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Astron. Astrophys. 353, 389-395 (2000)

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1. Introduction

There is evidence for at least three scales of motion in the solar photosphere: granulation, mesogranulation, and supergranulation. Granulation has been the subject of studies for more than a century, and its structure, physical properties and evolution are rather well known from both observational work and numerical models - except at the smallest spatial scales below 150 km on the Sun, which are unaccessible to present time ground-based and space-borne solar telescopes. Observed granular sizes range from the limit given by observational techniques, i.e. 150 km, to [FORMULA] km (e.g., Roudier & Muller 1986; Hirzberger et al. 1997). Supergranulation had been detected by Leighton et al. (1962); gas rises at the supergranule's center, flows horizontally outwards at speeds of 200-500 m [FORMULA], and sinks at the cell boundary (cf. Simon 2000). Mean diameters quoted for supergranules range from 32 Mm (Simon & Leighton 1964) down to 13-18 Mm (Hagenaar et al. 1997), and seem to depend strongly on the material and method used for the determination.

The term mesogranulation was first used by November et al. (1981); they described the observed vertical motions as a "fairly stationary pattern of cellular flow with a spatial scale of 5-10 Mm", a spatial rms velocity amplitude of about 60 m [FORMULA], and a lifetime of "at least 2 hr". In the next decade some authors noted that granular structure seems to vary on meso-scales. Oda (1984) described repeatedly fragmenting granules that form a cellular pattern of 7 Mm size. Koutchmy & Lebecq (1986) artificially blurred a series of white light granulation images and found quasi-stationary intensity modulations at similar scales. Muller et al. (1990) noted that large granules seem to form a cellular pattern of a characteristic scale of 5 Mm. Later Brandt et al. (1991) found that size, intensity, lifetime, and expansion (collapse) rate of granules change with their location in the mesogranulation pattern.

Since its first detection nearly two decades ago, the properties of the mesogranulation were studied by various methods, especially by local correlation tracking (LCT, for a description see e.g. November 1986) and by two-dimensional spectroscopy (e.g. Straus & Bonaccini 1997). However, there is still disagreement on the nature of this phenomenon: whether it represents waves (Dame 1985; Straus & Bonaccini 1997) or convection (e.g. Deubner 1989; Straus et al. 1992); whether it is a distinct spatial regime (Title et al. 1986; Simon et al. 1988a; Ginet & Simon 1992) or cannot be identified as a regime separated from granulation (Straus et al. 1992; Straus & Bonaccini 1997). Accordingly, there is also wide disagreement on such basic properties as size and lifetime. While Simon et al. (1988b) quote sizes ranging from 3 to 9 Mm, with a mean around 6 Mm, Ueno & Kitai (1998a) find a mean size of as much as 13 Mm. In his thesis Darvann (1991) cites lifetimes to range from less than one half to many hours derived in work prior to 1991; his own measurements yield values between 3.5 and 7 hours, which is in good agreement with the values obtained by Brandt et al. (1994). In a recent paper Roudier et al. (1998) find much shorter lifetimes, i.e., ranging from 16 to 185 min depending on the temporal window and the methods used. The cited uncertainties demonstrate two basic difficulties concerning the meso-scale flows: i) the results are strongly method-dependent, especially they depend on where the limit between granulation and meso-granulation is defined; ii) long time series of very high spatial resolution are needed for a reliable determination of the meso-scale characteristics - a requirement that is very hard to fulfill by ground-based observations.

Concerning the topic of the relation between convection and oscillations, the search for the sources of solar oscillations has received considerable attention in recent years, as has the question how flow fields modulate the oscillations. Although Zaqarashvili (1999) suggests that 5-min waves are invoked by the radiative core of the Sun, most research concentrates on regions at, or just below, the solar surface because the velocity field here possesses the highest Mach number: the convective velocities are maximal and the velocity of sound is relatively low as compared to the interior.

Especially the impact of the granulation has been the topic of ongoing research. Rast (1995) argues that the turbulent downflows in intergranular lanes, in particular locations where the downflows gather into high velocity fingers, are strong emitters of acoustic energy. Indeed several observational studies (e.g., Rimmele et al. 1995; Goode & Strous 1998; Hoekzema et al. 1998b) confirm that acoustic waves in intergranular lanes on average have much higher amplitudes than in granules. However, this does not necessarily imply that intergranular spaces also are major sources of acoustic waves: the waves may be refracted or diffracted into them (Zhugzhda & Stix 1994; Hoekzema et al. 1998a). Simulations by Cattaneo et al. (1990) and Malagoli et al. (1990) suggest that the outflow near the edges of granules may reach the speed of sound thus invoking strong acoustic waves. This may have been observed indirectly by Nesis et al. (1992) and Solanki et al. (1996).

Much less attention has been given to relations between oscillations and larger-scale flow fields; but since there is no very great difference between the flow velocities associated with granulation, meso-scale flows, and supergranulation - all are of the order of 0.5 to several km s-1 - it is worthwhile to compare their impacts on acoustic wave amplitudes. Only recently Hoekzema & Brandt (1998) and Ueno & Kitai (1998b) analysed the impact of meso-scale flows on oscillations. Here we present results of a search for relations between intensity oscillation amplitudes and meso-scale flow patterns, i.e., meso-scale convergent regions and meso-scale divergent regions.

This paper builds on a series of papers: Hoekzema et al. (1998a, Paper I; 1998b, Paper II) and Hoekzema & Rutten (1998). They employ the correspondence factor C to explore local relations between fine structure and intensity oscillation amplitudes in the quiet solar photosphere on the basis of image sequences obtained with the Swedish Vacuum Solar Telescope (SVST) on La Palma. The approach here follows that of the preceding three papers. We use similar reduction and measurement procedures, and apply our Fourier analysis technique on brightness histories (per pixel) of almost 90 min duration to produce Fourier amplitude maps for spatial and temporal correlation with the concurrent photospheric meso-scale divergence maps. We measure the amount of spatio-temporal alignment at varying time delays between different features through the statistical correspondence factor C that was introduced in Paper I. It is used to quantify the co-spatiality of high oscillatory amplitudes with meso-scale morphology as measured by its divergence.

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Online publication: December 8, 1999