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.

We present a Bayesian inference methodology for the estimation of orbital parameters on single-line spectroscopic binaries with astrometric data, based on the No-U-Turn sampler Markov chain Monte Carlo algorithm. Our approach is designed to provide a precise and efficient estimation of the joint posterior distribution of the orbital parameters in the presence of partial and heterogeneous observations. This scheme allows us to directly incorporate prior information about the system—in the form of a trigonometric parallax, and an estimation of the mass of the primary component from its spectral type—to constrain the range of solutions, and to estimate orbital parameters that cannot be usually determined (e.g., the individual component masses), due to the lack of observations or imprecise measurements. Our methodology is tested by analyzing the posterior distributions of well-studied double-line spectroscopic binaries treated as single-line binaries by omitting the radial velocity data of the secondary object. Our results show that the system’s mass ratio can be estimated with an uncertainty smaller than 10% using our approach. As a proof of concept, the proposed methodology is applied to 12 single-line spectroscopic binaries with astrometric data that lacked a joint astrometric–spectroscopic solution, for which we provide full orbital elements. Our sample-based methodology allows us also to study the impact of different posterior distributions in the corresponding observations space. This novel analysis provides a better understanding of the effect of the different sources of information on the shape and uncertainty in the orbit and radial velocity curve.

We present results from Speckle inteferometric observations of 15 visual binaries and one double-line spectroscopic binary, carried out with the HRCam Speckle camera of the SOAR 4.1 m telescope. These systems were observed as a part of an on-going survey to characterize the binary population in the solar vicinity, out to a distance of 250 pc. We obtained orbital elements and mass sums for our sample of visual binaries. The orbits were computed using a 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 their uncertainty. Their periods cover a range from 5 yr to more than 500 yr; and their spectral types go from early A to mid M, implying total system masses from slightly more than 4M⊙ down to 0.2M ⊙. They are located at distances between approximately 12 and 200 pc, mostly at low Galactic latitude. For the double-line spectroscopic binary YSC8, we present the first combined astrometric/radial-velocity orbit resulting from a self-consistent fit, leading to individual component masses of 0.897 ± 0.027 M ⊙ and 0.857 ± 0.026 M ⊙; and an orbital parallax of 26.61 ± 0.29 mas, which compares very well with the Gaia DR2 trigonometric parallax (26.55 ± 0.27 mas). In combination with published photometry and trigonometric parallaxes, we place our objects on an H-R diagram and discuss their evolutionary status. We also present a thorough analysis of the precision and consistency of the photometry available for them.

Partial measurements of relative position are a relatively common event during the observation of visual binary stars. However, these observations are typically discarded when estimating the orbit of a visual pair. In this article we present a novel framework to characterize the orbits from a Bayesian standpoint, including partial observations of relative position as an input for the estimation of orbital parameters. Our aim is to formally incorporate the information contained in those partial measurements in a systematic way into the final inference. In the statistical literature, an imputation is defined as the replacement of a missing quantity with a plausible value. To compute posterior distributions of orbital parameters with partial observations, we propose a technique based on Markov chain Monte Carlo with multiple imputation. We present the methodology and test the algorithm with both synthetic and real observations, studying the effect of incorporating partial measurements in the parameter estimation. Our results suggest that the inclusion of partial measurements into the characterization of visual binaries may lead to a reduction in the uncertainty associated to each orbital element, in terms of a decrease in dispersion measures (such as the interquartile range) of the posterior distribution of relevant orbital parameters. The extent to which the uncertainty decreases after the incorporation of new data (either complete or partial) depends on how informative those newly-incorporated measurements are. Quantifying the information contained in each measurement remains an open issue. 2 R. Claveria et al.observed, angular separations beyond the angular resolution of the telescope, etc. The latter case is arguably the most common source of partial information: in the vicinity of the periastron, the angular separation between the primary and secondary star (denoted by ρ hereafter) reaches its minimum values; if those values fall below the resolution threshold of the imaging device, then the angular separation is confined to a range (i.e., ρ ∈ (0, ρ max )) instead of being reduced to a single value (as occurs with regular, successfully resolved measurements), and usually no information about the position angle of the secondary with respect to the primary (denoted by ϑ hereafter) can be inferred either. In certain cases, databases of visual binary observations also report partial data of the form ρ = (0, ∞), ϑ = ϑ * , that is, the angular separation is missing but the position angle is well-defined. Many example of partially missing data (in ρ or ϑ) can be found by browsing either through the historical measurements database of the Washington Double Star Catalogue (WDS hereafter, Mason et al. (2001)) or the Catalog of Interferometric Measurements of Binary Stars (INT hereafter, Hartkopf et al. (2001)), both diligently curated by the Naval Observatory of the United States 1 .In a broader context, from population censuses to clinical research surveys, the presence of incomplete or missing data may occur in a wide ...

We present orbital elements, orbital parallaxes, and individual component masses for 14 spatially resolved double-line spectroscopic binaries derived doing a simultaneous fit of their visual orbit and radial velocity curve. This was done by means of a Markov Chain Monte Carlo code developed by our group that produces posterior distribution functions and error estimates for all of the parameters. Of this sample, six systems had high-quality previous studies and were included as benchmarks to test our procedures, but even in these cases, we could improve the previous orbits by adding recent data from our survey of southern binaries being carried out with the HRCam and ZORRO speckle cameras at the SOAR 4.1 m and Gemini South 8.1 m telescopes, respectively. We also give results for eight objects that did not have a published combined orbital solution, one of which did not have a visual orbit either. We could determine mass ratios with a typical uncertainty of less than 1%, mass sums with uncertainties of about 1%, and individual component masses with a formal uncertainty of 0.01 M ⊙ in the best cases. A comparison of our orbital parallaxes with available trigonometric parallaxes from Hipparcos and Gaia eDR3 shows a good correspondence, the mean value of the differences being consistent with zero within the errors of both catalogs. We also present observational H-R diagrams for our sample of binaries, which, in combination with isochrones from different sources, allowed us to assess their evolutionary status and the quality of their photometry.