Orbits for 18 Visual Binaries and Two Double-line Spectroscopic Binaries Observed with HRCAM on the CTIO SOAR 4 m Telescope, Using a New Bayesian Orbit Code Based on Markov Chain Monte Carlo^*

Abstract

We present orbital elements and mass sums for eighteen visual binary stars of spectral types B to K (five of which are new orbits) with periods ranging from 20 to more than 500 yr. For two doubleline spectroscopic binaries with no previous orbits, the individual component masses, using combined astrometric and radial velocity data, have a formal uncertainty of ∼ 0.1M . Adopting published photometry, and trigonometric parallaxes, plus our own measurements, we place these objects on an H-R diagram, and discuss their evolutionary status. These objects are part of a survey to characterize the binary population of stars in the Southern Hemisphere, using the SOAR 4m telescope+HRCAM at CTIO. Orbital elements are computed using a newly developed Markov Chain Monte Carlo algorithm that delivers maximum likelihood estimates of the parameters, as well as posterior probability density functions that allow us to evaluate the uncertainty of our derived parameters in a robust way. For spectroscopic binaries, using our approach, it is possible to derive a self-consistent parallax for the system from the combined astrometric plus radial velocity data ("orbital parallax"), which compares well with the trigonometric parallaxes. We also present a mathematical formalism that allows a dimensionality reduction of the feature space from seven to three search parameters (or from ten to seven dimensions -including parallax -in the case of spectroscopic binaries with astrometric data), which makes it possible to explore a smaller number of parameters in each case, improving the computational efficiency of our Markov Chain Monte Carlo code.

Visual Binary Stars with Partially Missing Data: Introducing Multiple Imputation in Astrometric Analysis

“…Its use in the characterization of orbits of binary stars, however, has been more limited, despite the high degree of formal similarity between exoplanets and multiple stellar sysrtems. Some examples of works addressing the estimation of orbital parameters of binary stars from a Bayesian perspective (but only using complete datasets) are Sahlmann et al (2013); Burgasser et al (2015) and Mendez et al (2017).…”

“…The approach described here is well-known within the astronomical literature, being Hartkopf et al (1989); Pourbaix (1994); Lucy (2014), and Mendez et al (2017) some examples of its use.…”

“…In this section, the methodology proposed in Section 3, and tested in Section 4 with synthetic data, is applied to a real object: the visual binary star HU177 (WDS J17305-1446AB = HIP 85679 = HD 158561). This object has been recently studied (using only complete data) by Mendez et al (2017). The reason for choosing HU177 for a case study is that, among objects with partial data, this is one for which the incorporation of partial measurements may make a relevant difference in terms of the results of the inference 11 .…”

“…However, the issue of partial measurements in orbital estimation has been systematically ignored. This work presents a novel extension of our previous Markov chain Monte Carlo-based method to estimate orbital parameters (Mendez et al (2017)), that fully incorporates partial data into the inference using an imputation approach. The cases addressed are those mentioned in the preceding paragraph, namely, ρ ∈ (0, ρ max ), ϑ ∈ (0, 2π) and ρ ∈ (0, ∞), ϑ = ϑ * .…”

“…In their Catalog of Orbits of Visual Binary Stars (available at https://www.usno.navy.mil/USNO/astrometry/optical-IRprod/wds/orb6), the US Naval Observatory has devised an orbit "grading" system, where grade 5 means an indeterminate or very uncertain orbit due to poor orbit coverage and/or bad data quality, while grade 1 means a definitive orbit. In the WDS Orbit catalogue HU177 has grade 5, butMendez et al (2017) proposed promoting it to grade 3 ("reliable") after incorporating more recent interferometric measurements.12Mendez et al (2017) and the Catalog of Orbits of Visual Binary Stars can be consulted for orbit estimates of this star.…”