The Photometric Study of Six W UMa Systems and Investigation of the Mass–Radius Relations for Contact Binary Stars

We present the photometric analysis of six short-period systems (EI Oct, V336 TrA, NX Boo, V356 PS and V2282 Cyg). This is first these except for TrA. Observations were conducted 27 nights at three observatories in northern southern hemispheres. calculated a new ephemeris each using our minimum times additional literature. The Markov Chain Monte Carlo (MCMC) approach was used to determine eclipse timing variation trends systems. found likely orbital growth TrA Boo; four other show linear trend period changes, which most due accumulation measurement errors their parameters. light curve performed Physics Eclipsing Binaries (PHOEBE) 2.3.59 version code with MCMC approach. absolute parameters by Gaia Early Data Release 3 (EDR3) parallax. positions also depicted on Hertzsprung-Russell (H-R) $logJ_0-logM$ diagrams. According sample, we able relations mass-radius (M-R) relationships contact binary There strong relationship between mass ratio radius W UMa provided relation. compared M-R updated this study seven studies obtained spectroscopic method. In addition, estimated some 1734 EW systems, based relationships.