First detailed study of two eccentric eclipsing binaries: TYC 5378-1590-1 and TYC 8378-252-1

Aims. The analysis of combined photometry and spectroscopy of eccentric eclipsing binary systems facilitates the derivation of very precise values for a large ensemble of physical parameters of the component stars and their orbits, thereby providing stringent tests of theories of stellar structure and evolution. In this paper two eccentric eclipsing binary systems, TYC 5378-1590-1 and TYC 8378252-1, are studied in detail for the first time. Methods. Radial velocities were obtained using cross-correlation methods applied to mid-resolution spectra covering almost the entire orbital phase domains of these two systems. TESS photometry was used for the analysis of TYC 5378-1590-1, whereas ASAS-SN photometry was used for the analysis of TYC 8378-252-1. Results. We obtained the first precise derivation of the physical parameters of these systems. Both systems display moderately eccentric orbits (e similar to 0:3 and 0:2) with periods of 3.73235 and 2.87769 days, respectively. The apsidal motion is very slow, with a duration of several centuries for both systems. We present two models for the apsidal motion of TYC 5378-1590-1. The internal structure constant derived from observations for TYC 8378-252-1 is approximately 11% lower than theoretical predictions. We discuss possible reasons for this discrepancy. Our analysis indicates that the components of both systems are on the main sequence. The components of TYC 5378-1590-1 are relatively young stars (age similar to 600 Myr) close to the ZAMS, whereas the components of TYC 8378-252-1 are relatively old stars (age similar to 4 Gyr) close to the TAMS. Our finding that the circularization timescale for TYC 5378-1590-1 is similar to 200 times longer than its evolutionary age is compatible with circularization theory; however, our finding that the evolutionary age of TYC 8378-252-1 is approximately ten times longer than the circulation age, while its orbital eccentricity is quite high (e similar to 0:2), challenges the present theories of circularization.