Overview of dynamos in stars and galaxies Axel Brandenburg (Nordita, Copenhagen) Collaborators: Nils Erland Haugen (Univ. Trondheim) Wolfgang Dobler (Freiburg  Calgary) Tarek Yousef (Univ. Trondheim) Antony Mee (Univ. Newcastle) Talk given in Cracow, Wednesday 29. Sept 2004

turbulent: large-scale and small -scale Dynamos kinematic laminar: fast and slow turbulent: large-scale and small -scale nonlinear self-killing quenching self-generating J.B-driven Fuchs et al (1999) Blackman & B (2002) Fuchs et al (1999) Blackman & Field (2004)

MRI: Local disc simulations Dynamo makes its own turbulence (no longer forced!) Hyperviscosity 1283

Important questions Does SN turbulence give dynamo? w/ shear w/ rotation Does SN turbulence give dynamo? Resolution too poor? Or because of shocks? How important is compressibility? Does the turbulence become “acoustic”? Is turbulent B-field a small scale feature? PPM, hyperviscosity, shock viscosity, etc Can they screw things up? Bottleneck effect (real or artifact?) Does the actual Prandtl number matter? We are never able to do the real thing Fundamental questions  more idealized simulations Korpi et al (1999) Sarson et al (2003)

1st Problem: compressibility? Shocks sweep up all the field: dynamo harder? -- or artifact of shock diffusion? Direct and shock-capturing simulations, n/h=1 Direct simulation, n/h=5  Bimodal behavior!

Potential flow subdominant Potential component more important, but remains subdominant Shock-capturing viscosity: affects only small scales

Flow outside shocks unchanged Localized shocks: exceed color scale Outside shocks: smooth

2nd problem: small-scale dynamo Kazantsev (1968) According to linear theory, field would be regenerated at the resistive scale Magn. spectrum Kin. spectrum Maron & Cowley (2001) magnetic peak: resistive scale?

Kazantsev spectrum (kinematic) Opposite limit, no scale separation, forcing at kf=1-2 Kazantsev spectrum confirmed (even for n/h=1) Spectrum remains highly time-dependent

instead: kpeak~Rm,crit1/2 kf ~ 6kf 256 processor run at 10243 -3/2 slope? Haugen et al. (2003, ApJ 597, L141) Result: not peaked at resistive scale -- Kolmogov scaling! instead: kpeak~Rm,crit1/2 kf ~ 6kf

3nd problem: deviations from Kolmogorov? compensated spectrum Porter, Pouquet, & Woodward (1998) using PPM, 10243 meshpoints Kaneda et al. (2003) on the Earth simulator, 40963 meshpoints (dashed: Pencil-Code with 10243 )

Comparison: hyper vs normal height of bottleneck increased Haugen & Brandenburg (PRE, 2004) onset of bottleneck at same position 2nd Result: inertial range unaffected by artificial diffusion

Helical MHD turbulence Helically forced turbulence (cyclonic events) Small & large scale field grows exponentially Past saturation: slow evolution  Explained by magnetic helicity equation

Slow saturation Brandenburg (2001, ApJ)

Connection with a effect: writhe with internal twist as by-product clockwise tilt (right handed) W  left handed internal twist Talk given at Thinkshop in May 2002 Yousef & Brandenburg A&A 407, 7 (2003)

Revised nonlinear dynamo theory (originally due to Kleeorin & Ruzmaikin 1982) Two-scale assumption Production of large scale helicity comes at the price of producing also small scale magnetic helicity

Express in terms of a  Dynamical a-quenching (Kleeorin & Ruzmaikin 1982) no additional free parameters Steady limit: consistent with Vainshtein & Cattaneo (1992) (algebraic quenching)

History of a quenching “catastrophic” a quenching Rm –dependent (Vainshtein & Cattaneo 1972, Gruzinov & Diamond 1994-96) “conventional” a quenching e.g., a~B-3, independent of Rm (Moffatt 1972, Rüdiger 1973) periodic box simulations: saturation at super-equipartition, but after resistive time (Brandenburg 2001) open domains: removal of magnetic waste by helicity flux (Blackman & Field 2000, Kleeorin et al 2000-2003) Dynamical quenching Kleeorin & Ruzmaikin (1982)

Current helicity flux Advantage over magnetic helicity <j.b> is what enters a effect Can define helicity density Rm also in the numerator

Full time evolution Significant field already after kinematic growth phase followed by slow resistive adjustment

Large scale vs small scale losses Diffusive large scale losses:  lower saturation level (Brandenburg & Dobler 2001) Periodic box with LL losses Small scale losses (artificial)  higher saturation level  still slow time scale Numerical experiment: remove field for k>4 every 1-3 turnover times (Brandenburg et al. 2002)

Significance of shear a  transport of helicity in k-space Shear  transport of helicity in x-space Mediating helicity escape ( plasmoids) Mediating turbulent helicity flux Expression for current helicity flux: (first order smoothing, tau approximation) Schnack et al. Vishniac & Cho (2001, ApJ) Expected to be finite on when there is shear Arlt & Brandenburg (2001, A&A)

Simulating solar-like differential rotation Still helically forced turbulence Shear driven by a friction term Normal field boundary condition

Helicity fluxes at large and small scales Negative current helicity: net production in northern hemisphere 1046 Mx2/cycle

Impose toroidal field  measure a previously:

Conclusions Homogeneous dynamos saturate resistively Entirely magnetic helicity controlled Inhomogeneous dynamo Open surface, equator Still many issues to be addressed Current helicity flux important Finite if there is shear Avoid magnetic helicity, use current helicity