1. Katarzyna Otmianowska-Mazur (UJ, Poland)‏ Grzegorz Kowal (UW-Madison/UJ, Poland)‏ Alex Lazarian (UW-Madison, USA)‏ Ethan Vishniac (McMaster, Canada)‏ Effects of resistivity on 3D and 2D turbulent reconnection Kraków, October 11th, 2008

2. MHD Reconnection Fast reconnection should have speed close to V A Sweet-Parker (1958, 1957) reconnection is slow ~ V A *R M -1/2 Petschek (1964) found the fast mechanism ~ (logR M )-1 Biskamp (1984, 1996) showed that the X-point region collapses to Sweet- Parker geometry for large R M In the original version of this model (Petschek) shocks are required in order to maintain such geometry. These shocks are, in turn, supported by the flows driven by fast reconnection, they fade if L x increases (Vishniac et al. 2002). In solar atmosphere and corona magnetic reconnection is found to work (Shibata 1999, Martens 2003, Isobe et al. 2005)

3. Turbulence as a Potential Answer for Fast MHD Reconnection Lazarian & Vishniac (e.g. 1999, 2000) suggested that the presence of a random magnetic field component substantially enhances the reconnection rate enabling fast reconnection, i.e. reconnection that does not depend on fluid resistivity. The main phenomena responsible for that : * the presence of turbulence enables many magnetic field lines to enter the reconnection zone simultaneously. A significant fraction of magnetic energy goes into the MHD turbulence. This enhances reconnection rates through an increase in the field stochasticity. In this way magnetic reconnection becomes fast when the field stochasticity is taken into account. Fan et al. (2004, 2005) obtained the increase of magnetic reconnection rate due to the presence of turbulence in the solar atmosphere.

4. This calculation performed in LV99 used the Goldreich-Sridhar (1995) model of MHD turbulence, the Kraichnan model (Iroshnikov 1963; Kraichnan 1965) and the MHD turbulence with an arbitrary spectrum. In all the cases the upper limit on V rec,global was greater than V A, so that the diffusive wandering of field lines imposed the relevant limit on reconnection speeds. For instance, for the Goldreich-Sridhar (1995) spectrum the upper limit on the reconnection speed was where l and V l are the energy injection scale and turbulent velocity at this scale respectively. V r,up = V A min[(L x / l) 1/2, (l / L x ) 1/2 ] (v l /V A ) 2 2D 3D V rec = (  4 V t 2 /  L 3 V A ) 1/6 V rec,SP

5. Turbulence as a Potential Answer for Fast Reconnection Numerical model of turbulent reconnection Evolution in 2.5D and 3D Dependence on power of turbulence and resistivity Grzegorz Kowal code 512 x 512, B x = -1, 1, B y = 0 B z = -0.5, V x, V y, V z = 0, D = 1

6. What Happens When Turbulence Appears? Evolution of magnetic field and current density Evolution of velocity and density Total mass conserved in the system even with open boundaries Small increase of energies after introduction of turbulence

7. Dependence on Resistivity Reconnection rates: 2.5D depend on anomalous and uniform resistivity

8. Dependence on Resistivity and Power of Turbulence Reconnection rates: higher for more powerful forcing depend on uniform resistivity Increase by 50% and100% η=2·10 -3 η=10 -3

9. Dependence on uniform Resistivity

10. Dependence on anomalous Resistivity

11. Results Turbulent MHD r econnection in 2.5D numerical simulations depends on diffusion Turbulent MHD r econnection in 3D numerical simulations does not depend on diffusion