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Left : one of 20 time-slice images of the complete time series. Right : bitmap image obtained after unsharp masking of the time-slice image to the left. Black pixels of the bitmap correspond to the intergranular space.
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From a series of 1400 white-light images of solar granulation spanning a time period of 8.2hours, skeletal plots of time-slice
diagrams are derived showing intergranular lane positions as a function of time. The diagrams permit to automatically track,
classify, and relate 42 186 granules. Recurrently fragmenting granules are found that survive by m...
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... order to highlight the tree structure of the intergranular lanes we next seek to obtain a skeleton, which replaces the dark lanes by single thin curves that delineate the middle of the lanes. This offers a way to apply automatic analysis tools with the help of which evolutionary properties of granules can be determined. To this aim the time-slice diagrams are first transformed to bitmap images by the following procedure. A diffuse version of the original image, obtained by a box-car average over 10 pixel, is subtracted from the original image (unsharp masking). Then, pixels in areas with a grey level higher than the global average (segmentation level) are given a value of 0, while pixels with a lower value are associated with 1 and constitute the intergranular space. The transformed version of Figure 2 (left) is shown in Figure 2 (right), where white pixels correspond to value 0 (granulum) and black ones to value 1 ...
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... order to highlight the tree structure of the intergranular lanes we next seek to obtain a skeleton, which replaces the dark lanes by single thin curves that delineate the middle of the lanes. This offers a way to apply automatic analysis tools with the help of which evolutionary properties of granules can be determined. To this aim the time-slice diagrams are first transformed to bitmap images by the following procedure. A diffuse version of the original image, obtained by a box-car average over 10 pixel, is subtracted from the original image (unsharp masking). Then, pixels in areas with a grey level higher than the global average (segmentation level) are given a value of 0, while pixels with a lower value are associated with 1 and constitute the intergranular space. The transformed version of Figure 2 (left) is shown in Figure 2 (right), where white pixels correspond to value 0 (granulum) and black ones to value 1 ...
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... points to which the same procedure is applied iteratively until none but skeletal points are left over. We use a modified version of the classical thinning algorithm described by Pavlidis (1982). We would like to caution against using the thinning algorithm that comes with the IDL software package 5.3, which uses erroneous patterns for the decision on skeletability. Finally, the skeleton is noise filtered by removing isolated branches (branches without connection to other branches) that are shorter than two minutes, since shorter-lived details cannot be reliably treated as intergranulum or granulum. Figure 4 (left) shows the result when applying the thinning algorithm to the bitmap of Figure 2 (right). Figure 4 (right) shows an enlarged section of the unsharp-masked grey-scale time-slice diagram, overlaid with the corresponding skeleton. It can be verified that the skeleton accurately renders the location of intergranular lanes. An MPEG-movie, showing the granular evolution within a neighborhood of ± 1 . 25 arc-sec of the slice together with the buildup of the corresponding time-slice diagram can be found on the ...
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... 3. Detail of Figure 2: unsharp-masked time-slice image ( left ) and corresponding bitmap image ( right ). The grey shaded area in the bitmap gives an impression of the sensitivity of the segmentation to the degree of unsharp masking. For more details see text.
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... 4. Left : skeleton of a section of the time-slice diagram shown in Figure 2 left . The skeleton is obtained by application of a thinning procedure on the bitmap image of Figure 2 right . Right : enlarged section of the skeleton superimposed on the corresponding unsharp-masked time-slice diagram.
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... 4. Left : skeleton of a section of the time-slice diagram shown in Figure 2 left . The skeleton is obtained by application of a thinning procedure on the bitmap image of Figure 2 right . Right : enlarged section of the skeleton superimposed on the corresponding unsharp-masked time-slice diagram.
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... explained in Section 1 we do not use the entire image but only 10 horizontal and 10 vertical slices of 4 pixel (0.5 arc sec) width, equidistantly distributed over each image. The ‘one-dimensional’ slice images, which we contract to 1 pixel width by averaging over the 4 pixels (no pixel averaging is done in the slice direction), are then assembled time step by time step in order to obtain a two-dimensional time- slice diagram of 43.4 Mm width over a time period of 8.2 hr. An example is shown in Figure 2 (left). The location of the dark intergranular lanes with time, as well as birth and destruction of granules can be clearly seen in the diagram. It is ...
