4 The pulsation period of P Cyg

Independently of the Fourier analysis, we determined the basic period of P Cyg using the classical method of establishing an ephemeris on the basis of times of photometric maximum (hereafter indicated by  $T_{\rm max}$) and minimum ( $T_{\rm min}$). Therefore, we have selected by visual inspection all well-observed extrema in Figs. 6 and 7. With well-observed extrema we understand those groups of data that consist of at least four measurements in the 5-day time interval centered on the visually estimated time of extremum, with the additional condition that a $T_{\rm min}$ or $T_{\rm max}$ should not be dominated by one single outlying measurement.

An important element in this approach is the establishment of the cycle-count scheme. A first inspection of the light curves shows that there are five blocks of almost contiguous cycles in which there is virtually no doubt as to the relative cycle-count patterns internal to each block: JD 46906-47095, 47294-47479, 47629-47834, 48738-48915 and 49145-49517. A linear ephemeris fitted to $T_{\rm min}$ for each of these groups yields, respectively P= 16.79, 18.83, 16.96, 17.85 and 17.68, thus a mean $P=17\hbox{$.\!\!^{\rm d}$ }6 \pm 0.4$. Therefore, we tried to extend the cycle-count scheme to all time intervals falling in between the determined  $T_{\rm min}$ and  $T_{\rm max}$. During this procedure, we also used other indications pointing to the presence of maxima and minima (such as less-well observed extrema).

From a number of pronounced minima, we derived a preliminary ephemeris, and then we determined the cycle number E for all obtained  $T_{\rm min}$; the zeropoint for E is arbitrary, but chosen in such a way that we deal with positive E-numbers only. The resulting ephemeris turned out to be

 

$${\rm HJD}_{\rm min} 2446189.9 + 17.34\,E$$ = (1)

$$\hbox{\phantom{446\,}} \pm 1.4 \hbox{\phantom{\,\ }} \pm 0.1.$$

The list of $T_{\rm min}$, Evalues is given in Table 3. Figure 9 gives the resulting O-C diagram. Note that this 17 $.\!\!^{\rm d}$3 cycle (0.0576 cd^-1) is absent in the amplitude spectrum of Fig. 8.

Figure 8: Frequency spectra of the light curve of P Cyg (1982-1999). The lower and upper panels give the same information at different frequency resolution.

Figure 9: O-C diagram for all $T_{\rm min}$ data listed in Table 3.

 

 

Table 3: Heliocentric times of minimum light of P Cyg and cycle number E.

$T_{\rm min}$	E	$T_{\rm min}$	E	$T_{\rm min}$	E
46554.6	21	47098.2	52	48042.2	107
46568.1	22	47294.5	64	48058.4	108
46590.2	23	47308.9	65	48360.9	125
46729.7	29	47349.0	67	48569.1	137
46906.3	41	47424.9	71	48569.1	137
46977.3	45	47447.4	72	48738.0	147
47006.9	47	47478.9	74	48758.2	148
47021.3	48	47796.1	93	48902.9	156
47034.5	49	47813.6	94	48915.0	157
47074.5	51	47834.3	95

In a way similar to the one followed in the previous Section, we derived the ephemeris

 

$${\rm HJD}_{\rm max} 2446199.5 + 17.35\,E$$ = (2)

$$\hbox{\phantom{446\,}} \pm 6.5 \hbox{\phantom{\,\ }} \pm 0.2.$$

The list of $T_{\rm max}$, E is given in Table 4. Figure 10 gives the resulting O-C diagram which, just like Fig. 9, illustrates that the observed time of extremum can strongly deviate from the calculated value, although no significant trends (linear or polynomial) are present.

 

 

Table 4: Heliocentric times of maximum light of P Cyg and cycle number E.

$T_{\rm max}$	E	$T_{\rm max}$	E	$T_{\rm max}$	E
47025.6	47	47470.9	74	48534.8	135
47088.6	51	47493.0	75	48750.1	147
47323.8	65	47845.9	95	48776.8	148
47436.5	71	48369.8	125

Figure 10: O-C diagram for all $T_{\rm max}$ data listed in Table 4.