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

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

  • 2.
    Asplund, Julia
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Jóhannesson, Guðlaugur
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA; Carnegie Mellon University, USA.
    On the Measurement of Handedness in Fermi Large Area Telescope Data2020In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 898, no 2, article id 124Article in journal (Refereed)
    Abstract [en]

    A handedness in the arrival directions of high-energy photons from outside our Galaxy can be related to the helicity of an intergalactic magnetic field. Previous estimates by Tashiro et al. and Chen et al. showed a hint of a signal present in the photons observed by the Fermi Large Area Telescope (LAT). An update on the measurement of handedness in Fermi-LAT data is presented using more than 10 yr of observations. Simulations are performed to study the uncertainty of the measurements, taking into account the structure of the exposure caused by the energy-dependent instrument response and its observing profile, as well as the background from the interstellar medium. The simulations are required to accurately estimate the uncertainty and to show that previously the uncertainty was significantly underestimated. The apparent signal in the earlier analysis of Fermi-LAT data is rendered nonsignificant.

  • 3. Babkovskaia, Natalia
    et al.
    Haugen, N. E. L.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    A high-order public domain code for direct numerical simulations of turbulent combustion2011In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, no 1, p. 1-12Article in journal (Refereed)
    Abstract [en]

    A high-order scheme for direct numerical simulations of turbulent combustion is discussed. Its implementation in the massively parallel and publicly available PENCIL CODE is validated with the focus on hydrogen combustion. This is the first open source DNS code with detailed chemistry available. An attempt has been made to present, for the first time, the full set of evolution and auxiliary equations required for a complete description of single phase non-isothermal fluid dynamics with detailed chemical reactions. Ignition delay times (0D) and laminar flame velocities (1D) are calculated and compared with results from the commercially available Chemkin code. The scheme is verified to be fifth order in space. Upon doubling the resolution, a 32-fold increase in the accuracy of the flame front is demonstrated. Finally, also turbulent and spherical flame front velocities are calculated and the implementation of the non-reflecting so-called Navier-Stokes Characteristic Boundary Condition is validated in all three directions.

  • 4.
    Barekat, A.
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. Max-Planck-Institut für Sonnensystemforschung, Germany.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Near-polytropic stellar simulations with a radiative surface2014In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 571, article id A68Article in journal (Refereed)
    Abstract [en]

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

  • 5. Bejarano, Cecilia
    et al.
    Gomez, Daniel O.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    SHEAR-DRIVEN INSTABILITIES IN HALL-MAGNETOHYDRODYNAMIC PLASMAS2011In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 737, no 2, p. 62-Article in journal (Refereed)
    Abstract [en]

    The large-scale dynamics of plasmas is well described within the framework of magnetohydrodynamics (MHD). However, whenever the ion density of the plasma becomes sufficiently low, the Hall effect is likely to become important. The role of the Hall effect has been studied in several astrophysical plasma processes, such as magnetic reconnection, magnetic dynamo, MHD turbulence, or MHD instabilities. In particular, the development of small-scale instabilities is essential to understand the transport properties in a number of astrophysical plasmas. The magneto-rotational instability (MRI), which takes place in differentially rotating accretion disks embedded in relatively weak magnetic fields, is just one example. The influence of the large-scale velocity flows on small-scale instabilities is often approximated by a linear shear flow. In this paper, we quantitatively study the role of the Hall effect on plasmas embedded in large-scale shear flows. More precisely, we show that an instability develops when the Hall effect is present, which we therefore term as the Hall magneto-shear instability. As a particular case, we recover the so-called MRI and quantitatively assess the role of the Hall effect on its development and evolution.

  • 6.
    Bhat, Pallavi
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Inter University Centre for Astronomy and Astrophysics, India; Princeton University, USA.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Hydraulic effects in a radiative atmosphere with ionization2016In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 587, article id A90Article in journal (Refereed)
    Abstract [en]

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

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

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

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

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

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

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

  • 8. Blanco, N.
    et al.
    Stafford, K. A.
    Lavoie, M. C.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Gorna, M. W.
    Merski, M.
    A simple model for the total number of SARS-CoV-2 infections on a national level2021In: Epidemiology and Infection, ISSN 0950-2688, E-ISSN 1469-4409, Vol. 149, article id e80Article in journal (Refereed)
    Abstract [en]

    This study aimed to identify an appropriate simple mathematical model to fit the number of coronavirus disease 2019 (COVID-19) cases at the national level for the early portion of the pandemic, before significant public health interventions could be enacted. The total number of cases for the COVID-19 epidemic over time in 28 countries was analysed and fit to several simple rate models. The resulting model parameters were used to extrapolate projections for more recent data. While the Gompertz growth model (mean R-2 = 0.998) best fit the current data, uncertainties in the eventual case limit introduced significant model errors. However, the quadratic rate model (mean R-2 = 0.992) fit the current data best for 25 (89%) countries as determined by R-2 values of the remaining models. Projection to the future using the simple quadratic model accurately forecast the number of future total number of cases 50% of the time up to 10 days in advance. Extrapolation to the future with the simple exponential model significantly overpredicted the total number of future cases. These results demonstrate that accurate future predictions of the case load in a given country can be made using this very simple model.

