3. Results from photometric monitoring
3.1. The long-term light-curve variability
Fig. 1 shows all differential V-band photometry of HD 51066 since the discovery of its light variability in 1992 by Henry et al. (1995b). The average light level increased by 0:m 08 until 1996 and the rotational-modulation amplitude reached a maximum of 0:m 05 when the system appeared brightest around 1996/97. The latest data from 1997/98 show now a stagnation of the long-term brightness increase and possibly even indicate a decrease. Not plotted in Fig. 1 are the check minus comparison star magnitudes but visual inspection showed them to be of constant value to within the expected external errors. Thus, the long-term brightness variation is real and most likely the sign of a starspot cycle probably similar to the Sun's 11-year cycle. Previous long-term photometry of spotted and evolved stars (e.g. Strassmeier et al. 1997a, Olàh et al. 1997, Cutispoto 1995, Rodonó et al. 1995, Henry et al. 1995a) indicate either more or less erratic variations or (pseudo)periodicities 1 of the order of 10-20 years. However, the interpretation of such variations is severely hampered because most of the targets are components of relatively close RS CVn binaries while HD 51066 is an effectively single star. In case the long-term brightness variation in Fig. 1 turns out to be periodic and the data in season 1992 (S1) represent the overall minimum then we may expect a long-term period near 11 years.
3.2. The rotational period
Since HD 51066 is effectively a single star we have no reference clock - like the orbital period in close binaries - and thus rely on the photometric variations to determine the rotational period. Our first attempt was to find the best seasonal periods by using a Fortran program that performs a multiple frequency search through minimization of the residuals with a Fourier option (Kollath 1990). Quoted errors are estimated from the width of the frequency peak at where n is the number of data points and the number of free parameters. Table 2 lists the best results for the data sets as indicated in Fig. 1. Note that season S3 was split into two parts due to a rapid increase of the light curve amplitude within approximately 20 days; one prior to 2,449,280 (S3a) and one therafter (S3b). The cause of this amplitude increase from 0:m 02 to 0:m 053 in V is likely caused by a redistribution of starspots but the phenomenon has not repeated in our data.
Since we did not have sufficient photometry to compute a period for the 1995 observing season - a season with spectroscopic data for Doppler imaging - we decided not to use the seasonal periods for phasing but rather use the period from the combined photometry from 1992-1997. Such a period likely represents an average rotation period and is probably even better suited for intercomparison of annual Doppler images than are the seasonal periods. To take into account the long-term trend seen in Fig. 1 we first prewhitened the data with two frequencies near 0.0003 (2800 days) but different amplitudes in order to eliminate the long-term trend in the data and then searched for the best-fitting period and found 16.0530.004 days (Fig. 2). All spectroscopic and photometric data in this paper were then phased with the ephemeris
where the zero point is just an arbitrary point in time.
3.3. The short-term light and color variations
The Wolfgang-Amadeus APT photometry from 1997 October through 1998 January (Fig. 3 a) is used to search for short-term variations of the light-curve shape due to intrinsic variations of the spot distribution. The folded seasonal V magnitudes and V-I colors (Fig. 3 b) show a peak-to-peak amplitude of 0:m 0290:m 002 and 0:m 0080:m 002, respectively and both curves have their minima at around phase 0:p35 and maxima at around phase 0:p95. The high quality of the data allows the application of a geometric starspot model to infer starspot positions and temperatures and we adopt the maximum V and I magnitudes observed so far, i.e. V=6:m 935 and V-I=0:m 95 during 1996/97, as the unspotted magnitudes. Only the spot positions and sizes are treated as free parameters of the Levenberg-Marquardt method used here to minimize the for a given bandpass (see, e.g. Kvári & Bartus 1997). The spot temperature is then obtained by simultaneously fitting the V-I color curve. As can be seen in the lower panel in Fig. 3 the observed light and color curves of HD 51066 deviate significantly from a sinusoid and our spot-modelling code finds the best fit with two, cool, circular spots with K, at longitudes of and , latitudes of and , and radii of and , respectively. The combined spotted area amounts to 2.0% of the total sphere. Errors in longitude and area are within 1-2%, while errors in latitude are certainly model dependent and can amount to 10% or even more. The error of the relative temperature, 500300 K, is also comparably large, mostly due to m 008 and the, therefore, barely discernable modulation the small V-I amplitude of just 0: due to wavelength dependent limb darking. The rms residual of the fit is below 5 mmag while the rms of a single data point is on average 2.5 mmag. Although formally larger than the observational error, considering that we combined observations from 90 continuous nights, i.e. more than five stellar rotations, it indicates a relatively stable light curve in 1997/98.
© European Southern Observatory (ESO) 1998
Online publication: July 20, 1998