1. 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

2. 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

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

4. 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

5. Homogeneous & incompressible MHD turbulence5

6. 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

7. 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~ K, n~ cm-3  Pm~3 but ambipolar diffusion important…
In the computer, no scale separation: Pm of order unity 7

8. 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

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

10. 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

11. 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

12. The case of the ISM: supersonic turbulence

13. 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)

14. 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

15. 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

16. 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