1999ApJS..121..547V

We present a set of 23 Doppler images of the spotted RS CVn star HR 1099 (V711 Tauri; HD 22468) obtained from 1981 to 1992. HR 1099 shows a large, cool polar spot that has persisted for the 11 yr of this study and other low-latitude spots that come and go on relatively short (less than 1 yr) timescales and can emerge anywhere on the star. The polar spot has variable protuberances that look very similar to the time-variable vertical extensions of the Sun's polar coronal hole. The area of the polar spot and its extensions shows marginal evidence of being variable, with a period of about 3 yr and an amplitude of about 1% that is perhaps indicative of a weak cycle, but this is not yet conclusive.

Comparison of our Doppler images with previously published ``few spot'' model fits to the light curves shows that such simple spot-model solutions, while sometimes in agreement, are often misleading and nonunique, particularly when the light-curve amplitude is small. Moreover, these spot-model fits do not recover the existence of the polar spot. The Doppler images show quite good agreement among multiple images at a given epoch and between different Doppler imaging research groups using completely independent data sets and imaging software. Our (cool spots only) Doppler imaging solutions, when properly thresholded, generally well reproduce the published light curves. However, in one instance the difficulty of fitting light curves suggests that at least one hot spot was present on HR 1099 during one observing season. Variations in the mean brightness of the system at the observed 0.05 mag level seem to correlate with spot area, particularly the polar spot, indicating that the mean light level is a pretty good proxy of spot area on HR 1099. While the polar spot with variable extensions was always present, isolated spots also frequently appeared at both mid- and low latitudes. On several occasions isolated prominent spots emerged and then disappeared on or near the equator.

The ``migrating photometric wave'' on HR 1099 is due not to a simple longitudinal migration of spots on a differentially rotating star but rather to changes in the spatial distribution of a few spots (some of which move but most of which are fixed in longitude) that emerge and then disappear. So, at least for HR 1099, the phase drift of this migrating photometric wave minimum contains very little unique information about differential rotation or spot migration. While the tracking of individual features involves some uncertainty and speculation because of our limited time sampling, the tracks of two long-lived spots suggest that some spots that emerge at low or intermediate latitudes may migrate up to the pole in a clockwise spiral (slower than the orbit), then apparently merge with the polar spot. If these dark spots trace magnetic flux, we speculate that some of the magnetic flux emerging at lower latitudes migrates poleward and merges with the polar spot flux. It is not yet clear whether this flux is of the same or opposite polarity to the polar spot and thus whether these poleward-migrating, low-latitude spots reinforce or cancel the polar spot field. One of the high-latitude spots also appeared to get stretched in longitude as it approached the polar spot, and its overall track is quite reminiscent of the annulus of toroidal field found by Donati et al. encircling the polar spot of HR 1099 in 1990.9.

In general, the spots appear to be very tightly locked to the orbital frame of the system, and most disappear before they have had a chance to migrate significantly. Like solar coronal holes, they show very little evidence for shear due to differential rotation. A few selected, long-lived features gave longitudinal migration rates of 1 part in 300 to 1 part in 3600 of the rotation period, in the sense that intermediate and low latitudes rotate slightly slower than the orbital angular velocity, while the pole and highest latitudes appear to be synchronized to the orbit. The implied differential rotation is thus of opposite sign and about a factor of 56 less than for the Sun. The rotation rate versus latitude behavior can be well fitted with a variety of formulae, including the Maunder formula. One of the best fits is provided by a rotation period versus latitude that is proportional to the surface strength of a centered axisymmetric magnetic dipole field, with the pole synchronized to the orbit and lower latitudes rotating more slowly. We believe that these starspots are not measuring photospheric differential rotation. Instead, like solar coronal holes, their relatively low degree of shearing and nearly solid body rotation may be enforced by a multikilogauss, axisymmetric, nearly current-free quasi-potential global magnetic field. Our Doppler images also agree very closely with the Zeeman-Doppler imagery of Donati et al. and support their finding that regions around the edge of the polar spot and within bright spots show largely monopolar fields of at least 300-700 G strength. The large, permanent cool polar spots, the very low observable differential rotation and shearing of starspots, and the evidence of strong, essentially unipolar magnetic fields associated with them leads us to believe that HR 1099 and other rapidly rotating RS CVn stars harbor quite strong (multikilogauss) axisymmetric global magnetic dipole fields. These fields have historically been largely hidden from view by their high degree of rotational symmetry, by being concentrated in the low surface brightness dark spots, and by these stars' high degree of rotational line broadening. We propose that the starspots on HR 1099 and other rapidly rotating RS CVn stars are, by analogy with solar coronal holes, large unipolar, magnetic regions that are tightly frozen into multikilogauss, axisymmetric global dipole fields in these stars. Since the large cool polar spots, the signature of these dipoles, are not present on more slowly rotating RS CVn stars, we believe that they must be dynamo-induced fields rather than remnant fossil fields.