Stochastic Reconnection in Partially Ionized Gas:Progress Report A. Lazarian (UW-Madison) Collaboration with J. Cho (UW-Madison and CITA) A.Esquivel (UW-Madison) H. Yan (UW-Madison) E. Vishniac (Johns Hopkins)

Questions to address? How does turbulence affect reconnection? What are the properties of turbulence in partially ionized gas? How does partial ionization change the expected reconnection rate?

Motivation: Interstellar Fields Turbulent: Re ~VL/ ~10 10 >> 1 ~ r L v th, v th < V, r L << L

Armstrong & Spangler (1995) Lazarian& Pogosyan (00) & Starnimirovic & Lazarian (01) showed Kolmogorov velocity spectrum of HI here. Slope ~ -5/3 Electron density spectrum AU pc

What is the effect of Interstellar Tubrulence? Makes boundary conditions difficult to control. X point reconnection is not feasible unless large scale field reconfigure themselves over hundreds of parsec scales. Fast local (e.g. X point) reconnection does not guarantee fast reconnection if the global outflow regions are narrow.

Relation to Center Activities Properties of turbulence: related to Magnetic Chaos and Transport Reconnection and properties of turbulence are related to Ion Heating. Reconnection is an essential part of the picture of Dynamo and Angular Momentum Transport

What is Stochastic Reconnection? Stochastic reconnection: The natural state of fluids is turbulence. Presence of an stochastic component of the B field. Magnetic field lines dissipate not on their entire scale length (L), but on a smaller scale ( || ) determined by turbulence statistics. Many simultaneous S-P reconnections. Lazarian & Vishniac (1999)

Properties of Stochastic Reconnection Can be both fast and slow (depending on the level of turbulence) ( B!) Allows flares of reconnection. Depends of the properties of turbulence

Partially ionzed gas:possible effects Free diffusion of neutrals out of the current sheet. Probably not so important (Vishniac & Lazarian 1998, Heitsch & Zweibel 2003). Turbulence is affected by damping caused by neutrals. Is it fatal?

Turbulence in partially ionized gas:Theoretical expectations (from Lazarian, Vishniac & Cho 2004) In partially ionized gas MHD turbulence does not vanish at the viscous damping scale. Magnetic intermittency increases with decrease of the scale. Turbulence gets resurrected at ion decoupling scale.

B Viscous magnetized fluid Viscosity is important while resistivity is not. ~0.3pc in WNM Does viscous damping scale is the scale at which MHD turbulence ends?

Viscosity Damped Turbulence: New Regime of MHD Turbulence Cho, Lazarian & Vishniac 2002b E(k)~k -1 intermittent Numerical testing confirms that magnetic turbulence does not die!!! Expected: k -1 for magnetic field k -4 for kinetic energy Scale dependent intermittency

Viscosity damped turbulence protrudes up to the scales at which neutrals decouple from ions. After that the normal MHD turbulence in ionic fluid is restored. Lazarian, Vishniac & Cho (2003) Yet to be tested with two fluid code

Results: Expected Reconnection Rates for Phases of ISM (from Lazarian, Vishniac & Cho 2004) Molecular cloud: 0.1 V A (L 30 /l 30 3/2 ) Dark cloud: 0.1 V T M A 1/2 L 30 /l 30 1/4 ) Cold Neutral Medium: 0.08 V T M 2 (L 30 /l 30 3/2 )

Some Astrophysical Implications Removal of magnetic field during star formation Solar flares and particle acceleration

Numerical Testings Numerical testing of the stochastic reconnection idea Further testing of the divergence of the field lines in the new regime of turbulence. Numerical testing of the resurrection of turbulence prediction (using two fluid code).

Summary Interstellar reconnection happens in turbulent medium and on very large scales. Turbulence and external forcing makes large scale X point not probable. Stochastic reconnection is fast, but it may also be slow. The research requires interaction with other directions of the Center.

Compressible MHD Turbulence: Stimulating Prior Work Higdon 1984 (anisotropy in compressible MHD turbulence) Goldreich & Shridhar 1995 (incompressible MHD theory, hints about compressibility) Lithwick & Goldreich 2001 (effects of compressibility) Choice is biased by authors preferences. Longer list is in Cho, Lazarian & Vishniac 2003.

Implication 1: CR transport Scattering efficiency (Kolmogorov) Fast modes Alfven modes are inefficient. Fast modes are efficient in spite of damping Big difference!!! From Yan & Lazarian 2002

What are the scattering rates for different ISM phases? Solid line is analytical results Symbols are numerical results (a)gyroresonance is dominant; (b)the scattering in partially ionized media is not important. From Yan & Lazarian 2004 Gyroresonance TTD

Implication 2: Dust Dynamics Gyroresonace with fast modes is most efficient Grains get supersonic Grains may get aligned From Yan & Lazarian 2003 Grain size

Cascade time follows Kolmogorov scaling t cas ~k -2/3 Cho, Lazarian, & Vishniac 2002a Implication 3: Decay of MHD turbulence Fast decay of MHD turbulence reported earlier is not due to coupling of compressible and incopressible motions! Incompressible MHD turbulence decays fast. Inportant for star formation.

Large scales Normal MHD Turbulence Viscosity damped regime Large Scales (Small k only) Small Scales (Large k only) Magnetic structures perpendicular to mean B. Intermittency is prominent for new regime at small scales. Intermittent structures Smaller and smaller structures forming at scales smaller than the damping scale. From Cho, Lazarian & Vishniac 2003

Ordinary MHDNew regime Viscosity damped turbulence exhibits scale-dependent intermittency! Cho, Lazarian & Vishniac 2003 Corresponds to prediction in Lazarian, Vishniac & Cho 2003

Viscosity damped MHD turbulence results in a shallow spectrum of density fluctuations. Could there be a relation to tiny scale structures observed in the ISM? From Cho & Lazarian 2003

Why E(k)~k -1 ? Magnetic fluctuations evolve due to shear at the damping scale. => Cascade of magnetic energy with the fixed rate: Expect to see a lot of magnetic structure below the viscous damping scale (e.g. below 0.3pc for WNM) Bl2Bl2 diss = const => B l 2 ~ const, or E(k)~k -1 kE(k)~B l

Genus analysis (cont.) A shift from the mean can reveal meatball or Swiss cheese topology. Genus curve of the HI in the SMC and from compressible MHD simulations. The SMC show a evident Swiss cheese topology, the simulations are more or less symmetric. Genus are a quantitative measure of the topology, allows to test simulations & observations. SMC MHD