COMMISSION 27 OF THE I. A. U. INFORMATION BULLETIN ON VARIABLE STARS Number 3564 Konkoly Observatory Budapest 15 February 1991 HU ISSN 0374 - 0676 Light Curves for AB Doradus AB Doradus (HD 36705) is a bright (V ~7.0 ), rapidly rotating (0.51d), chromospherically active single star possessing a highly variable light curve (see Innis et al., 1988). Only some of the Pleiades K dwarfs (Van Leeuwen and Alphenaar, 1982) rotate faster, and indeed the star's kinematical data and strong Lithium line (Rucinski, 1982) suggest that this is no coincidence with AB Doradus quite likely to be a member of the Local Association under going a late stage of Pre-Main Sequence contraction. It is widely accepted that the star's variability is due to large "star spots" which evolve rapidly, altering both the shape and amplitude of the light curve. Such a situation could be expected in such a rapidly rotating cool star, if the underlying magnetic field generation is essentially dynamo in nature (Weiss et al., 1984). Recently several light curves for AB Doradus have been analysed using a Chi2 minimisation Fortran program (see Banks and Budding, 1990, and Banks et al., 1991, for details of the methodology) which demonstrated that two dark circular regions could adequately account for the differential light curve. A general background of maculation effects distributed uniformly in longitude was assumed to explain the variation in AB Dor's "immaculate" (unspotted) magnitude - which has progressively dimmed since the stars discovery in 1979 (Pakull, 1981). A range of inclinations was trialed by these two studies, in the hope that a better fit to the data would be obtained at one value, which might be near to AB Dor's real inclination. It was tentatively concluded that a low inclination around 65 deg might be preferred. This bulletin details a small continuation of these previous spot modelling efforts, analysing the February 1987 UBVRI light curves obtained by Cutispoto (1990) using the 50 cm ESO Cassegrain telescope. Each waveband was modelled assuming two dark (i.e. 0 Kelvin) spots, Al-Naimiy's (1978) limb darkening coefficient appropriate for each passband, and a photospheric temperature of 5250 Kelvin (Allen, 1973) corresponding to Rucinski's (1985) spectral classification. The S/N ratio was arbitrarily assumed to be 100:1. Checking for indeterminacy using the Hessian matrix (see Budding and Najim, 1980) is an important part of our approach, preventing excessive over-parameterisation of the data (see also Banks and Budding, 1990a). Most of the fits (bar three) were determinate, indicating that the information content of the data was not being blatantly exceeded. A range of inclinations were trialed (90 deg, 80 deg, 70 deg, 60 deg, 50 deg) for each waveband, and their Chi2 values examined (see Table 1 ). Table 2 gives the "best fit" model parameters. Parameters for the larger, second spot are more consistent between the wave bands, as could be expected as its greater photometric effect defines the values better Observational noise in the few data points defining the first spot's effect has a considerable effect on its derived parameters (see Figures 1 and 2) - particularly as the spot's effect overlaps considerably with the other spot's. Innis et al. (1988) asserted that while two spot groups were apparent on AB Dor during the period 1979 to 1987, they remained ~180 deg apart in longitude, suggesting that the star might be an oblique-dipole rotator (see Stibbs, 1950). However the derived spots for February 1987 are closer to 120 degrees apart, as were those for January 1990 (Banks et al., 1991). Further quantitative modelling of other light curves is required to resolve this issue. Budding and Zeilik (1987) noted that starspots appear to be located at relatively high latitudes, and that this is a feature of chromospherically active, short period stars. Support is lent to this conclusion. However the rather tentative suggestion that a low inclination might be preferred by