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Astron. Astrophys. 351, 212-224 (1999)

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2. Light curve modelling

We model the V 1794 Cyg data between 1975 and 1995: 114 subsets (SET) of UBVRI photometry with an external accuracy of [FORMULA] in BVRI and [FORMULA] in U (Jetsu et al. 1999: Paper ii). The parameters of our second order ([FORMULA]) light curve model

[EQUATION]

are: the mean (M), the amplitudes ([FORMULA], [FORMULA]), and the frequency (f, i.e. the period [FORMULA]). The free parameter vector is [FORMULA] or [FORMULA] for fixed f. Only subsets with nonflare observations during at least 7 nights (nts) are modelled. In Sect. 3 this model for the original UBVRI magnitudes is linear with fixed f. The three stage period analysis (TSPA) by Jetsu & Pelt (1999: Paper i) with f as a free parameter is applied in Sect. 4 for the nonlinear modelling of the normalized magnitudes ([FORMULA]). The nonflare data ([FORMULA]) of every SET with [FORMULA] were normalized separately in each UBVRI passband with a relation based on the mean ([FORMULA]) and standard deviation ([FORMULA]) of [FORMULA] (Paper i: Eq. 17).

All V 1794 Cyg light curves are modelled with a varying [FORMULA]. The best P in each SET is determined with the TSPA applied to [FORMULA] from all available passbands, which also yields the primary and secondary minima epochs ([FORMULA], [FORMULA]). The ephemerides [FORMULA] are used for the linear modelling of the mean (M) and the total amplitude (A) of the light curve in each UBVRI passband. Both M and A are nearly independent of P, because [FORMULA] and [FORMULA] are accurate approximations for subsets with [FORMULA] (Paper i: Sect. 6.3). Like for any active star, the traditional constant P ephemeris for the whole data of V 1794 Cyg would overlook differential rotation and longitudinal shifts of activity centres. Our varying P approach adapts easily to these phenomena. Hence there is no unique phase for the whole data, but the phase dependent light curve features are unique in time , e.g. the [FORMULA] epoch does not depend strongly on P changes of a few percent (see Jetsu et al. 1993: Fig. 8). The phases are [FORMULA] within each SET, where [FORMULA] removes the integer part of [FORMULA]. In conclusion, first the nonlinear TSPA modelling of [FORMULA] yields P, [FORMULA] and [FORMULA] of each SET, and then the linear modelling of the UBVRI magnitudes with [FORMULA] gives [FORMULA], [FORMULA],..., [FORMULA], [FORMULA], [FORMULA],..., [FORMULA] and [FORMULA]. The M, A, [FORMULA], [FORMULA] and P errors are estimated with the bootstrap explained in Paper i (Sect. 4).

The results of this varying period analysis of V 1794 Cyg are presented in four separate tables. The mean and the total amplitude of the UBVR light curves during each SET are given in Table 1 (M and A). The analysis of a series of time points, the primary and secondary minima epochs of these lights curves, is summarized in Table 2. The results of the time series analysis of the normalized magnitudes within each SET are given in Table 3 (P, [FORMULA] and [FORMULA]). The last Table 4 presents the predictions for the changes in the yearly primary minima.


[TABLE]

Table 1. The means ([FORMULA], [FORMULA], [FORMULA] and [FORMULA]) and total amplitudes ([FORMULA], [FORMULA], [FORMULA] and [FORMULA]) for the modelled UBVR light curves of subsets with [FORMULA]



[TABLE]

Table 1. (continued)



[TABLE]

Table 2. The best P detected for [FORMULA] with the SD-, WSD-, K- and WK-methods. The critical levels for the P detected with the nonweighted SD- and K-methods are [FORMULA] and [FORMULA] (Paper iii: Eqs. 19 and 24)



[TABLE]

Table 3. The [FORMULA], [FORMULA] and P for the [FORMULA] of subsets with [FORMULA]. The [FORMULA] rejections are denoted with "r" in column [FORMULA], while the [FORMULA] rejections are applied to subsets with [FORMULA]. Finally, [FORMULA] rejects the [FORMULA] with [FORMULA]



[TABLE]

Table 4. The predicted [FORMULA] changes with [FORMULA]. The [FORMULA], [FORMULA], [FORMULA], [FORMULA], [FORMULA], [FORMULA] and RES parameters are explained Sect. 4.3


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© European Southern Observatory (ESO) 1999

Online publication: November 2, 1999
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