Visual Orbit Research Articles

Orbits of Binary Stars: from Visual Measures to Speckle Interferometry

Knowledge of the orbits of visual binary stars has always been one of the fundamentals of astronomy. Based historically on the visual measures, nowadays the orbits rely more (or exclusively) on the accurate speckle data. This prompts reconsideration of the methods of orbit calculation, undertaken here and illustrated by 20 examples, from accurate to drastically revised and tentative orbits. Good understanding and critical assessment of the input data is a key requirement, especially concerning visual measures. Combination of visual and speckle data is still needed for long-period binaries, but the relative weights must match their respective errors. When the orbit can be fully constrained only by accurate speckle data, the old measures should be ignored. Orbits can be classified into three grades: (A) fully constrained, (B) semiconstrained, and (C) preliminary or tentative. Typical use cases of visual orbits are listed. Accurate parallaxes from Gaia, together with the orbits, will greatly expand the data on stellar masses. Continued speckle monitoring will be an essential complement to Gaia, but the vast amount of new pairs will restrict future work on orbits to the most interesting or relevant objects.

A Study of Eight Visual-spectroscopic Southern Binaries Using Recent SOAR Observations

Speckle observations performed between 2019 and 2022 with the HRCam attached to the 4.1 m SOAR telescope (Cerro Pachón, Chile) permitted to improve visual orbits of the southern binaries WDS 01243-0655 (BU 1163), WDS 09275-5806 (CHR 240), WDS 12114-1647 (S 643 AaAb), WDS 13317-0219 (HDS 1895), WDS 15282-0921 (BAG 25 AaAb), WDS 17304-0104 (STF 2173), WDS 19598-0957 (HO 276), and WDS 21274-0701 (HDS 3053). All of them are spectroscopic binaries, of which six are SB2, so relevant information about their individual masses has been obtained. Moreover, comparison between different values of their parallaxes (orbital, dynamic, and ANAPAR, a color-dependent model suitable for binary systems attending to the exact locations of the components on the MS in the HR diagram) with those provided by Hipparcos and Gaia missions, along with comments for each binary are presented. The luminosity determination of the 16 components allowed us to estimate their approximate age and position on the HR diagram as well.

Mass Ratio of Single-line Spectroscopic Binaries with Visual Orbits Using Bayesian Inference and Suitable Priors* *Based in part on observations obtained at the Southern Astrophysical Research (SOAR) telescope, which is a joint project of the Ministério da Ciência, Tecnologia, e Inovaçãoes (MCTI) da República Federativa do Brasil, the U.S. National Optical Astronomy Observatory (NOAO), the University of North Carolina at

We present orbital elements for 22 single-line binaries, nine of them studied for the first time, determined from a joint spectroscopic and astrometric solution. The astrometry is based on interferometric measurements obtained with the HRCam Speckle camera on the SOAR 4.1 m telescope at Cerro Pachon, Chile, supplemented with historical data. The spectroscopic observations were secured using Echelle spectrographs (FEROS, FIDEOS, and HARPS) at La Silla, Chile. A comparison of our orbital elements and systemic velocities with previous studies, including Gaia radial velocities, shows the robustness of our estimations. By adopting suitable priors of the trigonometric parallax and spectral type of the primary component, and using a Bayesian inference methodology developed by our group, we were able to estimate mass ratios for these binaries. Combining the present results with a previous study of other single-line binaries from our team, we present a pseudo mass-to-luminosity relationship based on 23 systems (46 stars) in the mass range 0.6 ≤ M ⊙ ≤ 2.5. We find a reasonable correspondence with a fiducial mass-to-luminosity relationship. We conclude that our methodology does allow us to derive tentative mass ratios for these types of binaries.

Visual Orbits and Alignments of Planet-hosting Binary Systems

Roughly half of Solar-type planet hosts have stellar companions, so understanding how these binary companions affect the formation and evolution of planets is an important component to understanding planetary systems overall. Measuring the dynamical properties of planet host binaries enables a valuable test of planet formation in multistar systems and requires knowledge of the binary orbital parameters. Using high-resolution imaging, we have measured the relative astrometry and visual orbits of 13 binary systems where one of the stars is known to host a transiting exoplanet. Our results indicate that the mutual inclination between the orbits of the binary hosts and the transiting planets are well aligned. Our results for close binary systems (a < 100 au) complement past work for wide planet host binaries from Gaia.

