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Korpi-Lagg MJ, Mac Low MM, Gent FA. Computational approaches to modeling dynamos in galaxies. LIVING REVIEWS IN COMPUTATIONAL ASTROPHYSICS 2024; 10:3. [PMID: 38966754 PMCID: PMC11219407 DOI: 10.1007/s41115-024-00021-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/03/2024] [Accepted: 05/29/2024] [Indexed: 07/06/2024]
Abstract
Galaxies are observed to host magnetic fields with a typical total strength of around 15 μ G. A coherent large-scale field constitutes up to a few microgauss of the total, while the rest is built from strong magnetic fluctuations over a wide range of spatial scales. This represents sufficient magnetic energy for it to be dynamically significant. Several questions immediately arise: What is the physical mechanism that gives rise to such magnetic fields? How do these magnetic fields affect the formation and evolution of galaxies? In which physical processes do magnetic fields play a role, and how can that role be characterized? Numerical modelling of magnetized flows in galaxies is playing an ever-increasing role in finding those answers. We review major techniques used for these models. Current results strongly support the conclusion that field growth occurs during the formation of the first galaxies on timescales shorter than their accretion timescales due to small-scale turbulent dynamos. The saturated small-scale dynamo maintains field strengths at only a few percent of equipartition with turbulence. This is in contradiction with the observed magnitude of turbulent fields, but may be reconciled by the further contribution to the turbulent field of the large-scale dynamo. The subsequent action of large-scale dynamos in differentially rotating discs produces field strengths observed in low redshift galaxies, where it reaches equipartition with the turbulence and has substantial power at large scales. The field structure resulting appears consistent with observations including Faraday rotation and polarisation from synchrotron and dust thermal emission. Major remaining challenges include scaling numerical models toward realistic scale separations and Prandtl and Reynolds numbers.
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Affiliation(s)
- Maarit J. Korpi-Lagg
- Astroinformatics, Department of Computer Science, Aalto University, P.O. Box 15400, 00076 Espoo, Finland
- Nordic Institute for Theoretical Physics, Hannes Alfvéns väg 12, 106 91 Stockholm, Sweden
- Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3, 37707 Göttingen, Germany
| | - Mordecai-Mark Mac Low
- Department of Astrophysics, American Museum of Natural History, 200 Central Park West, New York, NY 10024 USA
| | - Frederick A. Gent
- Astroinformatics, Department of Computer Science, Aalto University, P.O. Box 15400, 00076 Espoo, Finland
- Nordic Institute for Theoretical Physics, Hannes Alfvéns väg 12, 106 91 Stockholm, Sweden
- KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, 106 91 Stockholm, Sweden
- School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, NE1 7RU UK
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2
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Sironi L, Comisso L, Golant R. Generation of Near-Equipartition Magnetic Fields in Turbulent Collisionless Plasmas. PHYSICAL REVIEW LETTERS 2023; 131:055201. [PMID: 37595224 DOI: 10.1103/physrevlett.131.055201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2023] [Accepted: 06/08/2023] [Indexed: 08/20/2023]
Abstract
The mechanisms that generate "seed" magnetic fields in our Universe and that amplify them throughout cosmic time remain poorly understood. By means of fully kinetic particle-in-cell simulations of turbulent, initially unmagnetized plasmas, we study the genesis of magnetic fields via the Weibel instability and follow their dynamo growth up to near-equipartition levels. In the kinematic stage of the dynamo, we find that the rms magnetic field strength grows exponentially with rate γ_{B}≃0.4u_{rms}/L, where L/2π is the driving scale and u_{rms} is the rms turbulent velocity. In the saturated stage, the magnetic field energy reaches about half of the turbulent kinetic energy. Here, magnetic field growth is balanced by dissipation via reconnection, as revealed by the appearance of plasmoid chains. At saturation, the integral-scale wave number of the magnetic spectrum approaches k_{int}≃12π/L. Our results show that turbulence-induced by, e.g., the gravitational buildup of galaxies and galaxy clusters-can magnetize collisionless plasmas with large-scale near-equipartition fields.
