Artificial granules in 2-D solar models

Two-dimensional, hydrodynamic, time-dependent models of solar granulation have been used to determine characteristics of artificial granules. It is found that the evolution of granules which subsequently fragment, respectively disappear, is fundamentally different. Dissolution of artificial granules is the basic process (48%–58%) in 2-D models. The number of small-scale and short-lived granules increases continuously toward the smaller scales. The main contributor to the total area are the granules with sizes about 900–1000 km. The mean lifetime of artificial granules is estimated to be 6–11 min.     

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     

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).

     

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.     

The spatial distribution of umbral dots and granules

A statistical analysis is made of the spatial distribution of umbral dots and photospheric granules. The dots and granules are more evenly spaced than random points, though dots mapped by different observers have different distributions.     

Time-dependent interaction of granules with magnetic flux tubes

The time-dependent interaction of the granulation velocity field with a magnetic flux tube is investigated here. It is seen that when a magnetic field line is displaced normal to itself so as to simulate thebuffeting action of granules, a flow of gas is initiated along the field. By choosing a lateral velocity field which is consistent with observations of granules, it is found that the resulting gas motion is a downward flow with a velocity compatible with the observed downflow in isolated photospheric flux tubes. It is therefore proposed that the observed photospheric downflow is a manifestation of the interaction of granules with flux tubes.     

Morphological properties and origin of the photospheric facular granules

From time series of high resolution photographs, morphological properties of the photospheric facular granules were derived. The facular granules are cells of the common granular pattern, brighter than the normal granules when seen between cos = 0.6 and the limb. Their apparent diameter, which decreases towards the limb, is smaller than that of the normal granules: 0.65 and 1.25 respectively at cos = 0.55; their lifetime is 25 min but their bright stage lifetime is only 15 min; they are visible closer to the limb than the normal granules: 1.2 compared to 2–5; the brightening of the facular granules occurs at a faster rate than their fading. From the great similitude of both morphological properties and temperature models of facular and normal granules, it appears possible that the photospheric facular granules are convective cells modified by the presence of a magnetic field of some hundreds Gauss.     

Soft X-ray line profiles in the impulsive phase of electron-heated solar flares

We have measured the motion of facular points and granules in the same region near a decaying sunspot. It is found that both features move away across the moat surrounding the sunspot. The mean speed of facular points is larger than that of granules: 0.65 km s^–1 and 0.4 km s^–1, respectively. These results are consistent with previous measurements of the speed of bright network features and moving magnetic fields, as well as of non-magnetic photospherical material. They support models in which a decaying sunspot is at the center of a supergranule, whose horizontal motions sweep out granules and magnetic flux tubes associated to the facular points. It is also found that granules are dragged by supergranular motions away of the moat.Contributions from the Kwasan and Hida Observatories, University of Kyoto.A part of this work was done while one of the authors (R.M.) was staying at the Kwasan and Hida Observatories, University of Kyoto, Japan, as a JSPS research fellow.     

The variation of the mean size of the photospheric granules close to and away from a sunspot

We study the mean size of granules as a function of distance from the boundaries of the sunspot penumbra. We use for the determination of the mean size two different methods, a visual and a photometric. In all cases the mean diameter of the granules away from the spot was greater than the mean diameter of the granules in the neighbourhood of the penumbra. Our study is based on an excellent sequence of photos, taken at the Pic-du-Midi Observatory on May 11, 1979.     

Heating of the solar corona

The suggestion is advanced that heating of the solar corona results from Landau damping of ion-acoustic waves generated in the motion of photospheric granules. Laboratory experiments relevant to the question of corona heating are discussed, together with the available observational information on the extent of energy deposition in the corona.Of the European Space Research Organization (ESRO).     

The large-scale pattern formed by the spatial distribution of granules

The spatial distribution of granule sizes at the surface of the sun is investigated. Granules have been separated into two classes: those larger than 1.37 and those smaller, where 1.37 is the critical scale defined by Roudier and Muller (1986). It is found that granules are not distributed at random: large granules appear to be clustered, forming a cellular pattern with a characteristic scale of 7; small granules form a similar and complementary pattern. These patterns are probably related to the mesogranulation.     

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.     

Structure and physics of solar faculae

The methods used and the results obtained in the measurement of the distances between the centers of chromospheric granules are described. A coincidence of these structures at two different altitudes was observed. Observations made in the K2v, or in the K3 and CN lines permit the comparison of two different altitudes: the upper and the lower chromosphere. These results include flocculi on the edge of the supergranules as well as plages. Two main results are obtained: (l)the most likely distance between two neighboring granules is, at the minimum of the solar cycle, of about 2. 60 for K3 and 2.45 for CN, and (2) this distance is decreasing with growing solar activity.     

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.     

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.     

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.     

