Statistical moments and multipoint magnetic field correlators in a galactic dynamo model with random turbulent diffusion




galactic dynamo, magnetic field, equations with random coefficients, intermittency, statistical moment


In this paper we consider a stochastic model of the galactic dynamo in which the coefficient of turbulent diffusion is considered as a random process with renewal. The numerical simulation of statistical moments as well as two-point and three-point correlators of the magnetic field showing the relation between its values at various time instants is performed. The presence of intermittency expressed in the progressive growth of moments and correlators in the case of "quiet" regions of galaxies with a small fraction of the ionized hydrogen component is shown. The numerical results are compared with the results obtained analytically earlier.

Author Biographies

D.A. Grachev

S.A. Elistratov

E.A. Mikhailov


  1. T. G. Arshakian, R. Beck, M. Krause, and D. Sokoloff, “Evolution of Magnetic Fields in Galaxies and Future Observational Tests with the Square Kilometre Array,” Astron. Astrophys. 494 (1), 21-32 (2009).
  2. R. Beck, A. Brandenburg, D. Moss, et al., “Galactic Magnetism: Recent Development and Perspectives,” Ann. Rev. Astron. Astrophys. 34, 155-206 (1996).
  3. E. A. Mikhailov, D. D. Sokoloff, and Yu. N. Efremov, “Star Formation Rate and Magnetic Fields in Spiral Galaxies,” Pis’ma Astron. Zh. 38 (9), 611-616 (2012) [Astron. Lett. 38 (9), 543-548 (2012)].
  4. M. E. Artyushkova and D. D. Sokoloff, “Modelling Small-Scale Dynamo by the Jacobi Equation,” Magnetohydrodynamics 42 (1), 3-20 (2006).
  5. M. R. E. Proctor, “Effects of Fluctuation on αΩ Dynamo Models,” Mon. Not. R. Astron. Soc. 382 (1), L39-L42 (2007).
  6. A. P. L. Newton and E. Kim, “Determining the Temporal Dynamics of the Solar α Effect,” Astron. Astrophys. 551 (2013).
    doi 10.1051/0004-6361/201219456
  7. D. Passos, D. Nandy, S. Hazra, and I. Lopes, “A Solar Dynamo Model Driven by Mean-Field Alpha and Babcock-Leighton Sources: Fluctuations, Grand-Minima-Maxima, and Hemispheric Asymmetry in Sunspot Cycles,” Astron. Astrophys. 563 (2014).
    doi 10.1051/0004-6361/201322635
  8. E. A. Mikhailov, “Star Formation and Galactic Dynamo Model with Helicity Fluxes,” Pis’ma Astron. Zh. 40 (7), 445-453 (2014) [Astron. Lett. 40 (7), 398-405 (2014)].
  9. S. Sur and K. Subramanian, “Galactic Dynamo Action in Presence of Stochastic α and Shear,” Mon. Not. R. Astron. Soc. 392 (1), L6-L10 (2009).
  10. E. A. Mikhailov and I. I. Modyaev, “Dynamo Equations with Random Coefficients,” Magnetohydrodynamics 51 (2), 285-292 (2015).
  11. F. Krause and K.-H. R854dler, Mean-Field Magnetohydrodynamics and Dynamo Theory (Pergamon, Oxford, 1980).
  12. D. Moss, “On the Generation of Bisymmetric Magnetic Field Structures in Spiral Galaxies by Tidal Interactions,” Mon. Not. R. Astron. Soc. 275 (1), 191-194 (1995).
  13. A. Phillips, “A Comparison of the Asymptotic and no-z Approximations for Galactic Dynamos,” Geophys. Astrophys. Fluid Dyn. 94 (1-2), 135-150 (2001).
  14. E. A. Mikhailov and V. V. Pushkarev, “Influence of Star Formation on Large Scale Structures of Galactic Magnetic Fields,” Astrofiz. Byull. 73 (4), 451-456 (2018) [Astrophys. Bull. 73 (4), 425-429 (2018)].
  15. E. A. Mikhailov and V. V. Pushkarev, “Fluctuations of the Turbulent Diffusion Coefficient in Galaxy Dynamo Equations,” Vychisl. Metody Programm. 17, 447-454 (2016).
  16. Ya. B. Zeldovich, S. A. Molchanov, A. A. Ruzmaikin, and D. D. Sokolov, “Intermittency in Random Media,” Usp. Fiz. Nauk 152 (1), 3-32 (1987) [Sov. Phys. Usp. 30 (5), 353-369 (1987)].
  17. Ya. B. Zel’dovich, A. A. Ruzmaikin, and D. D. Sokoloff, The Almighty Chance (World Scientific, Singapore, 1990).
  18. D. A. Grachev and D. D. Sokoloff, “Numerical Modeling of Growth of Multiplicative Random Quantities,” Vychisl. Metody Programm. 8, 1-5 (2007).
  19. M. E. Artyushkova and D. D. Sokolov, “Numerical Modeling of the Solutions of the Jacobi Equation on a Geodesic with Random Curvature,” Astron. Zh. 82 (7), 584-589 (2005) [Astron. Rep. 49 (7), 520-525 (2005)].
  20. D. A. Grachev, “A Relation between Numerical and Analytical Results for Stochastic Differential Equations,” Vychisl. Metody Programm. 9, 234-238 (2008).
  21. D. A. Grachev, “Averaging of Jacobi Fields along Geodesics on Manifolds of Random Curvature,” J. Math. Sci. 160 (1), 128-138 (2009).
  22. D. A. Grachev and E. A. Mikhailov, “Numerical Modeling of a Two-Point Correlator for the Lagrange Solutions of Some Evolution Equations,” Vychisl. Metody Programm. 18, 277-283 (2017).



How to Cite

Грачев Д.А., Елистратов С.А., Михайлов Е.А. Statistical Moments and Multipoint Magnetic Field Correlators in a Galactic Dynamo Model With Random Turbulent Diffusion // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2019. 20. 88-96. doi 10.26089/NumMet.v20r209



Section 1. Numerical methods and applications

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