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

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

  • 10. Bourdin, Philippe
    et al.
    Singh, Nishant K.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Max-Planck-Institut für Sonnensystemforschung, Germany.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Magnetic Helicity Reversal in the Corona at Small Plasma Beta2018In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 869, no 1, article id 2Article in journal (Refereed)
    Abstract [en]

    Solar and stellar dynamos shed small-scale and large-scale magnetic helicity of opposite signs. However, solar wind observations and simulations have shown that some distance above the dynamo both the small-scale and large-scale magnetic helicities have reversed signs. With realistic simulations of the solar corona above an active region now being available, we have access to the magnetic field and current density along coronal loops. We show that a sign reversal in the horizontal averages of the magnetic helicity occurs when the local maximum of the plasma beta drops below unity and the field becomes nearly fully force free. Hence, this reversal is expected to occur well within the solar corona and would not directly be accessible to in situ measurements with the Parker Solar Probe or SolarOrbiter. We also show that the reversal is associated with subtle changes in the relative dominance of structures with positive and negative magnetic helicity.

  • 11. Bourdin, Philippe-A
    et al.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Magnetic Helicity from Multipolar Regions on the Solar Surface2018In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 869, no 1, article id 3Article in journal (Refereed)
    Abstract [en]

    The emergence of dipolar magnetic features on the solar surface is an idealization. Most of the magnetic flux emergence occurs in complex multipolar regions. Here, we show that the surface pattern of magnetic structures alone can reveal the sign of the underlying magnetic helicity in the nearly force-free coronal regions above. The sign of the magnetic helicity can be predicted to good accuracy by considering the three-dimensional position vectors of three spots on the sphere ordered by their relative strengths at the surface and compute from them the skew product. This product, which is a pseudoscalar, is shown to be a good proxy for the sign of the coronal magnetic helicity.

  • 12.
    Bracco, Andrea
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Candelaresi, S.
    Del Sordo, F.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Is there a left-handed magnetic field in the solar neighborhood? Exploring helical magnetic fields in the interstellar medium through dust polarization power spectra2019In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 621, article id A97Article in journal (Refereed)
    Abstract [en]

    Context. The analysis of the full-sky Planck polarization data at 850 mu m revealed unexpected properties of the E- and B-mode power spectra of dust emission in the interstellar medium (ISM). The positive cross-correlations over a wide range of angular scales between the total dust intensity, T, and both E and (most of all) B modes has raised new questions about the physical mechanisms that affect dust polarization, such as the Galactic magnetic field structure. This is key both to better understanding ISM dynamics and to accurately describing Galactic foregrounds to the polarization of the cosmic microwave background (CMB). In particular, in the quest to find primordial B modes of the CMB, the observed positive cross-correlation between T and B for interstellar dust requires further investigation towards parity-violating processes in the ISM.

    Aims. In this theoretical paper we investigate the possibility that the observed cross-correlations in the dust polarization power spectra, and specifically the one between T and B, can be related to a parity-odd quantity in the ISM such as the magnetic helicity.

    Methods. We produce synthetic dust polarization data, derived from 3D analytical toy models of density structures and helical magnetic fields, to compare with the E and B modes of observations. We present several models. The first is an ideal fully helical isotropic case, such as the Arnold-Beltrami-Childress field. Second, following the nowadays favored interpretation of the T-E signal in terms of the observed alignment between the magnetic field morphology and the filamentary density structure of the diffuse ISM, we design models for helical magnetic fields wrapped around cylindrical interstellar filaments. Lastly, focusing on the observed T-B correlation, we propose a new line of interpretation of the Planck observations advocating the presence of a large-scale helical component of the Galactic magnetic field in the solar neighborhood.

    Results. Our analysis shows that: I) the sign of magnetic helicity does not affect E and B modes for isotropic magnetic-field configurations; II) helical magnetic fields threading interstellar filaments cannot reproduce the Planck results; and III) a weak helical left-handed magnetic field structure in the solar neighborhood may explain the T-B correlation seen in the Planck data. Such a magnetic-field configuration would also account for the observed large-scale T-E correlation.

    Conclusions. This work suggests a new perspective for the interpretation of the dust polarization power spectra that supports the imprint of a large-scale structure of the Galactic magnetic field in the solar neighborhood.

  • 13.
    Brandenburg, A.
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy.
    Kleeorin, N.
    Rogachevskii, I.
    Large-scale magnetic flux concentrations from turbulent stresses2010In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 331, no 1, p. 5-13Article in journal (Refereed)
    Abstract [en]

    % In this study we provide the first numerical demonstration of the effects of turbulence on the mean Lorentz force and the resulting formation of large-scale magnetic structures. Using three-dimensional direct numerical simulations (DNS) of forced turbulence we show that an imposed mean magnetic field leads to a decrease of the turbulent hydromagnetic pressure and tension. This phenomenon is quantified by determining the relevant functions that relate the sum of the turbulent Reynolds and Maxwell stresses with the Maxwell stress of the mean magnetic field. Using such a parameterization, we show by means of two-dimensional and three-dimensional mean-field numerical modelling that an isentropic density stratified layer becomes unstable in the presence of a uniform imposed magnetic field. This large-scale instability results in the formation of loop-like magnetic structures which are concentrated at the top of the stratified layer. In three dimensions these structures resemble the appearance of bipolar magnetic regions in the Sun. The results of DNS and mean-field numerical modelling are in good agreement with theoretical predictions. We discuss our model in the context of a distributed solar dynamo where active regions and sunspots might be rather shallow phenomena.} \begin{document

