Orbital period cut-off of W UMa-type contact binaries

Abstract

Period cut-off and period-color relation are two special characters of W UMa-type contact binaries. In the past, many authors noted these two properties, however, a comprehensive study was still lacking. In order to reveal a theoretical mechanism behind these two peculiarities, we collected 370 contact binaries whose orbital periods, mass ratios, masses and radii are compiled and attempted to make this idea come true by statistical means. Then, we obtained a lower limit (0.15 days) of orbital period by studying the correlation among four physical parameters (orbital period P, mass ratio q, mass of primary star M1 and separation between two components a). Furthermore, we used the most reliable parameters (P and q) to check our result, fortunately, all evidence indicated that our predicted value is credible. In the end, the reason why the period-color relation exist was also discussed.

Investigation of the Orbital Period and Mass Relations for W UMa-type Contact Systems

“…In order to study the characteristics of W UMa contact binaries, Zhang & Qian (2020) collected data for 369 contact binaries and fitted polynomials to their diagrams. By combining their obtained best-fit equations with Kepler's third law, they presented a P − a, and P − q relation.…”

“…If the selected system has only photometric analysis, we have chosen the most recent study of that system. We eventually used the 251 systems from a study by Zhang & Qian (2020) where we found referenced papers and added our sample in this study to the dataset.…”

“…This enhanced dataset was then used to obtain a new relation between orbital period and mass ratio. We define the mass ratio similar to Zhang & Qian (2020), and hereafter, we call it q * to avoid any confusion. In order to use the orbital periods as the input to our regressor, we first normalize them by dividing all values by the maximum value.…”

“…This has been done by studying samples of binaries to find a relationship between their orbital period and mass ratio using different models. Zhang & Qian (2020) presented formulations to describe how the orbital period is related to the semi-major axis (a) and the mass ratio by using the simplified Kepler's third law and fitting models to the data of a sample of contact binaries. In this study, the primary goal is to recalculate the absolute parameters of a sample of contact systems based on the Gaia EDR3 parallax.…”

“…Additionally, we employed the Zhang & Qian (2020) study sample, as well as our 118 systems, which summed up a total of 369 systems, to investigate P − q relationship.…”