5. Discussion and conclusions
In a 4 1/2 hour time series of excellent quality a sample of 662 UDs, obtained by an object-tracking procedure, was analyzed with the following results:
1. The observed filling factor of UDs in the umbral core was on average. This is consistent with the earlier estimate made by Sobotka et al. (1993). During the 4 1/2 hour period the number of UDs and the filling factor remained practically constant.
2. Large (diameter ) and long-lived (lifetime minutes) UDs appear mostly in regions with enhanced umbral diffuse background intensity. In such regions the magnetic field strength is expected to be smaller than in dark areas (Kopp & Rabin 1992, Martínez Pillet & Vázquez 1993, Solanki et al. 1993).
3. UDs do not have a "typical" size. Their number rapidly increases with decreasing diameter down to the resolution limit. This is a somewhat surprising result, in contradiction to several previous estimates of UD sizes (Koutchmy & Adjabshirzadeh 1981, Grossmann-Doerth et al. 1986, and Sobotka et al. 1993). The deficit of small UDs in those observations is probably due to the visual nature of the object search, so that selection effects led to discarding of smaller and less contrasty objects. (It can be demonstrated with our present sample of UDs that their observed contrast with respect to the local diffuse background decreases for due to the image degradation caused by blurring and telescope resolution.) Our result stems from a larger and better-quality data set and a new object-tracking algorithm, which we believe is more objective than previous methods. It is very interesting to compare the histogram of of UDs (Fig. 3) with that of photospheric granules (see e.g. Fig. 6 in Roudier & Muller 1986). These distributions have nearly identical shapes.
4. UDs do not have a "typical" lifetime. Short-lived UDs (lifetimes below 10 minutes) represent about 2/3 of the population, while only 1% live more than 2 hours. This is again a new and unexpected result, obtained by the object-tracking algorithm. It differs from the estimates of characteristic lifetimes of 15 to 60 minutes reported by Adjabshirzadeh & Koutchmy (1980), Kitai (1985), Kusoffsky & Lundstedt (1986), and Ewell (1992). Their data were based on small samples of UDs, probably influenced by visual selection effects, and had a low temporal resolution (5 minutes in the best case). Moreover, their measurements of lifetimes may also have been affected by temporal intensity variations of long-lived UDs. However, Kitai (1985) also reported a similar distribution of lifetimes for a sample of 55 "chromospheric umbral dots", bright features with sizes about , observed in H filtergrams.
© European Southern Observatory (ESO) 1997
Online publication: March 26, 1998