Astron. Astrophys. 342, 167-172 (1999)

## 4. The diagrams

Fig. 3 illustrates the diagram for resulting from applying a linear ephemeris to the over the last 150 years-that is, the time interval with an almost uninterrupted sequence of maxima and minima. The shape of the curve is cyclic, not strictly periodic. The 123 maxima wander between 6 weeks early and about 6 weeks late, in accord with Maraldi's early findings and with Argelander's attempt to fit a cyclic term. The minima follow the maxima by days on average. The agreement between the two trends is very good, while short-term differences may be due to measurement errors and cycle-to-cycle jitter in the period.

 Fig. 3. diagram covering the last 150 years, linear ephemeris. The top curve is for the times of maximum and corresponds to the left Y-axis, the lower curve is for the times of minimum and relates to the Y-axis on the right side (the were calculated with the linear ephemeris for the maxima given in the figure).

Fig. 4 illustrates the diagram resulting from applying a linear ephemeris over the time span of three centuries. For the sake of illustration, we have highlighted datapoints with that follow about the same sampling distribution as the data belonging to the cycle interval 1-140.

 Fig. 4. diagram over three centuries, linear ephemeris based on . Some data with have about the same time distribution as the data belonging to the cycle interval 1-140 (filled circles).

Fig. 5 shows cycle lengths derived from 110 successive times of light maximum of  Cygni for the last 150 years. The d 7, and the apparent standard deviation is 8:d9. Successive average period length is 408: maxima are connected by straight lines, the continuous curve is the running average (bin length 7 datapoints). The diagram shows sequences of intervals where the cycle length seems to be highly erratic ( d over 7 consecutive cycles: long cycles are typically followed by short ones) or much less fluctuating ( d over 7 consecutive cycles). The moving average also suggests that some real period variation is present.

 Fig. 5. Cycle lengths derived from 110 successive times of light maximum of  Cygni for the last 150 years. Average period is 408:d7, . Successive maxima are connected by straight lines, the continuous curve is the running average (bin length 7 datapoints).

© European Southern Observatory (ESO) 1999

Online publication: December 22, 1998