  • 14.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA; Carnegie Mellon University, USA.
    A Global Two-scale Helicity Proxy from pi-ambiguous Solar Magnetic Fields2019In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 883, no 2, article id 119Article in journal (Refereed)
    Abstract [en]

    If the alpha effect plays a role in the generation of the Sun's magnetic field, the field should show evidence of magnetic helicity of opposite signs at large and small length scales. Measuring this faces two challenges: (i) in weak-field regions, horizontal field measurements are unreliable because of the pi ambiguity, and (ii) one needs a truly global approach to computing helicity spectra in the case where one expects a sign reversal across the equator at all wavenumbers. Here we develop such a method using spin-2 spherical harmonics to decompose the linear polarization in terms of the parity-even and parity-odd E and B polarizations, respectively. Using simple one- and two-dimensional models, we show that the product of the spectral decompositions of E and B, taken at spherical harmonic degrees that are shifted by one, can act as a proxy of the global magnetic helicity with a sign that represents that in the northern hemisphere. We then apply this method to the analysis of solar synoptic vector magnetograms, from which we extract a pseudo-polarization corresponding to a pi-ambiguated magnetic field, i.e., a magnetic field vector that has no arrow. We find a negative sign of the global EB helicity proxy at spherical harmonic degrees of around 6. This could indicate a positive magnetic helicity at large length scales, but the spectrum fails to capture clear evidence of the well-known negative magnetic helicity at smaller scales. This method might also be applicable to stellar and Galactic polarization data.

  • 15.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Advances in mean-field dynamo theory and applications to astrophysical turbulence2018In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 84, no 4, article id 735840404Article in journal (Refereed)
    Abstract [en]

    Recent advances in mean-field theory are reviewed and applications to the Sun, late-type stars, accretion disks, galaxies and the early Universe are discussed. We focus particularly on aspects of spatio-temporal non-locality, which provided some of the main new qualitative and quantitative insights that emerged from applying the test-field method to magnetic fields of different length and time scales. We also review the status of nonlinear quenching and the relation to magnetic helicity, which is an important observational diagnostic of modern solar dynamo theory. Both solar and some stellar dynamos seem to operate in an intermediate regime that has not yet been possible to model successfully. This regime is bracketed by antisolar-like differential rotation on one end and stellar activity cycles belonging to the superactive stars on the other. The difficulty in modelling this regime may be related to shortcomings in simulating solar/stellar convection. On galactic and extragalactic length scales, the observational constraints on dynamo theory are still less stringent and more uncertain, but recent advances both in theory and observations suggest that more conclusive comparisons may soon be possible also here. The possibility of inversely cascading magnetic helicity in the early Universe is particularly exciting in explaining the recently observed lower limits of magnetic fields on cosmological length scales. Such magnetic fields may be helical with the same sign of magnetic helicity throughout the entire Universe. This would be a manifestation of parity breaking.

  • 16.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA; Carnegie Mellon University, USA,.
    Ambipolar diffusion in large Prandtl number turbulence2019In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 487, no 2, p. 2673-2684Article in journal (Refereed)
    Abstract [en]

    We study the effects of ambipolar diffusion (AD) on hydromagnetic turbulence. We consider the regime of large magnetic Prandtl number, relevant to the interstellar medium. In most of the cases, we use the single-fluid approximation where the drift velocity between charged and neutral particles is proportional to the Lorentz force. In two cases we also compare with the corresponding two-fluid model, where ionization and recombination are included in the continuity and momentum equations for the neutral and charged species. The magnetic field properties are found to be well represented by the single-fluid approximation. We quantify the effects of AD on total and spectral kinetic and magnetic energies, the ohmic and AD dissipation rates, the statistics of the magnetic field, the current density, and the linear polarization as measured by the rotationally invariant E and B mode polarizations. We show that the kurtosis of the magnetic field decreases with increasing AD. The E mode polarization changes its skewness from positive values for small AD to negative ones for large AD. Even when AD is weak, changes in AD have a marked effect on the skewness and kurtosis of E, and only a weak effect on those of B. These results open the possibility of employing E and B mode polarizations as diagnostic tools for characterizing turbulent properties of the interstellar medium.

  • 17.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Analytic solution of an oscillatory migratory alpha(2) stellar dynamo2017In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 598, article id A117Article in journal (Refereed)
    Abstract [en]

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

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

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

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

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

  • 18.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Chandrasekhar-Kendall functions in astrophysical dynamos2011In: Pramana (Bangalore), ISSN 0304-4289, E-ISSN 0973-7111, Vol. 77, no 1, p. 67-76Article in journal (Refereed)
    Abstract [en]

    Some of the contributions of Chandrasekhar to the field of magnetohydrodynamics are highlighted. Particular emphasis is placed on the Chandrasekhar-Kendall functions that allow a decomposition of a vector field into right- and left-handed contributions. Magnetic energy spectra of both contributions are shown for a new set of helically forced simulations at resolutions higher than what has been available so far. For a forcing function with positive helicity, these simulations show a forward cascade of the right-handed contributions to the magnetic field and nonlocal inverse transfer for the left-handed contributions. The speed of inverse transfer is shown to decrease with increasing value of the magnetic Reynolds number.

