The average PG velocities that we measure are in reasonably good agreement with those of Muller (1973a) and Tönjes & Wöhl (1982), but the character is very different. Whereas they find almost exclusively INW motions, we find both INW and OUT, with a strong dependence on position in the penumbra as described in Sect. 3.1. Although Muller (1973a) states in his summary that all motions are INW, careful examination of his Fig. 3 shows that he actually found a few OUT PGs at penumbral positions 0.25-0.80, and more OUT than INW PGs in the outermost penumbra (positions 0.8-1.0). Thus the qualitative difference in our results may not be as large as it first appears. All three of these observations show velocities far smaller than those of Schröter (1962).
The LCT flow maps calculated by Wang & Zirin (1992) show that both bright and dark penumbral structures in the inner part of the penumbra move toward the umbra, and those in the outer part move outward. This was observed in four of five sunspots, but in one very young spot inflow occurred in the whole penumbra. Since we found in Sect. 3.1 that the LCT flows seem to be consistent with the motions of individual PGs, we can infer that a part of the discrepancy between our work and Muller's (1973a) may simply be the physical properties of the particular sunspots studied. Our spot was of medium size, in the maximum phase of evolution; Muller's was very large. The character of the motions may vary significantly as function of size, age, evolutionary stage (young, old, growing, decaying), and location (unipolar, leading, following, simple or complex group), etc. Thus it is likely that Muller (1973a) and we are both correct despite our disparate results.
On the other hand, the difference may, at least in part, lie in the methods of analysis and/or quality of the observational data. Muller (1998, private communication) believes that "investigations based on visual identifications are superior to investigations based on computer identifications, because they are more `intelligent'; one can see the evolution of grains in more detail, understand better what happens and take some decisions; it is less sensitive to threshold effects, because the eyes can detect small contrasts." He acknowledges that his process "is tedious and time-consuming and might not be objective enough in the decisions." This last comment by Muller is the main reason that we prefer computer identification of features. Even though the algorithms may occasionally make mistakes, they are completely objective in their decision-making. Also they are not subject to two biases inherent in visual identification; namely, the tendency of the eye-brain interaction to selectively prefer brighter (higher contrast) and larger features. The computer is ideally suited to performing tedious tasks; thus it selects far more features for analysis than the human analyst is physically or psychologically prepared to do.
With regard to the shorter lifetimes that we measure, we agree with Muller "that the difference in lifetime we find in our respective investigations is mainly due to the different time interval between frames and to different ways we identify the penumbral grains." Our time interval (44.5 s) is about eight times shorter than Muller's (1973a, 6 minutes). It is clear that with lower temporal resolution the mean lifetime increases, because short-lived objects do not appear in the statistics and false coincidences of independent objects are more probable. Our time series is also 50 % longer than Muller's, and this, in combination with our smaller time intervals, means that our statistics are significantly better than Muller's. Concerning the identification and tracking methods, we also suggest that the human eye-brain system, compared to the computer, is more likely to look for long-lived objects.
One unsolved mystery which should be pursued with other data sets is the comet-like shape of many PGs. Muller (1973a,b) says their "heads" point toward the umbra. We agree that INW PGs show this behavior. But why, then, do not the heads of OUT PGs point toward the photosphere? We find that the shapes of OUT PGs are less regular than those of INW - sometimes the heads point toward the photosphere, sometimes toward the umbra, sometimes there are no tails, and sometimes no heads.
Finally, what is a penumbral grain? Since it is bright, it must represent localized heating within a penumbral filament. Since we see PGs "move", do these moving brightenings indicate mass motion of hot material or are they only phase velocities of brightness fluctuations? Perhaps these bright features are the loci of the intersections with the photosphere of hot, rising, flux tubes as suggested by Schlichenmaier et al. (1998a,b). Except for a brief acceleration at the beginning of a PG's life, their model predicts inward phase motions that decelerate in time. Only 25 % of PGs observed by us move in this particular way. We hope that the numerical simulations can be refined to account for the interaction of several flux tubes, for repeated travelling of individual PGs along "preferred" trajectories (as shown by the persistent filamentary pattern in time-averaged images), and to explain both the inward and outward observed motions.
© European Southern Observatory (ESO) 1999
Online publication: July 26, 1999