Multi-parametric effect of solar activity on cosmic rays

The long-term modulation of cosmic ray intensity (CRI) by different solar activity (SA) parameters and an inverse correlation between individual SA parameter and CRI is well known. Earlier, it has been suggested that the concept of multi-parametric modulation of CRI may play an important role in the study of long-term modulation of CRI. In the present study, we have tried to investigate the combined effect of a set of two SA parameters in the long-term modulation of CRI. For this purpose, we have used a new statistical technique called “Running multiple correlation method”, based on the “Running cross correlation method”. The running multiple correlation functions among different sets of two SA parameters (e.g., sunspot numbers and solar flux, sunspot numbers and coronal index, sunspot numbers and grouped solar flares, etc.) and CRI have been correlated separately. It is found that the strength of multiple correlation (among two SA parameters and CRI) and cross correlation (between individual SA parameter and CRI) is almost similar throughout the period of investigation (1955–2005). It is also found that the multiple correlations among various SA parameters and CRI is stronger during ascending and descending phases of the solar cycles and it becomes weaker during maxima and minima of the solar cycles, which is in accordance with the linear relationship between SA parameters and CRI. The values of multiple correlation functions among different sets of SA parameters and CRI fall well within the 95% confidence interval. In the view of odd-even hypothesis of solar cycles, the strange behaviour of present cycle 23 (odd cycle), as this is characterized by many peculiarities with double peaks and many quiet periods (Gnevyshev gaps) interrupted the solar activity (for example April 2001, October–November 2003 and January 2005), leads us to speculate that the solar cycle 24 (even cycle) might be of exceptional nature.     

Amplitude distributions of solar photospheric fluctuations

Amplitude distributions, which are nearly Gaussian, have been calculated for radial velocity, continuum brightness, spectral line equivalent width and spectral line central residual intensity fluctuations measured from high-dispersion high-resolution spectrograms taken at the center of the solar disk. The RMS and skewness S for each distribution have been calculated in a manner which allows testing of the homogeneity of the granulation pattern (i.e. variations in its statistics across the solar disk and with time). Pattern inhomogeneity across the disk is strongly indicated, and further evidence suggesting appreciable pattern persistence over time intervals 15 minutes is presented. The possibilities for investigations of S and its associated bi-spectrum are discussed. The qualitative values of S obtained are shown not to be due to unusually bright, rising granules (though a statistical tendency towards such granules is possible). An attempt to explain S for continuum brightness fluctuations in terms of the nonlinear effects of Planckian emission and opacity fluctuations in a stratified photosphere, leads to contradiction with the measured amplitude distributions, a contradiction which is probably due to an oversimplified treatment of radiative transfer in an inhomogeneous photosphere.     

Video image selection studies of granules,pores, and penumbral flows near a large sunspot

An excellent high-resolution movie in the green continuum was produced by shift-and-add treatment of two 60-min videotapes obtained at the Big Bear Solar Observatory. We have studied the digitized images by direct measurement, cross-correlation techniques, and correlation tracking. The seeing-limited resolution was about 0.3 arc sec.While the cross-correlation lifetime for granules is about five minutes, we find that actually tracking the growth and decay of a granule gives lifetimes from 10 to 22 minutes, the longest lifetimes pertaining to the largest granules. The longer lifetime comes from tracking the granule while it undergoes large changes in size and shape, while the cross-correlation lifetime is just the time in which it grows by a factor two. All the granules followed began as small elements, grew to some size, and either faded (88%), exploded (2%) or were hit by an exploding granule (10%). The major variation in granule structure appears to be due to substantial variations in the dark lanes, which often double in width.The granulation shows the typical exploding granule behavior; we find the probability that any granule will be affected by an exploding granule during its lifetime to be 10%. We also observed a larger scale explosion covering about 10 granules. This explosion was marked by rapid (1 km s^–1) outward flux of the granules.We tracked the development of six small pores, one of which could be followed for two hours. The latter showed four maxima of absorption separated by about 30 min each, virtually disappearing in between. Another was observed to form in about 20 min, but no changes occur in less than granule lifetime.We confirm the inflow in penumbral fibrils observed by Muller. The inflow velocity is about 0.5 km s^–1, and all bright spots disappear into the umbra. The inflow which affects bright and dark features in the penumbral fibrils, is also observed in the smaller spots. We surmise that the Evershed flow is limited to the areas between the bright fibrils. We confirm granular outflow outside the penumbra.     

Variation of the low-degree solar acoustic mode parameters over the solar cycle

VIRGO/SPM is a helioseismic sunphotometer on board SOHO that observes the disk-integrated sunlight irradiance at three different colors (red, green, and blue). The data obtained for SPM since the beginning of the SOHO mission, April 1996, to March 2001 have been used to study the differences of the p-mode parameters during the solar activity cycle. These time series have been divided in sub-series of 100 days, transformed to power spectra and averaged in sets of three to yield a total number of six averaged power spectra (around one per year). A new way of analyzing the power spectrum has been applied to the six power spectra of each color; it consists of fitting the whole p-mode spectrum at once with a unique background. The results for the frequencies, line widths, power, mode energy, energy rate fed in the mode and splittings along the activity cycle are found, compared and discussed.