  • 19.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Dissipation in dynamos at low and high magnetic Prandtl numbers2011In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 332, no 1, p. 51-56Article in journal (Refereed)
    Abstract [en]

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

  • 20.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Hall Cascade with Fractional Magnetic Helicity in Neutron Star Crusts2020In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 901, no 1, article id 18Article in journal (Refereed)
    Abstract [en]

    The ohmic decay of magnetic fields in the crusts of neutron stars is generally believed to be governed by Hall drift, which leads to what is known as a Hall cascade. Here we show that helical and fractionally helical magnetic fields undergo strong inverse cascading like in magnetohydrodynamics (MHD), but the magnetic energy decays more slowly with time t: proportional to t(-2/5) instead of proportional to t(-2/3) in MHD. Even for a nonhelical magnetic field there is a certain degree of inverse cascading for sufficiently strong magnetic fields. The inertial range scaling with wavenumber k is compatible with earlier findings for the forced Hall cascade, i.e., proportional to k(-7/3), but in the decaying cases, the subinertial range spectrum steepens to a novel k(5) slope instead of the k(4) slope in MHD. The energy of the large-scale magnetic field can increase quadratically in time through inverse cascading. For helical fields, the energy dissipation is found to be inversely proportional to the large-scale magnetic field and proportional to the fifth power of the rms magnetic field. For neutron star conditions with an rms magnetic field of a few times 10(14) G, the large-scale magnetic field might only be 10(11) G, while still producing magnetic dissipation of 10(33) erg s(-1) for thousands of years, which could manifest itself through X-ray emission. Finally, it is shown that the conclusions from local unstratified models agree rather well with those from stratified models with boundaries.

  • 21.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    Magnetic field evolution in simulations with Euler potentials2010In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 401, no 1, p. 347-354Article in journal (Refereed)
    Abstract [en]

    Using two- and three-dimensional hydromagnetic simulations for a range of different flows, including laminar and turbulent ones, it is shown that solutions expressing the field in terms of Euler potentials (EP) are in general incorrect if the EP are evolved with an artificial diffusion term. In three dimensions, standard methods using the magnetic vector potential are found to permit dynamo action when the EP give decaying solutions. With an imposed field, the EP method yields excessive power at small scales. This effect is more exaggerated in the dynamic case, suggesting an unrealistically reduced feedback from the Lorentz force. The EP approach agrees with standard methods only at early times when magnetic diffusivity did not have time to act. It is demonstrated that the usage of EP with even a small artificial magnetic diffusivity does not converge to a proper solution of hydromagnetic turbulence. The source of this disagreement is not connected with magnetic helicity or the three-dimensionality of the magnetic field, but is simply due to the fact that the non-linear representation of the magnetic field in terms of EP that depend on the same coordinates is incompatible with the linear diffusion operator in the induction equation.

  • 22.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA; Carnegie Mellon University, USA.
    Magnetic helicity and fluxes in an inhomogeneous alpha(2) dynamo2018In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 339, no 9-10, p. 631-640Article in journal (Refereed)
    Abstract [en]

    Much work on turbulent three-dimensional dynamos has been done using triply periodic domains, in which there are no magnetic helicity fluxes. Here, we present simulations where the turbulent intensity is still nearly homogeneous, but now there is a perfect conductor boundary condition on one end and a vertical field or pseudovacuum conditions on the other. This leads to migratory dynamo waves. Good agreement with a corresponding analytically solvable alpha(2) dynamo is found. Magnetic helicity fluxes are studied in both types of models. It is found that at moderate magnetic Reynolds numbers, most of the magnetic helicity losses occur on large scales. Whether this changes at even larger magnetic Reynolds numbers, as required for alleviating the catastrophic dynamo quenching problem, remains stillunclear.

  • 23.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Physics.
    MAGNETIC PRANDTL NUMBER DEPENDENCE OF THE KINETIC- TO- MAGNETIC DISSIPATION RATIO2014In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 791, no 1, p. 12-Article in journal (Refereed)
    Abstract [en]

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

  • 24.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    Nonlinear Small-scale Dynamos at Low Magnetic Prandtl Numbers2011In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 741, no 2, p. 92-Article in journal (Refereed)
    Abstract [en]

    Saturated small-scale dynamo solutions driven by isotropic non-helical turbulence are presented at low magnetic Prandtl numbers Pr M down to 0.01. For Pr M < 0.1, most of the energy is dissipated via Joule heat and, in agreement with earlier results for helical large-scale dynamos, kinetic energy dissipation is shown to diminish proportional to Pr1/2 M down to values of 0.1. In agreement with earlier work, there is, in addition to a short Golitsyn k -11/3 spectrum near the resistive scale, also some evidence for a short k -1 spectrum on larger scales. The rms magnetic field strength of the small-scale dynamo is found to depend only weakly on the value of Pr M and decreases by about a factor of two as Pr M is decreased from 1 to 0.01. The possibility of dynamo action at Pr M = 0.1 in the nonlinear regime is argued to be a consequence of a suppression of the bottleneck seen in the kinetic energy spectrum in the absence of a dynamo and, more generally, a suppression of kinetic energy near the dissipation wavenumber.