AB Dor is not clearly supported by this study. Table 1: The values of Chi2 are plotted for each waveband and inclination trialed. Gaps are left hen indeterminacy resulted. The actual numbers depend on the arbitrarily chosen observational error of 1%. An asterisk mark the best fit for each band. Inclination U Band B band V band R band I Band 90 deg 16.3 3.24 5.06 1.74* 4.01 80 deg 15.3 2.86 5.38 1.85 3.63* 70 deg 13.7 3.02 5.07 1.87 4.21 60 deg 13.6* 2.57* 4.79* ---- ---- 50 deg 13.7 --- 5.07 2.75 6.74 Table 2: The parameters for the best model fits from table 1 are given. All units are degrees. The number refers to the spot, i.e longitude 1 for the first spot's longitude. Passband longitude 1 latitude 1 radius 1 longitude 2 latitude 2 radius 2 U 69.2+-46.2 84.4+-0.6 30.2+-0.3 315.8+-16.5 55.6+-22.7 12.1+-7.2 B 82.8+-36.7 85.3+-2.6 30.1+-1.2 309.4+-30.1 44.8+-36.9 11.9+-2.5 V 88.9+-28.0 35.3+-4.3 17.8+-0.2 327.3+-1.3 46.2+-2.4 11.5+-0.2 R 38.0+-28.8 87.3+-3.0 30.1+-1.3 305.0+-14.0 62.9+-11.6 15.5+-1.8 I 34.5+-14.2 67.8+-5.0 15.9+-1.0 311.0+-22.2 58.7+-25.2 17.0+-3.5 The spot temperature method outlined by Zeilik et al. (1989), based on the assumption that both the surrounding photosphere and the spot radiate as black bodies, was used on the R and I band data with the best V band model as the reference. Spot temperatures of 3860 +- 470 (I) and 3980 +- 40 (R) Kelvin were reached, in reasonable agreement with the values of 3840 +- 150 (I) and 3710 +- 230 (R) Kelvin that Banks and Budding (1990) derived for Lloyd Evans' (1987) 1984 data using the same method. [FIGURE 1] Figure 1: The inclination 60deg V band model fit (smooth line) is plotted against the data (rings). [FIGURE 2] Figure 2: The inclination 80deg I band model is plotted against that waveband's data. It is hoped that this small contribution will be of use to the many other investigators studying AB Dor. It is unfortunate that the only published light curves close in time to this one are the January 1987 and Sept/Nov 1986 curves of Innis et al. (1988), followed by December 1988 (Thompson and Thompson, 1989) and Anders' (1990) November 1989 data. Thus only general trends in AB Dor's spot evolution will be identifiable over this period, although modelling should still be worthwhile, particularly of the December 1988 data which is of high quality and complete phase coverage. However incomplete phase coverage and the low number of observational points inhibited the analysis of the Feb 1987 light curves, allowing observational errors to become overly influential. Many literature light curves also (see Innis et al., 1988) exhibit these problems. To increase their information potential, future observations need to avoid these. Indeed, further observations are crucial, as AB Dor is a highly active star, and rightly deserves intensive scrutiny in the hope that a definitive spot evolution sequence can be obtained. Timothy Banks Physics Department Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand; and Carter Observatory, P.O. Box 2909, Wgtn, N.Z. References : Allen, C.W., Astrophysical Quantities, Third Edition University of London Press, London, 1973. [BIBCODE 1973asqu.book.....A ] Al-Naimiy, H., 1978, Astrophys. Spa. Sci., 53, 181,1978. [BIBCODE 1978Ap&SS..53..181A ] Anders G., IBVS #3437, 1990. [IBVS 3437] Banks, T., and Budding, E., Astrophys. Spa. Sci., 167, 221, 1990. [BIBCODE 1990Ap&SS.167..221B ] Banks, T., and Budding, E., Earth, Moon, and Planets 49, 15, 1990a. 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[BIBCODE 1950MNRAS.110..395S ] Thompson, K., and Thompson I., IBVS 3320, 1989. Van Leuuwen, F., and Alphenaar, P., in Activity in Red Dwarfs, Eds: M. Rodono and P.D. Byrne, IAU Colloq 71, 379, 1982. [BIBCODE 1983ASSL..102..189V ] Weiss, N.O., Cattaneo, F., and Jones, C.A., Geophys. Astrophys. Fluid Dynamics, 30, 305, 1984. [BIBCODE 1984GApFD..30..305W ] Zeilik, M., Cox, D.A., De Blasi, C., Rhodes, M., and Budding, E., Astrophys. J., 345, 991, 1989. [BIBCODE 1989ApJ...345..991Z ]