The Solar Surface Dynamo

Transcription

1 Overview of turbulent dynamo theory The Solar Surface Dynamo J. Pietarila Graham, 1 S. Danilovic, 1 M. Schüssler, 1 A. Vögler, 2 1 Max-Planck-Institut für Sonnensystemforschung 2 Sterrekundig Instituut, Utrecht University SGS

2 Overview of turbulent dynamo theory Outline 1 Overview of turbulent dynamo theory 2 3

3 Overview of turbulent dynamo theory Solar global dynamo Global dynamo 22 year cycle dipolar many models (Babcock-Leighton, flux-transport (Dikpati et al.), surface shear (Brandenburg 2005)) M. Dikpati, NCAR

4 Overview of turbulent dynamo theory Solar surface dynamo turbulent (small-scale) dynamo? Turbulent dynamo Stretching of B-field lines by turbulence (Batchelor 1950, Moffat 1978, Parker 1979) Fast dynamo for chaotic & sufficiently complex flows (Childress & Gilbert 1995) Near the surface layer of the sun? (e.g., Petrovay & Szakaly 1993) Stretching η t B = (v B) + η 2 B Re M = volo η > ReM C dynamo

5 Overview of turbulent dynamo theory Turbulent dynamos well studied Turbulent dynamos first demonstrated 20 years ago Realistic: Boussinesq (no sound waves), rotation, convection in spherical shell (Gilman and Miller 1981) Idealistic: periodic box N 3 = 64 3, Re M 100 (Meneguzzi et al. 1981) Homogeneity and isotropy recovered at small scales Helical and Non-helical

6 Turbulent dynamos large & small 2 types of turbulent dynamos Large-scale (LSD; helicity, α effect: mean-field) Small-scale (SSD; non-helical) solar surface dynamo (τ conv 10 min << τ rotation no net helicity)

7 Overview of turbulent dynamo theory Evidence for SSSD Arguments against SSSD Magnetic carpet (Title and Schrijver 1998; Title 2000) Lites et al (see also Hagenaar et al. 2003)

8 Evidence for SSSD Arguments against SSSD Convectively-Driven Small-Scale Dynamo (Cattaneo 1999) Temperature B z Re 200 Re M Re 9/4 M Boussinesq convection (no sound waves) no Coriolis force (SSD) (see also Cattaneo et al. 2003)

9 Overview of turbulent dynamo theory Evidence for SSSD Arguments against SSSD 1. Shredding of large-scale field by turbulence? Induced small-scale field Observation: Very small-scale bipolar regions (Φ < Mx) independent of the solar cycle and latitude (for low latitudes) (Hagenaar et al. 2003; Trujillo Bueno et al. 2004) Timescale for SSD much faster (e.g., Kulsrud & Anderson 1992; Kulsrud 1999) for open questions see Iskakov et al. (2007) τ SSD 10 min (theoretically) other dynamos Shredding is algebraic-in-time, SSD is exponential-in-time (e.g., Schekochihin et al. 2005)

10 Evidence for SSSD Arguments against SSSD 2. Re Re M (i.e., P M Re M Re = ν η 1) P M > 1 l η < l ν Schekochihin et al P M < 1 l η < l ν eddies l > l η stretch B eddies l < l η diffuse B

11 Evidence for SSSD Arguments against SSSD 2. Re Re M (i.e., P M Re M Re = ν η 1) 2 Theoretical possibilities (Rogachevskii & Kleeorin 1997) Schekochihin et al. 2005

12 Evidence for SSSD Arguments against SSSD 2. Re Re M (i.e., P M Re M Re = ν η 1) Dynamo at low P M Iskakov et al. 2007

13 Evidence for SSSD Arguments against SSSD 2. Re Re M (i.e., P M Re M Re = ν η 1) Dynamo at low P M P M 10 5 Iskakov et al. 2007

14 P M 10 5 No Problem Evidence for SSSD Arguments against SSSD VKS experiment (Monchaux et al. 2007) CEA-Saclay CNRS ENS-Lyon ENS-Paris

15 Overview of turbulent dynamo theory Evidence for SSSD Arguments against SSSD 3. Strong stratification & little recirculation Last argument against SSD (Stein et al. 2003) Strong stratification Little plasma is recirculated in the near-surface layers Realistic magneto-convection with open boundaries (Stein et al. 2003): Re M 600

16 Turbulent solar surface dynamo Comparing MURaM with obs.: Strong horizontal field Estimating true unsigned vertical flux The MURaM code (Vögler et al. 2005; Vögler 2003) Realistic magnetoconvection Strong stratification Fully compressible Partial ionization Radiative transfer Open lower boundary B z & brightness dv (vertical upflows, = 0 for downflows; B hor not advected dz into box) No rotation Parallelized

