Observational Criteria for Small-Scale Turbulent Dynamo in the Solar Photosphere

Valentina Abramenko, Philip Goode,

Vasyl Yurchyshyn, Kwangsu Ahn

Big Bear Solar Observatory of NJIT http://bbso.njit.edu/~avi/

The 220th AAS Meeting / SPD, Anchorage, Alaska - June 10-14, 2012 Abramenko et. al.

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Magnetic elements (color contours) against granulation in a coronal hole area.

Yellow – SOT FG/negative; Blue/red – NST/BBSO negative/positive Stokes V; Green – NST/BBSO Stokes (Q2+U2)1/2

1”

How to explore the turbulent dynamo from observations?

1 - From kinetic and magnetic energy spectra on small scales

2 - From diffusivity regime on small scales

3 - From observations of small-scale magnetic flux emergence

The 220th AAS Meeting / SPD, Anchorage, Alaska - June 10-14, 2012 Abramenko et. al.

1 - Kinetic and Magnetic Energy Spectra

Kinetic dissipation scales , λ ν

Spatial scale

Kinetic Spectrum

wavenumber

Pow

er S

pec

tru

m

Magnetic dissipation scales, λ η

Magnetic Spectrum

Batchelor 1959Nakagawa & Priest 1973Schekochinin+ 2003

The 220th AAS Meeting / SPD, Anchorage, Alaska - June 10-14, 2012 Abramenko et. al.

Magnetic dissipation scale is smaller than Kinetic dissipation scale Small-scale dynamo action is ensured

1 - Kinetic and Magnetic Energy Spectra (cont)

The 220th AAS Meeting / SPD, Anchorage, Alaska - June 10-14, 2012 Abramenko et. al.

0.8’’

0.16’’

0.10’’

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1 - Kinetic and Magnetic Energy Spectra (cont)

1 - Kinetic and Magnetic Energy Spectra (cont)

The 220th AAS Meeting / SPD, Anchorage, Alaska - June 10-14, 2012 Abramenko et. al.

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0.16’’

- Observed λ η<0.1’’

As the resolution improves, the observed magnetic dissipation scale - λ η might decrease

1 - Kinetic and Magnetic Energy Spectra (cont)

λ η ~ η – coefficient of turbulent magnetic diffusion. For a regime of super-diffusivity, η decreases as the scale decreases

10The 220th AAS Meeting / SPD, Anchorage, Alaska - June 10-14, 2012 Abramenko et. al.

2 – Turbulent Diffusion Regime

From trajectories of magnetic bright points we obtain their displacements , ∆l

∆l

Magnetic bright points trajectories

11The 220th AAS Meeting / SPD, Anchorage, Alaska - June 10-14, 2012 Abramenko et. al.

2 – Turbulent Diffusion Regime (cont)

Magnetic turbulent diffusivity:

η ~ ((∆l)2) (γ-1)/γ

12The 220th AAS Meeting / SPD, Anchorage, Alaska - June 10-14, 2012 Abramenko et. al.

2 – Turbulent Diffusion Regime (cont)

Magnetic turbulent diffusivity decreases with decreasing scale,creating favorable conditions for the small-scale turbulent dynamo

Magneti

c Tu

rbule

nt

Diff

usi

vit

y,

η, k

m2 /

s

13The 220th AAS Meeting / SPD, Anchorage, Alaska - June 10-14, 2012 Abramenko et. al.

3 – Small-scale magnetic elements statistics

NST/Near Infrared magnetogram of a coronal hole region

Pixel size: 0.”1; ticks separation is 1”

14The 220th AAS Meeting / SPD, Anchorage, Alaska - June 10-14, 2012 Abramenko et. al.

3 – Small-scale magnetic elements statistics (cont)

NST d

iff.

limit

N=2213

Power Law Index= – 1.86±0.10 down to 2x1016 Mx

Compare: Parnell et al. 2009: -1.85

84% are smaller than 500 km

93% - flux below 2· 1017 Mx

85% live shorter than 4 min

90% - magn energy below 5· 1024 erg

Parnell et al. 2009

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3 – Small-scale magnetic elements statistics

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Conclusions

We observe the following evidences for the small-scale turbulent dynamo action in the solar photosphere:

• The magnetic energy spectrum tends to be extended toward small scales and to overtake the kinetic energy spectrum on scales below 0.5-1.0 Mm;

•The magnetic turbulent diffusivity regime – super-diffusivity – is present in the QS photosphere, which ensures the shallow magnetic spectrum and favors the turbulent dynamo action;

• Distribution functions of size, flux, lifetime, and energy of the magnetic elements extend until the diffraction limit without any saturation, which supposed to be observed when the turbulent dynamo is at work.

•Total unsigned magnetic flux related to the turbulent dynamo action may consist of (6-13)·1014 Wb, which is about (20-50)% of the total solar flux during a solar minimum.

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3 – Small-scale magnetic elements statistics (cont)

Yellow – SOT/FG/-100G

Blue/red- NST negative /positive LOS

Green – NST B trans

10’’

FG:~500 km

NST: -50 kmx

z

Small loops closed below ~500km

Why magnetic elements are more numerous in NST magnetogram?

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