Bright-dark asymmetry in solar granulation

Although a positive print of solar granulation gives the impression of bright irregular areas on a dark background, this impression is highly subjective and depends upon the nature of the photographic process. We developed an objective method for comparing bright and dark features and applied it to 40 000 elements from a granulation photograph. Each element had dimensions of 150 km by 150 km. We found that dark features were fewer in number, larger, and had larger perimeter-to-area ratios than the bright features. The statistical confidence level of our results exceeded 99%. Our results are consistent with the subjective impression that granulation is composed of bright features separated by dark lanes.Publications of the Goethe Link Observatory, Indiana University, No. 120.     

Time-slice diagrams of solar granulation

From a series of 1400 white-light images of solar granulation spanning a time period of 8.2 hours, 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 means of their descendants for more than 3 hours. Such long-lived active granules tend to have a mean spatial distance along the slice of about 10 Mm. This distance decreases with decreasing minimal required lifetime. Since active granules are expected to generate a steadily divergent flow over a long period of time, it is suggested to identify them as a source of the mesogranular flow. Deficiencies of the time-slice analysis are discussed. The relative frequency of different types of granules and the granule decay time as derived from the time-slice diagrams are compared with corresponding results of previous works. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1013350505080     

Mesostructure of the solar granulation

Quasi-periodic variations in the thermodynamic and hydrodynamic fine-structure properties of the granulation field along the photospheric surface are estimated quantitatively. The darkest vast intergranular lanes, called the intergranular knots, are the most important indicator of their physical properties. The formulated new definitions of “granule” and “intergranular lane” require a revision of the previous results. The definition of mesogranulation is given, and the method of its detection in the granulation field is described. The following important quantitative results, which established the extent and nature of the physical relationship between the granulation and mesogranulation fields, have been obtained for the first time: (1) the intensity amplitude of granules in mesogranules (ΔI(gr)/I ₀)_msgr = +10.3% is a factor of 1.4 larger than that of granules in intermesogranular regions [(ΔI(gr)/I ₀)_imsgr = +7.3%], whereas the intensity amplitude of intergranular lanes in mesogranules [(ΔI(igr)/I ₀)_msgr = ?6.0%] is a factor of 1.4 smaller than that of intergranular lanes in intermesogranular regions [(ΔI(igr)/I ₀)_imsgr = ?8.4%]; (2) the mean intensities of photospheric granules and intergranular lanes are (ΔI(gr)/I ₀)_phot = +9.2% and (ΔI(igr)/I ₀)_phot = ?7.5%, respectively; (3) granules cover 59% of the area of mesogranules, 45% of the area of the photosphere, and 31 % of the area of intermesogranular regions, while intergranular lanes cover 41, 55, and 69% of these areas, respectively; (4) intergranular knots and bright granules virtually never formed and do not exist in mesogranules and intermesogranular regions, respectively; (5) the amplitudes of intensity fluctuations in mesogranules and intermesogranular regions, as well as the areas occupied by them (49.4 and 50.6%, respectively), essentially level off, ΔI(msgr)/I ₀ = +3.6% and ΔI(imsgr)/I ₀ = ?3.5%, respectively.     

Structure of the solar granulation

The structure of the solar granulation has been analysed using computer-processed images of two very high resolution (0.25) white-light pictures obtained at the Pic-du-Midi Observatory.The narrow dispersion in the distribution of granule sizes is not confirmed. On the contrary, it is found that the number of granules increases continuously toward smaller scales; this means that the solar granulation has no characteristic or mean scale. Nevertheless, the granules appear to have a critical scale of 1.37, at which drastic changes in the properties of granules occur; in particular the fractal dimension changes at the critical scale. The granules smaller than this scale could be of turbulent origin.     

Morphological study of the solar granulation

Time-sequential high quality photographs of the photospheric granule on a quiet region of the disc center obtained at the Pic-du-Midi Observatory by Kawaguchi are analyzed. The size variation of individual granules in the area of 54×52 on the photosphere are traced over a period of 4 min. The granules are classified according to their morphological features as follows. (1) Active granules, they repeat the expansion and the fragmentation. (2) Quiet granules, they do not alter the size noticeably during the observed time span. (3) Declining granules, they disappear without further fragmentation or merging.The distribution of active granules on the photosphere reveals a presence of a cellular pattern. The relationships between the cellular pattern and the brightness on the quiet photosphere are investigated. The results show that there is a good spatial correlation between them. The autocorrelation analysis shows a kind of periodicity on the photospheric intensity and its mean wavelengths are 11.3. The size of the cellular pattern is comparable, in magnitude, to that of mesogranulation found by Novemberet al. (1981) on the velocitygram obtained at the Sacramento Peak Observatory. Then the cellular pattern revealed by the chain of granules in the present study may be bentatively identified as the mesogranulation. The possible physical connection between the mesogranulation and the clumpy assemblage of active granules is briefly discussed.     