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... Detailed spectropolarimetric observations of the photospheric lines along the solar surface and its time evolution tightly constrain the properties of the solar convection in terms of spatial and temporal scales, plasma upflows and downflows, as well as its horizontal motion and its thermodynamical properties. Granular convective cells have typical diameters of ∼1 Mm, bright and thus hot central areas, where upflows are located (∼1 km s −1 ), and dark, and thus cooler, lanes, that separate adjacent convective cells and where downflows (∼−1.5 km s −1 ) are located (e.g., [27][28][29][30][31][32][33][34] and references therein). The emergence of distinct scales of plasma motion on larger scales-mesogranulation [35] and supergranulation [36][37][38]-is highlighted by spatio-temporal filters applied by the observation techniques (e.g., time averaging) and by tracking the horizontal motion of the plasma. ...
The turbulent thermal convection on the Sun is an example of an irreversible non-equilibrium phenomenon in a quasi-steady state characterized by a continuous entropy production rate. Here, the statistical features of a proxy of the local entropy production rate, in solar quiet regions at different timescales, are investigated and compared with the symmetry conjecture of the steady-state fluctuation theorem by Gallavotti and Cohen. Our results show that solar turbulent convection satisfies the symmetries predicted by the fluctuation relation of the Gallavotti and Cohen theorem at a local level.
... To check the validation of this normalization approach, we draw November & Simon (1988) 0.5-1.0 km s −1 Brandt et al. (1988) 0.67 km s −1 Title et al. (1989) 0.37 km s −1 Berger et al. (1998) 1.1 km s −1 Shine et al. (2000) 0.49 km s −1 Müller et al. (2001) 0.6 km s −1 Matsumoto & Kitai (2010) 1.1 km s −1 Verma & Denker (2011) 0.54 km s −1 Chitta et al. (2012) 1.3 km s −1 histograms of the normalized continuum intensity in each data set at the disk center to the most off-disk center accessed in our study, μ=0.6. These histograms (not shown) do not differ from each other, indicating that a continuum intensity normalized within each data set represents more or less an identical location. ...
Gas convection is observed in the solar photosphere as granulation, i.e., having highly time-dependent cellular patterns, consisting of numerous bright cells called granules and dark surrounding channels called intergranular lanes. Many efforts have been made to characterize the granulation, which may be used as an energy source for various types of dynamical phenomena. Although the horizontal gas flow dynamics in intergranular lanes may play a vital role, they are poorly understood. This is because the Doppler signals can be obtained only at the solar limb, where the signals are severely degraded by a foreshortening effect. To reduce such a degradation, we use Hinode 's spectroscopic data, which are free from a seeing-induced image degradation, and improve the image quality by correcting for stray light in the instruments. The data set continuously covers from the solar disk to the limb, providing a multidirectional line-of-sight (LOS) diagnosis against the granulation. The obtained LOS flow-field variation across the disk indicates a horizontal flow speed of 1.8–2.4 km s ⁻¹ . We also derive the spatial distribution of the horizontal flow speed, which is 1.6 km s ⁻¹ in granules and 1.8 km s ⁻¹ in intergranular lanes, and where the maximum speed is inside intergranular lanes. This result newly suggests the following sequence of horizontal flow: a hot rising gas parcel is strongly accelerated from the granular center, even beyond the transition from the granules to the intergranular lanes, resulting in the fastest speed inside the intergranular lanes, and the gas may also experience decelerations in the intergranular lane.
... The physical properties and the temporal evolutions of granules have been reported in numerous studies (Roudier & Muller 1986;Hirzberger et al. 1997;Roudier et al. 2003;Oba et al. 2017aOba et al. , 2017b. Some small granules fade out without any fragmentation or merger, whereas large granules principally fragment into multiple smaller granules (Hirzberger et al. 1999;Müller et al. 2001;Lemmerer et al. 2017). ...
