The Most Probable 3D Orbit for Spectroscopic Binaries

Abstract

Binary stars are a very important source of astronomical information. Those short-period binaries observed by means of both spectroscopy and interferometry can provide, through their corresponding orbits, precise values regarding individual masses as well as orbital parallaxes. For this reason, it is fundamental to attempt to optically resolve double-lined spectroscopic binaries. In the present article, we used the elaboration of a specific algorithm in order to determine the necessary telescope aperture to resolve a concrete spectroscopic binary. To that end, using available photometric and spectroscopic information, we established a 3D model for each spectroscopic binary with an orbit from which we deduced the most probable maximum and minimum separations between the components. In this manner, using the obtained calibrations in our study, we also deduced different physical parameters of the components of each system. The methodology presented here was tested satisfactorily with a list of spectroscopic binaries that had been optically resolved and that have both the spectroscopic and visual orbits.

Orbital elements and individual component masses from joint spectroscopic and astrometric data of double-line spectroscopic binaries

“…If we scale our masses to the Gaia parallax instead of our orbital parallax, the individual component masses turn out to be 1.10 and 0.98 M respectively, quite close to those from the isochrones. However, the spectral type of the primary (G0IV to G5IV) implies a mass between 1.26 to 1.20 M (see Table 19 on Abushattal et al (2020)), closer to the masses derived from our orbital parallax. The photometry suggests that the primary is leaving the main-sequence; in our HR diagrams the isochrone that best fits both components is the PARSEC 9 Gyr (see Figure 5).…”

“…Unfortunately, all our latest observations cover the same sector of the orbit (see Figure 7). As a final note, the F8V spectral type for the primary implies a mass of 1.23±0.05 M (Abushattal et al (2020), Table 18), within 1σ of our dynamical mass (with prior) as shown in Table 4. .…”

“…Note also that the V -band photometry for this target does not exhibit such a large variance according to Tables 1 and 2. Our individual masses seem more consistent with a G7V to G8V spectral type (according to Abushattal et al (2020), their Table 18), rather than with the earlier types given in WDS (G0V) and SIMBAD (G1V) which imply larger masses. However, given our 10% mass uncertainty, the earlier types are consistent within 1σ of our mass interquartile range (see Table 4).…”

“…Our formal errors are however significantly smaller (see Table 4). Given the spectral type of the primary (F0V) Abushattal et al (2020) predict for it a mass of 1.64 ± 0.05 M , which differs by less than 1σ of our dynamical mass.…”

“…If we scale down the individual masses reported on Table 4 to the Hipparcos parallax instead of our orbital parallax, the individual masses become 1.49 and 1.11 M respectively, closer to the values inferred from the isochrones but still too large. The spectral type (F7V-F8V) for the primary implies a mass between 1.23 to 1.29 M , while for the secondary (G4V, see Table 1) it should be 1.06 M (see Table 18 on Abushattal et al (2020)). These numbers are still slightly larger than the masses implied by the isochrones, but more in line with the larger Hipparcos parallax than with our orbital parallax.…”