On the nature of the eccentric eclipsing binary star SY Phe with a pulsating γ Dor component

Spectroscopic observations of the eccentric binary system SY Phe were made at the South African Astronomical Observatory in 2019, 2020, and 2021, and its mid-resolution spectra were obtained. The radial velocities of the component stars were measured using the cross-correlation method and Fourier disentangling of the spectra. The spectral type (hence the effective temperature) of the primary star was determined from a model-atmosphere analysis. The radial velocity and Transiting Exoplanet Survey Satellite (TESS) light curves of the system were analysed, and its absolute parameters were derived. A strong (5.2 mmag) periodic signal with a frequency typical of $\gamma$ Dor stars (1.169 cycles per day) dominates the Fourier spectrum of the light curve between the eclipses. Apsidal motion parameters of SY Phe were calculated by studying eclipse timing variations. The Geneva evolution models indicate an evolutionary age of 2 Gyr and solar metallicity for the primary component; however, although the position of the secondary component in the H-R diagram matches the isochrone of 2 Gyr, it appears to have a larger radius and higher effective temperature than expected for its determined mass. Here, the secondary component has too large a radius, which is in accordance with the radius discrepancy problem that has been encountered in other studies, especially in late-type dwarfs, and has not been solved for half a century.