17 Turbulent solar surface dynamo Comparing MURaM with obs.: Strong horizontal field Estimating true unsigned vertical flux Strong stratification & little recirculation No Problem Vögler & Schüssler 2007 Run Nhor 2 N Z Re M A B C Re C M < 2600 Run C: E M 3%E K

18 Turbulent solar surface dynamo Comparing MURaM with obs.: Strong horizontal field Estimating true unsigned vertical flux Turbulent small-scale solar surface dynamo for Re M > Re C M Run C Simulation Comparison Result Grid pts. Re M P M BC SSD Run A open N Stein open N Run B open N Cattaneo closed Y Run C open Y (Vögler & Schüssler 2007)

19 Turbulent solar surface dynamo Comparing MURaM with obs.: Strong horizontal field Estimating true unsigned vertical flux Pervasive horizontal magnetic flux (Lites et al. 2008) B L app 11 Mx cm 2 B T app 55 Mx cm 2 Bapp L 50 Mx cm 2 Bapp T 200 Mx cm 2

20 Turbulent solar surface dynamo Comparing MURaM with obs.: Strong horizontal field Estimating true unsigned vertical flux Strong horizontal photospheric magnetic field in SSD (Schüssler & Vögler 2008) Run C: log B hor Shallow narrow loops (integranular lanes) (see also Steiner et al. 2008) Extended loops (above granules) Average vertical field decreases faster with height than horizontal field

21 Overview of turbulent dynamo theory Distribution of vertical field strength Turbulent solar surface dynamo Comparing MURaM with obs.: Strong horizontal field Estimating true unsigned vertical flux Hinode Bapp L 220 Mm 110 Mm (Lites et al. 2008) Run C: B ave 4.9 Mm 4.9 Mm

22 Turbulent solar surface dynamo Comparing MURaM with obs.: Strong horizontal field Estimating true unsigned vertical flux Observed PDF derived from Stokes V (Lites et al. 2008) Simulated PDFs Simulations have prevalent weak field

23 Turbulent solar surface dynamo Comparing MURaM with obs.: Strong horizontal field Estimating true unsigned vertical flux Observed PDF derived from Stokes V (Lites et al. 2008) Simulated PDFs Synthetic observation is also peaked

24 Turbulent solar surface dynamo Comparing MURaM with obs.: Strong horizontal field Estimating true unsigned vertical flux Observed PDF derived from Stokes V (Lites et al. 2008) Simulated PDFs Observed PDF is compatible with monotonic PDF of the actual field

25 Vertical radiative transfer & turbulence Turbulent solar surface dynamo Comparing MURaM with obs.: Strong horizontal field Estimating true unsigned vertical flux Fe I Å (a Hinode SP line) Vertically averaged field = 0 Absorption profiles Doppler shifted

26 Vertical radiative transfer & turbulence Turbulent solar surface dynamo Comparing MURaM with obs.: Strong horizontal field Estimating true unsigned vertical flux B ave < 0.1 G Synthetic Magnetogram Effect increases with variance(v z ) 1/2 along line of sight

27 Overview of turbulent dynamo theory Turbulent solar surface dynamo Comparing MURaM with obs.: Strong horizontal field Estimating true unsigned vertical flux From fractal geometry to true unsigned vertical flux (Sorriso-Valvo et al. 2002) Fractal = self-similar = power-law N(l) l D Koch fractal χ(l) P R i Ai (l) Bz da R B da z A χ(l) l κ (Ott et al. 1992) χ(l) measures the portion of flux remaining after averaging over boxes of length l

28 Cancellation is self-similar Turbulent solar surface dynamo Comparing MURaM with obs.: Strong horizontal field Estimating true unsigned vertical flux Hinode Bapp L (Lites et al. 2008) P R i A i (l) Bzda χ(l) R A Bz da Fractal extrapolation B Z A B z da/ A da P R i B Z l B Z = B Z l χ(lη ) χ(l) A i (l) Bzda R A da = χ(l) B Z «0.26 = 11G 220km lη η 10 8 cm 2 s 1 (Kovitya & Cram 1983) K41 l η 80 m < 800 m B Z 46 G

29 Better agreement with Hanle estimates Turbulent solar surface dynamo Comparing MURaM with obs.: Strong horizontal field Estimating true unsigned vertical flux The flux remaining at l = 200 km follows a power-law scaling. Extrapolation to solar values, Re M , yields χ(200 km) = 0.2. B Z 50 G B Z 50 G B hor > B Z (Lites et al. 2008) B 130 G Hanle (Trujillo Bueno et al. 2004)

30 Overview of turbulent dynamo theory Conclusions Turbulent solar surface dynamo Comparing MURaM with obs.: Strong horizontal field Estimating true unsigned vertical flux A small-scale solar surface dynamo (SSSD) is likely Evidence seen in observations MURaM dynamo simulations in agreement with observations Arguments against fail: stratified, compressed, little recirculation, P M 1 all seem OK Whatever its source, small-scale B-field is turbulent & fractal - we should use this to interpret observations arxiv: