5. Summary and conclusions
We present a time-series of Doppler images of the RS CVn binary V711 Tau from a 57-day observing interval in late 1996. From these data, we obtained a phase-dependent time resolution on the stellar surface of between a few hours and 10 days. This allows to follow the rapid evolution of individual surface features.
The first important result is that low to intermediate-latitude spots indeed migrate toward the pole as claimed earlier by Vogt & Hatzes (1996) and Vogt et al. (1999). Although this seems to be a general trend for all spots on the surface, it can be sometimes completely masked by local spot rearrangements, mostly the merging of already existing spots or the emerging of a new spot at approximately the same location. A redistribution of magnetic flux from crosstalk between individual spots seems to be a plausible explanation for the short-term morphological evolution of a particular feature.
Vogt et al. (1999) explained the poleward migration with a non-solar differential rotation law, i.e. where the polar regions rotate faster than the equatorial regions. However, our results are only partially consistent with that differential-rotation interpretation because at least one of our spots (spot E , but possibly also D ; see Fig. 9) migrated in a counter-clockwise direction while a (symmetric) differential rotation pattern should make all spots at a given latitude migrate in the same longitudinal direction. A poleward directed meridional flow is an alternative interpretation but would predict a constant latitudinal migration rate for spots at all longitudes which, again, is not observed (see again Fig. 9b and Table 6). Possibly, both mechanisms change their behavior at latitudes near the stellar rotation pole so that an extrapolation above, say, 60o may not be applicable. Most likely, however, is a combination of all of these mechanisms - crosstalk between magnetic features, differential rotation, and meridional flows (and who knows what else) - which cause the complex (short-term) spot migrations on V711 Tau. We caution that our total time coverage is not sufficient to conclusively decide upon the true mechanism and we emphasize that very high time resolution observations over a long interval are needed to unambiguously determine the differential rotation.
The second result is that an individual spot may change its temperature and size on a relatively short time scale. Possibly even much shorter than the time resolution of an average Doppler image. This verifies the earlier findings of Vogt et al. (1999). In case of spot B , we saw a cooling of 300 K within less than 3 days, or one stellar rotation, shortly before it merged with the larger and already cooler feature A . Is the (magnetic) energy transport by Alfvén waves efficient enough to observe such fast cooling rates? If we adopt a field strength of 300 G from the Zeeman-Doppler maps of Donati (1999), and an average electron density for V711 Tau of cm-3, i.e. the value for the deep solar photosphere at according to the models of Vernazza et al. (1976), we get an Alfvén velocity of 210 km s-1 (this value increases by a factor of 100 if we adopt the electron density predicted for the upper photosphere at a height of 800 km). At 210 km s-1 it takes a wave approximately one day to cross spot B and is thus at least of correct order.
If this was a regular spot behavior, it would render all Doppler images from data taken more than 2-3 rotations apart (5-8 days) just an average of the actual spot distribution. Although these average maps still contain very useful information as demonstrated in the paper by Vogt et al. (1999), care must be taken not to overinterpret their time-dependent behavior. We note that some of the 23 Doppler images presented by Vogt et al. (1999) were obtained from data taken over a time range of up to two months.
From both main results in this paper - the poleward migration and the rapid cooling and redistribution of individual spots - we may speculate that magnetic reconnection between individual spots plays a significant role in a spot's life. Reconnection may initiate a field diffusion from the stronger field areas (i.e. presumably the cooler spots) to the weaker field areas (i.e. the less cool spots) and, as a consequence, increase the supression of the convective motion in the warmer spots and thus lower the energy flow from inside the star and effectively cool the spot. This would not necessarily imply that the two spotted areas are of opposite polarity but that they are at least of mixed polarity. A flux element from within a spot would disperse in a random way according to a diffusion equation with a diffusion constant given by (Leighton 1969), where L is a characteristic length and a characteristic time scale. In case of the increasing separation of spots D and E from map 17 to 18, the distance between the rims of the two spots suggests L is approximately 450,000 km (assuming a stellar radius of 3.7 ; Donati 1999), and approximately 3 days (2.6105 sec). The diffusion constant would thus be km2 s-1, compared to 300 km2 s-1 from the motion of network elements on the Sun (Zirin 1985). Even if we allow for higher diffusion rates due to larger field gradients and the larger photospheric volume for V711 Tau compared to the Sun, it is more likely that the rapid spot changes on V711 Tau are governed by violent magnetic-field reconnections rather than by simple diffusion. There are numerous small-scale examples on the Sun where a type of "siphon" flow between magnetic regions of opposite polarity is an efficient way to transport flux from a spot to the surrounding photosphere and thereby cause a small spot's relatively short lifetime (e.g. Schmidt 1991, Thomas & Montesinos 1997). Such interactions between individual magnetic regions will likely cause a very complicated and time-variable surface field geometry that may even include azimuthal fields at photospheric levels despite that the current picture of emerging flux tubes on the Sun suggests predominantly radial photospheric fields.
© European Southern Observatory (ESO) 2000
Online publication: February 9, 2000