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2 Observations

The observations of FG Hya in the V-band were carried out over 4 nights in March, 1999, with the PI1024 TKB CCD photometric system attached to the 100-cm reflector telescope at the Yunnan Observatory in China. The effective field of view of the photometric system is 6.5 square arc minutes at the Cassegrain focus and its BV color system approximates the standard Johnson BV photometric system (Yang & Li 1999). The coordinates of the comparison star and the check star used are listed in Table 1, respectively. The comparison star and the check star are so close to the variable that they are in the same field of the observation together with the program star.

 

 
Table 1: The coordinates of the variable, comparison star and check star

star
R.A.(1999.0) Dec.(1999.0)

variable
$08^{\rm h}27^{\rm m}01^{\rm s}$ $03^{\rm o}31'02''$
comparison star 08 26 57 03 32 08
check star 08 26 56 03 29 46


The integration time for each image is 100 s. A total of 207 images in Vband were obtained for 4 nights in March, 1999. The aperture photometry package of IRAF was used to reduce the images. The reduced results show that the difference between the magnitude of the check star and that of the comparison star is constant within probable error of $\pm 0.006$ magnitude. Extinction corrections were not made since the comparison star was so close to the variable.

From the observations, four times of minimum light were derived using parabola fitting. The new times of the minimum light are listed in Table 2, in which the (O-C)1 values are calculated by means of the light element formula given by Smith (1963)


\begin{displaymath}{\rm Min.I}= {\rm HJD\ 2436968.7067}+0\hbox{$.\!\!^{\rm d}$ }32783433E.
\end{displaymath} (1)


 

 
Table 2: The times of minimum light of FG Hya
HJD 2451240+ Min. (O-C)1 (O-C)2

5.2079(4)
I -0.0282 -0.0007
6.1925(3) I -0.0261 0.0004
7.1762(9) I -0.0269 0.0006
8.1592(4) I -0.0274 0.0001


From 36 photoelectric times of minimum light collected in the references and the new ones in the present article, the (O-C) values of the minima computed with the above ephemeris are plotted in Fig. 1. This diagram shows that several sudden jumps in the orbital period of FG Hya may occur. The timings of Mahdy et al. (1985) may be crucial in the O-C diagram (see Fig. 1). When their observations were checked, one of their timings (the first one listed) was found to be incorrect. They gave -0.0017 for the O-C whereas the calculated O-C is -0.031! Their other values are correct as given. But the question remains, their light curves appear to be distorted by heavy and asymmetrical spot(s). Therefore, the timings from the most extreme light curves could be suspected to be off because of the substantial spot(s). If the timings near epoch 28000 from Mahdy et al.'s observations are not taken into account, one can see clearly that the period of FG Hya was decreasing (see Fig. 2) and then a parabola ephemeris can be derived as the following:


  \begin{figure}
\includegraphics[width=8.8cm,clip]{9343FIG1.EPS}\end{figure} Figure 1: The sudden changes in the orbital period of FG Hya


  \begin{figure}
\includegraphics[width=8.8cm,clip]{9343FIG2.EPS}\end{figure} Figure 2: Lone-term decrease of the orbital period for FG Hya


\begin{displaymath}{\rm Min.I}\!=\!{\rm HJD\ 2436968.7345}+0\hbox{$.\!\!^{\rm d}$ }32783966E\!-\!1.4\ {10^{-10}}E^{2}.
\end{displaymath} (2)

The period change rate of FG Hya is $\delta{p}/p=-2.8\ {10^{-10}}.$However, since 1989 the period has been quite stable. From our times and the ones after 1989, a new linear ephemeris, more consistent with the period from 1989 to 1999, was derived:


\begin{displaymath}{\rm Min. I} = {\rm HJD}\ 2451248.1591(6)+0\hbox{$.\!\!^{\rm d}$ }32782743(20)E,
\end{displaymath} (3)

which was used to compute the phases of our observations and the (O-C)2values in Table 2.

A total of 207 individual observations have been obtained and listed in Table 4 with their Heliocentric Julian Day, phases and magnitude differences between the variable and the comparison star. The light curve of the system is shown as the solid circle points in Fig. 3. Since the period of FG Hya is close to one third of a day, it is difficult to obtain a complete light curve in a season. Most of the phases of the present light curve were covered in the four observing sessions, but an interval of 0.1 in phase (from 0.35p to 0.45p) is still is not covered.

  \begin{figure}
\includegraphics[width=8.8cm,clip]{9343FIG3.EPS}\end{figure} Figure 3: The light curve of FG Hya. The solid circle points indicate the observations and the line shows those from the model (see the text)


  \begin{figure}
\includegraphics[width=8.8cm,clip]{9343FIG4.EPS}\end{figure} Figure 4: The variation of the lignt curves of FG Hya. The explanation of the different synbols used can be seen in the text

As noted by Binnendijk (1963), the shape of the light curve of the system was changing. A graphical depiction of the variable shape of the light curves in Vband is shown in Fig. 4, which gives the observations carried out by Smith (X's) in 1955, by Binnendijk (open circles) in 1961-62, by Yang et al. (solid circles) in 1982, by Mahdy et al. (open diamonds) in 1985 and by the present authors (solid diamonds) in 1999. For comparison, all light curves are reduced assuming that they could have the same light level at the phase of 0.5. This level was chosen to normalize all of the light curves to simply demonstrate the substantial variability of the light curve over time. As shown in Fig. 4, the variation of the light curve of the system is very obvious. Some parameters of the light curves for FG Hya are listed in Table 3, from which one can see that the difference of the eclipsing depth between the primary eclipse and the secondary one is considerably changing while neither the O'Connell effect (two maxima in the light curves are unequal), nor its variation is obvious.


   
Table 3: The parameters of the V light curve properties of FG Hya

obs. date
1955 1961-62 1982 1985 1999

Max.I-Min.I
-0.350 -0.339 -0.369 -0.397 -0.357
Max.I-Min.II -0.333 -0.310 -0.314 -0.327 -0.350
Max.II-Min.I -0.372 -0.352 -0.363 -0.394 -0.353
Max.II-Min.II -0.355 -0.323 -0.314 -0.324 -0.346
Max.I-Max.II 0.022 0.013 -0.006 -0.003 -0.004
Min.I-Min.II 0.017 0.029 0.055 0.070 0.007


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