Doin' the twist: secular changes in the surface differential rotation on AB Doradus

We present measurements of the rotation rates of individual starspots on the rapidly rotating young K0 dwarf AB Doradus, at six epochs between 1988 December and 1996 December. The equatorial rotation period of the star decreased from 0.5137 to 0.5129 d between 1988 December and 1992 January. It then increased steadily, attaining a value of 0.5133 d by 1996 December. The latitude dependence of the rotation rate mirrored the changes in the equatorial rotation rate. The beat period between the equatorial and polar rotation periods dropped from 140 to 70 d initially, then rose steadily. The most rigid rotation, in 1988 December, occurred when the starspot coverage was at a maximum. The time-dependent part of the differential rotation is found to have     , which should alter the oblateness of the star enough to explain the period changes observed in several close binaries via the Applegate mechanism.     

Modelling surface magnetic field evolution on AB Doradûs due to diffusion and surface differential rotation

From Zeeman–Doppler images of the young, rapidly-rotating K0 dwarf AB Doradûs, we have created a potential approximation to the observed radial magnetic field and have evolved it over 30 d subject to the observed surface differential rotation , meridional flow and various diffusion rates. Assuming that the dark polar cap seen in Doppler images of this star is caused by the presence of a unipolar field, we have shown that the observed differential rotation will shear this field to produce the observed high-latitude band of unidirectional azimuthal field. By cross-correlating the evolved fields with the initial field each day we have followed the decay with time of the cross-correlation function. Over 30 d it decays by only 10 per cent. This contrasts with the results of Barnes et al. , who show that on this time-scale the spot distribution of He699 is uncorrelated. We propose that this is due to the effects of flux emergence changing the spot distributions.     

The global magnetic topology of AB Doradus

We have used Zeeman–Doppler maps of the surface field of the young, rapid rotator AB Dor  ( P _rot=0.514 d)  to extrapolate the coronal field, assuming it to be potential. We find that the topology of the large-scale field is very similar in all three years for which we have images. The corona divides cleanly into regions of open and closed field. The open field originates in two mid-latitude regions of opposite polarity separated by about 180° of longitude. The closed field region forms a torus extending almost over each pole, with an axis that runs through these two longitudes. We have investigated the effect on the global topology of different forms of flux in the unobservable hemisphere and in the dark polar spot where the Zeeman signal is suppressed. The flux distribution in the unobservable hemisphere affects only the low-latitude topology, whereas the imposition of a unidirectional polar field forces the polar cap to be open. This contradicts observations that suggest that the closed field corona extends to high latitudes and leads us to propose that the polar cap may be composed of multipolar regions.     

Stellar differential rotation from direct star-spot tracking

On the Sun, the rotation periods of individual sunspots not only trace the latitude-dependence of the surface rotation rate, but also provide clues as to the amount of subsurface fluid shear. In this paper we present the first measurements of stellar differential rotation made by tracking the rotation of individual star-spots with sizes comparable to the largest sunspots. To achieve this we re-analyse four sequences of densely sampled, high signal-to-noise ratio echelle spectra of AB Doradus spanning several stellar rotations in 1996 December. Using spectral subtraction, least-squares deconvolution and matched-filter analysis, we demonstrate that it is possible to measure directly the velocity amplitudes and rotation periods of large numbers of individual star-spots at low to intermediate latitude. We derive values for the equatorial rotation rate and the magnitude of the surface differential rotation, both of which are in excellent agreement with those obtained by Donati & Collier Cameron from cross-correlation of Doppler images derived a year earlier in 1995 December, and with a re-analysis of the 1996 data by the χ ² landscape method. The differences between the rotation rates of individual spots and the fitted differential rotation law are substantially greater than the observational errors. The smaller spots show a greater scatter about the mean relation than the larger ones, which suggests that buffeting by turbulent supergranular flows could be responsible.     

