Variable Stars Common Observation

Mission in Particular Areas of the Sky

**Eclipsing binary systems with eccentric orbits**

*by Ivan Adamin*in November-December 2013 (#3)

Eccentric eclipsing binaries are a subgroup of detached binary stars that have provided new and important information for the study of internal stellar structure. Eccentric systems display the phenomenon of Apsidal motion. In particular, apsidal motions in this type of binary systems has proven to be highly rewarding during the past decades, allowing to get valuable astrophysics parameters of the binary system.

Currently there are more than a hundred eccentric eclipsing systems known. Many of them still require extensive observations for creation of reliable astrophysical models of their systems. Below one can read a short overview of this kind of systems and their examples

### The apsidal motion effect

The study of apsidal motion effect in detached eclipsing binary systems with eccentric orbits (EEB) is an important source of information on the stellar internal structure as well as for the possibility of verification of the theory of General Relativity (Claret & Gimenez 1993; Claret 1997). It is the rotation of the line of apses of the orbit of an eccentric or elliptical two body system. The rate of motion of the apsis is dependent on the internal structure of each component. Determination of the characteristics of a binary thus provides an observational test of the theory of stellar structure and evolution.

The first theoretical explanation of apsidal motion (the precession of an eccentric orbit in its own plane) extends back to the beginning of the 20th century. The history of apsidal motion studies based on observations of times of minima of eclipsing binary stars is long and interesting. It began with the recognition by Duner (1892) that there were two separate types of minima of Y Cyg with significantly different periods, and he correctly atrributed this effect to a rotating line of apsides. This massive binary is one of the best-known cases of apsidal motion among eclipsing binaries.

The initial idea to measure the motion of the periastron of binary stars in order to have some insight into their internal structure was given by Russell (1928). In eccentric binaries, the behavior of the orbit is influenced by the distortion of the components. This is a function of the internal density concentration as well as the mass ratio and the separation of the components. Stellar distortion, or deviation from the point-like behavior, is responsible for the secular movement of the periastron and its observational measurement should obviously lead to an empirical measurement of the level of the density concentration. A fairly good historic introduction can be found in (Gimenez, 2006).

From the observational point of view, the study of this effect requires a more or less continuous monitoring of times of minimum light of the candidate systems. The necessarily long time basis of the observations requires a careful preparation of programs and targets.

This means that a large amount of observing time is generally needed which is not available at large instruments. Since only accurate timings of relatively deep eclipses are needed, a moderate or even small telescopes equipped with a photoelectric photometer or a CCD camera can be perfectly suited to this kind of project.

There are some advantages and disadvantages of the use of this effect (Hegedus et al. 2005):

Advantages:

–its basic study requires only very simple techniques (timing of eclipsing minima).

–the effect includes information not only about the internal mass distribution, but the gravitational theory itself as well.

Disadvantages:

–generally one needs to wait for quite a long time until the effect can be revealed;

–by the study of minima time observations (or by changes in the spectroscopic orbital elements), because the typical periods of this effect are from several hundred to several thousand years;

–the individual internal structure parameters remain unknown, only the weighted average of the two components can be determined.

A detailed analysis of the period variations can be performed using times of minimum light observed throughout the apsidal motion cycle, and from this both the orbital eccentricity and the period of rotation of the periastron can be obtained with a high accuracy. Moreover, this provides independent information for the analysis of the light curves (Gimenez, 1994).

Similar photometric studies of apsidal motion in EEB’s were published regularly during the seventies by Helmut Busch, Hartha observatory, and later e.g. by Kh. F. Khaliullin, Moscow University, or J. V. Clausen, Copenhagen University (Wolf et al., 2004). A catalogue of eclipsing binaries that are suitable for photometric monitoring was provided by Hegedus (2000) while a catalogue of known binaries with apsidal motion was published by Petrova & Orlov (1999).

### The theory behind the effect

Suitable numerical methods for the apsidal motion analysis were described by Gimenez & Garca-Pelayo (1983), Lacy (1992), and Wolf &? Sarounova (1995).

Below some basic concepts behind the core of the theory are provided just to recap of the method. There are five independent variables (T0, Ps, e, ω1, ω0) determined in this procedure. e represents the eccentricity of an orbit. The periastron position ωat epoch E is defined by the famous linear equation: = ωω0 + ω1* E, where ω1 is the rate of periastron advance (in degrees per sidereal cycle or in degrees per year), and the position of periastron for the zero epoch T0 is denoted as ω0. On a shorter timescale, the precession of an eccentric orbit in its own plane can produce an observable rate of change in the longitude of periastron: ω1 = d / ωdt.

The sidereal and anomalistic periods of the binary, Ps and Pa, are connected by the following equation: Ps = Pa (1 −ω1 / 360°), and the period of apsidal motion can be represented via U = 360° Pa / ω1

The rate of motion of the apsis is dependent on the internal structure of each component. Determination of the characteristics of a binary thus provides an observational test of the theory of stellar structure and evolution. The apsidal motion in relatively close binary systems can be studied by means of an O−C diagram analysis (for details see, e.g., Wolf et al. 1996, 1997).See Fig.2 and Fig.3 as examples of this kind of research.

In the case of deep, narrow eclipses the rate of apsidal motion can be determined by the analysis of primary and secondary eclipse timings and by measuring the change in the displacement of the secondary minimum from the half point (0.5 phase) according to D = (t2 - t1) - P / 2 where t2 and t1 are times of secondary and primary minima, respectively (GM85). D, in turn is related to the longitude of periastron ωby the formula given by Sterne (1939, a, b): For a short recap of the method: the individual equations for computing the time of primary and secondary minima are given in Giménez & García-Pelayo (1983). This is a weighted least squares iterative procedure, including terms in the eccentricity up to the fifth order.

### Eclipsing Binary with Eccentric Orbits Catalog

In 2007 there was a catalog containing a list of binary systems with eccentric orbits published (Bulut+). The catalog lists the physical parameters (including apsidal motion parameters) of 124 eclipsing binaries with eccentric orbits. In addition, the catalog also contains a list of 150 candidate systems, about which fewer details are known at present.

The catalog can be found at http://cdsarc.u-strasbg.fr/viz-bin/Cat?J/MNRAS/378/179

J/MNRAS/378/179 - Eclipsing Binary with Eccentric Orbits Catalog (Bulut I., Demircan O., 2007)

References for further reading:

- Giménez, A., García-Pelayo, J. M. 1983, Ap&SS, 92, 203
- Giménez, A., 2006; Proc. of the IAU, Symp. S240, 290
- Sterne, T. E. 1940, Proc. Natl. Acad. Sci., 26, 36
- Gimenez, A. & Claret, A.; Evolutionary Processes in Interacting Binary Stars, 1992, 277
- Lacy, C. H. S. 1992, AJ, 104, 2213
- Wolf, M., Claret, A., Kotková, L., et al. 2010, A&A, 509, A18
- Benvenuto, O. G., et al., 2002, MNRAS, 330, 435
- Hegedüs, T., et al. 2005, ASP Conf. Ser., 333, 88
- Wolf, M.; 2000, Astron. Astrophys. 356, 134
- Wolf, M., et al.; 2008, MNRAS 388, 1836
- Pribulla, T. 2012, Proceedings of IAU Symp.282

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