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

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4. The [FORMULA] diagrams

Fig. 3 illustrates the [FORMULA] diagram for [FORMULA] resulting from applying a linear ephemeris to the [FORMULA] 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 [FORMULA] 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.

[FIGURE] Fig. 3. [FORMULA] 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 [FORMULA] were calculated with the linear ephemeris for the maxima given in the figure).

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

[FIGURE] Fig. 4. [FORMULA] diagram over three centuries, linear ephemeris based on [FORMULA]. Some data with [FORMULA] 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 [FORMULA] 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 ([FORMULA] d over 7 consecutive cycles: long cycles are typically followed by short ones) or much less fluctuating ([FORMULA] d over 7 consecutive cycles). The moving average also suggests that some real period variation is present.

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

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© European Southern Observatory (ESO) 1999

Online publication: December 22, 1998
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