  • 25.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Piecewise quadratic growth during the 2019 novel coronavirus epidemic2020In: Infectious Disease Modelling, ISSN 2468-0427, Vol. 5, p. 681-690Article in journal (Refereed)
    Abstract [en]

    The temporal growth in the number of deaths in the COVID-19 epidemic is subexponential. Here we show that a piecewise quadratic law provides an excellent fit during the thirty days after the first three fatalities on January 20 and later since the end of March 2020. There is also a brief intermediate period of exponential growth. During the second quadratic growth phase, the characteristic time of the growth is about eight times shorter than in the beginning, which can be understood as the occurrence of separate hotspots. Quadratic behavior can be motivated by peripheral growth when further spreading occurs only on the outskirts of an infected region. We also study numerical solutions of a simple epidemic model, where the spatial extend of the system is taken into account. To model the delayed onset outside China together with the early one in China within a single model with minimal assumptions, we adopt an initial condition of several hotspots, of which one reaches saturation much earlier than the others. At each site, quadratic growth commences when the local number of infections has reached a certain saturation level. The total number of deaths does then indeed follow a piecewise quadratic behavior.

  • 26.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC). Carnegie Mellon University, United States of America; Ilia State University, Georgia.
    Quadratic growth during the COVID-19 pandemic: merging hotspots and reinfections2023In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 56, no 4, article id 044002Article in journal (Refereed)
    Abstract [en]

    The existence of an exponential growth phase during early stages of a pandemic is often taken for granted. However, for the 2019 novel coronavirus epidemic, the early exponential phase lasted only for about six days, while the quadratic growth prevailed for forty days until it spread to other countries and continued, again quadratically, but with a shorter time constant. Here we show that this rapid phase is followed by a subsequent slow-down where the coefficient is reduced to almost the original value at the outbreak. This can be explained by the merging of previously disconnected sites that occurred after the disease jumped (nonlocally) to a relatively small number of separated sites. Subsequent variations in the slope with continued growth can qualitatively be explained as a result of reinfections and variations in their rate. We demonstrate that the observed behavior can be described by a standard epidemiological model with spatial extent and reinfections included. Time-dependent changes in the spatial diffusion coefficient can also model corresponding variations in the slope.

  • 27.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Simulations of Galactic Dynamos2015In: Magnetic Fields in Diffuse Media / [ed] Lazarian, A.; DalPino, E.M.D.; Melioli, C., Dordrecht: Springer, 2015, Vol. 407, p. 529-555Chapter in book (Refereed)
    Abstract [en]

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

  • 28.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    STELLAR MIXING LENGTH THEORY WITH ENTROPY RAIN2016In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 832, no 1, article id 6Article in journal (Refereed)
    Abstract [en]

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

  • 29.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy.
    The critical role of magnetic helicity in astrophysical large-scale dynamos2009In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 51, no 12, p. 4043-Article in journal (Refereed)
    Abstract [en]

    The role of magnetic helicity in astrophysical large-scale dynamos is reviewed and compared with cases where there is no energy supply and an initial magnetic field can only decay. In both cases magnetic energy tends to get redistributed to larger scales. Depending on the efficiency of magnetic helicity fluxes the decay of a helical field can speed up. Likewise, the saturation of a helical dynamo can speed up through magnetic helicity fluxes. The astrophysical importance of these processes is reviewed in the context of the solar dynamo and an estimated upper limit for the magnetic helicity flux of 1046 Mx2/cycle is given.

  • 30.
    Brandenburg, Axel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. JILA and Laboratory for Atmospheric and Space Physics, USA; Carnegie Mellon University, USA.
    The Limited Roles of Autocatalysis and Enantiomeric Cross-Inhibition in Achieving Homochirality in Dilute Systems2019In: Origins of life and evolution of the biosphere, ISSN 0169-6149, E-ISSN 1573-0875, Vol. 49, no 1-2, p. 49-60Article in journal (Refereed)
    Abstract [en]

    To understand the effects of fluctuations on achieving homochirality, we employ a Monte-Carlo method where autocatalysis and enantiomeric cross-inhibition, as well as racemization and deracemization reactions are included. The results of earlier work either without autocatalysis or without cross-inhibition are reproduced. Bifurcation diagrams and the dependencies of the number of reaction steps on parameters are studied. In systems with 30,000 molecules, for example, up to a billion reaction steps may be needed to achieve homochirality without autocatalysis.

  • 31.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Ashurova, Mohira B.
    Jabbari, Sarah
    Compensating Faraday Depolarization by Magnetic Helicity in the Solar Corona2017In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 845, no 2, article id L15Article in journal (Refereed)
    Abstract [en]

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

  • 32.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA; Carnegie Mellon University, USA.
    Boldyrev, Stanislav
    The Turbulent Stress Spectrum in the Inertial and Subinertial Ranges2020In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 892, no 2, article id 80Article in journal (Refereed)
    Abstract [en]

    For velocity and magnetic fields, the turbulent pressure and, more generally, the squared fields such as the components of the turbulent stress tensor, play important roles in astrophysics. For both one and three dimensions, we derive the equations relating the energy spectra of the fields to the spectra of their squares. We solve the resulting integrals numerically and show that for turbulent energy spectra of Kolmogorov type, the spectral slope of the stress spectrum is also of Kolmogorov type. For shallower turbulence spectra, the slope of the stress spectrum quickly approaches that of white noise, regardless of how blue the spectrum of the field is. For fully helical fields, the stress spectrum is elevated by about a factor of two in the subinertial range, while that in the inertial range remains unchanged. We discuss possible implications for understanding the spectrum of primordial gravitational waves from causally generated magnetic fields during cosmological phase transitions in the early universe. We also discuss potential diagnostic applications to the interstellar medium, where polarization and scintillation measurements characterize the square of the magnetic field.