In quiet regions on the solar surface, turbulent convective motions of granulation play an important role in creating small-scale magnetic structures, as well as in energy injection into the upper atmosphere. The turbulent nature of granulation can be studied using spectral line profiles, especially line broadening, which contain information on the flow field smaller than the spatial resolution of an instrument. Moreover, the Doppler velocity gradient along a line of sight (LOS) causes line broadening as well. However, the quantitative relationship between velocity gradient and line broadening has not been understood well. In this study, we perform bisector analyses using the spectral profiles obtained using the spectropolarimeter of the Hinode /Solar Optical Telescope to investigate the relationship of line broadening and bisector velocities with the granulation flows. The results indicate that line broadening has a positive correlation with the Doppler velocity gradients along the LOS. We found excessive line broadening in fading granules, that cannot be explained only by the LOS velocity gradient, although the velocity gradient is enhanced in the process of fading. If this excessive line broadening is attributed to small-scale turbulent motions, the averaged turbulent velocity is obtained as 0.9 km s ⁻¹ .
... The methods enable the study of the lifetime of individual granules from the point the granule evolves, up until it dies. A different approach to deriving the lifetime of granules is the calculation of time-slice diagrams (see, e.g., Rast 1999;Ploner et al. 1998;Müller et al. 2001). The position of the prior detected intergranular lanes are followed in a time-series of thin-slit filtergrams. ...
Previous studies have discovered a population of small granules with diameters less than 800 km showing differing physical properties. High resolution simulations and observations of the solar granulation, in combination with automated segmentation and tracking algorithms, allow us to study the evolution of the structural and physical properties of these granules and surrounding vortex motions with high temporal and spatial accuracy. We focus on the dynamics of granules (lifetime, fragmentation, size, position, intensity, vertical velocity) over time and the influence of strong vortex motions. Of special interest are the dynamics of small granules compared to regular-sized granules. We developed a temporal tracking algorithm based on our developed segmentation algorithm for solar granulation. This was applied to radiation hydrodynamics simulations and high resolution observations of the quiet Sun by SUNRISE/IMaX. The dynamics of small granules differ in regard to their diameter, intensity and depth evolution compared to regular granules. The tracked granules in the simulation and observations reveal similar dynamics (lifetime, evolution of size, vertical velocity and intensity). The fragmentation analysis shows that the majority of granules in simulations do not fragment, while the opposite was found in observations. Strong vortex motions were detected at the location of small granules. Regions of strong vertical vorticity show high intensities and downflow velocities, and live up to several minutes. The analysis of granules separated according to their diameter in different groups reveals strongly differing behaviors. The largest discrepancies can be found within the groups of small, medium-sized and large granules and have to be analyzed independently. The predominant location of vortex motions on and close to small granules indicates a strong influence on the dynamics of granules.
... Direct observations (e.g., Title et al., 1989;Wilken et al., 1997;Krieg et al., 2000;Müller et al., 2001;Berrilli et al., 2001;Löfdahl et al., 2001;Hirzberger, 2002;Nesis et al., 2002;Hirzberger, 2002;Roudier et al., 2003b;Del Moro, 2004;Puschmann et al., 2005;Nesis et al., 2006;Stodilka and Malynych, 2006, and references therein), have given a wealth of information about the morphology and evolution of the granulation pattern, and about how it is influenced and advected by larger scale flows. However, direct observations of sub-arcsecond size structures are unavoidably affected by image degradation, caused by limited instrumental resolution, scattering in the instrument and, in the case of Earth-based observations, atmospheric blurring and image distortion. ...
... They matched the patterns to generalized Voronoi foams and concluded that the two patterns are very similar. Roudier et al. (2003a) and Roudier and Muller (2004) demonstrated that a significant fraction of the granules in the photosphere are organized in the form of 'trees of fragmenting granules', which consists of families of repeatedly splitting granules, originating from single granules at their beginnings (see also Müller et al., 2001). Trees of fragmenting granules can live much longer than individual granules, with lifetimes typical of mesogranulation; this illustrates that larger scale flows are able to influence and modulate the evolution of smaller scale flows. ...
Electronic supplementary material:
Supplementary material is available for this article at 10.12942/lrsp-2009-2.
... Mesogranular intensity fluctuations are reported to have correlations with vertical velocity consistent with convection (Deubner 1989;Straus et al. 1992), but it is unclear whether these occur on a scale distinct from or part of the broad granular distribution. This uncertainty is particularly important in the light of numerous observations which demonstrate that granule properties vary on mesogranular scales (Oda 1984;Dialetis et al. 1988;Title et al. 1989;Muller, Roudier, & Vigneau 1990;Brandt et al 1991;Abdussamatov 1993Abdussamatov , 2000Abdussamatov & Zlatopol'skii 1997;Hoekzema & Brandt 2000;Mü ller et al. 2001). Although such observations are most often interpreted to mean that granular dynamics are influenced by the underlying mesogranular flow, they alternatively suggest that mesogranulation is a secondary property of granulation itself (Rast 1995(Rast , 1999Rieutord et al. 2000;Mü ller et al. 2001;Cattaneo, Lenz, & Weiss 2001). ...