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Affiliation(s)
- Lorenzo Sironi
- Department of Astronomy and Columbia Astrophysics Laboratory, Columbia University, New York, New York 10027, USA
| | - Luca Comisso
- Department of Astronomy and Columbia Astrophysics Laboratory, Columbia University, New York, New York 10027, USA
| | - Ryan Golant
- Department of Astronomy and Columbia Astrophysics Laboratory, Columbia University, New York, New York 10027, USA
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3
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Bott AFA, Chen L, Boutoux G, Caillaud T, Duval A, Koenig M, Khiar B, Lantuéjoul I, Le-Deroff L, Reville B, Rosch R, Ryu D, Spindloe C, Vauzour B, Villette B, Schekochihin AA, Lamb DQ, Tzeferacos P, Gregori G, Casner A. Inefficient Magnetic-Field Amplification in Supersonic Laser-Plasma Turbulence. PHYSICAL REVIEW LETTERS 2021; 127:175002. [PMID: 34739267 DOI: 10.1103/physrevlett.127.175002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2020] [Revised: 06/07/2021] [Accepted: 09/17/2021] [Indexed: 06/13/2023]
Abstract
We report a laser-plasma experiment that was carried out at the LMJ-PETAL facility and realized the first magnetized, turbulent, supersonic (Ma_{turb}≈2.5) plasma with a large magnetic Reynolds number (Rm≈45) in the laboratory. Initial seed magnetic fields were amplified, but only moderately so, and did not become dynamically significant. A notable absence of magnetic energy at scales smaller than the outer scale of the turbulent cascade was also observed. Our results support the notion that moderately supersonic, low-magnetic-Prandtl-number plasma turbulence is inefficient at amplifying magnetic fields compared to its subsonic, incompressible counterpart.
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Affiliation(s)
- A F A Bott
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Department of Astrophysical Sciences, University of Princeton, 4 Ivy Lane, Princeton, New Jersey 08544, USA
| | - L Chen
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - G Boutoux
- CEA-DAM, DIF, F-91297 Arpajon, France
| | | | - A Duval
- CEA-DAM, DIF, F-91297 Arpajon, France
| | - M Koenig
- LULI, CNRS, CEA, Ecole Polytechnique, UPMC, Sorbonne Universités, Institut Polytechnique de Paris, F-91128 Palaiseau cedex, France
- Graduate School of Engineering, Osaka University, Suita, Osaka 565-0871, Japan
| | - B Khiar
- Department of Astronomy and Astrophysics, University of Chicago, 5640 S. Ellis Avenue, Chicago, Illinois 60637, USA
| | | | | | - B Reville
- Max-Planck-Institut für Kernphysik, Postfach 10 39 80, 69029 Heidelberg, Germany
| | - R Rosch
- CEA-DAM, DIF, F-91297 Arpajon, France
| | - D Ryu
- Department of Physics, School of Natural Sciences, UNIST, Ulsan 44919, Korea
| | - C Spindloe
- Central Laser Facility, STFC Rutherford Appleton Laboratory, Chilton, Didcot OX11 0XQ, United Kingdom
| | - B Vauzour
- CEA-DAM, DIF, F-91297 Arpajon, France
| | | | - A A Schekochihin
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Merton College, Merton Street, Oxford OX1 4JD, United Kingdom
| | - D Q Lamb
- Department of Astronomy and Astrophysics, University of Chicago, 5640 S. Ellis Avenue, Chicago, Illinois 60637, USA
| | - P Tzeferacos
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Department of Astronomy and Astrophysics, University of Chicago, 5640 S. Ellis Avenue, Chicago, Illinois 60637, USA
- Department of Physics and Astronomy, University of Rochester, 206 Bausch & Lomb Hall, Rochester, New York 14627, USA
- Laboratory for Laser Energetics, University of Rochester, 250 East River Road, Rochester, New York 14623, USA
| | - G Gregori
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - A Casner
- CEA-DAM, DIF, F-91297 Arpajon, France
- Université de Bordeaux-CNRS-CEA, CELIA, UMR 5107, F-33405 Talence, France
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4
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Varma V, Müller B. 3D simulations of oxygen shell burning with and without magnetic fields. MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 2021; 504:636-647. [PMID: 33935581 PMCID: PMC8056252 DOI: 10.1093/mnras/stab883] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/01/2021] [Revised: 03/03/2021] [Accepted: 03/25/2021] [Indexed: 06/12/2023]
Abstract
We present a first 3D magnetohydrodynamic (MHD) simulation of convective oxygen and neon shell burning in a non-rotating [Formula: see text] star shortly before core collapse to study the generation of magnetic fields in supernova progenitors. We also run a purely hydrodynamic control simulation to gauge the impact of the magnetic fields on the convective flow and on convective boundary mixing. After about 17 convective turnover times, the magnetic field is approaching saturation levels in the oxygen shell with an average field strength of [Formula: see text], and does not reach kinetic equipartition. The field remains dominated by small-to-medium scales, and the dipole field strength at the base of the oxygen shell is only [Formula: see text]. The angle-averaged diagonal components of the Maxwell stress tensor mirror those of the Reynolds stress tensor, but are about one order of magnitude smaller. The shear flow at the oxygen-neon shell interface creates relatively strong fields parallel to the convective boundary, which noticeably inhibit the turbulent entrainment of neon into the oxygen shell. The reduced ingestion of neon lowers the nuclear energy generation rate in the oxygen shell and thereby slightly slows down the convective flow. Aside from this indirect effect, we find that magnetic fields do not appreciably alter the flow inside the oxygen shell. We discuss the implications of our results for the subsequent core-collapse supernova and stress the need for longer simulations, resolution studies, and an investigation of non-ideal effects for a better understanding of magnetic fields in supernova progenitors.
