Alex Lazarian

1. 3D Reconnection of Weakly Stochastic Magnetic Field and its Implications Alex Lazarian Astronomy Department and Center for Magnetic Self-Organization in Astrophysical and Laboratory Plasmas Collaboration: Ethan Vishniac, Grzegorz Kowal and Otminowska-Mazur

2. Solar Flares and Coronal Mass Ejections arise from magnetic reconnection

3. Gamma Ray Bursts, Dynamo and Magnetotail activity are other examples of reconnection But the problem is more fundamental.

4. Without the proof of fast reconnection all MHD numerical research is a “naked emperor” from the famous tale H.C. Andersen:”Not only was the material so beautiful, but the clothes made from it had the special power of being invisible to everyone who was stupid or not fit for his post.” Turkish version: "A turban such than one born in wedlock will see it, while the bastard will see it not" But reconnection should be slow to explain accumulation of flux required for solar flares.

5. Handwavingreconnection by D. Uzdensky Astrophysical reconnection was always associated with a particular kind of waves It is good to see whether other types of waves or non-linear interactions can do the job

6. Vin B Vout Vout Vin RECONNECTION RATE For ISM Rm>1012. Sweet-Parker model exhibits long and thin current sheets; very slow speed ~ 10-6 VA for ISM Ohmic diffusion Mass conservation Free outflow

7. Petschek model does not work for uniform resistivities X point Both dimensions are comparable. VR~VA Fast reconnection

8. Anomalous effects stabilize Petschek model, but are very restrictive Hall MHD Petcheck + anomalous effects ion current e current (Drake et al. ‘98) Very stringent requirement: mean free path of an electron is comparable with astrophysical L Is reconnection slow otherwise? Bad news for most of astrophysical simulations.

9. While electrons make many gyrations over a collision time, reconnection is collisional for interstellar medium Thus the interstellar gas is in collisionless if and the current sheet length of sheets Too small!!! >> 1. For ISM the collisionality parameter is But the condition for the reconnection to be “collisionless” is different, i. e. , is resistive width. is ion inertial length and <1

10. The idea of different mechanism responsible for fast reconnection in different media does not correspond to the principle of parsimony Ockham’s razor: “entities should not be multiplied needlessly” William Ockham 1288-1348

11. Astrophysical fluids are turbulent and magnetic field lines are not laminar Modified from Armstrong, Rickett & Spangler(1995) Density fluctuations ISM Turbulence Spectrum Slope ~ -5/3 WHAM emission: density fluctuations Chepurnov & Lazarian 2010 Electron density spectrum Scincillations and scattering pc AU

12. emission Doppler shifted velocity exhibits turbulent spectrum as revealed by the VCS technique VCS technique by Lazarian & Pogosyan (00, 06, 08) Sensitive to supersonic turbulence is cold gas. Reveals E(k)~k-1.85 for Arecibo high latitude data (Chepurnov et al. 10)

13. Turbulence was discussed in terms of reconnection, but results were inconclusive Microturbulence affects the effective resistivity by inducing anomalous effect Some papers which attempted to go beyond this: Speizer (1970) --- effect of line stochasticity in collisionless plasmas Jacobs & Moses (1984) --- inclusion of electron diffusion perpendicular mean B Strauss (1985), Bhattacharjee & Hameiri (1986) --- hyperresistivity Matthaeus & Lamkin (1985) --- numerical studies of 2D turbulent reconnection On the contrary, Kim & Diamond (2001) conclude that turbulence makes any reconnection slow, irrespectively of the local reconnection rate

14. Reconnection of 3D weakly turbulent magnetic fields involves many simultaneous reconnection events Turbulent reconnection: 1. Outflow is determined by field wandering. 2. Reconnection is fast with Ohmic resistivity only. B dissipates on a small scale || determined by turbulence statistics. Key element: L/l|| reconnection simultaneous events Lazarian & Vishniac (1999)

15. l||= Valfenlperp Vrec, local Vrec, local=h/ lperp Local reconnection rate is slow for Alfvenic turbulence due to eddy anisotropy Conservative scenario: Local reconnection is Sweet-Parker lperp l|| Vrec, local=Vl Rm -1/4 ifl||scales asl2/3perp (as in Goldreich-Sridhar 95)

16. The general requirement: Constraint due to Ohmic diffusion provides reconnection velocity faster than VA l|| L V rec, global =L/l|| Vrec, local For Goldreich-Shridhar 95 model of MHD turbulence the reconnection rate is V rec, global = Valfven Rm1/4> Valfven !!!!!!

