A critical review of period analyses and implications for mass exchange in W UMa eclipsing binaries: Paper 3

Abstract

This is the third of a series of four papers, the goal of which is to identify the overcontact eclipsing binary star systems for which a solid case can be made for mass exchange. To reach this goal, it is necessary first to identify those systems for which there is a strong case for period change. We have identified 60 candidate systems; in the first two papers (Nelson et al., 2014, Nelson et al., 2016) we discussed 40 individual cases; this paper continues with the last 20. For each system, we present a detailed discussion and evaluation concerning the observational and interpretive material presented in the literature. At least one eclipse timing (ET) diagram, commonly referred to as an “O–C diagram”, that includes the latest available data, accompanies each discussion. In paper 4, we will discuss the mechanisms that can cause period change and which of the 60 systems can be reliably concluded to exhibit mass exchange; we will also provide a list of marginal and rejected cases – suitable for future work.

Introduction

This is the third in a series of papers reviewing the status of our knowledge of period changes in W UMa binary stars. The overall goal of this review is to provide an accurate assessment of period changes in a sample of well-studied systems for which a solid case can be made for mass exchange between the two stars. A brief summary of the nature of overcontact eclipsing binaries, including problems with the determination of times of minima, and a number of relevant equations was presented in paper 1, Nelson et al. (2014). We refer the reader to that paper, for a more detailed discussion of our motivation and terminology, especially our justification for the use of the term “eclipse timing (ET) diagram” as opposed to “O–C diagram”.

An indispensable tool in the study of period change is the eclipse timing (ET) diagram. As the alternate name ‘O–C’ implies, it is the difference between the observed timings (O) and those calculated (C) under the assumption that the eclipses are perfectly regular. The O–C values (in days) are then plotted versus cycle number, n. The plot is thus sensitive to small changes in the period.

The essential elements for the calculated values are the epoch (or heliocentric Julian date, HJD₀, for a particular instant of primary minimum, often the earliest in the data set) and the period. If the period is constant, the plotted data will lie on a straight line, the slope of which can be used to refine the period until the slope is essentially zero. If however the period is changing at a constant rate, the points will then follow a parabola (or quadratic relationship). Other possible relationships are piece-wise linear, sinusoidal, quasi-periodic or some other, more complex function.

There are several possible causes for a quadratic relationship: there may be a mass transfer from one star to its companion (the subject of this series of papers); there may be a steady mass loss from the system as a whole (via a stellar wind for example) resulting in a loss in angular momentum of the system; or the apparent parabola may be a small part of a long-term period modulation resulting from magnetic cycles (the Applegate mechanism, Applegate, 1989, Applegate, 1992) or from variation in timings due to the light time effect (LiTE). The latter is the delay or advance of the eclipse times as the binary pair moves in its orbit around the centre of mass of the multiple star system (Irwin, 1952, Irwin, 1959).

A piece-wise linear relationship may be explained by an episodic mass exchange or by LiTE. A system exemplifying the latter is AC Boo, discussed in paper 1, but with a possible LiTE explanation (Nelson 2015a). Another notable example of LiTE is that of TZ Boo, amongst numerous other systems, to be discussed in this paper.

As we have stated in the abstract, in order to establish a list of candidates for which a solid case for mass exchange can be made, it is necessary first to narrow the list to only those displaying a definite quadratic relationship in the ET diagram. Next, as we are interested in mass exchange, it is necessary to eliminate those for which an alternate explanation to mass exchange exists.

Readers interested in details of any of the analyses should consult Nelson (2015b).