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

2

3 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 (Q 2 +U 2 ) 1/2 1”

How to explore the turbulent dynamo from observations? 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 220 th 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 Power Spectrum Magnetic dissipation scales, λ η Magnetic Spectrum Batchelor 1959 Nakagawa & Priest 1973 Schekochinin The 220 th 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 220 th AAS Meeting / SPD, Anchorage, Alaska - June 10-14, 2012 Abramenko et. al. 0.8’’ 0.16’’ 0.10’’

7 The 220 th AAS Meeting / SPD, Anchorage, Alaska - June 10-14, 2012 Abramenko et. al. 1 - Kinetic and Magnetic Energy Spectra (cont)

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

9 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

10 The 220 th 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∆l Magnetic bright points trajectories

11 The 220 th 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

12 The 220 th 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 Magnetic Turbulent Diffusivity, η, km 2 /s

13 The 220 th 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”

14 The 220 th AAS Meeting / SPD, Anchorage, Alaska - June 10-14, 2012 Abramenko et. al. 3 – Small-scale magnetic elements statistics (cont) NST diff. limit N=2213 Power Law Index= – 1.86±0.10 down to 2x10 16 Mx Compare: Parnell et al. 2009: % are smaller than 500 km 93% - flux below 2· Mx 85% live shorter than 4 min 90% - magn energy below 5· erg Parnell et al. 2009

15 The 220 th AAS Meeting / SPD, Anchorage, Alaska - June 10-14, 2012 Abramenko et. al. 3 – Small-scale magnetic elements statistics

16 The 220 th AAS Meeting / SPD, Anchorage, Alaska - June 10-14, 2012 Abramenko et. al. Conclusions 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 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)·10 14 Wb, which is about (20-50)% of the total solar flux during a solar minimum.

17 The 220 th AAS Meeting / SPD, Anchorage, Alaska - June 10-14, 2012 Abramenko et. al. 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 km x z Small loops closed below ~500km Why magnetic elements are more numerous in NST magnetogram?

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

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