Astron. Astrophys. 347, 212-224 (1999)

6. Summary and conclusions

Vogt (1988) presented the first Doppler image of HD199178 from observations in 1985 and found a big cool polar cap and one, also rather cool, equatorial spot. Our maps show basically the same morphology but with several "equatorial" spots at a given time. In the following we will discuss the spot lifetimes and the involved variability time scales on HD 199178 in more detail.

6.1. The low-latitude spots

The maps in Fig. 3 and 4 indicate a generally weak, but persistent, spot coverage at low latitudes. Only the 1990 map revealed a low-latitude spot with a temperature comparable to that of the polar spot. The lifetime of these features is possibly so short that we cannot follow their evolution and unambiguously distinguish between them based on our mostly annual maps. The average latitude of 30^o remained the same throughout the baseline of our observations from 1988 through 1997. Unfortunately, Doppler imaging is not capable of reliably reconstructing features that appear "below" the stellar equator at negative latitudes; such features will always be weakly mirrored to higher latitudes. The weaker "northern"-latitude spots may well be artifacts of such mirroring.

Tables 4 and 5 identify the positions ( = longitude, b = latitude) and the minimum temperatures, i.e. the temperature in the central region of a feature. Note that the temperatures and longitudes and latitudes just refer to an estimated spot center and were based on our Ca I Doppler maps. The positional precision is likely no better than ^o, while the minimum temperatures () are only good to within, say, 50 K.

When we compare our two maps from 1989, just about one month apart, we see that some rearranging of emerging flux at both the polar and the equatorial regions took place. The cross-correlation image in Fig. 5 shows peaks for almost the full range of phase shifts. The individual spots can obviously change fairly rapidly, e.g., the most significant spot (spot C) in April 1989 was not seen anymore in May-June 1989, while other features migrated in longitude and/or latitude (spots A and E), or remained more or less identical (spots B and F), or significantly increased in contrast (spot D). Although we have to live with the uncertainty of the spot identification from map to map, it seems clear that the short end of the variability time scale is of the order of one month or even less. This is in agreement with time-series Doppler imaging of other stars, e.g., for EI Eri (Strassmeier et al. 1991, Hatzes & Vogt 1992, Washüttl et al. 1999), or AB Dor (Collier-Cameron & Unruh 1994, Donati & Collier-Cameron 1997).

Fig. 5. Cross-correlation images. The temperature variation along each 5o latitude bin is cross correlated in the two consecutive maps in 1989 (left panel ), and 1989b and 1990 (right panel ). The grey scale indicates the correlation coefficient (from 0 to 1) in the sense that the better the correlation the darker the grey scale. The horizontal axis is the relative phase shifts. Correlations above latitudes of 60o and below -20o are only very poorly determined.

6.2. The polar spot and its appendages

There is striking evidence for the existence of a polar feature in all our maps in agreement with Vogt's (1988) map from 1985. Nevertheless, we tried several "dirty tricks" to remove the polar cap during our line-profile reconstructions but without much success (see also, e.g., Hatzes et al. 1996). First, we applied various shifts to the continua of all line profiles within a data set to mimic deeper and shallower lines, respectively. Second, the same shifts were applied but with different (integrated) values for the chemical surface abundances as well as microturbulence and macroturbulence velocities. Third, we recomputed local line profiles from a grid of lower and higher model atmospheres () in combination with various values for microturbulence (between 0 and 2.5 km s^-1) as well as relative and absolute photometry. Some of these combinations indeed resulted in a weakening of the polar feature, especially when we neglect microturbulence or adopt too high a , but none would remove it. We emphasize that blending does not affect our line profile models and therefore cannot account for the existence of the polar feature.

As an additional test, we phased all our line profiles with other photometric periods. None of the periods cited in Sect. 4.3, nor the ones actually adopted (Eqs. 1-4), would remove the polar spot, or produce maps with convincing evidence for the existence of prefered longitudes. This excludes Jetsu et al.'s (1990a) simple model for HD 199178 where starspots form only around two main active longitudes separated by approximately 180^o. Just recently, Jetsu et al. (1999a) arrived at the same conclusion from an updated time-series analysis of 20 years of photometry.

Given that the polar spot and its variations are real, we may conclude that its lifetime is at least as long as the time of our observations, i.e. almost nine years. However, it is most likely that we observed the same polar spot that was already seen by Vogt (1988) in 1985. Its overall lifetime would then be at least 12 years. On the contrary, one low-latitude spot seems to have vanished, or at least significantly changed, on a time scale of the order of less than one month.

From a theoretical point of view, a persistent large-scale morphology would be expected because it is predominantly the stellar rotation rate, the field strength in the overshoot layer, and the structure of the convection zone that determine the latitude of emerging magnetic flux (e.g. Schüssler et al. 1996), and these parameters remain stable for a long period of time. From an observational point of view, it is somewhat unexpected though because sudden phase shifts of light-curve minima, as observed for HD 199178 in late 1990 (Jetsu et al. 1999a), are usually explained by the extinction of a particular spot cycle and the begin of a new cycle with new spots at some other longitude (e.g. Berdyugina & Tuominen 1998, Oláh et al. 1997, Henry et al. 1995). This is not what we generally observe on HD 199178. Instead, we see a mixture of the growth and decay of individual features with simultaneous, likely random, redistribution of others; at time scales that are possibly longer for the polar regions. Our inadequate time resolution of basically one map per year does not permit to follow the evolution of individual features, not even at the pole. However, we strongly suspect that determining an individual starspot's lifetime by simply identifying the beginning and the ending of a consistent light-curve pattern, usually representing just a constant migration rate, will grossly overestimate spot lifetimes by up to a factor of 2-5 and possibly even more depending on the rotation rate of the star.

6.3. Evidence for differential surface rotation?

Fig. 5 shows the cross-correlation images for the maps from 1989a and 1989b, and 1989b and 1990. Identifying the highest correlation coefficients, we find mostly more than one significant peak per latitude bin. This ambiguity suggests that the spot distribution changed within our maps. We fitted Gaussians to the most significant peaks of the cross-correlation functions of each latitude bin but found no conclusive evidence for the existence of a consistent migration pattern; neither from our annual Doppler images, nor from the two 1989 maps only one month apart. This is surprising because differential surface rotation is commonly used to explain the observed photometric period variations of spotted stars (Hall 1972, 1996). However, we believe that our non detection does not necessarily mean that there is no differential surface rotation on HD 199178 but merely that its spot distribution is rather dominated by short-term surface field reconnections that mask the differential-rotation signature. A similar result was obtained for the single G8III-II giant HD 51066 (Strassmeier et al. 1998), while consecutive Doppler images of the young K2V-star AB Dor (Donati & Collier Cameron 1997), the K0III giant IL Hya (Weber & Strassmeier 1998) and the T Tauri star V410 Tau (Rice & Strassmeier 1996) gave positive results, indicating solar-like differential rotation. Cases where the polar regions rotate faster than the equatorial zones, i.e. opposite to the solar case, were also found: for V711 Tau (Vogt et al. 1999), UX Ari (Vogt & Hatzes 1991) and HU Vir (Strassmeier 1994, Hatzes 1998); and also from time-series analysis of the Mt. Wilson Ca II H&K data of Com (Donahue & Baliunas 1992). At the moment, Doppler imaging provides no conclusive evidence for differential surface rotation on HD 199178.

© European Southern Observatory (ESO) 1999

Online publication: June 18, 1999
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