Morphological study of the solar granulation

High resolution images of the solar granulation show the presence of the small dot-like dark regions in the granulation cells. From the study of the characteristics of these dark regions, it is found that the dark regions are formed without any relations to the presence of the magnetic field. Moreover, it is observed that a granulation cell splits in a few minutes after the formation of the dark regions in the cell. Similarities and differences between the granules with the dark regions and the so-called exploding granules are discussed.     

Shift-and-add reconstruction of solar granulation images

To restore an atmospherically degraded image of solar granulation the shift-and-add (SAA) method is applied to its specklegrams. It is the first time, to the best of our knowledge, that such a technique has been used for image reconstruction of solar granulation, a largely extended target. SAA, therefore, enables us to monitor restored images of solar granulation in a simple and fast way.     

Morphological study of the solar granulation

A time sequence of granulation images of 46 min long has allowed us to make a detailed study of the evolution of granules in an area of approximately 17″ × 17″ on the solar surface. It is found that the granules evolve by repeated fragmentation into smaller granules or merging with adjacent ones and that there are few granules which appear in the intergranular lanes as new granules (Table III). The statistical nature of granules is as follows:

1. A family of granules is defined as a group of granules produced from a single granule by fragmentation or merging. The lifetime is estimated for single granules and for families of granules. The lifetime shows a close correlation with the maximum size of a single granule or with that of the largest granule belonging to a family (Figures 5 and 7).
2. The smaller the size, the more probably a granule will disappear without further fragmentation or merging. The granule whose size is larger than 2″ will certainly split or merge as the next evolutional step (Table IV).

     

Statistical analysis of a solar granulation plate

Two-dimensional autocorrelation function and power spectrum per unit area are given for a solar granulation plate taken at the Pic-du-Midi Observatory. A comparison is made between our result and the power per unit wave number taken from the Schwarzschild stratoscope data.     

Center to limb variation of solar granulation

The density dependence of solar EUV line intensity ratios from Mg VIII, Si VII, S IX and Si IX ions have been used to determine electron densities in the quiet Sun and coronal holes. The line intensity values have been computed using a model atmosphere of Kopp and Orrall (1976) in order to emphasize the utility of the lines studied which could be compared with observational data that future missions might provide.     

Two-dimensional spectroscopic time series of solar granulation

In this paper we investigate the dynamics of the solar granulation by analyzing time series of 2D spatially highly resolved spectrograms. These were obtained by spatial scans covering a field of 12 8″ × 20″. The advantage of this method is a high spectral resolution, however, the data are not taken simultaneously and to cover the field described above 50 exposures taken sequentially in time are necessary. Therefore, to obtain one map about 2 minutes are required. Plots of the evolution of different line parameters are given as well as the decay of correlation functions. The correlations between the first map of line parameters and successive maps (which are separated by about 2 minutes) were investigated showing a rapid decay down to a correlation coefficient of 0.4 within 4 minutes, the velocity pattern in the field observed varies on smaller time scales. The temporal variation of correlation between the line parameters for the different lines shows a periodic signal related to 5-min oscillations which could not be totally filtered. The evolution of the correlation functions between line parameters is analyzed which gives an error estimate of all correlation values found in the literature. For the first time it is explicitly shown how evolution in a selected photospheric field influences the evolution of granular/intergranular structures.     

Two-dimensional spectroscopic time series of solar granulation

In this paper we investigate the dynamics of the solar granulation by analyzing time series of 2D spatially highly resolved spectrograms. These were obtained by spatial scans covering a field of 12 8″ × 20″. The advantage of this method is a high spectral resolution, however, the data are not taken simultaneously and to cover the field described above 50 exposures taken sequentially in time are necessary. Therefore, to obtain one map about 2 minutes are required. Plots of the evolution of different line parameters are given as well as the decay of correlation functions. The correlations between the first map of line parameters and successive maps (which are separated by about 2 minutes) were investigated showing a rapid decay down to a correlation coefficient of 0.4 within 4 minutes, the velocity pattern in the field observed varies on smaller time scales. The temporal variation of correlation between the line parameters for the different lines shows a periodic signal related to 5-min oscillations which could not be totally filtered. The evolution of the correlation functions between line parameters is analyzed which gives an error estimate of all correlation values found in the literature. For the first time it is explicitly shown how evolution in a selected photospheric field influences the evolution of granular/intergranular structures.     

