr 8, s. 797-806Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The effects of uniform horizontal shear on a stably stratified layer of gas is studied. The system is initially destabilized by a magnetically buoyant flux tube pointing in the cross-stream direction. The shear amplifies the initial field to Lundquist numbers of about 200-400, but then its value drops to about 100-300, depending on the value of the sub-adiabatic gradient. The larger values correspond to cases where the stratification is strongly stable and nearly isothermal. At the end of the runs the magnetic field is nearly axisymmetric, i.e. uniform in the streamwise direction. In view of Cowling's theorem the sustainment of the field remains a puzzle and may be due to subtle numerical effects that have not yet been identified in detail. In the final state the strength of the magnetic field decreases with height in such a way that the field is expected to be unstable. Low amplitude oscillations are seen in the vertical velocity even at late times, suggesting that they might be persistent.

  • 244. Viviani, M.
    et al.
    Warnecke, J.
    Käpylä, M. J.
    Käpylä, Petri J.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Leibniz Institute for Astrophysics Potsdam, Germany; Aalto University, Finland; Max Planck Institute for Solar System Research, Germany.
    Olspert, N.
    Cole-Kodikara, E. M.
    Lehtinen, J. J.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Transition from axi- to nonaxisymmetric dynamo modes in spherical convection models of solar-like stars2018Ingår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 616, artikel-id A160Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Context. Both dynamo theory and observations of stellar large-scale magnetic fields suggest a change from nearly axisymmetric configurations at solar rotation rates to nonaxisymmetric configurations for rapid rotation. Aims. We seek to understand this transition using numerical simulations. Methods. We use three-dimensional simulations of turbulent magnetohydrodynamic convection in spherical shell wedges and considered rotation rates between 1 and 31 times the solar value. Results. We find a transition from axi- to nonaxisymmetric solutions at around 1.8 times the solar rotation rate. This transition coincides with a change in the rotation profile from antisolar- to solar-like differential rotation with a faster equator and slow poles. In the solar-like rotation regime, the field configuration consists of an axisymmetric oscillatory field accompanied by an m = 1 azimuthal mode (two active longitudes), which also shows temporal variability. At slow (rapid) rotation, the axisymmetric (nonaxisymmetric) mode dominates. The axisymmetric mode produces latitudinal dynamo waves with polarity reversals, while the nonaxisymmetric mode often exhibits a slow drift in the rotating reference frame and the strength of the active longitudes changes cyclically over time between the different hemispheres. In the majority of cases we find retrograde waves, while prograde waves are more often found from observations. Most of the obtained dynamo solutions exhibit cyclic variability either caused by latitudinal or azimuthal dynamo waves. In an activity-period diagram, the cycle lengths normalized by the rotation period form two different populations as a function of rotation rate or magnetic activity level. The slowly rotating axisymmetric population lies close to what in observations is called the inactive branch, where the stars are believed to have solar-like differential rotation, while the rapidly rotating models are close to the superactive branch with a declining cycle to rotation frequency ratio and an increasing rotation rate. Conclusions. We can successfully reproduce the transition from axi- to nonaxisymmetric dynamo solutions for high rotation rates, but high-resolution simulations are required to limit the effect of rotational quenching of convection at rotation rates above 20 times the solar value.

  • 245. Warnecke, J.
    et al.