Investigation of the Orbital Period and Mass Relations for W UMa-type Contact Systems by Using Gaia EDR3 Parallax

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 star catalogue 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 d 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 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 network method. Additionally, we present a model for the relationship between the orbital period and the mass ratio (P–q) by fitting a multilayer perceptron regression model to a sample of the data collected from the literature.