  • 33.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA; Carnegie Mellon University, USA.
    Bracco, Andrea
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kahniashvili, Tina
    Mandal, Sayan
    Pol, Alberto Roper
    Petrie, Gordon J. D.
    Singh, Nishant K.
    E and B Polarizations from Inhomogeneous and Solar Surface Turbulence2019In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 870, no 2, article id 87Article in journal (Refereed)
    Abstract [en]

    Gradient- and curl-type or E- and B-type polarizations have been routinely analyzed to study the physics contributing to the cosmic microwave background polarization and galactic foregrounds. They characterize the parity-even and parity-odd properties of the underlying physical mechanisms, such as, for example, hydromagnetic turbulence in the case of dust polarization. Here, we study spectral correlation functions characterizing the parity-even and parity-odd parts of linear polarization for homogeneous and inhomogeneous turbulence to show that only the inhomogeneous helical case can give rise to a parity-odd polarization signal. We also study nonhelical turbulence and suggest that a strong non-vanishing (here negative) skewness of the E polarization is responsible for an enhanced ratio of the EE to the BB (quadratic) correlation in both the helical and nonhelical cases. This could explain the enhanced EE/BB ratio observed recently for dust polarization. We close with a preliminary assessment of using the linear polarization of the Sun to characterize its helical turbulence without being subjected to the pi ambiguity that magnetic inversion techniques have to address.

  • 34.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA; Carnegie Mellon University, USA.
    Brüggen, Marcus
    Hemispheric Handedness in the Galactic Synchrotron Polarization Foreground2020In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 896, no 1, article id L14Article in journal (Refereed)
    Abstract [en]

    The large-scale magnetic field of the Milky Way is thought to be created by an alpha omega dynamo, which implies that it should have opposite handedness north and south of the Galactic midplane. Here we attempt to detect a variation in handedness using polarization data from the Wilkinson Microwave Anisotropy Probe. Previous analyzes of the parity-even and parity-odd parts of linear polarization of the global dust and synchrotron emission have focused on quadratic correlations in spectral space of, and between, these two components. Here, by contrast, we analyze the parity-odd polarization itself and show that it has, on average, opposite signs in northern and southern Galactic hemispheres. Comparison with a Galactic mean-field dynamo model shows broad qualitative agreement and reveals that the sign of the observed hemispheric dependence of the azimuthally averaged parity-odd polarization is not determined by the sign of alpha, but by the sense of differential rotation.

  • 35.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Candelaresi, Simon
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Chatterjee, Piyali
    Small-scale magnetic helicity losses from a mean-field dynamo2009In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 398, no 3, p. 1414-1422Article in journal (Refereed)
    Abstract [en]

    Using mean-field models with a dynamical quenching formalism, we show that in finite domains magnetic helicity fluxes associated with small-scale magnetic fields are able to alleviate catastrophic quenching. We consider fluxes that result from advection by a mean flow, the turbulent mixing down the gradient of mean small-scale magnetic helicity density or the explicit removal which may be associated with the effects of coronal mass ejections in the Sun. In the absence of shear, all the small-scale magnetic helicity fluxes are found to be equally strong for both large- and small-scale fields. In the presence of shear, there is also an additional magnetic helicity flux associated with the mean field, but this flux does not alleviate catastrophic quenching. Outside the dynamo-active region, there are neither sources nor sinks of magnetic helicity, so in a steady state this flux must be constant. It is shown that unphysical behaviour emerges if the small-scale magnetic helicity flux is forced to vanish within the computational domain.

  • 36.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Chatterjee, P.
    Del Sordo, Fabio
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Hubbard, A.
    Käpylä, P. J.
    Rheinhardt, M.
    Turbulent transport in hydromagnetic flows2010In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T142, article id 14028Article in journal (Refereed)
    Abstract [en]

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

  • 37.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, Colorado.
    Chatterjee, Piyali
    Strong nonlocality variations in a spherical mean-field dynamo2018In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 339, no 2-3, p. 118-126Article in journal (Refereed)
    Abstract [en]

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

  • 38.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA; Carnegie Mellon University, USA.
    Chen, Long
    The nature of mean-field generation in three classes of optimal dynamos2020In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 86, no 1, article id 905860110Article in journal (Refereed)
    Abstract [en]