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Affiliation(s)
- Vishnu Varma
- School of Physics and Astronomy, 10 College Walk, Monash University, Clayton VIC 3800, Australia
| | - Bernhard Müller
- School of Physics and Astronomy, 10 College Walk, Monash University, Clayton VIC 3800, Australia
- ARC Centre of Excellence for Gravitational Wave Discovery – OzGrav, Monash University, Clayton, VIC 3800, Australia
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Sharda P, Federrath C, Krumholz MR, Schleicher DRG. Magnetic field amplification in accretion discs around the first stars: implications for the primordial IMF. MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 2021; 503:2014-2032. [PMID: 33782632 PMCID: PMC7987533 DOI: 10.1093/mnras/stab531] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2020] [Revised: 02/17/2021] [Accepted: 02/22/2021] [Indexed: 06/12/2023]
Abstract
Magnetic fields play an important role in the dynamics of present-day molecular clouds. Recent work has shown that magnetic fields are equally important for primordial clouds, which form the first stars in the Universe. While the primordial magnetic field strength on cosmic scales is largely unconstrained, theoretical models strongly suggest that a weak seed field existed in the early Universe. We study how the amplification of such a weak field can influence the evolution of accretion discs around first stars, and thus affect the primordial initial mass function (IMF). We perform a suite of 3D ideal magneto-hydrodynamic simulations with different initial field strengths and numerical resolutions. We find that, in simulations with sufficient spatial resolution to resolve the Jeans scale during the collapse, even initially weak magnetic fields grow exponentially to become dynamically important due to both the so-called small-scale turbulent dynamo and the large-scale mean-field dynamo. Capturing the small-scale dynamo action depends primarily on how well we resolve the Jeans length, while capturing the large-scale dynamo depends on the Jeans resolution as well as the maximum absolute resolution. Provided enough resolution, we find that fragmentation does not depend strongly on the initial field strength, because even weak fields grow to become strong. However, fragmentation in runs with magnetic fields differs significantly from those without magnetic fields. We conclude that the development of dynamically strong magnetic fields during the formation of the first stars is likely inevitable, and that these fields had a significant impact on the primordial IMF.
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Affiliation(s)
- Piyush Sharda
- Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia
- Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia
| | - Christoph Federrath
- Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia
- Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia
| | - Mark R Krumholz
- Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia
- Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia
| | - Dominik R G Schleicher
- Departamento de Astronomía, Facultad Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción, Chile
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Achikanath Chirakkara R, Federrath C, Trivedi P, Banerjee R. Efficient Highly Subsonic Turbulent Dynamo and Growth of Primordial Magnetic Fields. PHYSICAL REVIEW LETTERS 2021; 126:091103. [PMID: 33750146 DOI: 10.1103/physrevlett.126.091103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2020] [Revised: 12/11/2020] [Accepted: 01/14/2021] [Indexed: 06/12/2023]
Abstract
We present the first study on the amplification of magnetic fields by the turbulent dynamo in the highly subsonic regime, with Mach numbers ranging from 10^{-3} to 0.4. We find that for the lower Mach numbers the saturation efficiency of the dynamo (E_{mag}/E_{kin})_{sat} increases as the Mach number decreases. Even in the case when injection of energy is purely through longitudinal forcing modes, (E_{mag}/E_{kin})_{sat}≳10^{-2} at a Mach number of 10^{-3}. We apply our results to magnetic field amplification in the early Universe and predict that a turbulent dynamo can amplify primordial magnetic fields to ≳10^{-16} G on scales up to 0.1 pc and ≳10^{-13} G on scales up to 100 pc. This produces fields compatible with lower limits of the intergalactic magnetic field inferred from blazar γ-ray observations.