Projected spin–orbit alignments from Kepler asteroseismology and Gaia astrometry

ABSTRACT The angle between the rotation and orbital axes of stars in binary systems – the obliquity – is an important indicator of how these systems form and evolve, but few such measurements exist. We combine the sample of astrometric orbital inclinations from Gaia Data Release 3 with a sample of solar-like oscillators in which rotational inclinations have been measured using asteroseismology. We supplement our sample with one binary whose visual orbit has been determined using speckle interferometry and present the projected spin–orbit alignments in five systems. We find that each system, and the overall sample, is consistent with alignment but there are important caveats. First, the asteroseismic rotational inclinations are fundamentally ambiguous and, secondly, we can only measure the projected (rather than true) obliquity. If rotational and orbital inclinations are independent and isotropically distributed, the likelihood of drawing our data by chance is less than a few per cent. Though small, our data set argues against uniformly random obliquities in binary systems. We speculate that dozens more measurements could be made using data from NASA’s Transiting Exoplanet Survey Satellite mission, mostly in red giants. ESA’s PLAnetary Transits and Oscillations mission will likely produce hundreds more spin–orbit measurements in systems with main-sequence and subgiant stars.

The Physical Parameters, Stability, and Habitability of some Double-lined Spectroscopic Binaries

Large ground telescopes can now resolve most double-lined binaries optically at some point in their orbit due to the improvement of imaging techniques in recent decades. Using additional information about these systems, such as astrometric parallax, even a single precise visual observation can provide a 3D orbit and the primary physical parameters. Furthermore, both the visual and spectroscopic orbits can be determined. We combine the Edward method with the visual solution and the spectroscopic orbit parameters: period (P), periastron epoch (T), eccentricity (e), semimajor axis (a1,2) and inclination (i), we also know the mass ratio of the system. The developed method allows us to select doublelined spectroscopic systems with recently calculated orbits. We calculate the individual masses, orbital parallax, and other fundamental astrophysical parameters. The purpose of these parameters is to verify the reliability of the data received from space missions and to calculate the stability and habitability, which is the primary goal of this study. Astronomical information can be obtained from binary stars. By observing short period binaries using both spectroscopy and interferometry, we can determine the individual masses and orbital parallaxes of the objects based on their corresponding orbits. Spectroscopic binaries with double-lines are therefore fundamentally important to optically resolve. To determine the required telescope aperture for the resolution of a spectroscopic binary, we developed a specific algorithm. Wedetermined the most probable maximum and minimum separations between each spectroscopic binary based on photometric and spectroscopic information. Thus, we also determined the different physical parameters of each system by using the calibrations we obtained in our study. Based on optically resolved spectroscopic binaries with both spectroscopic and visual orbits, the methodology presented here was successfully tested.

Visual Orbits of Spectroscopic Binaries with the CHARA Array. IV. HD 61859, HD 89822, HD 109510, and HD 191692

We present the visual orbits of four spectroscopic binary stars, HD 61859, HD 89822, HD 109510, and HD 191692, using long baseline interferometry with the CHARA Array. We also obtained new radial velocities from echelle spectra using the APO 3.5 m, CTIO 1.5 m, and Fairborn Observatory 2.0 m telescopes. By combining the astrometric and spectroscopic observations, we solve for the full, three-dimensional orbits and determine the stellar masses to 1%–12% uncertainty and distances to 0.4%–6% uncertainty. We then estimate the effective temperature and radius of each component star through Doppler tomography and spectral energy distribution analyses. We found masses of 1.4–3.5 M ⊙, radii of 1.5–4.7 R ⊙, and temperatures of 6400–10,300 K. We then compare the observed stellar parameters to the predictions of the stellar evolution models, but found that only one of our systems fits well with the evolutionary models.

Bayesian Inference in Single-line Spectroscopic Binaries with a Visual Orbit

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.

Orbital Elements and Individual Component Masses from Joint Spectroscopic and Astrometric Data of Double-line Spectroscopic Binaries*

Abstract 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.

