4 Variation in the orbital period of AK Ser

AK Ser is an EA-type eclipsing binary with sectral type of A5. 32 visual and photographic times of light minimum published in BBSAG bulletin have been collected at Eclipsing Minimum Database and 1 timing 2436348.472 was published by Szczepanowska (1959). Using the linear ephemeris given in the fourth edition of the "General Catalogue of Variable Stars":

$${\rm MinI}=2446255.462+1\hbox{$.\!\!^{\rm d}$ }922580\times{E}$$ (11)

the O-C residuals of all times of light minimum were computed and listed in Table 4. These O-C values are presented in Fig. 5.

Figure 5: O-C curve of AK Ser and its description by a quadratic ephemeris

As displayed in Fig. 5, the orbital period of the system is variable. Based on all the times of light minimum, a least square solution yields the following quadratic ephemeris:

$$% {\rm Min I}\!=\!2446255.4624\!+\!1.92258268\!\times\!{E} \!+\!2.09\ {10^{-9}}\!\times\!{E^{2}}$$ (12)

$\pm{3}$ $\pm{34}$ $\pm{8}$

and a period increase rate of ${\rm d}P/{\rm d}t=+7.94\ {10^{-7}}$ days/ year. Since the time interval between the first timing and the other times of light minimum is large (about 4200 cycles or 22 years), if the first time of light minimum is not used in the least square solution, we can obtain another quadratic ephemeris:

$$% {\rm Min I}\!=\!2446255.4631\!+\!1.92258273\!\times\!{E} \!+\!1.70\ {10^{-9}}\!\times\!{E^{2}}$$ (13)

$\pm{135}$ $\pm{80}$ $\pm{60}$

and a period increase rate of ${\rm d}P/{\rm d}t=+6.46\ {10^{-7}}$ days/ year which is nearly equal to that value obtained by using all timings.