Exploring Contact Binaries: Observational Analysis of four W Uma Binaries Using Photometry and Spectroscopy

We present the multi-band photometric and low-resolution spectroscopic analysis of four W Ursae Majoris eclipsing binaries (EWs) - J080510.1+141528 (hereinafter as J0805a), J080516.3+143138 (hereinafter as J0805b), J143358.7+053953 (hereinafter as J1433), and J143458.4+054143 (hereinafter as J1434). The multi-band ground based photometric data are collected using the 1.3-m Devasthal Fast Optical Telescope (DFOT) while we also make use of TESS photometric observations. The spectroscopic analysis is based on the low-resolution observations by 4-m Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). The ephemeris of these systems are updated using the photometric data from TESS and other photometric surveys. The system J0805b shows a secular change in the orbital period with a period change rate of 4.2 ($\pm$ 0.1) $\times10^{-7}$ days per year while the orbital period change rate for J1433 is calculated as -1.1 ($\pm$ 0.1) $\times10^{-6}$ days per year. The mass-transfer rate for J0805b is found to be dM$_{1}$/dt = -1.56($\pm$0.07) $\times 10^{-6}$ M$_{\odot}$/year and dM$_{1}$/dt = -7.95($\pm$0.87) $\times 10^{-7}$ M$_{\odot}$/year for J1433. All the systems have inclination > 79$^{\circ}$ except J1433 which has inclination of 72.8$^{\circ}$. The mass-ratios (less massive to more massive component) for these targets are < 0.5. All the system except J0805b are A-subtype contact binaries. The absolute parameters of the systems are determined using GAIA DR3 parallax and reddening information. The LAMOST spectra are analyzed using spectral subtraction technique. A small excess emission is detected for J1433 in H$_{\alpha}$ and H$_{\beta}$ region. The systems are plotted on Hertzsprung-Russell (HR) diagram and compared with previously studied systems. The mass-ratio vs radius-ratio relation is also investigated for these systems.