Observations with the Differential Speckle Survey Instrument. X. Preliminary Orbits of K-dwarf Binaries and Other Stars

Abstract This paper details speckle observations of binary stars taken at the Lowell Discovery Telescope, the WIYN telescope, and the Gemini telescopes between 2016 January and 2019 September. The observations taken at Gemini and Lowell were done with the Differential Speckle Survey Instrument (DSSI), and those done at WIYN were taken with the successor instrument to DSSI at that site, the NN-EXPLORE Exoplanet Star and Speckle Imager (NESSI). In total, we present 378 observations of 178 systems, and we show that the uncertainty in the measurement precision for the combined data set is ∼2 mas in separation, ∼1°–2° in position angle depending on the separation, and ∼0.1 mag in magnitude difference. Together with data already in the literature, these new results permit 25 visual orbits and one spectroscopic-visual orbit to be calculated for the first time. In the case of the spectroscopic-visual analysis, which is done on the ternary star HD 173093, we calculate masses with a precision of better than 1% for all three stars in that system. Twenty-one of the visual orbits calculated have a K dwarf as the primary star; we add these to the known orbits of K-dwarf primary stars and discuss the basic orbital properties of these stars at this stage. Although incomplete, the data that exist so far indicate that binaries with K-dwarf primaries tend not to have low-eccentricity orbits at separations of one to a few tens of astronomical units, that is, on solar system scales.

The First Dynamical Mass Determination of a Nitrogen-rich Wolf–Rayet Star Using a Combined Visual and Spectroscopic Orbit

Abstract We present the first visual orbit for the nitrogen-rich Wolf–Rayet binary, WR 133 (WN5o + O9I), based on observations made with the CHARA Array and the MIRC-X combiner. This orbit represents the first visual orbit for a WN star and only the third Wolf–Rayet star with a visual orbit. The orbit has a period of 112.8 days, a moderate eccentricity of 0.36, and a separation of a = 0.79 mas on the sky. We combine the visual orbit with an SB2 orbit and Gaia parallax to find that the derived masses of the component stars are and , with the large errors owing to the nearly face-on geometry of the system combined with errors in the spectroscopic parameters. We also derive an orbital parallax that is identical to the Gaia-determined distance. We present a preliminary spectral analysis and atmosphere models of the component stars, and find the mass-loss rate in agreement with polarization variability and our orbit. However, the derived masses are low compared to the spectral types and spectral model. Given the close binary nature, we suspect that WR 133 should have formed through binary interactions, and represents an ideal target for testing evolutionary models given its membership in the cluster NGC 6871.

ARMADA. I. Triple Companions Detected in B-type Binaries α Del and ν Gem

Abstract Ground-based optical long-baseline interferometry has the power to measure the orbits of close binary systems at ∼10 μas precision. This precision makes it possible to detect “wobbles” in the binary motion due to the gravitational pull from additional short-period companions. We started the ARrangement for Micro-Arcsecond Differential Astrometry (ARMADA) survey with the Michigan Infra-Red Combiner (MIRC)/MIRC-X instrument at the Center for High Angular Resoloution Astronomy (CHARA) array for the purpose of detecting giant planets and stellar companions orbiting individual stars in binary systems. We describe our observations for the survey, and introduce the wavelength calibration scheme that delivers precision at the tens of microarcseconds level for &lt;02 binaries. We test our instrument performance on a known triple system, κ Peg, and show that our survey is delivering a factor of 10 better precision than previous similar surveys. We present astrometric detections of tertiary components to two B-type binaries: a 30 day companion to α Del, and a 50 day companion to ν Gem. We also collected radial velocity data for α Del with the Tennessee State University Automated Spectroscopic Telescope at Fairborn Observatory. We are able to measure the orbits and masses of all three components in these systems. We find that the previously published radial velocity orbit for the inner pair of ν Gem is not consistent with our visual orbit. The precision achieved for these orbits suggests that our ARMADA survey will be successful at discovering new compact triple systems to A/B-type binary systems, leading to better statistics of hierarchical system architectures and formation history.

