5. Discussion and conclusions
Our observations of HD 12545 in 1997/98 caught this spotted star in its, so far, most active state. The light and color curves had a full V amplitude of 0:m 63, a V-I amplitude of 0:m 17, and B-V and U-B amplitudes of 0:m 10, respectively. At the same time, the star was at its brightest magnitude ever, 15% brighter than the previously detected high (see Fig. 1). Unexpected for a very active K0 giant, this indicates some solar analogy because the Sun also appears brighter during sunspot maximum due to an increased facular component. Dorren & Guinan (1990) observed a similar correlation for the RS CVn star HR 1099 and suggested that the long-term light variation is produced by competition between the blocking effect of the cool starspots and enhancement from white-light faculae. If true, and solar analogy applies, the U-brightness should increase with respect to the B-brightness during times when white-light faculae are visible on the stellar disk, i.e. during light-curve maximum, and the U-B index should appear bluer. Fig. 1c shows that this is indeed the case.
The observational phase of the warm spot coincides approximately with the region of the sub-stellar point, that is the part on the K giant facing the secondary star. Could the warm feature be the hot spot of the inner Lagrangian point due to ongoing mass transfer? If the inclination of 60o is approximately right (within deviations of -20o and +40o), then HD 12545 is significantly far from filling its Roche lobe and appears practically spherical; its radius of 11.4 is barely 50% of the critical radius and the secondary star is over four times less massive and almost exactly four stellar radii away from the primary. We also do not see systematic blue nor red shifts of high-excitation emission lines or of photospheric absorption lines in excess of 3-4 km s-1 that would be expected due to the mass stream between the stars. Furthermore, the observed annual variations of the light-curve maximum suggests a time-variable phenomenon while a hot spot due to mass transfer should be a relatively stable phenomenon and brighten the system continuously. We can thus safely conclude that the warm feature must be due to solar-type plage or facular activity.
Because the light-curve amplitude of HD 12545 remained around 0:m 6 in V throughout the entire observing season, we estimate that the lifetime of both the warm and the large cool surface feature is at least as long, roughly 220 days, but could be even one year (Fig. 1a). Previous light-curve modeling with the usual assumption of only cool spots is thus relatively meaningless in this case. Also, the notion that the brightest magnitude ever observed is the unspotted magnitude of the star can be severely wrong, and would produce a false areal spot coverage for HD 12545.
Our Doppler images recovered a gigantic cool starspot. With a linear extension of 1220 solar radii, it is 60 times larger than a very large sunspot group (230,000 km as observed on Sept. 4, 1998; Schleicher & Wöhl 1998) and appears 10 times larger than the projected solar disk. Its area is thereby 10,000 times the area of the largest sunspot group. It is clearly non-symmetric with respect to the rotation axis and its central longitude is approximately 180o different to the warm spot; the cool spot is located on the hemisphere facing away from the secondary star. Because the rotation of HD 12545 is synchronized to the orbital motion, we may suspect that these spot positions are persistent active longitudes. Such an activity persistency has been found for other RS CVn binaries, e.g. for II Peg (Berdyugina et al. 1998), and could be tested with further Doppler images of HD 12545. If true, it could be interpreted as being due to a magnetic field connection with the red-dwarf secondary, which itself should be fully convective and thus harbor a magnetic field as well, and thus resembling the interacting magnetospheres originally discussed by Uchida & Sakurai (1985) to explain the activity of RS CVn binaries.
HD 12545 is currently the star with the longest rotation period that has been mapped and shows no polar cap-like spot but an asymmetric spot craddling the pole. This might hint toward a relation with the long stellar rotation period of HD 12545 (or the low equatorial rotational velocity). A relation between the emerging latitudes of magnetic flux tubes and the stellar rotation period is predicted by the models originally put forward by Schüssler et al. (1996). For a single flux tube in a rotating star, the effect of the Coriolis force over the buoyancy force becomes smaller the longer the rotation period. The net force is then unable to deflect a magnetic flux tube off the radial rising path and toward the stellar rotation axis, which leads to predominantly mid-to-low latitude spots in case of a main-sequence star. However, if the convection zone is deep enough, as expected for a K0 giant, moderate rotation rates are already sufficient to deflect magnetic flux closer to the rotation poles.
There are still two puzzles with this scenario and HD 12545 left to be solved. First, the models of Schüssler et al. (1996) assume an equatorial-plane symmetry of the flux-tube generation and evolution. However, the polar spot on HD 12545 is large enough so that it could be detected if it had a similar counterpart on the invisible pole, but this is not obvious from our maps. Piskunov & Wehlau (1994) presented numerical simulations to detect such polar caps on the invisible pole. Although they concluded that it is currently not feasible to see the other cap, the polar spot on HD 12545 is not a symmetric cap and also reaches down to a latitude of +30o on the stellar surface, a configuration which was not included in the simulations of Piskunov & Wehlau (1994). We take this as evidence that there is no other polar counterpart on HD 12545 and speculate that the warm spot harbors a field of opposite polarity.
Second, both the warm and the large cool feature on HD 12545 are
thought to be concentrations of magnetic fields originating from flux
tubes that surfaced in the stellar photosphere. Their lifetimes are at
least the 220 days for which we had photometry and they thus appear to
be relatively long lived. Why then is the warm feature at the stellar
equator while the cool feature appears close to the pole? One
explanation could be that the two features were formed from fields
that originated from different dynamo modes. They could be of
different field strength and thus become unstable at different
latitudes. A similar phenomenon is predicted for pre-main-sequence
star models with a comparable ratio of radiative-core to
convective-envelope dimensions as for a K giant (Granzer et al. 1999).
In such a model, flux tubes at low latitudes may become unstable at
low field strengths, their magnetic buoyancy is then small and their
rise to the surface almost axiparallel due to the dominance of the
Coriolis force. The consequence is that the flux tubes surface in two
latitudinally distinct zones. On HD 12545, where the spots are so
large that they fill up part of a hemisphere, the "preferred zones"
are probably just the equatorial regions and the polar regions. Of
course, a completely different explanation would be that such active
regions are formed due to random effects of magnetoconvection near the
stellar photosphere. A Zeeman-Doppler image of the surface field
topology of HD 12545 could possibly resolve this issue if the star can
be reobserved in a similarly favorable state of high activity. Recent
advances in and applications of this technique by Donati (1999),
together with the advent of 8m-class telescopes, may shed new light on
the issue of stellar magnetism.
© European Southern Observatory (ESO) 1999
Online publication: June 18, 1999