    In recent years, several optimal dynamos have been discovered. They minimize the magnetic energy dissipation or, equivalently, maximize the growth rate at a fixed magnetic Reynolds number. In the optimal dynamo of Willis (Phys. Rev. Lett., vol. 109, 2012, 251101), we find mean-field dynamo action for planar averages. One component of the magnetic field grows exponentially while the other decays in an oscillatory fashion near onset. This behaviour is different from that of an $\unicode[STIX]{x1D6FC}<^>{2}$ dynamo, where the two non-vanishing components of the planar averages are coupled and have the same growth rate. For the Willis dynamo, we find that the mean field is excited by a negative turbulent magnetic diffusivity, which has a non-uniform spatial profile near onset. The temporal oscillations in the decaying component are caused by the corresponding component of the diffusivity tensor being complex when the mean field is decaying and, in this way, time dependent. The growing mean field can be modelled by a negative magnetic diffusivity combined with a positive magnetic hyperdiffusivity. In two other classes of optimal dynamos of Chen et al. (J. Fluid Mech., vol. 783, 2015, pp. 23-45), we find, to some extent, similar mean-field dynamo actions. When the magnetic boundary conditions are mixed, the two components of the planar averaged field grow at different rates when the dynamo is 15 % supercritical. When the mean magnetic field satisfies homogeneous boundary conditions (where the magnetic field is tangential to the boundary), mean-field dynamo action is found for one-dimensional averages, but not for planar averages. Despite having different spatial profiles, both dynamos show negative turbulent magnetic diffusivities. Our finding suggests that negative turbulent magnetic diffusivities may support a broader class of dynamos than previously thought, including these three optimal dynamos.

  • 39.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. Ilia State University, Georgia; Carnegie Mellon University, USA.
    Clarke, Emma
    He, Yutong
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy.
    Kahniashvili, Tina
    Can we observe the QCD phase transition-generated gravitational waves through pulsar timing arrays?2021In: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 104, no 4, article id 043513Article in journal (Refereed)
    Abstract [en]

    We perform numerical simulations of gravitational waves (GWs) induced by hydrodynamic and hydromagnetic turbulent sources that might have been present at cosmological quantum chromodynamic (QCD) phase transitions. For turbulent energies of about 4% of the radiation energy density, the typical scale of such motions may have been a sizable fraction of the Hubble scale at that time. The resulting GWs are found to have an energy fraction of about 10(-9) of the critical energy density in the nHz range today and may already have been observed by the NANOGrav Collaboration. This is further made possible by our findings of shallower spectra proportional to the square root of the frequency for nonhelical hydromagnetic turbulence. This implies more power at low frequencies than for the steeper spectra previously anticipated. The behavior toward higher frequencies depends strongly on the nature of the turbulence. For vortical hydrodynamic and hydromagnetic turbulence, there is a sharp drop of spectral GW energy by up to five orders of magnitude in the presence of helicity, and somewhat less in the absence of helicity. For acoustic hydrodynamic turbulence, the sharp drop is replaced by a power law decay, albeit with a rather steep slope. Our study supports earlier findings of a quadratic scaling of the GW energy with the magnetic energy of the turbulence and inverse quadratic scaling with the peak frequency, which leads to larger GW energies under QCD conditions.

  • 40.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Das, Upasana
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    The time step constraint in radiation hydrodynamics2020In: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 114, no 1-2, p. 162-195Article in journal (Refereed)
    Abstract [en]

    Explicit radiation hydrodynamic simulations of the atmospheres of massive stars and of convection in accretion discs around white dwarfs suffer from prohibitively short time steps due to radiation. This constraint is related to the cooling time rather than the radiative pressure, which also becomes important in hot stars and discs. We show that the radiative time step constraint is governed by the minimum of the sum of the optically thick and thin contributions rather than the smaller one of the two. In simulations with the Pencil Code, their weighting fractions are found empirically. In three-dimensional convective accretion disc simulations, the Deardorff term is found to be the main contributor to the enthalpy flux rather than the superadiabatic gradient. We conclude with a discussion of how the radiative time step problem could be mitigated in certain types of investigations.

  • 41.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. Carnegie Mellon University, USA; Ilia State University, Georgia.
    Das, Upasana
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Turbulent radiative diffusion and turbulent Newtonian cooling2021In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 33, no 9, article id 095125Article in journal (Refereed)
    Abstract [en]

    Radiation transport plays an important role in stellar atmospheres, but the effects of turbulence are being obscured by other effects such as stratification. Using radiative hydrodynamic simulations of forced turbulence, we determine the decay rates of sinusoidal large-scale temperature perturbations of different wavenumbers in the optically thick and thin regimes. Increasing the wavenumber increases the rate of decay in both regimes, but this effect is much weaker than for the usual turbulent diffusion of passive scalars, where the increase is quadratic for small wavenumbers. The turbulent decay is well described by an enhanced Newtonian cooling process in the optically thin limit, which is found to show a weak increase proportional to the square root of the wavenumber. In the optically thick limit, the increase in turbulent decay is somewhat steeper for wavenumbers below the energy-carrying wavenumber of the turbulence, but levels off toward larger wavenumbers. In the presence of turbulence, the typical cooling time is comparable to the turbulent turnover time. We observe that the temperature takes a long time to reach equilibrium in both the optically thin and thick cases, but in the former, the temperature retains smaller scale structures for longer.

  • 42.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Del Sordo, Fabio
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Turbulent diffusion and galactic magnetism2009In: Proceedings of the International Astronomical Union, ISSN 1743-9213, E-ISSN 1743-9221, Vol. 5, p. 432-433Article in journal (Other academic)
    Abstract [en]

    Using the test-field method for nearly irrotational turbulence driven by spherical expansion waves it is shown that the turbulent magnetic diffusivity increases with magnetic Reynolds numbers. Its value levels off at several times the rms velocity of the turbulence multiplied by the typical radius of the expansion waves. This result is discussed in the context of the galactic mean-field dynamo.

