The Solar Surface Dynamo - Los Alamos National Laboratorycnls.lanl.gov/~jgraham/manuscripts/Hinode2.pdf · Overview of turbulent dynamo theory Is there a small-scale solar surface

Overview of turbulent dynamo theoryIs there a small-scale solar surface dynamo (SSSD)?

MURaM solar surface dynamo

The Solar Surface Dynamo

J. Pietarila Graham,1 S. Danilovic,1 M. Schssler,1

A. Vgler,2

1Max-Planck-Institut fr Sonnensystemforschung2Sterrekundig Instituut, Utrecht University

2nd Hinode Science Meeting 30.09.08



Outline

1 Overview of turbulent dynamo theory

2 Is there a small-scale solar surface dynamo (SSSD)?

3 MURaM solar surface dynamo



Solar global dynamo

Global dynamo22 year cycle dipolarmany models(Babcock-Leighton,flux-transport (Dikpati et al.),surface shear (Brandenburg2005))

M. Dikpati, NCAR



Solar surface dynamo turbulent (small-scale) dynamo?

Turbulent dynamoStretching of B-field linesby turbulence (Batchelor 1950, Moffat1978, Parker 1979)

Fast dynamo for chaotic& sufficiently complexflows (Childress & Gilbert 1995)Near the surface layer ofthe sun? (e.g., Petrovay & Szakaly 1993)

Stretching tB = (v B) + 2BReM = vo lo > Re

CM dynamo



Turbulent dynamos well studied

Turbulent dynamos first demonstrated 20 years agoRealistic: Boussinesq, rotation, convection in sphericalshell (Gilman and Miller 1981)Idealistic: periodic boxN3 = 643, ReM 100 (Meneguzzi et al. 1981)

Homogeneity and isotropy recovered at small scalesHelical and Non-helical



Turbulent dynamos large & small

2 types of turbulentdynamos

Large-scale (LSD;helicity, effect:mean-field)

Small-scale (SSD;non-helical)

solar surfacedynamo(conv 10 min



Evidence for SSSDArguments against SSSD

Magnetic carpet (Title and Schrijver 1998; Title 2000)

Lites et al. 2008

(see also Hagenaar et al. 2003)




Convectively-Driven Small-Scale Dynamo (Cattaneo 1999)

Temperature

Boussinesq convection

no Coriolis force (SSD)

Bz

(see also Cattaneo et al. 2003)

Re 200ReM 1000

512 512 97 5 Re9/4M




1. Shredding of large-scale field by turbulence?

Induced small-scale fieldTimescale for SSD much faster (e.g., Kulsrud & Anderson 1992; Kulsrud 1999)

SSD 10 min (theoretically) other dynamosShredding is algebraic-in-time, SSD is exponential-in-time(e.g., Schekochihin et al. 2005)

Observation: Very small-scale bipolar regions( < 30 1018 Mx) independent of the solar cycle andlatitude (for low latitudes) (Hagenaar et al. 2003)




2. Re ReM (i.e., PM ReMRe = 1)

PM > 1Schekochihin et al. 2004

eddies l > l stretch B

PM < 1

eddies l < l diffuse B





2 Theoretical possibilities

Schekochihin et al. 2005





No dynamo at low PM

Schekochihin et al. 2005

Dynamo at low PM

Ponty et al. 2005




PM 105 No Problem

VKS experiment (Monchaux et al. 2007) CEA-Saclay CNRS ENS-Lyon ENS-Paris




3. Strong stratification & little recirculation

Last argument against SSD (Stein et al. 2003)

Strong stratificationLittle plasma is recirculated in the near-surface layersRealistic magneto-convection with open boundaries(Stein et al. 2003): 253 253 163 ReM 600



Turbulent solar surface dynamoComparing MURaM with obs.: Strong horizontal fieldPrevalent weak vertical fieldEstimating true unsigned vertical flux

The MURaM code (Vgler et al. 2005; Vgler 2003)

Realistic magnetoconvection

Strong stratification

Fully compressible

Partial ionization

Radiative transfer

Open lower boundary(vertical upflows, dv

dz= 0 for downflows; Bhor not advected

into box)