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Affiliation(s)
- Radhika Achikanath Chirakkara
- Department of Physics, Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Pune 411008, India
- Research School of Astronomy and Astrophysics, Australian National University, Canberra, Australian Capital Territory 2611, Australia
- Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
| | - Christoph Federrath
- Research School of Astronomy and Astrophysics, Australian National University, Canberra, Australian Capital Territory 2611, Australia
| | - Pranjal Trivedi
- Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
- Universität Hamburg, II. Institut für Theoretische Physik, Luruper Chaussee 149, 22761 Hamburg, Germany
- Department of Physics, Sri Venkateswara College, University of Delhi, New Delhi 110020, India
| | - Robi Banerjee
- Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
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7
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Synthesizing Observations and Theory to Understand Galactic Magnetic Fields: Progress and Challenges. GALAXIES 2019. [DOI: 10.3390/galaxies8010004] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Constraining dynamo theories of magnetic field origin by observation is indispensable but challenging, in part because the basic quantities measured by observers and predicted by modelers are different. We clarify these differences and sketch out ways to bridge the divide. Based on archival and previously unpublished data, we then compile various important properties of galactic magnetic fields for nearby spiral galaxies. We consistently compute strengths of total, ordered, and regular fields, pitch angles of ordered and regular fields, and we summarize the present knowledge on azimuthal modes, field parities, and the properties of non-axisymmetric spiral features called magnetic arms. We review related aspects of dynamo theory, with a focus on mean-field models and their predictions for large-scale magnetic fields in galactic discs and halos. Furthermore, we measure the velocity dispersion of H i gas in arm and inter-arm regions in three galaxies, M 51, M 74, and NGC 6946, since spiral modulation of the root-mean-square turbulent speed has been proposed as a driver of non-axisymmetry in large-scale dynamos. We find no evidence for such a modulation and place upper limits on its strength, helping to narrow down the list of mechanisms to explain magnetic arms. Successes and remaining challenges of dynamo models with respect to explaining observations are briefly summarized, and possible strategies are suggested. With new instruments like the Square Kilometre Array (SKA), large data sets of magnetic and non-magnetic properties from thousands of galaxies will become available, to be compared with theory.
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8
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Abstract
The origin and maintenance of coherent magnetic fields in the Universe is reviewed with an emphasis on the possible challenges that arise in their theoretical understanding. We begin with the interesting possibility that magnetic fields originated at some level from the early universe. This could be during inflation, the electroweak, or the quark-hadron phase transitions. These mechanisms can give rise to fields which could be strong, but often with much smaller coherence scales than galactic scales. Their subsequent turbulent decay decreases their strength but increases their coherence. We then turn to astrophysical batteries which can generate seed magnetic fields. Here the coherence scale can be large, but the field strength is generally very small. These seed fields need to be further amplified and maintained by a dynamo to explain observed magnetic fields in galaxies. Basic ideas behind both small and large-scale turbulent dynamos are outlined. The small-scale dynamo may help to understand the first magnetization of young galaxies, while the large-scale dynamo is important for the generation of fields with scales larger than the stirring scale, as observed in nearby disk galaxies. The current theoretical challenges that turbulent dynamos encounter and their possible resolution are discussed.
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Martins Afonso M, Mitra D, Vincenzi D. Kazantsev dynamo in turbulent compressible flows. Proc Math Phys Eng Sci 2019; 475:20180591. [PMID: 31007546 DOI: 10.1098/rspa.2018.0591] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2018] [Accepted: 01/25/2019] [Indexed: 11/12/2022] Open
Abstract
We consider the kinematic fluctuation dynamo problem in a flow that is random, white-in-time, with both solenoidal and potential components. This model is a generalization of the well-studied Kazantsev model. If both the solenoidal and potential parts have the same scaling exponent, then, as the compressibility of the flow increases, the growth rate decreases but remains positive. If the scaling exponents for the solenoidal and potential parts differ, in particular if they correspond to typical Kolmogorov and Burgers values, we again find that an increase in compressibility slows down the growth rate but does not turn it off. The slow down is, however, weaker and the critical magnetic Reynolds number is lower than when both the solenoidal and potential components display the Kolmogorov scaling. Intriguingly, we find that there exist cases, when the potential part is smoother than the solenoidal part, for which an increase in compressibility increases the growth rate. We also find that the critical value of the scaling exponent above which a dynamo is seen is unity irrespective of the compressibility. Finally, we realize that the dimension d = 3 is special, as for all other values of d the critical exponent is higher and depends on the compressibility.
