Recently Published (ApJ 756, 2012): Mini-granulation in the Solar Photosphere Read More ...

Observations of the solar surface granulation with the NST with a broad-band TiO filter showed a presence of two populations of the solar granulation: regular granules of 600-2000 km extent and mini-granules of less than 600 km extent. The two populations show different size distribution functions and different preferable location on the solar surface.

A data set of 36 images of solar granulation in a quiet sun area on the solar disk center was analyzed. The data were obtained with the 1.6~m clear aperture New Solar Telescope (NST) at Big Bear Solar Observatory (BBSO) and with a broad-band filter centered at the TiO (705.7~nm) spectral line. A histogram of normalized intensity image (left) derived from 648 images of 755x700 pixels each shows that the NST imager is able to capture a wide dynamical spectra of intensities ranging from 0.4 to 2.5. A very high spatial resolution of the data (diffraction limit of 77~km and pixel scale of 0.0375'') augmented by the very high contrast of the observed granulation (15.5±0.6%) allowed us to detect for the first time a distinct population of mini-granules. On spatial scales below 600~km, mini-granules dominate the granulation field. Their size is distributed log-normally with no predominant scale. Conversely, regular (large) granules display a Gaussian (normal) size distribution with a mode of 1100~km.

Mini-granules contribute significantly to the total granule area. They are predominantly confined to the wide dark lanes between regular granules and often form chains and clusters, see the movie (link) where mini-granules are outlined by yellow contours.

A multi-fractality test reveals that intensity structures smaller that 600~km represent a multi-fractal, whereas larger features show no multi-fractality and can be considered as a Gaussian random field. The origin, properties and role of the newly discovered population of mini-granules in the solar magneto-convection are yet to be explored.

Figure 1: A histogram of normalized intensity derived from 648 images of 755x700 pixels each. The NST imager is able to capture a wide dynamical spectra of intensities ranging from 0.4 to 2.5. (click picture to zoom in) Figure 2: Probability density functions (PDFs) of the granule equivalent diameter derived from 15 various detection runs (gray lines). They are overplotted with their average (thick red line). The green line segments and numbers show the best linear fit and the average slope within the corresponding scale range. The most right frame is decomposition of the observed averaged PDF into two components: a log-normal approximation, (f1) and a Gaussian approximation (f2). Their sum (f1+f2) fits the observed data very well. Figure 3: Flatness functions calculated from 36 independent granulation images (gray) and their average (turquoise) are shown in the figure to the left. The dashed segments show the best linear fits to the data points. The blue arrow divides the multi-fractality range of mini-granules (where the flatness function varies as a power law) from the Gaussian range of regular granules (where the flatness function is independent from scales).

We believe that there exists a smooth transition from the normal granulation to mini-granulation. The association between the mini-granulation and magnetic and velocity fields, as well as efforts to detect mini-granulation in numerical simulations of solar magneto-convection are subjects for future research. As for now, it is evident that the complex picture of solar near-surface magneto-convection became even more complex.

Recent Published: Super-diffusivity in the Quiet Sun Photosphere Read More ...

Figure 1: Example of bright points detection

Diffusion of magnetic elements on the solar surface was explored via tracking of photospheric bright points (BPs) visible in broad-band images. The data sets for a quiet sun area (QS), coronal hole (CH) and active region's plage area (ARP) were obtained with the NDT with a TiO broad-band filter. All data sets showed a regime of super-diffusivity in a good agreement with the diffusivity from simulated data provided by R. Stein. BPs were automatically detected (an example of detection is shown in Fifure 1). Examples of BPs trajectories are shown in Figure 2. Resudual juttering of the telecsope was very small as compared to measured displacements of BPs, see Figure 3.

Figure 2: Example of trajectories of bright poins (click picture to zoom in) Figure 3: x- and y-coordinates of a BP overplotted with co-temporal variations of the offset between two consecutive images (red lines, right axes) Figure 4: Trajectories (red) of all BPs detected from the QS data set and persisted longer than 3 time steps (30 sec). Background is the first image of the data set.
By tracking the BPs we were able to measure their displacements as a function of time. Displacements were calculated for time intervals between a given moment and the moment when a PB was first detected. We then calculated the average (over all BPs) displacement for each time interval to obtain the average squared displacement as a function of time.
Figure 5: Qualitative illustration of different regimes of diffusivity. In the case of normal diffusion, the power index gamma is equal to unity (dashed line). For sub-diffusivity gamma is less than unity (green; - example: results of Cadavid et al. 1999). For super-diffusivity, gamma is larger than unity (blue, this study). Figure 6: Displacement spectra determined for the CH data (green), QS area (blue), and ARP area (red). The super-diffusion regime is persistent in all three magnetic areas. The ARP spectrum shows the shallowest slope and smallest displacements, indicating the lowest level of turbulent diffusion. The CH data show the steepest spectrum and largest displacements. Figure 7: Displacement spectra for the QS area calculated as a displacements from the start point (Drift) and as a separation between pairs of BPs (pair separation). The displacement spectrum (drift) obtained from simulated data is shown in green.
Figure 8: A sketch illustrating how the turbulent diffusion coefficient varies as a function of time scale for three different regimes of diffusivity. A dependence of the coefficient from the spatial scale is similar. Figure 9: Turbulent diffusion coefficient plotted as a function of time scale. Figure 10: Turbulent diffusion coefficient plotted as a function of spatial scale. The present study (solid lines) shows that as the temporal and spatial scales decrease, the diffusion coefficient decreases, too.

Modern models of the small-scale turbulent dynamo in the photosphere (Boldyrev and Cattaneo 2004; Vogler and Schussler 2007; Pietarila Graham et al. 2009) utilize the collisional value of magnetic diffusivity (0.01 - 10 kilometers squared per second) based on the electric conductivity in the photosphere. At the same time, utilizing the turbulent magnetic diffusivity would be more justified physically, as long as the turbulent diffusivity determines the minimum scale for magnetic elements. The measured so far value of turbulent magnetic diffusivity (70-350 kilometers squared per second) and been interpreted as a scale-independent parameter, leave a very slim chance to successfully model the small-scale turbulent dynamo in the photosphere. Thus, in the case of very high diffusivity on very small scales (sub-diffusivity), chances for tiny magnetic field concentrations to resist the spreading action of turbulent flows are small, so that the dynamo is restrained. A super-diffusion regime on very small scales is very favorable for pictures assuming the turbulent dynamo action since it assumes decreasing diffusivity with decreasing scales.

The result is published in The Astrophysical Journal, 743, p. 133, 2011, Arxiv, also see NASA ADS