Dynamo action & MHD turbulence (in the ISM, hopefully…) Impact of dissipation on MHD turbulence (in disks) COSMIS project, page 17 S. Fromang (CEA Saclay, France) 1

Yes: Stretch, twist & fold! Basic question: can we grow a magnetic field in the ISM? Yes: Stretch, twist & fold! Properties Exponential growth of B Requires dissipation No mean field needed By contrast, when compressed: B2/3

Dimensionless numbers & MHD turbulence Reynolds number: Re =csH/ Magnetic Reynolds number: ReM=csH/ Magnetic Prandtl number: Pm= / Energy k Viscous length Kinetic energy Magnetic energy Resistive length >> Resistive length Magnetic energy >> 3

What are its properties?  The key questions Does it grow? When does it grow (under what conditions)? How does it grow? When does it saturate? What are its properties? Power spectra, intermittency 4

Homogeneous & incompressible MHD turbulence 5

Magnetic field structure Schekochihin et al. (2007) Pm=/>>1 Viscous length >> Resistive length Velocity Magnetic field Pm =/ <<1 Viscous length << Resistive length Velocity Magnetic field Very different flow structure for Pm<<1 and Pm>>1 Potentially important for star formation related issues… 6

What is Pm? In the computer, no scale separation: Pm of order unity Balbus & Henri (2008) Schekochihin et al. (2002) Warm ISM Molecular clouds T~10-100 K, n~100-1000 cm-3  Pm~310-4 - 30 but ambipolar diffusion important… In the computer, no scale separation: Pm of order unity 7

Small scale dynamo properties Mechanism for Pm=/>>1 Schekochihin et al. (2007) Critical magnetic Reynolds number Rem Schekochihin et al. (2004) Schekochihin et al. (2002) 8

Subsonic MHD turbulence The case of accretion disks (my work…) 9

the magnetorotational instability (MRI) Conditions for instability Keplerian rotation Gas &B field coupling Vertical velocity Azimuthal B-field Fromang (2010) - Case Pm=4 Main results Outward angular momentum transport Subsonic MHD turbulence v/v~/~10% Magnetic field Pmag/Pth~10% MHD numerical simulations

Parameter survey Pm=1 Results similar to homogeneous turbulence Fromang et al. (2007) ? Pm=1 Results similar to homogeneous turbulence  the effect of dissipation is robust High Re - High Rem behavior uncertain see Bodo et al. (2011) 11

The case of the ISM: supersonic turbulence

Naive expectations and basic results Presence of shocks… …eddies are affected and Bfield might be dissipated in shocks Kinetic energy dissipates in shocks… …but no so clear what happens to Bfield High Mach numbers Critical Rem for dynamo increased (Haugen et al. 2004) Compressive forcing Growth rate & saturation reduced (Federrath et al. 2011) In agreement with the analytic results of Schober et al. (2011)

BEWARE: NO EXPLICIT DIFFUSION INCLUDED!!! Solenoidal vs. Compressive motions (Federrath et al. 2011) High fraction of the energy in solenoidal modes (between 40% and 80%) BEWARE: NO EXPLICIT DIFFUSION INCLUDED!!! Large importance of solenoidal motions  small scale dynamo expected… but with a Pm dependence (Schekochihin 2004) 14

The effect of dissipation…not much! Pm=1 Pm=5 Haugen et al. (2004) Lower critical Rem at larger Pm (as expected…) Power spectrum - Case Pm=1 (Haugen et al. 2004) No systematic study so far… 15

Where does it saturate? What are its properties? Conclusions IN SIMULATIONS, THE RESOLUTION IS LOW: No scale separation Pm is of order unity DISSIPATION IMPORTANT IN THE SIMULATIONS…IF NOT IN REALITY! Does it grow? YES, especially when Pm>>1 Where does it saturate? What are its properties? UNKNOWN… …although forcing (solenoidal vs. compressive) important