No rotation

Parallelized

Bz & brightness

bz_dyn2.mpgMedia File (video/mpeg)

i_dyn2.mpgMedia File (video/mpeg)




Strong stratification & little recirculation No Problem

Vgler & Schssler 2007

Run N2hor NZ ReMA 2882 100 300B 5762 100 1300C 6482 140 2600

1300 / ReCM < 2600

Run C: EM 3%EK




Turbulent small-scale solar surface dynamo forReM > ReCM

Run C

(Vgler & Schssler 2007)

Simulation Comparison

Result Grid pts. ReM PM BC SSD

Run A 2882 100 300 / 1 open N

Stein+ 2532 163 600 1 open N

Run B 5762 100 1300 / 1 open N

Cattaneo 5122 97 1000 5 closed Y

Run C 6482 140 2600 / 1 open Y




Pervasive horizontal magnetic flux (Lites et al. 2008)

|BLapp| 50 Mx cm2 BTapp 200 Mx cm

2

< |BLapp| > 11 Mx cm2 < BTapp > 55 Mx cm2




Strong horizontal photospheric magnetic field in SSD(Schssler & Vgler 2008)

(see also Steiner et al. 2008)

Run C: log Bhor

Shallow narrow loops (integranular lanes)

Extended loops (above granules) Average vertical field decreases faster with height than

horizontal field




Distribution of vertical field strength

Hinode BLapp 220 Mm 110 Mm (Lites et al. 2008)

Run C: Bave 4.9 Mm 4.9 Mm




Prevalent weak vertical field

Observed PDF derived from Stokes V (Lites et al. 2008) Simulated PDFs

Simulations have prevalent weakfield






Synthetic observation is alsopeaked






Observed PDF is compatible withmonotonic PDF of the actual field




Vertical radiative transfer & turbulence

Vertically averaged field = 0

Fe I 6302.5 (a Hinode SP line)

Absorption profiles Dopplershifted




Vertical radiative transfer & turbulence

Bave < 0.1 G

SyntheticMagnetogram

Effect increases with variance(vz)1/2 along line of sight




From fractal geometry to true unsigned vertical flux

Fractal = self-similar = power-law

N(l) lD

Koch fractal

(l)

Pi

RAi(l)

Bzda

RA|Bz|da

(l) l(Ott et al. 1992)

(Sorriso-Valvo et al. 2002)

(l) measures the portion of fluxremaining after averaging over

boxes of length l




Cancellation is self-similar

Hinode BLapp (Lites et al. 2008)

(l)

Pi

RAi(l)

Bzda

RA|Bz|da

Fractal extrapolation

< |BZ| >A

Bzda/A da< |BZ| >l

Pi

RAi(l)

Bzda

RAda

= (l) < BZ >

< |BZ| >=< |BZ| >l (l )(l) = 12G

100km

l

0.26 108 cm2s1 (Kovitya & Cram 1983)K41 l 80 m < 800 m< |BZ | > 40 G




Better agreement with Hanle estimates

The flux remaining atl = 200 km follows a power-lawscaling. Extrapolation to solarvalues, ReM 3 105, yields(200 km) = 0.2.< |BZ | > 50 G

< |BZ | > 40 or 50 G< Bhor > > < |BZ | > (Lites et al. 2008)< B > 130 G Hanle (Trujillo Buenoet al. 2004)




Conclusions

A small-scale solar surface dynamo (SSSD) is likely

Seen in Hinode observationsDynamo simulations in agreement with observationsArguments against fail: stratified, compressed, littlerecirculation, PM 1 all seem OK

Whatever its source, small-scale B-field is turbulent &fractal- we should use this to interpret observations

Overview of turbulent dynamo theoryIs there a small-scale solar surface dynamo (SSSD)?Evidence for SSSDArguments against SSSD

MURaM solar surface dynamoTurbulent solar surface dynamoComparing MURaM with obs.: Strong horizontal fieldPrevalent weak vertical fieldEstimating true unsigned vertical flux

Documents

The Solar Surface Dynamo - Los Alamos National Laboratorycnls.lanl.gov/~jgraham/manuscripts/Hinode2.pdf · Overview of turbulent dynamo theory Is there a small-scale solar surface