A seismic and gravitationally bound double star observed by Kepler Implication for the presence of a convective core

Context. Solar-like oscillations have been observed by Kepler and CoRoT in many solar-type stars, thereby providing a way to probe stars using asteroseismology. Aims. The derivation of stellar parameters has usually been done with single stars. The aim of the paper is to derive the stellar parameters of a double-star system (HIP 93511), for which an interferometric orbit has been observed along with asteroseismic measurements. Methods. We used a time series of nearly two years of data for the double star to detect the two oscillation-mode envelopes that appear in the power spectrum. Using a new scaling relation based on luminosity, we derived the radius and mass of each star. We derived the age of each star using two proxies: one based upon the large frequency separation and a new one based upon the small frequency separation. Using stellar modelling, the mode frequencies allowed us to derive the radius, the mass, and the age of each component. In addition, speckle interferometry performed since 2006 has enabled us to recover the orbit of the system and the total mass of the system. Results. From the determination of the orbit, the total mass of the system is 2.34(-0.33)(+0.45) M-circle dot. The total seismic mass using scaling relations is 2.47 +/- 0.07 M-circle dot. The seismic age derived using the new proxy based upon the small frequency separation is 3.5 +/- 0.3 Gyr. Based on stellar modelling, the mean common age of the system is 2.7-3.9 Gyr. The mean total seismic mass of the system is 2.34-2.53 M-circle dot consistent with what we determined independently with the orbit. The stellar models provide the mean radius, mass, and age of the stars as R-A = 1.82-1.87 R-circle dot, M-A = 1.25-1.39 M-circle dot, Age(A) = 2.6-3.5 Gyr; R-B = 1.22-1.25 R-circle dot, M-B = 1.08-1.14 M-circle dot, Age(B) = 3.35-4.21 Gyr. The models provide two sets of values for Star A: [1.25-1.27] M-circle dot and [1.34-1.39] M-circle dot. We detect a convective core in Star A, while Star B does not have any. For the metallicity of the binary system of Z approximate to 0.02, we set the limit between stars having a convective core in the range [1.14-1.25] M-circle dot.