A morphological study of the solar granulation

Some properties of the photospheric granulation near the centre of the quiet sun have been investigated on the basis of two high-definition Stratoscope photographs. We obtain (1) a number density of 54 granules per 10 × 10, (2) a total number of granules on the whole surface of 6.3 × 10⁶, (3) a mean cell diameter of 1.5 or 1100 km and a mean granule diameter of 1.2 or 850 km, the difference of 250 km being ascribed to the mean width of the dark intergranular lanes, (4) frequency distributions of cell diameters and granule diameters (Figures 1 and 2), and (5) an isophotal map in relative intensity (Figure 3). In general, larger granules are brighter than smaller granules (Figure 4). Cross-section profiles are shown for some granules and intergranular lanes (Figures 5 and 6). These quantities have not yet been corrected for the finite resolution of the telescope.     

The effect of finite resolution on solar granulation

Some numerical experiments were performed in order to simulate the effect of finite resolution on solar granulation. When a two-dimensional pattern is smeared, another pattern emerges whose nature depends on the width of the smearing function rather than the original pattern. The size of the structures present in a typical granulation photograph is about that which would be expected from the smearing of smaller structures by the effect of atmospheric seeing. Only Stratoscope photographs appear to have unambiguously determined the nature of solar granulation.     

On the rms intensity fluctuation of solar granulation

Using a selected high definition granulation photograph obtained with a 40 cm aperture telescope from the ground, a new determination of the rms intensity fluctuation is attempted. We find, at 5500 Å, a value of 0.058 without, of 0.067 with correction for theoretical diffraction only, and 0.095 ± 0.015 as the most probable value, if the differences between our power spectrum and those given in the literature is interpreted as due to a residual seeing of = 0.3 in our photograph.Mitteilungen aus dem Fraunhofer Institut Nr. 104.     

High-resolution models of solar granulation: the two-dimensional case

Using advanced numerical schemes and grid refinement, we present 2D high-resolution models of solar granulation with particular emphasis on downflowing plumes. In the high-resolution portion of our simulation, a box measuring 1.97 × 2.58 Mm² (vertical × horizontal), the grid size is 1.82 × 2.84 km². Calculations at the resolution usually applied in this type of simulations amount to only a few horizontal gridpoints for a downflowing plume. Due to the increased number of gridpoints in our high-resolution domain, the simulations show the development of vigorous secondary instabilities of both the plume's head and stem. The plume's head produces counterrotating vortex patches, a topology due to the 2D nature of the simulations. Below a depth of about 1 Mm, the plume's head and stem instabilities produce, in these 2D models, patches of low density, temperature, pressure and high vorticity which may last for all of our simulation time, ∼10 min, and probably considerably longer. Centrifugal forces acting in these patches counteract the strong inward pressure. Probably most importantly, the plume's instabilities give rise to acoustic pulses created predominantly down to ∼1.5 Mm. The pulses proceed laterally as well as upwards and are ubiquitous. Ultimately, most of them emerge into the photosphere. A considerable part of the photospheric 'turbulence' in these models is due to those pulses rather than to some sort of eddies. The upflows in granules are smooth where they reach the photosphere from below even in the present calculations; however, the pulses may enter in the photosphere also in granular upflows.     

Photoelectric photometry of solar granulation in several regions of the continuum

Photospheric brightness fluctuations were recorded photoelectrically across a part of the sun near the center of the disk, and simultaneously for two regions of the continuous spectrum chosen at various wavelengths between λ3500 Å and λ5500 Å. The auto-correlation functions and spatial power spectra were derived for each recording, and the cross-correlation functions, spatial relative phase and coherence spectra were computed for each pair of recordings. The main results are:

1. (1)
   The cross-correlation between any two recordings obtained for various regions of the continuous spectrum, is a function of the wavelength distance Δλ between these regions. The decrease of the cross-correlation with increasing Δλ is due to the fact that separate photometric inhomogeneities radiate in limited spectral ranges.     
   
   

An analysis of the observed contrast of solar surface granulation

The contrast of the solar surface granulation detected in the focal plane of the observing system as well as its relations with the aperture of the observing system, the coherent length of atmospheric turbulence and the sensitivity of the detecting system are analyzed. The results of numerical calculation of the granulation contrast as functions of aperture, coherent length of atmospheric turbulence and sensitivity of the detecting system are presented. Results of a related observation are also given.