Research on O-C diagrams


University of Athens Observatory participated in several observational monitoring campaigns on eclipsing binary systems and pulsating stars with the aim of determining the precise time of minimum and maximum light, respectively. These timings give the absolutely necessary information for the determination of orbital behavior of the members in a binary system, through the O-C diagrams (Observed - Calculated). Specialized observing programs aim to study the O-C diagrams and extract information about the Light-Time effect (LITE), basically due to the presence of a third body orbiting a binary system or a second body orbiting around a single star.

The long-term monitoring of the pulsating star V1162 Ori

The international campaign on the pulsating star V1162 Ori was initiated in 1999 by Chris Sterken, and its goal was follow-up observations on this High-amplitude delta Scuti Star (HADS), in order to recover its multiple periodicities. The target appeared to have many pulsation frequencies as expected, as well as a very interesting O-C diagram, which show the presence of an orbiting star around V1162 Ori.

V1162 Ori is a High-amplitude delta Scuti Star (HADS), which was the first target ever observed from the University of Athens Observatory (images after Arentoft et al. 2001). The O-C diagram of the times of maxima revealed the presence of an orbiting star around it.

The binary nature of the pulsating star SZ Lyn

The pulsating star SZ Lyn is a perfect example of a HADS within a binary system. This target was observed for several years (2001-2015) and the O-C diagram has revealed the binary nature of this system (Gazeas et al., 2004, CoAst, Vol. 145, 49 and Gazeas et al., 2004, CoAst, Vol. 144, 26).

The High Amplitude delta Scuti Star SZ Lyn is a member of a binary system. The O-C diagram uncovered an invisible companion, with an orbital period of ∼1180 days.

The O-C diagrams for the multiple systems UX Her and AT Peg. These diagrams uncovered the existance of an invisible companion, orbiting each system in an eccentric orbit.

Disentangling the O-C behavior

The way that various physical processes act in binary systems can be disentangled by interpreting their orbital period changes. Especially in the case of eclipsing binary systems, this may happen by analyzing their O-C diagrams, i.e. by monitoring their eclipse timing variations (ETV).

A dedicated study of O-C diagrams was conducted in 2011, in the frame of a PhD dissertation. It addresses the way these mechanisms -acting individually or combined- modulate the O-C differences and, consequently, fix the morphology of the O-C diagrams. It was achieved to specify the minimum time interval (i.e. number of orbital cycles) over which a pure O-C signal could be observable under the action of physical processes such as wind-driven mass loss, magnetic braking, non-conservative mass transfer of various types, and gravitational radiation at a given noise level.

To investigate how the noise level is affected by the photometric noise, the number of observations, the wavelength, the asymmetry degree of the minimum profile and even the method for the determination of its timing, a statistical study was properly designed. It was performed based on 114 CCD minima timings, most of them obtained at UOAO, and concerned two particular short-period eclipsing binaries, namely CG Cyg and RT And, because of their similar light and orbital parameters (same orbital period, equal minima depths). The analysis shown that high asymmetry and low observations quality increase considerably the O-C noise level when a mixture of methods such as the - most widely used - Kwee & van Woerden (1956, BAN, 12, 327) and the typical polynomial regression are employed along the whole O-C time-series length. An upper bound of 0.008 days was found from purely statistical reasons, that is without considering intrinsic stellar effects such as moving spots.

Beside the main goals of the above study, a long-term multiband monitoring of GSC 2696:2622 was carried out from UOAO. This target is a suspected variable star which served several times in the past as comparison star of CG Cyg. The star proved to be a low amplitude \delta Sct-type pulsator with a dominant frequency at 10.86 c/d and two less prominent peaks at 16.45 and 19.2 c/d. The first frequency was found consistent with a radial excitation mode, while the rest ones with non-radial oscillating modes. The two stronger peaks presented variations over time both in amplitude and phase, while the O-C diagram analysis based on all available maxima timings revealed considerable changes of the dominant frequency over the monitoring period, possibly attributed to the light-travel time effect of an unseen companion.

Synthetic O-C diagrams, showing long-term mechanisms, applied on stellar systems.

The magnetic activity of the eclipsing binary system DV Psc

Photometric investigation of the magnetically active eclipsing binary system DV Psc reveiled an interesting O-C behavior. After a long-term photometric monitoring of the light curve asymmetries on this system between the years 2005-2017, it was noticed that the O-C values undergo periodic variations with an estimated period of ∼9.2 days. This could be explained by the presence of a third body orbiting the system, as it is very common for a close binary system to have a tertiary component. However, spectroscopic observations did not show any presence of a third body, therefore the periodic variability on O-C values can be explained by the periodic magnetic activity of the system. Such an activity, causes the members of the eclipsing binary to show cool spots on their surfaces, frequently accompaigned with bright chromospheric flares, expressed as hot spots on the stellar surfaces. The resulted light curve asymmetries cause the time of minima (eclipses) to be slightly shifted in time, and therfore a periodic variation on O-C values every 9.2 years. The above phenomenon is fully explained and presented in the plots below.

The long-term monitoring of the magnetically active eclipsing system DV Psc, resulted in a complicated O-C diagram (plot on the left), which shows a cyclic variation of the observed times of minima (red for primary minima, green for secondary minima, grey for all minima). The time difference between the O-C values of primary and secondary minima (plot on the right), indicates the seasons when the magnetic activity is low (zero difference) or high (large difference), i.e. when the light curves are symmetric or not.

The periodic variability of the O-C values shows different amplitude for the primary (I) and secondary (II) minima (red and green curves, respectively). Such a behavior indicates a periodic magnetic activity, in parallel to the observed light curve asymmetries, expressed as the so called O' Connell Effect.

The University of Athens Observatory participated in several observations on O-C diagrams, which resulted in publications and scientific announcements in refereed journals.

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