A solar surface dynamo

Transcription

1 MPS Solar Group Seminar May 8, 2007 A solar surface dynamo Alexander Vögler (Univ. of Utrecht) & Manfred Schüssler

2 A lot of magnetic flux in the `quiet Sun Observation: Flux replenishment rates increase with increasing spatial resolution sensitive Zeeman magnetometry shows much flux in intergranular lanes Hanle depolarization indicates large amounts of small-scale, mixed-polarity flux in quiet photospheric regions Zeeman: B G Hanle: B 130 G? (Domίnguez Cerdena et al., 2003)

3 Local dynamo action based on granulation? Possible origin of quiet-sun magnetism: `turbulent surface dynamo Idealized simulations by Cattaneo (1999) Boussinesq, closed box self-excited dynamo action R m,crit 1000 (for Re = 200.) E mag / E kin 20% growth rate turnover time (Cattaneo 1999) Temperature (top) B z (top) B z (middle)

4 Local dynamo under solar conditions? Stein & Nordlund (2003) don t find dynamo action and argue: Little recirculation in the solar surface layers Downward pumping of magnetic flux no local dynamo

5 The MURaM (MPS/UofC Radiation MHD) code Developed by the MPS MHD group (A. Vögler, R. Cameron, S. Shelyag, M. Schüssler) in cooperation with F. Cattaneo, Th. Emonet, T. Linde (Univ. of Chicago) 3D compressible MHD Cartesian fixed grid 4th order centered spatial difference scheme explicit time stepping: 4th order Runge-Kutta MPI parallelized (domain decomposition) radiative transfer: short characteristics non-grey (opacity binning), LTE partial ionisation (11 species) and: extensive diagnostic tools to compare with observations (e.g. continuum & spectral line & polarization diagnostics)

6 The MURaM code: equations Continuity equation Momentum equation Q rad = F = 4πρ κν ( Jν Sν ) dν Energy equation di ds ν = κ ν ρ ( Iν Sν ) Induction equation Radiative Transfer Equation

7 Simulation setup Grid Resolution up to 648 x 648 x km 800 km τ=1 1.4 Mm 6 (4.9)Mm 6 (4.9) Mm closed, stress-free top boundary vertical field vertical at bottom & top bottom boundary open start with non-magnetic convection introduce 0.01 G vertical seed field (4 4 checkerboard, zero net flux) 3runs:

8 Time evolution of magnetic energy Emag open boundary: Rm 2600 no artificial recirculation free downward transport of magnetic flux no advection of flux from below seed field B0 = 0.01 G Rm 1300 Rm 300 Turbulent diffusivity from field decay experiments: ηt (τ k 2 ) cm 2 s -1 Æ Emag / Ekin < 1% Æ growth rate 10 min (turnover time) effective critical Reynolds number of O(10)

9 Structure of the near-surface field 4.9 Mm vertical magnetic field near <τ>=1 (greyscale saturates at Bz =50 G) Generation of small-scale flux, preferentially near long-lived downflows Unsigned vertical flux corresponds to ~25 G near the visible solar surface

10 Height dependence and relation to granulation pattern 4.9 Mm Magnetic field at τ R =1. B z = 25 G, saturation ±250 G Brightness Magnetic field at τ R =0.01 Bz = 3 G, saturation ±50 G

11 Probability density function (PDF) for B z as f(height) ~450 km below τ R =1. τ R 1. τ R 0.01

12 Energy spectra (B z, v z ) near the solar surface granules E kin E mag horizontal wave number

13 Poynting flux and energy balance Poynting Flux Energy Balance F = ( u B) B F ( j B) W = u Q J = η B 2 Negative Poynting flux Convective pumping into deeper layers F ( W Q ) 0. 8 J 80% of net energy input lost due to downward pumping Conclusion: There is sufficient local recirculation to overcome the drain of energy into the subsurface layers!

14 Summary & Outlook Local dynamo action demonstrated for realistic solar conditions Field amplitude not far below observed values Intermittent field structure (stretched exponential PDF) inefficient dynamo: downward pumping removes 80% of the magnetic energy input This is just the beginning... further clarification of the generation/amplification process existence of an inverse cascade? dependence of amplitude on magnetic Reynolds number dependence on Prandtl number (viscosity/magn. diffusivity) dependence on lower boundary condition (depth & specification) effect of a large-scale background field