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*Astron. Astrophys. 351, 212-224 (1999)*
## 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
in BVRI and
in U (Jetsu et al. 1999:
Paper ii). The parameters of our second order
() light curve model
are: the mean (*M*), the amplitudes
(,
), and the frequency (*f*, i.e.
the period ). The free parameter
vector is or
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
(). The nonflare data
() of every SET with
were normalized separately in each
UBVRI passband with a relation based on the mean
() and standard deviation
() of
(Paper i: Eq. 17).
All V 1794 Cyg light curves are modelled with a varying
. The best *P* in each SET is
determined with the TSPA applied to
from all available passbands, which also yields the primary and
secondary minima *epochs* (,
). The ephemerides
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 and
are accurate approximations for
subsets with (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 epoch does not
depend strongly on *P* changes of a few percent (see Jetsu et al.
1993: Fig. 8). The phases are within
each SET, where removes the integer
part of . In conclusion, first the
nonlinear TSPA modelling of yields
*P*, and
of each SET, and then the linear
modelling of the UBVRI magnitudes with
gives
,
,...,
, ,
,...,
and
. The *M*, *A*,
, 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*, and
). The last Table 4 presents the
predictions for the changes in the yearly primary minima.
**Table 1.** The means (, , and ) and total amplitudes (, , and ) for the modelled UBVR light curves of subsets with
**Table 1.** (continued)
**Table 2.** The best *P* detected for with the SD-, WSD-, K- and WK-methods. The critical levels for the *P* detected with the nonweighted SD- and K-methods are and (Paper iii: Eqs. 19 and 24)
**Table 3.** The , and *P* for the of subsets with . The rejections are denoted with "r" in column , while the rejections are applied to subsets with . Finally, rejects the with
**Table 4.** The predicted changes with . The , , , , , and RES parameters are explained Sect. 4.3
© European Southern Observatory (ESO) 1999
Online publication: November 2, 1999
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