Multisite observations of surface structures on AB Doradus in 1994 November

We present time-resolved optical spectroscopy and broad-band photometry of the rapidly rotating southern K0 dwarf star AB Doradus, obtained during 1994 November. The data were obtained as part of a collaboration dedicated to MUlti-SIte COntinuous Spectroscopy (MUSICOS), and entailed coordinated observations on three continents to obtain the fullest phase coverage possible subject to limitations of local weather conditions. The Doppler images from the three consecutive nights of the run show excellent mutual agreement, with a dark polar cap and numerous intermediate- and low-latitude features. Simultaneous optical photometry showed numerous short-duration U -band flares, and two longer duration optical flares with durations of the order of hours. The latter produced broad-band continuum enhancements throughout the optical spectrum. Where simultaneous spectroscopy was available, both types of flare were seen to have counterparts in H and the Ca  ii H line. Simultaneous time-resolved ultraviolet spectroscopy from the Goddard High Resolution Spectrograph (GHRS) aboard the Hubble Space Telescope , reported elsewhere, shows that at least one of the short-duration U -band flares was also observed in C  iv with the GHRS. Time-series H spectra showed significant evolution of the circumstellar prominence system over five consecutive stellar rotations. One prominence underwent a dramatic increase in distance from the stellar rotation axis. We speculate that this event may have been associated with one of the long-duration flares.     

Modelling the time variation of the surface differential rotation in AB Doradus and LQ Hydrae

Sequences of Doppler images of the young, rapidly rotating late-type stars AB Dor and LQ Hya show that their equatorial angular velocity and the amplitude of their surface differential rotation vary versus time. Such variations can be modelled to obtain information on the intensity of the azimuthal magnetic stresses within stellar convection zones. We introduce a simple model in the framework of the mean-field theory and discuss briefly the results of its application to those solar-like stars. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the time dependence of differential rotation in young late-type stars

A model for the angular momentum transfer within the convection zone of a rapidly rotating star is introduced and applied to the analysis of recent observations of temporal fluctuations of the differential rotation on the young late-type stars AB Doradus (AB Dor) and LQ Hydrae (LQ Hya). Under the hypothesis that the mean magnetic field produced by the stellar dynamo rules the angular momentum exchanges and that the angular velocity depends only on the distance s from the rotation axis and the time, the minimum azimuthal Maxwell stress  | B_sB _φ|  , averaged over the convection zone, is found to range from ∼0.04 to  ∼0.14 T²  . If the poloidal mean magnetic field   B _s   is of the order of 0.01 T, as indicated by the Zeeman–Doppler imaging maps of those stars, then the azimuthal mean field   B _φ  can reach an intensity of several teslas, which significantly exceeds equipartition with the turbulent kinetic energy. Such strong fields can account also for the orbital period modulation observed in cataclysmic variables and RS Canum Venaticorum systems with a main-sequence secondary component. Moreover, the model allows us to compute the kinetic energy dissipation rate during the maintenance of the differential rotation. Only in the case of the largest surface shear observed on LQ Hya may the dissipated power exceed the stellar luminosity, but the lack of a sufficient statistic on the occurrence of such episodes of large shear does not allow us to estimate their impact on the energy budget of the convection zone.     

Recent observations of AB Dor and interpretation

We use minimal empirical modelling techniques to interpret recent (2006–2007) photometry and spectroscopy of AB Dor. We compare, in particular, broadband (B and V) maculation effects with emission features in high‐resolution Ca II K‐line spectroscopy. We also compare emission effects in the Ca II Kand Hα lines observed at different rotational phases. We refer to a broader multiwavelength campaign, of which these optical data were a part, involving X‐ray and microwave observations to be published later. The broadband light curves are characterized by one outstanding macula, whereas the emission lines suggest 4 possible main chromospheric activity sites (‘faculae’). These appear at a similar latitude and with comparable size to the main umbra, but there are significant displacements in longitude. However, one strong facular concentration near phase zero may have a physical relationship to the main macula. The derived longitudes of these features would have been affected by differential rotation operating over the several months between the spectroscopic and photometric observations, but the difference of at least ∼30° between facula and umbra appears too great to allow their coincidence. The possibility of a large bipolar surface structure is considered, keeping in mind the bipolar character of solar activity centres: the activity of rapidly rotating cool stars being generally compared with that of the Sun, scaled up by a few orders of magnitude. Observed microwave activity may link to this same main photospheric and chromospheric centre picked up by the optical analysis. Characterization of macular and facular contributions in stellar activity sites would be improved with a closer timing of observations and higher signal to noise ratios in emission line data (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral line profile variations in the γ Doradus variable HD 164615: non-radial pulsations versus star-spots