Orbits and Structure of the Quadruple Systems GJ 225.1 and FIN 332

Only a handful of quadruple systems with two accurate inner visual orbits are known. Architecture of two such systems is studied here to determine period ratios, mutual orbit orientation, and other parameters; updated orbital elements and their errors are derived. Gliese 225.1 (HIP 28442) is composed of three K-type and one M-type dwarfs and has inner orbital periods of 67.2+-0.2 and 23.4+-0.5 yr. Its inner orbits have small mutual inclination and are likely coplanar with the outer orbit of ~2 kyr period. The quadruple system FIN 332 (HIP 92037) consists of four early A type stars with similar masses and magnitudes. Both its inner orbits with periods of 27.6+-0.2 and 39.8+-0.4 yr have large eccentricities (0.82 and 0.84). Their orientation in the sky is remarkably similar. In contrast, the outer orbit with a period of ~5 kyr has a large relative inclination to the inner orbits. Dynamics and formation of these quadruple systems are briefly discussed.

Visual Orbits of Spectroscopic Binaries with the CHARA Array. III. HD 8374 and HD 24546

Abstract We present the visual orbits of two long-period spectroscopic binary stars, HD 8374 and HD 24546, using interferometric observations acquired with the CHARA Array and the Palomar Testbed Interferometer. We also obtained new radial velocities from echelle spectra using the APO 3.5 m and Fairborn 2.0 m telescopes. By combining the visual and spectroscopic observations, we solve for the full, three-dimensional orbits and determine the stellar masses and distances to within 3% uncertainty. We then estimate the effective temperature and radius of each component star through Doppler tomography and spectral energy distribution analyses, in order to compare the observed stellar parameters to the predictions of stellar evolution models. For HD 8374, we find masses of M 1 = 1.636 ± 0.050M ⊙ and M 2 = 1.587 ± 0.049M ⊙, radii of R 1 = 1.84 ± 0.05R ⊙ and R 2 = 1.66 ± 0.12R ⊙, temperatures of K and K, and an estimated age of 1.0 Gyr. For HD 24546, we find masses of M 1 = 1.434 ± 0.014M ⊙ and M 2 = 1.409 ± 0.014M ⊙, radii of R 1 = 1.67 ± 0.06R ⊙ and R 2 = 1.60 ± 0.10R ⊙, temperatures of K and K, and an estimated age of 1.4 Gyr. HD 24546 is therefore too old to be a member of the Hyades cluster, despite its physical proximity to the group.

Nearby Quintuple Systems κ Tucanae and ξ Scorpii

Abstract Architecture and parameters of two wide, nearby hierarchical systems containing five solar-type stars each, κ Tuc and ξ Sco, are studied. Using Gaia astrometry and photometry, masses are determined from visual orbits and isochrones, and effective temperatures from spectra or colors. Both systems are ∼2 Gyr old. Their spatial motion corresponds to a young disk but does not match any known kinematic group. Internal proper motions relative to the center of mass and radial velocities show that wide ∼8 kau outer pairs are bound. No correlation between orbit orientations in the inner subsystems is observed. All masses except one are confined to the narrow range from 0.8 to 1.5 solar. Strongly correlated masses and wide orbits can be explained if those systems formed by fragmentation in relative isolation and their components accreted gas from a common source, as expected in a hierarchical collapse. Young moving groups could be formed in similar environments, and many of them contain high-order hierarchies.

Observations of Binary Stars with the Differential Speckle Survey Instrument. IX. Observations of Known and Suspected Binaries, and a Partial Survey of Be Stars

Abstract We report 370 measures of 170 components of binary and multiple-star systems, obtained from speckle imaging observations made with the Differential Speckle Survey Instrument at Lowell Observatory’s Discovery Channel Telescope in 2015 through 2017. Of the systems studied, 147 are binary stars, 10 are seen as triple systems, and 1 quadruple system is measured. Seventy-six high-quality nondetections and 15 newly resolved components are presented in our observations. The uncertainty in relative astrometry appears to be similar to our previous work at Lowell, namely, linear measurement uncertainties of approximately 2 mas, and the relative photometry appears to be uncertain at the 0.1–0.15 mag level. Using these measures and those in the literature, we calculate six new visual orbits, including one for the Be star 66 Oph and two combined spectroscopic–visual orbits. The latter two orbits, which are for HD 22451 (YSC 127) and HD 185501 (YSC 135), yield individual masses of the components at the level of 2% or better, and independent distance measures that in one case agrees with the value found in the Gaia DR2 and in the other disagrees at the 2σ level. We find that HD 22451 consists of an F6V+F7V pair with orbital period of 2401.1 ± 3.2 days and masses of 1.342 ± 0.029 and . For HD 185501, both stars are G5 dwarfs that orbit one another with a period of 433.94 ± 0.15 days, and the masses are 0.898 ± 0.012 and . We discuss the details of both the new discoveries and the orbit objects.

