The Araucaria Project: High-precision orbital parallax and masses of the eclipsing binary TZ Fornacis

Abstract

Context. Independent distance estimates are particularly useful to check the precision of other distance indicators, while accurate and precise masses are necessary to constrain evolution models. Aims. The goal is to measure the masses and distance of the detached eclipsing-binary TZ For with a precision level lower than 1% using a fully geometrical and empirical method. Methods. We obtained the first interferometric observations of TZ For with the VLTI/PIONIER combiner, which we combined with new and precise radial velocity measurements to derive its three-dimensional orbit, masses, and distance. Results. The system is well resolved by PIONIER at each observing epoch, which allowed a combined fit with eleven astrometric positions. Our derived values are in a good agreement with previous work, but with an improved precision. We measured the mass of both components to be M 1 = 2.057 ± 0.001 M and M 2 = 1.958 ± 0.001 M . The comparison with stellar evolution models gives an age of the system of 1.20 ± 0.10 Gyr. We also derived the distance to the system with a precision level of 1.1%: d = 185.9 ± 1.9 pc. Such precise and accurate geometrical distances to eclipsing binaries provide a unique opportunity to test the absolute calibration of the surface brightness-colour relation for late-type stars, and will also provide the best opportunity to check on the future Gaia measurements for possible systematic errors.

The Araucaria project: High-precision orbital parallax and masses of eclipsing binaries from infrared interferometry

“…Such large shift is unlikely to be due to convective blueshift as observed sometimes (see e.g. Pilecki et al 2018;Gallenne et al 2016), but probably due to the determination of the radial velocities. Our orbital parameters are consistent with the estimates of Andersen & Vaz (1984), except the orbital inclination where we found the solution > 90 • , for the same reason as we explained before for AI Phe.…”

“…To extract the RVs we used the Broadening Function (BF) formalism (Rucinski 1992) implemented in the RaveSpan software 4 (Pilecki et al 2017, see also e.g. Pilecki et al 2018;Gallenne et al 2016;Graczyk et al 2015;Pilecki et al 2013). The measurements errors were estimated using the uncertainties of the broadening profiles fits.…”

“…We employed the same fitting method as in Gallenne et al (2018bGallenne et al ( , 2016 Choi et al 2016) isochrone models to estimate the stellar age of our systems. These models are well suited as they include the horizontal and asymptotic giant branch evolutionary phases, and contain a wide range of initial masses and metallicities.…”

The Surface Brightness-color Relations Based on Eclipsing Binary Stars: Toward Precision Better than 1% in Angular Diameter Predictions

“…Even so, there are just a few eclipsing binaries in our sample with high precision trigonometric parallaxes (fractional uncertainty σ π /π < 2%). In the case of one system, TZ For, we utilized the orbital parallax determined by Gallenne et al (2016) which is by a factor of 5 more precise than the Gaia DR1 parallax.…”

“…One can note the clear dependency of uncertainty on angular size and color (V − K) 0 , with bluer (hotter) stars having angular diameters more poorly determined. From all the sample only one star, the cooler component of TZ For, had its angular diameter measured directly with interferometry (Gallenne et al 2016), however with much lower precision, and two components of β Aur were barely resolvable (Hummel et al 1995). Figure 3 shows the relation between the V-band surface brightness S V and color (V − K) 0 against some interferometric SBC relations (Challouf et al 2014;Boyajian et al 2014;di Benedetto 2005;Kervella et al 2004).…”