Fundamental Parameters for Totally Eclipsing Contact Binaries Observed by TESS

Totally eclipsing contact binaries provide a unique opportunity to accurately determine mass ratios through photometric methods alone, eliminating the need for spectroscopic data. Studying low mass ratio (LMR) contact binaries is crucial for advancing our understanding of binary star evolution and the formation of rare optical transients known as red novae. We identified 143 totally eclipsing contact binaries from the Transiting Exoplanet Survey Satellite. These high-precision light curves reveal a distinct O'Connell effect, which we interpret by introducing a cool spot on the primary star. Training a neural network model that includes cool spot parameters can generate a high-precision light curve 2 orders of magnitude faster than Phoebe. Utilizing the neural network (NNnol3) model combined with the Markov Chain Monte Carlo algorithm, we rapidly derived the fundamental parameters of these systems. By leveraging the relationship between orbital period and semimajor axis using the Random Sample Consensus algorithm, we estimated their absolute parameters. Our analysis identified 96 targets with mass ratios below 0.25, all of which were not listed in any previous catalog, thus signifying the discovery of new LMR system candidates. Assuming all 143 binary systems are affected by a third light during parameter estimation, we train a neural network (NNl3) model considering the third light. Then we calculate the residuals between the mass ratio ql3 (considering the third light) and qnol3 (neglecting it). For these residuals, the 25th percentile (Q1) is 0.012, the median (Q2) is 0.026, and the 75th percentile (Q3) is 0.05.