Signatures of Intermittent Turbulence in Hinode Quiet Sun PhotosphereSignatures of Intermittent Turbulence in Hinode Quiet Sun Photosphere Valentina Abramenko, Big Bear Solar Observatory, USA, www.bbso.njit.edu/~avi

Plasma turbulence is ubiquitous in astrophysics in general and in the solar photosphere, in particular. It is a fundamental physical process that plays an important role in the near-surface turbulent dynamo and plasma heating through dissipation. Turbulence acquires intermittent nature when extremely high fluctuations (in both temporal and spatial domains) become not rare and they thus determine the energy release dynamics: significant contribution to the traditional turbulent energy cascade appears in the intermittent medium. We estimated signatures of intermittent turbulence in the quiet sun photosphere utilizing Hinode/SOT data. We found that at scales below 1 Mm the QS structures are highly intermittent, which open possibilities for enhanced energy release dynamics at small scales.

What is the Intermittency

A turbulent medium can display a property of intermittency: a tendency to concentrate into strong blobs (sometimes in a shape of sheets , or tubes) of all scales intermittent with vast areas of low intensity, a presence of extremely strong fluctuations and a burst-like behavior in time evolution.

Intermittent structure is a multufractal. Generally, intermittency and multifractality are two different terms for the same phenomenon. Historically, the former term (intermittency) is usually applied to time series Analysis, whereas the later one (multifractality) is used for spatial objects (Takayasu, 1989; Frisch, 1995). In scale intervals, where intermittency presence, it can reinforce the energy release dynamics.

How to measure the degree of intermittency

r

Structure functions were first introduced by Kolmogorov (1941).

The ratio of the squared second structure function, S2( r ) (red), over the forth structure function, S4( r ) (blue), gives us the Filling Factor, f(r ) .The Filling Factor does not depend on the scale, r, For non-intermittent (or, monofractal) structures and time series.

For intermittent structures, the filling factor decreases as the scale decreases. For non-intermittent structures (like a Gaussian process) the filling factor does not depend on scale.

The steeper the slope of decrease, the more intermittent the structure is.In the multifractal terminology, the steeper the filling factor means the more complex multifractal,which is a superposition of a set of monofractals.

For example, in the solar wind turbulence, the presence of interminnency implies the presence of magnetic field discontinuities, shocks and current sheets of various scales. All these phenomena contribute significantly into the energy release dynamics, along with the usual turbulent cascade.

Intermittency of the magnetic field from SOHO/MDI high resolution data

We first applied the filling factor technique to magnetograms from SOHO/MDI obtained in the high resolution mode. Areas of three types we analyzed: Active Region (AR) area ( red), Plage area (green) and two areas in the quiet sun, which were mostly located inside small coronal holes (blue and turquoise). Middle figure – the filling factor function (linear axes) for the AR data. The interval of decreasing filling factor is well pronounced: 5 – 30 Mm. Below 5 Mm the filling factor increases, which is caused by the noise influence and poor resolution of the magnetogram.Right figure – the filling factor as a function of a spatial scale (double logarithmic plot) for three types of magnetic structures. For all of then, the filling factor function starts to increase at small scales as a result of insufficient data resolution. Note that while both the AR and the plage data display an intermittent nature of the magnetic field at scales above 2 Mm, the quiet sun data seems to display no intermittency at these scales. If we ignore the noise-related hooks and contunuously extend the AR and plage curves (dotted curve with the arrow) below the base lane of the quiet sun plateu, we may conclude that at scales below 1000 km one may expect the decreasing behavior of the filling factor in the quiet sun areas, i.e., the intermittent property of the QS magnetic field. Note, that here a special type of the filling factor formula was used: f( r ) = S6( r ) /( S3 ( r ) )2 , which is more sensitive to intermittency.

Quiet sun

Hinode SOT/SP: Intermittency in magnetic structures

Sot/SP data for the coronal hole area (blue curve) indicates that at scales larger than 2 Mm, the magnetic field structure seems to be non-intermittent (monofractal). Only a very slight slope (0.024) of the lower-law linear fit is observed. For comparison, we plotted the filling factor for an AR (red) and a plage area (green). Data for the AR and plage show a steeper slope of the power-law linear fit with indice 0.18 and 0.09, which implies intermittency at scales > 2 Mm.

What is interesting is that Hinode data do not show the behavior similar to that observed from MDI magnetograms at scales less than 3 Mm. Instead, the Hinode SOT/SP filling factor displays a rapid decrease with scale for all data types, which means enhanced intermittency in the magnetic structures at small scales.

Hinode SOT/FG: Intermittency in G-band and Ca II images

G-band:

Ca II:

Active Region Weak Plage Quiet Sun

At scales of 1 Mm and smaller the decrease of the filling factor is observed for both the G-band and Ca II images. Intermittent nature of the solar granulation and low-chromosphere structures is proved from the Hinode observations.

In monofractals, large fluctuations of the parameters (say, energy release events) are rare and do not determine mean values. In other words, time profiles are non-intermittent and evolution proceeds without catastrophes. On the contrary, in multifractals, the time profiles are highly intermittent, large fluctuations are not rare, and they determine mean values. The temporal energy release process is burst-like.

If so, the monofractal property of QS structures explains their quiet temporal behavior at scales above 2 Mm. The bulk of energy release dynamics (needed, in particular, for the solar wind acceleration) occurs at smaller scales, where the magnetic field structure is entirely different. In a way, one might say that below 1 Mm the complexity and structural organization of the QS magnetic field is similar to what we observe in active regions at scales of 10-100 Mm: same shear motions, energy built-up and release through explosions, but 2-3 order of magnitude weaker.

Many new phenomena will be discovered now, when the spatial scales less than 1 Mm are available from Hinode instruments.

ReferencesAbramenko, V. 2005, Solar Phys. 288.29Abramenko,V., Yurchyshyn, V., Watanabe, H. 2009, Solar Phys., 260, 43.Balke, A.C. et. Al., 1993, Solar Phys. 143, 215Berger, T.E., et al., 1995, ApJ,454,531Frisch, U. 1995, Turbulence, The legacy of A.N. Kolmogorov, Cambridge Univ. Press, Cambridge, 296.Takayasu, 1989, Fractals in the Physical Science, Manchester Univ. Press, Manchester and New York.

SOT/SP Bz-component/ fast mode/ HAO calibration; 2006 Dec 11SOT/SP Bz-component/ fast mode/ HAO calibration; 2008 Nov 30