Orbital and physical parameters of eclipsing binaries from the All-Sky Automated Survey catalogue - VI. AK Fornacis - a rare, bright K-type eclipsing binary
We present the results of the combined photometric and spectroscopic analysis of a bright (V=9.14), nearby (d=31 pc), late-type detached eclipsing binary AK Fornacis. This P=3.981 d system has not been previously recognised as a double-lined spectroscopic binary, and this is the first full physical model of this unique target. With the FEROS, CORALIE and HARPS spectrographs we collected a number of high-resolution spectra in order to calculate radial velocities of both components of the binary. Measurements were done with our own disentangling procedure and the TODCOR technique, and were later combined with the photometry from the ASAS and SuperWASP archives. We also performed an atmospheric analysis of the component spectra with the Spectroscopy Made Easy (SME) package. Our analysis shows that AK For consists of two active, cool dwarfs having masses of $M_1=0.6958 \pm 0.0010$ and $M_2=0.6355 \pm 0.0007$ M$_\odot$ and radii of $R_1=0.687 \pm 0.020$ and $R_2=0.609 \pm 0.016$ R$_\odot$, slightly less metal abundant than the Sun. Parameters of both components are well reproduced by the models. AK For is the brightest system among the known eclipsing binaries with K or M type stars. Its orbital period is one of the longest and rotational velocities one of the lowest, which allows us to obtain very precise radial velocity measurements. The precision in physical parameters we obtained places AK For among the binaries with the best mass measurements in the literature. It also fills the gap in our knowledge of stars in the range of 0.5-0.8 M$_\odot$, and between short and long-period systems. All this makes AK For a unique benchmark for understanding the properties of low-mass stars.