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4. Period variation

All times of minima of V 839 Oph available in the literature have been compiled, which altogether contain 71 times of minimum light (24 visual, 3 photographic and 44 photoelectric), cover about 45000 orbital revolutions, and thus provides important new information about the change of the orbital period of the system. There are however 2 big gaps in the data. One, following the discovery by Rigollet (1947), contain tex2html_wrap_inline2185 cycles, while the other, between the first group of photometric times of minima and the second visual time of minima, contains tex2html_wrap_inline2187 cycles. The first minimum is visual, as are many around E=-20000. However, one can see that the visual estimates in general show a large amount of scatter. Rigollet's minimum is of good quality, because his light curve contains 131 visual estimates.

The tex2html_wrap_inline2191 diagram which is calculated using the present work's linear ephemeris are shown in Fig. 2 (click here) and are listed as tex2html_wrap_inline2193 in Table 5 (click here) (available in electronic form). This form of the tex2html_wrap_inline2191 diagram indicates clearly that the orbital period of V 839 Oph is increasing. Both primary and secondary times of minima follow the same trend on the tex2html_wrap_inline2191 diagram.

Figure 2: The (tex2html_wrap_inline1697) diagram of V 839 Oph is shown is a quadratic fit through the data points. Photometric data (asteriscs), photographic data (squares) and visual data (diamonds) are shown

We fitted a quadratic function to the distribution of tex2html_wrap_inline2191 variations using all photometric and photographic times of minima together with the first visual time (see Fig. 2 (click here)). The following quadratic ephemeris was obtained:
where the coefficient of the square term represent the rate of change of the period (tex2html_wrap_inline1693), which is acceptable. In fact, such a representation of the tex2html_wrap_inline2191 data is statistically much better than the alternative (linear) representation. The tex2html_wrap_inline2207 residuals from the quadratic ephemeris are also listed in Table 5 (click here) and displayed Fig. 3 (click here)a. We found for the goodness of fit tex2html_wrap_inline2209=tex2html_wrap_inline2211=0.000033. If the period increase is purely due to the conservative mass transfer from the less massive to the more massive component (from tex2html_wrap_inline2215 to tex2html_wrap_inline2217 (Al-Naimy et al. 1989)) then with the equation tex2html_wrap_inline2219, such a transfer rate would be about tex2html_wrap_inline2221 for the period variation. After fitting the parabolic form, we also applied to the residuals a sinusoidal fit of the form

Figure 3: The calculated residuals from a) the quadratic ephemeris, b) the best sinusoidal fit

to all photographic and photoelectric times of minimum light include first Rigollet's visual time. Here tex2html_wrap_inline2223, tex2html_wrap_inline2225 and tex2html_wrap_inline2227 are the half-amplitude (in days), the period (in days), and a minimum time (in units of E) of the proposed sine curve of the tex2html_wrap_inline2191 diagram, respectively. We found that the data are best represented by the following sinusoidal ephemeris:
The best-fitting parabolic and sinusoidal curves are displayed, superimposed on the observational data, in Fig. 4 (click here). The tex2html_wrap_inline2233 residuals from the best fit, which are listed in Table 5 (click here) and displayed in Fig. 3 (click here)b and the goodness of fit of the representation, tex2html_wrap_inline2235 is much better than that of the previous quadratic one. The period of the cyclic variation is 19.62 yrs.

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