High-resolution spectral data of the Fe  II 5318 Å line in the γ Doradus star HD 164615 are presented. These show systematic changes in the spectral lineshapes with the photometric period of 0.8133 d which are modelled using either non-radial pulsations or cool star-spots. The non-radial modes that can fit the lineshape changes have m degree of 2–4. However, only the m = 2 mode seems to be consistent with the amplitude of the radial velocity variations measured for this star. The star-spot model, although it can qualitatively fit the lineshape changes, is excluded as a possible hypothesis on the basis of (1) poorer fits to the observed spectral line profiles, (2) an inability to account for the large changes in the spectral linewidth as a function of phase, (3) a predicted radial velocity curve that looks qualitatively different from the observed one, and (4) a predicted photometric curve that is a factor of 5 larger than the observed light curve (and with the wrong qualitative shape). Finally, a 'Doppler image' (assuming cool spots) derived from a sequence of synthetic line profiles having non-radial pulsations results in an image that is almost identical to the Doppler image derived for HD 164615. These results provide strong evidence that non-radial pulsations are indeed the explanation for the variability of HD 164615 as well as the other γ Dor variables.     

LO Peg in 1998: star-spot patterns and differential rotation

We present Doppler images of the young K5V–K7V rapid rotator LO Peg from seven nights of continuous spectroscopy obtained in 1998 from July 04 to July 10. The images reveal the presence of a strong polar cap with appendages extending to mid-latitudes, but no star-spots are seen below 15°. We briefly discuss the distribution of spots in light of recent flux transport simulations, which are able to reproduce the observed latitude dependence. With the full time series of spectra, of which 314 are useful, many phases are observed three times over the seven nights of observations. Using star-spots as tracers of a solar-like latitudinal differential rotation in our image reconstructions, we find that the equatorial regions complete one more rotation than the polar regions every  181 ± 35 d  . LO Peg is the second coolest star for which such a measurement has been made using indirect imaging methods. The degree of latitudinal shear is less than that seen in G and early K dwarfs, suggesting a trend in which differential rotation decreases with stellar mass in (pre-)main-sequence objects.     

Differential rotation of cool active stars: the case of intermediate rotators

In this paper, we present a new method for measuring the surface differential rotation of cool stars with rotation periods of a few days, for which the sparse phase coverage achievable from single-site observations generally prevents the use of more conventional techniques. The basic idea underlying this new analysis is to obtain the surface differential rotation pattern that minimizes the information content of the reconstructed Doppler image through a simultaneous fit of all available data.
Simulations demonstrate that the performance of this new method in the case of cool stars is satisfactory for a variety of observing strategies. Differential rotation parameters can be recovered reliably as long as the total data set spans at least 4 per cent of the time for the equator to lap the pole by approximately one complete cycle. We find in particular that these results hold for potentially complex spot distributions (as long as they include a mixture of low- and high-latitude features), and for various stellar inclination angles and rotation velocities. Such measurements can be obtained from either unpolarized or polarized data sets, provided their signal-to-noise ratio is larger than approximately 500 and 5000 per 2 km s⁻¹ spectral bin, respectively.
This method should therefore be very useful for investigating differential rotation in a much larger sample of objects than what has been possible up to now, and should hence give us the opportunity of studying how differential rotation reacts to various phenomena operating in stellar convective zones, such as tidal effects or dynamo magnetic field generation.