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Affiliation(s)
- Marco Martins Afonso
- Centro de Matemática (Faculdade de Ciências) da Universidade do Porto, Rua do Campo Alegre 687, Porto 4169-007, Portugal
| | - Dhrubaditya Mitra
- Nordita, KTH Royal Institute of Technology and Stockholm University, Stockholm, Sweden
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THE LINK BETWEEN TURBULENCE, MAGNETIC FIELDS, FILAMENTS, AND STAR FORMATION IN THE CENTRAL MOLECULAR ZONE CLOUD G0.253+0.016. ACTA ACUST UNITED AC 2016. [DOI: 10.3847/0004-637x/832/2/143] [Citation(s) in RCA: 111] [Impact Index Per Article: 13.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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11
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Yang Y, Shi Y, Wan M, Matthaeus WH, Chen S. Energy cascade and its locality in compressible magnetohydrodynamic turbulence. Phys Rev E 2016; 93:061102. [PMID: 27415197 DOI: 10.1103/physreve.93.061102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2016] [Indexed: 06/06/2023]
Abstract
We investigate energy transfer across scales in three-dimensional compressible magnetohydrodynamic (MHD) turbulence, a model often used to study space and astrophysical plasmas. Analysis shows that kinetic and magnetic energies cascade conservatively from large to small scales in cases with varying degrees of compression. With more compression, energy fluxes due to pressure dilation and subscale mass flux are greater, but conversion between kinetic and magnetic energy by magnetic line stretching is less efficient. Energy transfer between the same fields is dominated by local contributions regardless of compressive effects. In contrast, the conversion between kinetic and internal energy by pressure dilation is dominated by the largest scale contributions. Energy conversion between the velocity and magnetic fields is weakly local.
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Affiliation(s)
- Yan Yang
- State Key Laboratory for Turbulence and Complex Systems, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, People's Republic of China
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - Yipeng Shi
- State Key Laboratory for Turbulence and Complex Systems, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, People's Republic of China
| | - Minping Wan
- Department of Mechanics and Aerospace Engineering, South University of Science and Technology of China, Shenzhen, Guangdong 518055, People's Republic of China
| | - William H Matthaeus
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - Shiyi Chen
- State Key Laboratory for Turbulence and Complex Systems, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, People's Republic of China
- Department of Mechanics and Aerospace Engineering, South University of Science and Technology of China, Shenzhen, Guangdong 518055, People's Republic of China
- Collaborative Innovation Center of Advanced Aero-Engine, Beijing 100191, People's Republic of China
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12
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Schober J, Schleicher DRG, Federrath C, Bovino S, Klessen RS. Saturation of the turbulent dynamo. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:023010. [PMID: 26382506 DOI: 10.1103/physreve.92.023010] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2015] [Indexed: 06/05/2023]
Abstract
The origin of strong magnetic fields in the Universe can be explained by amplifying weak seed fields via turbulent motions on small spatial scales and subsequently transporting the magnetic energy to larger scales. This process is known as the turbulent dynamo and depends on the properties of turbulence, i.e., on the hydrodynamical Reynolds number and the compressibility of the gas, and on the magnetic diffusivity. While we know the growth rate of the magnetic energy in the linear regime, the saturation level, i.e., the ratio of magnetic energy to turbulent kinetic energy that can be reached, is not known from analytical calculations. In this paper we present a scale-dependent saturation model based on an effective turbulent resistivity which is determined by the turnover time scale of turbulent eddies and the magnetic energy density. The magnetic resistivity increases compared to the Spitzer value and the effective scale on which the magnetic energy spectrum is at its maximum moves to larger spatial scales. This process ends when the peak reaches a characteristic wave number k☆ which is determined by the critical magnetic Reynolds number. The saturation level of the dynamo also depends on the type of turbulence and differs for the limits of large and small magnetic Prandtl numbers Pm. With our model we find saturation levels between 43.8% and 1.3% for Pm≫1 and between 2.43% and 0.135% for Pm≪1, where the higher values refer to incompressible turbulence and the lower ones to highly compressible turbulence.
