Multiband photometric investigations for eight binary systems of the W Ursae Majoris (W UMa)-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 (PHOEBE) 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 semi-major axis was updated using a sample consisting of 414 contact binary systems and the Monte Carlo Markov Chain (MCMC) approach. Also, using Machine Learning (ML) and the Artificial Neural Network (ANN) 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.

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 multi-color CCD photometric study of 27 δ Scuti stars is presented. By using approximately three years of photometric observations, we obtained the times of maxima and magnitude changes during the observation time interval for each star. The ephemerides of our δ Scuti stars were calculated based on the Markov Chain Monte Carlo (MCMC) method using the observed times of maxima and the period of the stars’ oscillations. We used the Gaia EDR3 parallaxes to calculate the luminosities and also the absolute magnitudes of these δ Scuti stars. The fundamental physical parameters of all the stars in our sample such as masses and radii were estimated. We determined the pulsation modes of the stars based on the pulsation constants. Moreover, the period–luminosity (P–L) relation of δ Scuti stars was investigated and discussed. Then, by using a machine learning classification, new P–L relations for fundamental and overtone modes are presented.