17. Bottle neck is the outflow width: field wandering determines the reconnection rate (tested by Kowal et al. 09, next talk) Predictions in Lazarian & Vishniac (1999): No dependence on anomalous or Ohmic resistivities! As it translates into

18. In 10 years a substantial convergence between the models occured Hall MHD 1999 Our model Lazarian & Vishniac 1999 Hall MHD 2009 Our model is the one of volume filled reconnection. John Raymond attempted to test our model searching for volume reconnection, but by that time the Hall MHD model also evolved… Drake et al. 2006

19. Stochastic reconnection accelerates energetic particles without appealing to plasma effects GL03 versus Drake et al. 06: Cosmic rays get spectrum steeper than from shocks Drake et al. 2006 is 2D model with collapsing islands. The backreaction of accelerated electrons is accounted for. De Gouveia Dal Pino & Lazarian 2003 Applications to pulsars, microquasars, solar flare acceleration (De Gouveia Dal Pino & Lazarian 00, 03, 05, Lazarian 05).

20. In the presence of reconnection regular increase of energy is clearly seen 3D turbulent reconnection Pure Turbulence

21. Effect of solar cycle Effect of rotation Reconnection can provide a solution to anomalous cosmic ray measurements by Voyagers and to observed anisotropies of CR Lazarian & Opher 2009: Sun rotation creates B-reversals in the heliosheath inducing acceleration via reconnection. Lazarian & Desiati 2010: Sun 11 year cycles creates B-reversals in the heliotail inducing CR acceleration.

22. Hoang et al. Reconnection rate for flux in the box without external driving Time Turbulent reconnection produces flares when the initial state of field is laminar If field is laminar, the reconnection is slow and field accumulates. As turbulence level increases, the reconnection increases enhancing turbulence further (LV99). The finite time instability develops. Vishniac & Lazarian 1999 Ciaravella & Raymond 08 observed thick extended outflow regions associated with flares. Corresponds to what we expect and contradicts to Petscheck.

23. Allegoric summary: Emperor is not naked, reconnection is fast in most cases of realistically turbulent astro fluids. Many implications are to be explored.

24. We used both an intuitive measure, Vinflow, and a new measure of reconnection New measure:

25. Laminar Sweet-Parker reconnection Stochastic reconnection Initial reconnection without inflow: formation of Sweet-Parker layer Old measure is slightly larger due to diffusion Coincide assymptotically Calculations using the new measure are consistent with those using the intuitive one Intuitive, “old” measure is the measure of the influx of magnetic field New measure probes the annihilation of the flux

26. Reconnection layer structure depends on the scale of energy injection k=8 Turbulence with different scales - k=16 Laminar Sweet-Parker reconnection

27. Turbulence can enhance reconnection even in 2D via ejecting of islands -- forcing --outlfow Slower than in 3D as no multiple reconnection events are possible. The rate depends on both forcing and resistivity.

28. The range of direct applicability of collisionless reconnection is rather limited Reconnection is collisionless if Sweet-Parker sheet thickness Which translates into a restrictive: for Yamada et al. (2006) Which makes a lot of astrophysical environments, e.g. ISM, disks, stars collisional! Does it mean that all numerics in those fields is useless?

29. VR Voutflow outflow Cosmic ray bouncing back and forth B mirrow Turbulent reconnection efficiently accelerates cosmic rays by first order Fermi process Model of acceleration in De Gouveia Dal Pino & Lazarian 00 Applications to pulsars, microquasars, solar flare acceleration (De Gouveia Dal Pino & Lazarian 00, 04, Lazarian 04).

30. Original Petschek reconnection fails for generic astrophysical situations X point over many parsecs? Large scale fields: Inflow of matter Outflow of matter If the outflow slotis very small reconnection is slow because of the mass conservation constraint. Observations suggest that Solar reconnection layers are thick and not X-points (Raymond et al. 07). Also in most of ISM, stars, protostellar disks the reconnection is in collisional regime.

31. Tests of new measure: no effect of flux diffusion Reconnection of weakly stochastic field New measure gives zero for no field reversal Reconnection of weakly stochastic field Coincide within fluctuations