  • 43.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA; Carnegie Mellon University, USA; Ilia State University, Georgia.
    Durrer, Ruth
    Huang, Yiwen
    Kahniashvili, Tina
    Mandal, Sayan
    Mukohyama, Shinji
    Primordial magnetic helicity evolution with a homogeneous magnetic field from inflation2020In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 102, no 2, article id 023536Article in journal (Refereed)
    Abstract [en]

    Motivated by a scenario of magnetogenesis in which a homogeneous magnetic field is generated during inflation, we study the magnetohydrodynamic evolution of the primordial plasma motions for two kinds of initial conditions-(i) a spatially homogeneous field with an unlimited correlation length, and (ii) a zero flux scale-invariant statistically homogeneous magnetic field. In both cases, we apply, for a short initial time interval, monochromatic forcing at a certain wave number so that the correlation length is finite, but much smaller than the typical length scale of turbulence. In particular, we investigate the decay of nonhelical and helical hydromagnetic turbulence. We show that, in the presence of a homogeneous magnetic field, the decay of helical and nonhelical small-scale fields can occur rapidly. This is a special property of a system with a perfectly homogeneous magnetic field, which is sometimes considered as a local approximation to a slowly varying background field. It can never change and acts as an imposed magnetic field. This is in sharp contrast to the case of a statistically homogeneous magnetic field, where we recover familiar decay properties: a much slower decay of magnetic energy and a faster growth of the correlation length, especially in the case with magnetic helicity. The result suggests that a homogeneous magnetic field, if generated during inflation, should persist under the influence of small-scale fields and could be the origin of the large-scale magnetic field in the Universe.

  • 44.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, U.S.A; Carnegie Mellon University, U.S.A..
    Durrer, Ruth
    Kahniashvili, Tina
    Mandalc, Sayan
    Yin, Weichen Winston
    Statistical properties of scale-invariant helical magnetic fields and applications to cosmology2018In: Journal of Cosmology and Astroparticle Physics, E-ISSN 1475-7516, no 8, article id 034Article in journal (Refereed)
    Abstract [en]

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

  • 45.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA; Carnegie Mellon University, USA.
    Furuya, Ray S.
    Application of a helicity proxy to edge-on galaxies2020In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 496, no 4, p. 4749-4759Article in journal (Refereed)
    Abstract [en]

    We study the prospects of detecting magnetic helicity in galaxies by observing the dust polarization of the edge-on galaxy NGC 891. Our numerical results of mean-field dynamo calculations show that there should be a large-scale component of the rotationally invariant parity-odd B polarization that we predict to be negative in the first and third quadrants, and positive in the second and fourth quadrants. The large-scale parity-even E polarization is predicted to be negative near the axis and positive further away in the outskirts. These properties are shown to be mostly a consequence of the magnetic field being azimuthal and the polarized intensity being maximum at the centre of the galaxy and are not a signature of magnetic helicity.

  • 46.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Colorado, USA.
    Giampapa, Mark S.
    Enhanced Stellar Activity for Slow Antisolar Differential Rotation2018In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 855, no 2, article id L22Article in journal (Refereed)
    Abstract [en]

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

  • 47.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. Carnegie Mellon University, United States of America; Ilia State University, Georgia.
    Gogoberidze, Grigol
    Kahniashvili, Tina
    Mandal, Sayan
    Pol, Alberto Roper
    Shenoy, Nakul
    The scalar, vector, and tensor modes in gravitational wave turbulence simulations2021In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 38, no 14, article id 145002Article in journal (Refereed)
    Abstract [en]

    We study the gravitational wave (GW) signal sourced by primordial turbulence that is assumed to be present at cosmological phase transitions like the electroweak and quantum chromodynamics phase transitions. We consider various models of primordial turbulence, such as those with and without helicity, purely hydrodynamical turbulence induced by fluid motions, and magnetohydrodynamic turbulence whose energy can be dominated either by kinetic or magnetic energy, depending on the nature of the turbulence. We also study circularly polarized GWs generated by parity violating sources such as helical turbulence. Our ultimate goal is to determine the efficiency of GW production through different classes of turbulence. We find that the GW energy and strain tend to be large for acoustic or irrotational turbulence, even though its tensor mode amplitude is relatively small at most wave numbers. Only at very small wave numbers is the spectral tensor mode significant, which might explain the efficient GW production in that case.

  • 48.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Gressel, O.
    Jabbari, Sarah
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Kleeorin, N.
    Rogachevskii, I.
    Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field2014In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 562, article id A53Article in journal (Refereed)
    Abstract [en]

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

  • 49.
    Brandenburg, Axel
    et al.
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Gressel, Oliver
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Käpylä, Petri J.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Helsinki, Finland.
    Kleeorin, Nathan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    Mantere, M. J.
    Rogachevskii, Igor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Ben-Gurion University of the Negev, Israel.
    NEW SCALING FOR THE ALPHA EFFECT IN SLOWLY ROTATING TURBULENCE2013In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 762, no 2, article id 127Article in journal (Refereed)
    Abstract [en]

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

  • 50.
    Brandenburg, Axel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Astronomy. University of Colorado, USA.
    Haugen, N. E. L.
    Li, Xiang-Yu
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Stockholm University, Faculty of Science, Department of Meteorology . University of Colorado, USA.
    Subramanian, K.
    Varying the forcing scale in low Prandtl number dynamos2018In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 479, no 2, p. 2827-2833Article in journal (Refereed)
    Abstract [en]

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

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