We use photometric and spectroscopic observations of the eclipsing binaries V65, V66 and V69 in the field of the globular cluster M4 to derive masses, radii, and luminosities of their components. The orbital periods of these systems are 2.29, 8.11 and 48.19 d, respectively. The measured masses of the primary and secondary components (Mp and Ms) are 0.8035+-0.0086 and 0.6050+-0.0044 Msun for V65, 0.7842+-0.0045 and 0.7443+-0.0042 Msun for V66, and 0.7665+-0.0053 and 0.7278+-0.0048 Msun for V69. The measured radii (Rp and Rs) are 1.147+_0.010 and 0.6110+-0.0092 Rsun for V66, 0.9347+_0.0048 and 0.8298+-0.0053 Rsun for V66, and 0.8655+-0.0097 and 0.8074+-0.0080 Rsun for V69. The orbits of V65 and V66 are circular, whereas that of V69 has an eccentricity of 0.38. Based on systemic velocities and relative proper motions, we show that all the three systems are members of the cluster. We find that the distance to M4 is 1.82+-0.04 kpc - in good agreement with recent estimates based on entirely different methods. We compare the absolute parameters of V66 and V69 with two sets of theoretical isochrones in mass-radius and mass-luminosity diagrams, and for an assumed [Fe/H] = -1.20, [alpha/Fe] = 0.4, and Y = 0.25 we find the most probable age of M4 to be between 11.2 and 11.3 Gyr. CMD-fitting with the same parameters yields an age close to, or slightly in excess of, 12 Gyr. However, considering the sources of uncertainty involved in CMD fitting, these two methods of age determination are not discrepant. Age and distance determinations can be further improved when infrared eclipse photometry is obtained.
تحميل البحث