The existence of fine structure in sunspots is well-known: bright and dark filaments in the penumbra, light bridges, umbral dots (UDs), and dark nuclei observed in the umbra. Exceptionally good observational conditions are needed to obtain reliable information about these structures, which are probably related to the interactions of small-scale plasma motions with magnetic fields of different strengths and inclinations. Detailed knowledge of the physical characteristics and the dynamical behaviour of these structures is crucial for our understanding of the origin and evolution of sunspots.
The umbrae and penumbrae of sunspots are dynamical objects; therefore, long time series of high spatial resolution images are required for thorough studies. This is an extremely difficult task because adverse combinations of effects can often thwart such observations: seeing that deteriorates too soon, clouds that appear, instruments that fail, or sunset. Time series of sunspots with appropriate spatial resolution have been obtained only at very few sites around the world: Pic du Midi (e.g. Muller 1973, Kitai 1986), Sacramento Peak (Adjabshirzadeh & Koutchmy 1980), Big Bear (e.g. Ewell 1992, Wang & Zirin 1992), and Canary Islands (e.g. Kusoffsky & Lundstedt 1986). All these authors had to make a rigorous post facto selection of frames, and used only a small fraction of the original observing material due to strong variations of image quality. In recent years, the Swedish Vacuum Solar Telescope (SVST, see Scharmer et al. 1985) at La Palma, Canary Islands, has been equipped with an on-line frame-selection system (Scharmer 1989) and a sunspot tracker, which have been continuously improved since their first installation. This has made it possible to acquire several high-quality time series (e.g. Shine et al. 1994, Molowny-Horas 1994, Simon et al. 1994, Sobotka et al. 1995).
UDs are tiny bright features embedded in the dark umbral background. This background itself has a complex structure with smoothly varying intensity, forming brighter and darker regions with diffuse transitions. For this reason we call it diffuse background. The darkest regions in the diffuse background, which are almost void of UDs, are termed dark nuclei (see Sobotka et al. 1993 for more details concerning the terminology used in this paper). UDs are usually divided into two classes (Grossmann-Doerth et al. 1986): "peripheral" UDs, located in the vicinity of the umbra-penumbra border, and "central" ones in the inner parts of umbra. The "peripheral" UDs are usually brighter than the "central" ones.
Since UDs can be observed only near the resolution limit of contemporary telescopes, their real brightness and size cannot be measured directly. First estimates of the real intensity of UDs, made on the basis of colour temperatures (Beckers & Schröter 1968, Kneer 1973, Koutchmy & Adjabshirzadeh 1981), indicated the brightness of UDs to be close to that of the photosphere. More recent observations revealed intensities in a broader range, often lower than those of the photosphere (Aballe Villero 1992). High spatial resolution spectra made it possible to derive the real brightnesses of UDs from local two-component semi-empirical models and to calibrate a large photometric sample of UDs observed in white-light images (Sobotka et al. 1993). The result showed that, on average, the real brightness of UDs, , is proportional to the local brightness of the surrounding diffuse background , i.e. . Wiehr (1994) found that the contrast of UDs (with respect to ) decreases with increasing geometrical height. This means that either the intensities of UDs or their sizes, or both, decrease with height.
The real sizes of UDs must be smaller than the observed ones. Their determination is closely related to the estimate of the real brightnesses: if one knows the real and observed brightnesses and the observed size one can calculate the real size from flux conservation. Taking the real brightness equal to the photospheric one, Koutchmy & Adjabshirzadeh (1981) concluded that the diameters of UDs are very small: 0:0014-0:0028 (100-200 km). Aballe Villero (1992), from colour temperature analysis, found the diameters to vary in a broader range: 0:0015-0:0060 (110-440 km). Grossmann-Doerth et al. (1986) and Lites et al. (1991) tried to measure the sizes of UDs in white-light images restored for the estimated instrumental point-spread functions. They obtained 0:004-0:009 (290-650 km) and 0:0017-0:0039 (120-280 km), respectively. In the former case, Grossmann-Doerth et al. probably observed clusters of UDs rather than individual ones. Sobotka et al. (1993), using their approximate relation between the and , derived the diameters to be in the range 0:0025-0:0041 (180-300 km). They also found that the size and brightness of UDs were uncorrelated.
UDs are not static objects. Time series show that they change their brightness and move about. The first estimates of their lifetimes were about 25 minutes (Beckers & Schröter 1968, Adjabshirzadeh & Koutchmy 1980). More recent observations made by Kitai (1986) and Kusoffsky & Lundstedt (1986) indicated longer typical lifetimes of 40 and 60 minutes, respectively. Ewell (1992) reported a mean lifetime of only 15 minutes. Several UDs were observed to exist for more than 2 hours (Kusoffsky & Lundstedt 1986, Ewell 1992). It should be noted that the time resolution of all above mentioned observations was not better than 5 minutes. Those UDs that are located at the periphery of the umbra and sometimes associated with bright penumbral grains, move towards the center of the umbra (Ewell 1992, Molowny-Horas 1994). Ewell suggested distinguishing between "central" and "peripheral" UDs on the basis of their proper motions - "central" UDs were stationary, while "peripheral" UDs drifted inwards. The motion of umbral dots appears to be controlled by the distribution of dark nuclei in the umbra (Sobotka et al. 1995).
In this paper we analyze part of the time series obtained by Simon et al. (1994). This 11 hour series was taken to study horizontal motions in the quiet photosphere, but during 4 1/2 hours a medium-size sunspot was also present in the field-of-view (FOV). The observations and data reduction are summarized in Sect. 2. An automatic identification and tracking algorithm applied to UDs, described in Sect. 3, made it possible to measure intensity variations, effective diameters, lifetimes, and proper motions, of a large number of umbral dots. In Sect. 4 we present the results concerning the filling factor, sizes, and lifetimes of UDs, and summarize and discuss them in Sect. 5. Further results (intensity variations and proper motions of UDs) will be published in a subsequent paper.
© European Southern Observatory (ESO) 1997
Online publication: March 26, 1998