Orbital Characteristics of the Subdwarf-B and F V Star Binary EC~20117-4014(=V4640 Sgr)
Among the competing evolution theories for subdwarf-B (sdB) stars is the binary evolution scenario. EC~20117-4014 (=V4640~Sgr) is a spectroscopic binary system consisting of a pulsating sdB star and a late F main-sequence companion (O'Donoghue et al. 1997), however the period and the orbit semi-major axes have not been precisely determined. This paper presents orbital characteristics of the EC 20117-4014 binary system using 20 years of photometric data. Periodic Observed minus Calculated (O-C) variations were detected in the two highest amplitude pulsations identified in the EC 20117-4014 power spectrum, indicating the binary system's precise orbital period (P = 792.3 days) and the light-travel time amplitude (A = 468.9 s). This binary shows no significant orbital eccentricity and the upper limit of the eccentricity is 0.025 (using 3 $σ$ as an upper limit). This upper limit of the eccentricity is the lowest among all wide sdB binaries with known orbital parameters. This analysis indicated that the sdB is likely to have lost its hydrogen envelope through stable Roche lobe overflow, thus supporting hypotheses for the origin of sdB stars. In addition to those results, the underlying pulsation period change obtained from the photometric data was $\dot{P}$ = 5.4 ($\pm$0.7) $\times$ $10^{-14}$ d d$^{-1}$, which shows that the sdB is just before the end of the core helium-burning phase.