... This uncertainty is particularly important in the light of numerous observations which demonstrate that granule properties vary on mesogranular scales (Oda 1984;Dialetis et al. 1988;Title et al. 1989;Muller, Roudier, & Vigneau 1990;Brandt et al 1991;Abdussamatov 1993Abdussamatov , 2000Abdussamatov & Zlatopol'skii 1997;Hoekzema & Brandt 2000;Mü ller et al. 2001). Although such observations are most often interpreted to mean that granular dynamics are influenced by the underlying mesogranular flow, they alternatively suggest that mesogranulation is a secondary property of granulation itself (Rast 1995(Rast , 1999Rieutord et al. 2000;Mü ller et al. 2001;Cattaneo, Lenz, & Weiss 2001). In x 3 below we demonstrate how the latter may indeed be the case, not only for mesogranulation but also for the larger scale supergranular motions. ...
... It has been suggested, on the basis of simple advection models (Rast 1999), observations (Rieutard et al. 2000Mü ller et al. 2001), and three-dimensional convection models (Rast 1995;Cattaneo et al. 2001), that mesogranulation results from the collective interaction of granular flows. We investigate here whether both mesogranular and supergranular scales can result from the collective advective interaction of granular downflow plumes. ...
Solar granulation is described as an advection-fragmentation process in the upper layers of the convection zone. The fundamental hydrodynamic unit is the downflow plume, and from its structure the granular scale follows. Moreover, through the collective advective interaction of many small-scale and short-lived granular plumes, large spatial and long temporal mesogranular and supergranular scales naturally arise. We illustrate and examine this process of scale selection using a simplified n-body advective-interaction model. For parameters set by granulation observations and numerical plume simulations, clustering scales remarkably close to observed mesogranulation and supergranulation result.
... We will compare the final and initial positions of the corks, which will give us information about the motion of downflows in the field of view. Corks are tracked for ∼ 16 minutes (a time sufficiently longer than the characteristic time scale of photospheric fields (Müller et al., 2001;Berrilli et al., 2002) to let the cork settle in a downflow feature and track it for a while) and their initial and final position are stored. As corks tend to accumulate in long lasting downflow structures, new corks are added each ∼ 5 minutes in order to also track structures forming during the observations. ...
We investigate the plasma flow properties inside a Supergranular (SG) cell, in particular its interaction with small scale magnetic field structures. The SG cell has been identified using the magnetic network (CaII wing brightness) as proxy, applying the Two-Level Structure Tracking (TST) to high spatial, spectral and temporal resolution observations obtained by IBIS. The full 3D velocity vector field for the SG has been reconstructed at two different photospheric heights. In order to strengthen our findings, we also computed the mean radial flow of the SG by means of cork tracing. We also studied the behaviour of the horizontal and Line of Sight plasma flow cospatial with cluster of bright CaII structures of magnetic origin to better understand the interaction between photospheric convection and small scale magnetic features. The SG cell we investigated seems to be organized with an almost radial flow from its centre to the border. The large scale divergence structure is probably created by a compact region of constant up-flow close to the cell centre. On the edge of the SG, isolated regions of strong convergent flow are nearby or cospatial with extended clusters of bright CaII wing features forming the knots of the magnetic network. Comment: 7 pages, submitted to A&A, referee's comments included
... granules of short lifetimes) show a slight tendency to be located in downflow regions and larger granules in upflow regions of the MG. A connection of active granules and the mesogranular flow was also suggested by Müller et al. (2001). They compared the mean distance of long-lived active granules and the mesogranular scale. ...
... Roudier et al. (2003) confirm the suggestions of Straus & Bonaccini (1997) and Rieutord et al. (2000), that MG is not a "specific scale of convection" ... "but just the largescale extension of granulation". From a two-dimensional analysis of the granular intensity field they found that a "significant fraction of granules" form so-called trees of fragmenting granules, which are very long-lived, a result that was previously found from a one-dimensional time-slice analysis by Müller et al. (2001). ...
