1. New Mechanism of Generation of Large-Scale Magnetic Field in Turbulence with Large-Scale Velocity Shear I. ROGACHEVSKII, N. KLEEORIN, E. LIVERTS Ben-Gurion University of the Negev, Beer Sheva, ISRAEL

2. Outline  Introduction  Physics of new “shear-current” effect and comparison with alpha effect (hydrodynamic helicity)  Generation of large-scale magnetic field due to the “shear-current” effect (kinematic and nonlinear dynamos)  Application to Astrophysics: magnetic fields in merging protostellar clouds, protogalactic clouds, etc.  Conclusions and future studies

3. Mean-Field Dynamo Is it possible to generate a large-scale magnetic field in a non-helical and non- rotating homogeneous turbulence ? Is it possible to generate a large-scale magnetic field in a non-helical and non- rotating homogeneous turbulence ?

4. Alpha-Omega Dynamo (Mean-Field Approach)  Induction equation for mean magnetic field:  Electromotive force:

5. Generation of the mean magnetic field due to the dynamo Dynamo number: Mean magnetic field:

6. Physics of the alpha-effect  The -effect is related to the hydrodynamic helicity in an inhomogeneous turbulence.  The deformations of the magnetic field lines are caused by upward and downward rotating turbulent eddies.  The inhomogeneity of turbulence breaks a symmetry between the upward and downward eddies.  Therefore, the total effect of the upward and downward eddies on the mean magnetic field does not vanish and it creates the mean electric current parallel to the original mean magnetic field.

7. Mean-Field Dynamo Do one need hydrodynamic helicity in order to generate a large-scale magnetic field in a homogeneous turbulent flow ? Do one need hydrodynamic helicity in order to generate a large-scale magnetic field in a homogeneous turbulent flow ?

8. Mean-Field Approach  Induction equation for mean magnetic field:  Electromotive force:

9. The ''shear-current" effect  The large-scale shear motions implies a nonzero mean vorticity :  The ''shear-current" effect is related to the term, the term,  Therefore, the term determines the ''shear-current" effect. the ''shear-current" effect.

10. Comparison of the alpha-effect with the ''shear-current" effect  The effect is caused by a uniform rotation and inhomogeneity of turbulence:, where, where  The ''shear-current" effect is related to the term and is caused by mean shear and nonuniform mean magnetic field,, where, where  Therefore,

11. Physics of ''shear-current" effect  In a turbulent flow with the mean velocity shear, the inhomogeneity of the original mean magnetic field breaks a symmetry between the influence of the upward and downward turbulent eddies on the mean magnetic field.  The deformations of the magnetic field lines in the ''shear-current" dynamo are caused by the upward and downward turbulent eddies which result in the mean electric current parallel to the mean magnetic field and produce the magnetic dynamo.

12. Generation of the mean magnetic field due to the shear-current effect Mean velocity shear:

13. Necessary condition for the shear-current dynamo The parameter :The growth rate of B: The Kolmogorov Scaling (large Re and Rm): Small Re and Rm (weak turbulence): Rogachevskii and Kleeorin (2003): there is shear-current dynamo In a good agreement with: Rädler and Stepanov (2006) there is no dynamo for: Rüdiger and Kitchatinov (2006) (SOCA)

14. Generation of the mean magnetic field (kinematic dynamo) Solution for the symmetric mode: The growth rate of B: Critical dynamo number: The magnetic scale at maximum :

15. Generation of the mean magnetic field (kinematic dynamo) Solution for the antisymmetric mode: The growth rate of B: Critical dynamo number: The magnetic scale at maximum :

16. Generation of the mean vorticity and magnetic field in sheared turbulence Mean velocity shear: The growth rate of The mean vorticityThe mean magnetic field The growth rate of B

17. Generation of the mean vorticity in turbulence with mean velocity shear Mean velocity shear: The growth rate of the mean vorticity Elperin, Kleeorin and Rogachevskii, PRE, 68, 016311 (2003)

18. The shear-current nonlinear dynamo (algebraic nonlinearity) Dynamo number: Nonlinear shear-current effect: Mean magnetic field: Shear number:

19. Nonlinear shear-current effect Weak magnetic field: Strong mean magnetic field: There is no quenching of the nonlinear "shear-current" effect contrary to the quenching of the nonlinear alpha effect, the nonlinear turbulent magnetic diffusion, etc.

