2 Variation in the orbital period of UW Cygni

For the period study of UW Cyg, all available times of light minimum have been compiled. 18 of the timings published before 1959 have been collected and tabulated in the paper of Whitney (1959). Many times of light minimum are obtained from the Eclipsing Minimum Database by Internet (www.oa.uj.edu.pl/ktt/ktt.html). In all, 112 timings are collected. Unfortunately, all of the timings are visual or photographic. In this section, with these times of light minimum, the change in the orbital period of the neglected system is studied. In order to see the general behavior of the variations in the period of the system, the O-C residuals of all times of light minimum were computed by the linear ephemeris given in the fourth edition of the "General Catalogue of Variable Stars", as

$${\rm MinI}=2443690.0355+3\hbox{$.\!\!^{\rm d}$ }4507805\times{E}$$ (1)

and listed as $({\rm O{-}C})_{1}$ in Table 2. The $({\rm O{-}C})_{1}$ values are presented graphically against epoch number in Fig. 1. During the calculation, times of light minimum with the same epoch have been averaged and some timings listed in the first and sixth columns are the mean values. Two photographic times of light minimum 2445201.434 and 49166.000 are discarded, because their O-C values show large deviations from the general O-C trend formed by other points.

Figure 1: The O-C curve of UW Cyg from the ephemeris given by GCVS. The solid line refers to a new ephemeris

Since the form of the O-C diagram depends very much on the choice of the ephemeris used in the calculation of the "C" epochs, the general trend of the $({\rm O{-}C})_{1}$ diagram may show a downward straight line, indicating that this ephemeris need to be revised. Based on all times of light minimum, a least-squares solution yields the following mean ephemeris:

$${\rm Min I}=2443690.0670(31)+3.4507620(13)\times{E}.$$ (2)

The residuals $({\rm O{-}C})_{2}$, calculated with this ephemeris, are listed in fifth and tenth columns of Table 2 and are plotted graphically against epoch number in Fig. 2, from which the following results can be drawn: (i) the orbital period of the system is variable; (ii) its variation may show a wavelike fluctuation. With least-square method, a periodic ephemeris is obtained, as:

$$({\rm O{-}C})_{2}=-0.0055+0.0383\sin(0\hbox{$.\!\!^\circ$ }0691\times{E}+147.1^{\circ})$$ (3)

which can give a good fit to the general trend of the $({\rm O{-}C})_{2}$values (solid line in Fig. 2). This formula clearly indicates a periodic variation with a period of about T=49.2year and an amplitude of about $A=0\hbox{$.\!\!^{\rm d}$ }0383$. The cyclic variation of the O-C curve strongly suggests that the change of the orbital period is periodic.

Figure 2: O-C residuals based on the new ephemeris. The solid line refers to its description by a periodic function