2. Observations and results
Fig. 1 shows a visual light curve of AG Dra from 6810 eye estimates by amateurs. It ranges from 1973 till mid 1997, i.e. over 24 years. The data were taken from the public data base of the Association Francaise des Observateurs d'Etoiles Variables (AFOEV) at CDS, Strasbourg (ftp://cdsarc.u-strasbg.fr/pub/afoev). The figure displays 22-day means over the individual magnitudes. The tick marks show the times of maxima as predicted by the ephemeris derived below. Ten maxima adhering to this ephemeris can clearly be seen. One of them, no. 8, is very small, and one of them, no. 2, is a hump on the declining slope of the preceding one. Maximum no. 16 was used in the analysis although it had not been fully completed at the time of data extraction. Maxima nos. 9 and 10 are insignificant in the visual data. They are marked for comparison with Fig. 2 only. The decrease of the scatter in the diagram around 1980, and again around 1995, is due to strongly increasing numbers of magnitude estimates. The two outburst episodes have drawn much observational attention on this object.
The Hipparcos satellite (ESA 1997) observed AG Dra photometrically from 1989 to 1993. The Hipparcos measurements started shortly after maximum no. 8 and included maxima nos. 9 to 11 (counting as in Fig. 1). The spectral response of the main instrument on board comprised the range of the Johnson B and V bands, plus a low red wing extending to about 700 nm. The results are shown in Fig. 2. It is obvious that the 380-day variability is also present during this time span, but too small to be detected by eye estimates. The phase agrees perfectly with that of the stronger bursts seen by the amateurs (see also Fig. 3, to be discussed further below). The three slight oscillations observed by Hipparcos are not perfectly periodic, but have definitely differing shapes.
There are two more independent data sets indicating the 380-day periodicity: One is the photoelectric V photometry of Skopal and Chochol (1994). Close inspection of their Fig. 1 reveals maxima nos. 6 to 10 as very slight humps. - The other one is the radial-velocity data compiled by Mikolajewska et al. (1995). After removing the radial-velocity effect of a best-fit spectroscopic orbit, a 380-day wave with a full amplitude of about 3 km/s is seen in the residuals between JD 2448500 and 2449300. (H.M. Schmid, Heidelberg, 1997, private communication). Like the Hipparcos observations, these data cover a part of the quiet phase before the start of the 1994-6 outburst phase.
An ephemeris for the periodic brightness maxima of AG Dra was derived in the following way: The times of the ten obvious maxima from Fig. 1 were manually read from a large-scale plot, as were the three maxima nos. 9, 10 and 11 from Fig. 2. A constant period was adjusted to the 13 maxima, using equal weights. The result is:
with standard errors of 2.1 days in the period and 11 days in the starting epoch. The latter corresponds to maximum no. 9 in Figs. 1 and 2. The rms scatter of the individual maxima timings around the ephemeris is 37 days. This value is to be compared with an expectation value of 110 days for a random distribution of timings relative to a 380-day ephemeris. Thus the statistical significance of the periodicity is confirmed.
Not surprisingly, the largest timing residuals (see Fig. 3) are due to maxima nos. 2 (the hump) and 8 (the smallest visual maximum). Omitting these two, an improved ephemeris results:
where now the standard errors of the period and starting epoch are 1.6 days and 9 days, respectively. The rms scatter of the individual maxima is reduced to 27 days.
© European Southern Observatory (ESO) 1998
Online publication: December 16, 1997