20. Method of Derivation The spectral  -approximation (the third-order closure procedure) Equations for the correlation functions for:  The velocity fluctuations  The magnetic fluctuations  The cross-helicity tensor

21. The shear-current nonlinear dynamo (algebraic nonlinearity) Dynamo number: Nonlinear shear-current effect: Mean magnetic field: Shear number:

22. Nonlinear “shear-current” dynamo (algebraic nonlinearity)

24. Magnetic Helicity Magnetic part of alpha effect : Total magnetic helicity is conserved for very large magnetic Reynolds numbers Dynamics of small-scale magnetic helicity: The nonlinear function:

25. Dynamics of magnetic helicity In the absence of the magnetic helicity flux, In the presence of the flux of magnetic helicity: i.e., catastrophic quenching (Vainshtein and Cattaneo, 1992) Kleeorin and Ruzmaikin (1982); Gruzinov and Diamond (1994); Kleeorin and Rogachevskii (1999); Kleeorin, Moss, Rogachevskii and Sokoloff (2000); Blackman and Field (2000).

26. The shear-current nonlinear dynamo (algebraic and dynamic nonlinearities) Magnetic part of alpha effect: Dynamical nonlinearity: magnetic helicity evolution Mean magnetic field: The nonlinear function:

27. The shear-current nonlinear dynamo (algebraic and dynamic nonlinearities) Mean magnetic field:

28. Direct Numerical Simulations  A. Brandenburg, Astrophys. J. 625, 539-547 (2005).  A. Brandenburg, N.E.L. Haugen, P.J. Käpylä, C. Sandin, Astron. Nachr. 326, 174-185 (2005). 1. Non-helical forcing 2. Imposed mean velocity shear 3. Open boundary conditions (non-zero flux of magnetic helicity) (non-zero flux of magnetic helicity)

29. Astrophysical clouds  We apply the universal mechanism of generation of large-scale magnetic fields due to shear-current effect to several astrophysical objects: merging protostellar clouds merging protostellar clouds merging protogalactic clouds merging protogalactic clouds colliding giant galaxy clusters colliding giant galaxy clusters  Interactions of protostellar clouds, or colliding protogalactic clouds or giant galaxy clusters produce large-scale shear motions which are superimposed on small-scale turbulence.

30. ParametersParameters Protostellar Clouds Protogalactic Clouds Giant Galaxy Clusters Mass R (pc) V (cm/s)

31. Chernin (1993). Non-central collision

32. Different cloud sizes, Chernin (1993)

33. ParametersParameters Protostellar Clouds Protogalactic Clouds Giant Galaxy Clusters (cm/s) (cm/s) (cm) (cm) u (cm/s) u (cm/s) (cm) (cm) (years) (years)

34. ParametersParameters Protostellar Clouds Protogalactic Clouds Giant Galaxy Clusters (cm/s) (cm/s) (cm) (cm) (years) (years)

35. References  I. Rogachevskii and N. Kleeorin, Phys. Rev. E 68, 036301 (2003).  I. Rogachevskii and N. Kleeorin, Phys. Rev. E 70, 046310 (2004).  I. Rogachevskii, N. Kleeorin, A. D. Chernin and E. Liverts, Astron. Nachr. 327, 591-594 (2006).  I. Rogachevskii, N. Kleeorin and E. Liverts, to be submitted to GAFD (2006). to be submitted to GAFD (2006).

36. Conclusions  Generation of large-scale magnetic field is caused by a new ''shear-current" effect which acts even in a nonrotating and nonhelical homogeneous turbulence.  During the growth of the mean magnetic field, the nonlinear ''shear-current" effect is not quenched and it only changes its sign at some value of the mean magnetic field which can determine the level of the saturated mean magnetic field.

37. Conclusions  We have taken into account the transport of magnetic helicity as dynamical nonlinearity. The magnetic helicity flux strongly affects the magnetic field dynamics during the nonlinear shear-current dynamo. The level of the saturated mean magnetic field is of the order of the equipartition field.  The estimated saturated large-scale magnetic field for merging protogalactic clouds and colliding giant galaxy clusters is about several microgauss, and for merging protostellar clouds is of the order of several tenth of microgauss.

38. THE END