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Affiliation(s)
- J Schober
- Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Strasse 2, D-69120 Heidelberg, Germany and Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
| | - D R G Schleicher
- Departamento de Astronomía, Facultad Ciencias Físicas y Matemáticas, Universidad de Concepción, Avenida Esteban Iturra s/n Barrio Universitario, Casilla 160-C, Concepción, Chile
| | - C Federrath
- Research School of Astronomy & Astrophysics, The Australian National University, Canberra, ACT 2611, Australia
| | - S Bovino
- Hamburger Sternwarte, Gojenbergsweg 112, D-21029 Hamburg, Germany and Institut für Astrophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
| | - R S Klessen
- Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Strasse 2, D-69120 Heidelberg, Germany
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13
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Schober J, Schleicher D, Bovino S, Klessen RS. Small-scale dynamo at low magnetic Prandtl numbers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:066412. [PMID: 23368064 DOI: 10.1103/physreve.86.066412] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2012] [Indexed: 06/01/2023]
Abstract
The present-day Universe is highly magnetized, even though the first magnetic seed fields were most probably extremely weak. To explain the growth of the magnetic field strength over many orders of magnitude, fast amplification processes need to operate. The most efficient mechanism known today is the small-scale dynamo, which converts turbulent kinetic energy into magnetic energy leading to an exponential growth of the magnetic field. The efficiency of the dynamo depends on the type of turbulence indicated by the slope of the turbulence spectrum v(ℓ)∝ℓ^{ϑ}, where v(ℓ) is the eddy velocity at a scale ℓ. We explore turbulent spectra ranging from incompressible Kolmogorov turbulence with ϑ=1/3 to highly compressible Burgers turbulence with ϑ=1/2. In this work, we analyze the properties of the small-scale dynamo for low magnetic Prandtl numbers Pm, which denotes the ratio of the magnetic Reynolds number, Rm, to the hydrodynamical one, Re. We solve the Kazantsev equation, which describes the evolution of the small-scale magnetic field, using the WKB approximation. In the limit of low magnetic Prandtl numbers, the growth rate is proportional to Rm^{(1-ϑ)/(1+ϑ)}. We furthermore discuss the critical magnetic Reynolds number Rm_{crit}, which is required for small-scale dynamo action. The value of Rm_{crit} is roughly 100 for Kolmogorov turbulence and 2700 for Burgers. Furthermore, we discuss that Rm_{crit} provides a stronger constraint in the limit of low Pm than it does for large Pm. We conclude that the small-scale dynamo can operate in the regime of low magnetic Prandtl numbers if the magnetic Reynolds number is large enough. Thus, the magnetic field amplification on small scales can take place in a broad range of physical environments and amplify week magnetic seed fields on short time scales.
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Affiliation(s)
- Jennifer Schober
- Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Überle-Strasse 2, D-69120 Heidelberg, Germany.
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14
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Schober J, Schleicher D, Federrath C, Klessen R, Banerjee R. Magnetic field amplification by small-scale dynamo action: dependence on turbulence models and Reynolds and Prandtl numbers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:026303. [PMID: 22463313 DOI: 10.1103/physreve.85.026303] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2011] [Indexed: 05/31/2023]
Abstract
The small-scale dynamo is a process by which turbulent kinetic energy is converted into magnetic energy, and thus it is expected to depend crucially on the nature of the turbulence. In this paper, we present a model for the small-scale dynamo that takes into account the slope of the turbulent velocity spectrum v(ℓ)proportional ℓ([symbol see text])V}, where ℓ and v(ℓ) are the size of a turbulent fluctuation and the typical velocity on that scale. The time evolution of the fluctuation component of the magnetic field, i.e., the small-scale field, is described by the Kazantsev equation. We solve this linear differential equation for its eigenvalues with the quantum-mechanical WKB approximation. The validity of this method is estimated as a function of the magnetic Prandtl number Pm. We calculate the minimal magnetic Reynolds number for dynamo action, Rm_{crit}, using our model of the turbulent velocity correlation function. For Kolmogorov turbulence ([symbol see text] = 1/3), we find that the critical magnetic Reynolds number is Rm(crit) (K) ≈ 110 and for Burgers turbulence ([symbol see text] = 1/2) Rm(crit)(B) ≈ 2700. Furthermore, we derive that the growth rate of the small-scale magnetic field for a general type of turbulence is Γ proportional Re((1-[symbol see text])/(1+[symbol see text])) in the limit of infinite magnetic Prandtl number. For decreasing magnetic Prandtl number (down to Pm >/~ 10), the growth rate of the small-scale dynamo decreases. The details of this drop depend on the WKB approximation, which becomes invalid for a magnetic Prandtl number of about unity.
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Affiliation(s)
- Jennifer Schober
- Institut für Theoretische Astrophysik, Zentrum für Astronomie der Universität Heidelberg, Albert-Überle-Strasse 2, D-69120 Heidelberg, Germany.
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