1. Magnetic dynamo over different astrophysical scales Axel Brandenburg & Fabio Del Sordo (Nordita) with contributions from many others seed field primordial (decay) diagnostic interest (CMB) AGN outflows MRI driven SS dynamo galactic LS dynamo helicity losses

2. 2 Early-Universe B-field may have been helical: 3-D decay simulations Initial slope E~k 4 Christensson et al. (2001, PRE 64, 056405) helical vs nonhelical cosmological scale: ~3 cm

3. 3 Proposed helical decay law H not exactly constant Assume power law, not const H follows power law iff r=1/2; then M. Christensson, M. Hindmarsh, A. Brandenburg: 2005, AN 326, 393

4. 4 Many astrophysical sources of turbulence are potential No dynamo action in nearly potential flows (at least not so far)  and  t are also small Examples: EW phase transition bubbles, SN explosions

5. 5 Nearly potential flows neither  nor B is produced, unless … Mee & Brandenburg (2006, MNRAS 370, 415)

6. 6 Baroclinic and battery terms Analogy between  and B eqns  even with baroclinicity Kulsrud et al. (1996)  relevance to oblique cosmological shocks degree of ionisation

7. 7 Alternative: Magnetisation from quasars? 10,000 galaxies for 1 Gyr, 10 44 erg/s each Similar figure also for outflows from protostellar disc B. von Rekowski, A. Brandenburg, W. Dobler, A. Shukurov, 2003 A&A 398, 825-844 Poynting flux

8. 8 To maintain equipartition-strength fields  need dynamos: small-scale vs large-scale B-scale larger than U-scale B-scale smaller than U-scale Wavenumber =1/scale energy injection scale

9. 9 Small-scale vs large-scale dynamo

10. 10 Growth rate, applied to galaxy l =2 x 10 -9 yr -1 u rms =10 km/s k f =2 p /70 pc=0.1 pc -1 u rms k f =10 -6 s -1 Re=10 9 l =3 x 10 -2 yr -1 (very fast) Amplication factors: exp( l t)=10 4 for 5 Gr

11. 11 Kick-start the GBF with strong B Forced turbulence with shear and strong initial field at k=6

12. 12 Weaker initial field Kazantsev slope, exponential growth

13. 13 Reach full saturation: need helicity fluxes  evidence from different simulations Convective dynamo in a box with shear and rotation Käpylä, Korpi, Brandenburg (2008, A&A 491, 353) Only weak field if box is closed Forced turbulence in domain with solar-like shear Brandenburg (2005, ApJ 625, 539) 3-D simulations, no mean-field modeling

14. 14 Saturation phase: here for convection Käpylä et al (2008, A&A 491, 353) with rotationwithout rotation

15. 15 It can take some time… Rm=121, B y, 512 3 LS dynamo not always excited

16. 16 Conclusion 70 pc 10 pc factor 500 slope 3/2 factor 10,000