Investigation of the orbital period and mass relations for W UMa-type contact systems

Abstract

New relationships between the orbital period and some parameters of W Ursae Majoris (W UMa) type systems are presented in this study. To investigate the relationships, we calculated the absolute parameters of a sample of 118 systems. For this purpose, we used the parallax values obtained from the Gaia Early Data Release 3 (Gaia EDR3) star catalog for more precise calculations. The other required parameters, including the light curve solutions and the orbital period were derived from previous research. For some relationships, we added 86 systems from another study with an orbital period of less than 0.6 days to our sample, allowing us to increase the number of systems to 204. Therefore, the mass (M) values of each component along with all the other absolute parameters were recalculated for these contact systems. We used the Markov Chain Monte Carlo (MCMC) approach in order to gain the new orbital period-mass relations (P − M) per component, and added the temperature (T) to the process to acquire the new orbital period-temperature (P − T1) relation. We presented the orbital period behaviour in terms of log(g) by new relations for each component. We have also obtained a model between the orbital period, the mass of the primary component and temperature (P − M1 − T1) using the Artificial Neural Networks (ANN) method. Additionally, we present a model for the relationship between the orbital period and the mass ratio (P − q) by fitting a Multi-Layer Perceptron (MLP) regression model to a sample of the data collected from the literature.

The First Photometric Study of AH Mic Contact Binary System

“…(2) The result of the B − V index obtained from this work's light curves to be 0.73 ± 0.04 after calibration (Høg et al 2000) and as a result we found the effective temperature 5470 Flower (1996) study; (3) The effective temperature from the result of Poro et al (2022) analysis of the relationship between orbital period and the primary (hotter) temperature for contact systems is 5681 80) K. We chose Gaia DR2's temperature as a fixed parameter for the hotter star. In the continuation, we performed the initial light curve analysis.…”

“…Lindegren et al 2021;Ren et al 2021). The range of these corrections appears to include the value of observational and light curve solution uncertainties (Poro et al 2022). Therefore, in order to properly estimate the absolute parameters of the stars of AH Mic binary system, we used the Gaia EDR3 parallax method.…”

“…Therefore, in order to properly estimate the absolute parameters of the stars of AH Mic binary system, we used the Gaia EDR3 parallax method. This is a well-known method, which is fully described in the Poro et al (2022) study. To perform the estimation, we first obtained the absolute magnitude (M v ) of the system using the maximum light of apparent magnitude V max = 12.79(5) from our observation, the star's distance from Gaia EDR3 d (pc) = 470.2(6.5), and the extinction coefficient A v = 0.08 from the Schlafly & Finkbeiner (2011) study.…”

“…The reliable value of mass ratio through photometric light curve analysis is still under many investigations to approach the accuracy of this value using the spectroscopy method. However, investigations have been conducted, one of which is based on the Machine Learning methods using the Multi-Layer Perceptron (MLP) regression model and was carried out by the Poro et al (2022) study.…”

“…According to this method, we find the estimated range of mass ratio for AH Mic to be 0.408 to 0.572 with a mean of 0.485, which includes our calculated mass ratio of 0.431 from the light curve solutions. It's worth mentioning that the q specified in the Poro et al (2022) study is the ratio of the less massive star mass to the more massive star mass, hence q is never more than unity.…”