6 Discussion and summary

We detected a complex surface differential-rotation law for KU Peg with acceleration along the equator and possibly also near a latitude of $\approx$50$^\circ$, and deceleration in between and above. KU Peg's lap time $1/\Delta\Omega$ is $\approx$70 days for the $\pm$25$^\circ$ range around the equator, but 260 days for the entire equator-to-pole range. This differs from the solar case and from the findings of Collier Cameron et al. (2001) for the three ultra-fast rotators RXJ1508-4423 (G2), ABDor (K0/2V), and PZTel (K0IV/V) with rotation periods of 0.31, 0.515, and 0.94 days, respectively, in that these stars show a uniform differential rotation that follows a simple solar-like $\sin^2 b$ law. Their lap times $1/\Delta\Omega$ are 40, 110, and 80 days, respectively, which are all shorter than the solar value of 120 days. LO Peg (K5-7V, $P_{\rm rot}=0.424$ days) on the other hand, does show signs for the equator lagging behind (Lister et al. 1999). These authors argue though that the absence of mid-latitude features together with the short time between the two images (one day) possibly prevents the detection of significant differential rotation. Rice & Strassmeier (1996) detected differential rotation on the weak-lined TTauri star V410Tau ( $P_{\rm rot}=1.87$ days) in the same sense as on the Sun but with a laptime of 1800 days, a factor of 15 weaker, which is significantly different from the stars above. Either each star with a given mass, rotation period, and evolutionary status has its own distinct differential surface rotation, as e.g. indicated by the theoretical models from Kitchatinov & Rüdiger (1999), or the observations are masked by local and rapid magnetic-field reconfigurations that just mimic a differential rotation law.

Differential rotation was reported for several other evolved stars: Weber & Strassmeier (1998) found equatorial acceleration on the RSCVn binary ILHya for latitudes below 45$^\circ$ and about a factor of 30 smaller than on the Sun, as measured from two images taken $\approx$28 stellar rotations apart. Strassmeier (1994) and Hatzes (1998) derived a differential-rotation law for HUVir (also a RSCVn star) from the comparison of two temperature maps taken 2 stellar rotations and 4 years apart, respectively, and combined with contemporaneous photometric modeling included in Strassmeier (1994). Both authors found differential rotation of inverse behavior than on the Sun - polar regions rotate faster than low-latitude regions - and a factor of 10 slower. However, the spot features used in both studies were all at $b \geq 30\hbox{$^\circ$ }$ and thus no reliable information for the equatorial region was available. Hatzes & Vogt (1992) found solar-like differential rotation on the short-period (1.95 days) RSCVn binary EIEri, i.e. equatorial acceleration and similarity in strength, but an inverse behavior, and about a factor of 10 smaller than on the Sun, on the 6.4-days RSCVn binary UXAri (Vogt & Hatzes 1991).

So far, there is cumulative evidence that differential rotation profiles on evolved stars (and possibly also on pre-main-sequence stars) appear to be more complicated than on solar-type main-sequence or ZAMS stars. A recent study of the RSCVn binary HR1099 by Strassmeier & Bartus (2000) reveals a general poleward spot migration of the order of 0.4$^\circ$day^-1simultaneously to longitudinal spot migrations with both signs at the same time, i.e. spots migrating faster and slower than the orbital period but are located at approximately the same latitude. This is in agreement with an earlier claim by Vogt et al. (1999) based on 23 Doppler images taken throughout 11 years. KU Peg also shows evidence, like HR1099, for poleward spot migration and even of the same amount. There is also some similarity of our KU Peg result to the recently obtained rotation profile for the rapidly-rotating long-period K0III binary $\sigma$ Gem ( $P_{\rm rot}\approx20$ days, Kövári et al. 2001). For $\sigma$ Gem, they found a differential rotation law in quadratic form with acceleration in two latitudinal bands centered at approximately $\pm$40$^\circ$ around the equator, but deceleration along the equator and near the one visible pole. We believe that all of these observations hint toward a general dependence of differential rotation upon rotational period. Giants seem to show a mixture of solar-like and anti-solar profiles of various strengths, which seems to be partially in conflict with the recent differential-rotation models of Kitchatinov & Rüdiger (1999) who predict larger differential rotation in giants than in dwarfs. It is also indicative that differential rotation is not the only way to explain spot migrations and that the associated meridional flow may play a stronger role on giants than, e.g., for the Sun.

The Sun, for comparison, has a very weak latitudinal flow pattern of $\pm$0.03$^\circ$ day^-1 (Howard & Gilman 1986). This flow transports magnetic flux from mid-latitude spots up to the rotation poles where its opposite polarity causes the polarity reversal and the end of an old magnetic cycle and the start of a new one. So far, stellar observations of a poleward flow exist only for stars with high-latitude active regions but are in agreement with the picture first presented by Schüssler & Solanki (1992). In that picture, the flux tubes can arise at latitudes up to $\approx$60$^\circ$ if the star rotates rapidly enough. However, an additional transportation mechanism is necessary to move the spot towards the pole once it has emerged. This is different from the very young stars, where a truly polar spot can emerge without the additional need of a meridional flow (see Granzer et al. 2000 for a recent discussion).

For some of the previously discussed stars, the time between the individual maps was usually many rotations, and thus spot changes with timescales less than a few rotations could not be determined. Only spots close to the poles seem to be persistent enough to be seen throughout many rotations and this may bias our meridional-flow detections. However, if some mechanism does transport active regions towards the pole, where they make up for a large torodial field that, in return, inhibits differential rotation, then the difficulty of detecting differential rotation on such stars is not a surprise. One such star is the 16-day G8II-III giant CMCam (Strassmeier et al. 1998), where cross correlations of Doppler images from four observing seasons with one year in between did not reveal a clear differential-rotation signal, despite that there is evidence for phase shifts on its surface. A very similar case is the single G5 giant HD199178 (Strassmeier et al. 1999b), where images taken one month and images taken one year apart were cross-correlated but no systematic migration pattern was found. Whether the time the magnetic field needs to reconfigure on these stars is too short to be detected or, whether an existing differential rotation pattern is simply masked by short-term field configuration changes, could not be answered in those two cases.

Acknowledgements

Thanks to Trudy Tilleman for operating the McMath telescope half of the time and for providing gourmet coffee all of the time, to the Austrian Fond zur Förderung der wissenschaftlichen Forschung (FWF) for support under grants S7301-AST and S7302-AST, and to the German Forschungsgemeinschaft (DFG) for grant HU 532/8. We thank the referee, Dr. J. R. De Medeiros, for his constructive criticism.