Multiband photometric investigations for eight binary systems of the W Ursae Majoris-type are presented. Six systems are presented for the first time to analyze their light curves. All the analyzed systems have a temperature below 5000 K and an orbital period of less than 0.28 days. We extracted primary and secondary minima from the ground-based observations of these systems. According to a few observations reported in the literature, linear fits were considered in the O − C diagrams, and new ephemerides were presented. Light curve solutions were performed using the PHysics Of Eclipsing BinariEs code. The results of the mass ratio and fillout factor indicate that the systems are contact binary stars. Six of them showed the O’Connell effect, and a cold starspot on each companion was required for light curve solutions. Their absolute parameters were estimated and evaluated by two other methods. In this study, the empirical relationship between the orbital period and semimajor axis was updated using a sample consisting of 414 contact binary systems and the Monte Carlo Markov Chain approach. Also, using Machine Learning and the Artificial Neural Network model, the relationship between P–T ₁–M ₁ was updated for a better estimation of the mass of the primary star.

Reviewing the empirical and theoretical parameter relationships between various parameters is a good way to understand more about contact binary systems. In this investigation, two-dimensional (2D) relationships for P–M _V(system), P–L _1,2, M _1,2–L _1,2, and q–L _ratio were revisited. The sample used is related to 118 contact binary systems with an orbital period shorter than 0.6 days whose absolute parameters were estimated based on the Gaia Data Release 3 parallax. We reviewed previous studies on 2D relationships and updated six parameter relationships. Therefore, Markov chain Monte Carlo and Machine Learning methods were used, and the outcomes were compared. We selected 22 contact binary systems from eight previous studies for comparison, which had light curve solutions using spectroscopic data. The results show that the systems are in good agreement with the results of this study.

This is the first in-depth study of seven total-eclipse W Ursae Majoris-type contact binary systems using photometric light curves. The ground-based observations were conducted with four observatories in the Northern and Southern hemispheres. We also used the Transiting Exoplanet Survey Satellite for four target systems. We presented the analysis of orbital period variations of six systems and found that they display parabolic variations. The material transfer rates between the stars of the systems were calculated. Also, the results show that four systems have a long-term increase, while two have a long-term decrease in their orbital periods. We analysed light curves using the PHysics Of Eclipsing BinariEs python code and the Markov chain Monte Carlo algorithm to estimate different parameters of target systems and their uncertainties. Six of the target systems required the addition of a cold or hot star-spot. We estimated absolute parameters using the empirical relationship between the orbital period and the semimajor axis ($P\!\!-\!\!a$). According to each component’s effective temperature and mass, it was recognized that the studied systems are W subtype. We examined the dynamic stability of two targets, which were low mass ratio contact binary systems. We also showed the evolution of stars in the $M\!\!-\!\!R$ and $M\!\!-\!\!L$ diagrams. Finally, we showed that the hotter stars in contact systems have a temperature difference of less than ${\approx} 400$ K compared to the Gaia Data Release 3 temperature report.

Light curve analysis of W UMa-type contact binary systems using MCMC or MC methods can be time-consuming, primarily because the repeated generation of synthetic light curves tends to be relatively slow during the fitting process. Although various approaches have been proposed to address this issue, their implementation is often challenging due to complexity or uncertain performance. In this study, we introduce the BSN application, whose name is taken from the BSN project. The application is designed for analyzing contact binary system light curves, supporting photometric data, and employing an MCMC algorithm for efficient parameter estimation. The BSN application generates synthetic light curves more than 40 times faster than PHOEBE during the MCMC fitting process. The BSN application enhances light curve analysis with an expanded feature set and a more intuitive interface while maintaining compliance with established scientific standards. In addition, we present the first light curve analyses of four contact binary systems based on the TESS data, utilizing the BSN application version 1.0. We also conducted a light curve analysis using the PHOEBE Python code and compared the resulting outputs. Two of the target systems exhibited asymmetries in the maxima of their light curves, which were appropriately modeled by introducing a cold starspot on one of the components. The estimated mass ratios of these total-eclipse systems place them within the category of low mass ratio contact binary stars. The estimation of the absolute parameters for the selected systems was carried out using the $P-a$ empirical relationship. Based on the effective temperatures and masses of the components, three of the target systems were classified as A-subtype, while TIC 434222993 was identified as a W-subtype system.

We present the photometric analysis of six short-period systems (EI Oct, V336 TrA, NX Boo, V356 Boo, PS Boo, and V2282 Cyg). This is the first photometric analysis of these systems except for V336 TrA. Observations were conducted for 27 nights at three observatories in the northern and southern hemispheres. We calculated a new ephemeris for each of the systems using our minimum times and additional literature. The Markov Chain Monte Carlo (MCMC) approach was used to determine the eclipse timing variation trends of the systems. We found a likely orbital growth for V336 TrA and PS Boo; four other systems show a linear trend in orbital period changes, which is most likely due to the accumulation of measurement errors in their linear ephemeris parameters. The light curve analysis was performed using the Physics of Eclipsing Binaries (PHOEBE) 2.3.59 version code with the MCMC approach. The absolute parameters of the systems were calculated by using the Gaia Early Data Release 3 (EDR3) parallax. The positions of the systems were also depicted on the Hertzsprung–Russell (H-R) and log J 0 – log M diagrams. According to a sample, we were able to present relations for the mass–radius (M–R) relationships of contact binary systems. There is also a strong relationship between the mass ratio and the radius ratio in the W UMa systems for which we also provided a new relation. We compared the M–R updated relationships in this study with seven systems in other studies obtained using the spectroscopic method. In addition, we estimated some of the absolute parameters for 1734 EW systems, based on the new relationships.

The lower limit of the mass ratio in contact binaries remains uncertain, with observations suggesting systems exist below theoretical predictions. The stability of such very-low-mass-ratio systems is still debated. Based on our review of systems within the mass-ratio cutoff range, we reanalyzed TYC 3801-1529-1 and found it to have the lowest known mass ratio, q = 0.02 4 − ( 1 ) + ( 2 ) , among analyzed contact binaries. The reanalysis of this target was carried out using the BSN (Binary Systems of South and North ) application and the Markov Chain Monte Carlo method. We then compared our light-curve solution obtained from TESS observations with the results of a previous study. We studied the period variations of this system and identified a cyclic trend over the past 6 yr. After the third-body contribution has been removed, the system’s period variations can be described either by a linear trend with a negative slope or by a quadratic trend with a downward curvature. These results indicate that it is still not possible to definitively determine whether the orbital period is increasing or decreasing, underscoring the importance of future observations. By considering the challenges of detecting the faint secondary in extremely low-mass-ratio systems, we estimated the absolute parameters of the target. Based on our analysis, the secondary component of the binary is likely a brown dwarf, while the third body appears to be a low-mass M-type dwarf. According to our analysis, TYC 3801-1529-1 is dynamically unstable and thus represents a remarkable candidate for a binary merger.