Using a 45.5-h time series of photospheric flow fields generated from a set of high-resolution continuum images (SOHO/MDI) we analyze the dynamics of solar mesogranule features. The series was prepared applying a local correlation tracking algorithm with a 4.8´´ FWHM window. By computing 1-h running means in time steps of 10 min we generate 267 averaged divergence maps that are segmented to obtain binary maps. A tracking algorithm determines lifetimes and barycenter coordinates of regions of positive divergence defined as mesogranules (MGs). If we analyze features of lifetimes $\geq$1 h and of areas $\geq$5 Mm${^2}$ we find a mean drift velocity of 304 m s$^{-1}$ (with $\pm$$ 1\sigma$ variation of 180 m s$^{-1}$), a mean travel distance of $2.5 \pm 1.8$ Mm, a mean lifetime of $2.6 \pm 1.8$ h, and a $1/e$ decay time of 1.6 h for a total of 2022 MGs. The advective motion of MGs within supergranules is seen for 50 to 70% of the long-lived ($\geq$$4$ h) MGs while the short-lived ones move irregularly. If only the long-lived MGs are further analyzed the drift velocities reduce to 207 m s$^{-1}$ and the travel distances increase to 4.1 Mm on average, which is an appreciable fraction of the supergranular radius. The results are largely independent of the divergence segmentation level.
... From his 2D numerical model Ploner (1994) concluded that fragmenting granules can split repeatedly for several generations and discussed the link between these long-lived structures and the mesogranulation. Using time-slice of the Sun surface, Müller et al. (2001), found that fragmenting granules can survive by means of their descendants for more than 3 h. Their works suggest that mesogranular flow fields may be generated by actives granules. ...
3D analysis (x,y,t) of the granular intensity field (11-hour time sequence from the Swedish Vacuum Solar Telescope on La Palma, Canary Islands), demonstrates that a significant fraction of the granules in the photosphere are organized in the form of "Trees of Fragmenting Granules" (TFGs). A TFG consists of a family of repeatedly splitting granules, originating from a single granule at its beginning. A striking result is that TFGs can live much longer ( up to 8 h) than individual granules (10 min). We find that 62% of the area covered by granules belongs to TFGs of a lifetime >1.5 h. When averaged in time, such long-lived TFGs correspond to coherent diverging flows which may be identified as mesogranules. We also find a correlation between the network and the spatial distribution of TFGs.
... These granular cells are characterized by a typical horizontal extent of ∼1.4 Mm (Lawrence et al. 1999), and their typical lifetime ranges from few minutes to ∼15 min. However, in spite of these short lifetimes, a prolonged persistence of the granulation pattern and/or of related photospheric structures has been reported in several studies (Baudin et al. 1997;Roudier et al. 1997;Hoekzema et al. 1998;Müller et al. 2001;Getling & Brandt 2002). In particular, averaging many hours (∼1 ÷ 8) of observations, Getling & Brandt (2002) revealed quasi-regular structures of the photospheric and subphotospheric flows, that suggests the existence of a previously unknown type of selforganization resembling the so-called target patterns observed in experiments on Rayleigh-Bénard convection. ...
The existence of a quasi-regular pattern in solar photospheric convective fields is an open question. In the present work, this problem is quantitatively approached by means of the normalised information entropy measure H'(r) as introduced by Van Siclen (\cite{VanSic97}), which reports on the information content at different scales. Images were acquired at the THEMIS telescope of the European Northern Observatory by the IPM observing mode, and at the Richard B. Dunn Solar Telescope of the National Solar Observatory. The evaluation of H'(r) in the case of photospheric intensity binarized images shows the presence of maxima which are evidence of different prominent scales in the photospheric pattern. The relative positions of these maxima defines an ordering scale ~ 1.6 Mm in both instantaneous and average images. This is read as the evidence of a spatio-temporal organization in the evolution of convective pattern. The emergence of an ordering scale is discussed in the framework of pattern formation in random systems and in connection with the findings of previous works. By averaging images with time, an increase of the information content characterized by a coherence time of ~ 1 h is observed in the range of scales from 5.0 Mm to 10.0 Mm.
