6 Variation in the orbital period of UW Vir

Many visual and photographic times of light minimum of UW Vir observed by many amateurs have been compiled at Eclipsing Minimum Database and 4 timings are from Kreiner (1976). In order to analyze the changes in the orbital period of the system, the $({\rm O{-}C})_{1}$ residuals of these timings are calculated with the following ephemesris:

$${\rm MinI}=2444345.413+1\hbox{$.\!\!^{\rm d}$ }8107755\times{E}.$$ (17)

These $({\rm O{-}C})_{1}$ values are listed in Table 6 and presented graphically against epoch number in Fig. 8. During the calculation, timings with the same epoch have been averaged. Three times of light minimum 2442545.480, 2442545.489 and 2447192.566 with large deviations from the general O-C trend formed by other points in Fig. 8 were discarded and not used further in the discussion of the period variation.

Figure 8: O-C observations of UW Vir and the description of its general trend (solid line)

As displayed in Fig. 8, the orbital period of the system is variable, and as in the cases of RX Hya and AC Tau, its variation is in a complex way. Since the general trend of the $({\rm O{-}C})_{1}$diagram may display a roughly parabolic distribution indicating a long-time increase in the orbital period, a second-order least-squares solution of the $({\rm O{-}C})_{1}$ values leads to the following ephemeris:

$$% {\rm Min I}\!=\!2444345.4056\!+\!1.81075972\!\times\!{E} \!+\!4.29\ {10^{-9}}\!\times\!{E^{2}}$$ (18)

$\pm{9}$ $\pm{28}$ $\pm{4}.$

With the coefficient of the square term, a continuous period increase of ${\rm d}P/{\rm d}E=+8.58\ {10^{-9}}$days/cycle $=+1.73\ {10^{-6}}$ days/year is obtained which is equivalent to a period increase of 14.9 s/century. As shown in Fig. 8, the secular increase only indicates the general trend of the $({\rm O{-}C})_{1}$ diagram without describing any particular characteristics.

The $({\rm O{-}C})_{2}$ residuals from the quadratic ephemeris (18) are also listed in Table 6 and displayed in Fig. 9. The $({\rm O{-}C})_{2}$ values in Fig. 9 clearly show a cyclic oscillation. The circular orbit of UW Vir (Lucy & Sweeney 1980) indicates that the periodic oscillation of the $({\rm O{-}C})_{2}$ residuals is not caused by apsidal motion. This kind of variation can be explained by the light time effect via the presence of a third body. The sine-like variation of the $({\rm O{-}C})_{2}$ curve indicates that the third body is moving in a circular orbit. With the least-squares method, the following periodic ephemeris is obtained:

$$({\rm O{-}C})_{2}=-0.0155+0.0306\sin(0\hbox{$.\!\!^\circ$ }0389\times{E}+48.67^{\circ})$$ (19)

which can give a good description to the general trend of the $({\rm O{-}C})_{2}$ values (solid line in Fig. 9). This ephemeris describes a periodic variation with a period of about T=45.9year and an amplitude of about $A=0\hbox{$.\!\!^{\rm d}$ }0306$.

Figure 9: O-C residuals of UW Vir from the quadratic ephemeris (18)