The Gemini Planet Imager Exoplanet Survey: Dynamical Mass of the Exoplanet β Pictoris b from Combined Direct Imaging and Astrometry

Abstract We present new observations of the planet β Pictoris b from 2018 with the Gemini Planet Imager (GPI), the first GPI observations following conjunction. Based on these new measurements, we perform a joint orbit fit to the available relative astrometry from ground-based imaging, the Hipparcos Intermediate Astrometric Data (IAD), and the Gaia DR2 position, and demonstrate how to incorporate the IAD into direct imaging orbit fits. We find a mass consistent with predictions of hot-start evolutionary models and previous works following similar methods, though with larger uncertainties: 12.8+5.3 −3.2 M Jup. Our eccentricity determination of disfavors circular orbits. We consider orbit fits to several different imaging data sets, and find generally similar posteriors on the mass for each combination of imaging data. Our analysis underscores the importance of performing joint fits to the absolute and relative astrometry simultaneously, given the strong covariance between orbital elements. Time of conjunction is well-constrained within 2.8 days of 2017 September 13, with the star behind the planet’s Hill sphere between 2017 April 11 and 2018 February 16 (±18 days). Following the recent radial velocity detection of a second planet in the system, β Pic c, we perform additional two-planet fits combining relative astrometry, absolute astrometry, and stellar radial velocities. These joint fits find a significantly smaller mass (8.0 ± 2.6 M Jup) for the imaged planet β Pic b, in a somewhat more circular orbit. We expect future ground-based observations to further constrain the visual orbit and mass of the planet in advance of the release of Gaia DR4.

A study of the physical properties of SB2s with both the visual and spectroscopic orbits

ABSTRACT The study of a selected set of 69 double-lined spectroscopic binaries (SB2) with well-defined visual and spectroscopic orbits was carried out. The orbital parallax, the mass, the colour, and the luminosity of each component were derived from observational data for almost all of these systems. We have also obtained an independent estimation of the component masses by comparing the colour–magnitude diagram (CMD) to the stellar evolution tracks reported by Pietrinferni. Nearly all of the observational points on the CMD are located between two tracks of slightly different mass or which fall very close to the one corresponding to a unique mass value. The masses obtained from the stellar model are in good agreement with their empirical values determined by parallax techniques (orbital, Gaia, and dynamical). This means that our adopted model is rather reliable and can therefore be used to infer further information, such as the age of each component in the studied systems. Our results indicate a fair correspondence between the age of primaries and secondary stars within 3σ. Nevertheless, we caution that these age indications suffer of uncertainties due to both inhomogeneities/low precision of the adopted photometric data and possible systematics. Finally, it is statistically shown that along with the orbital and trigonometric parallaxes, the dynamical parallax can serve as a reliable tool for distance estimates.

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.

An Updated Visual Orbit of the Directly Imaged Exoplanet 51 Eridani b and Prospects for a Dynamical Mass Measurement with Gaia

Abstract We present a revision to the visual orbit of the young, directly imaged exoplanet 51 Eridani b using four years of observations with the Gemini Planet Imager. The relative astrometry is consistent with an eccentric ( ) orbit at an intermediate inclination ( °), although circular orbits cannot be excluded due to the complex shape of the multidimensional posterior distribution. We find a semimajor axis of au and a period of yr, assuming a mass of 1.75 for the host star. We find consistent values with a recent analysis of VLT/SPHERE data covering a similar baseline. We investigate the potential of using the absolute astrometry of the host star to obtain a dynamical mass constraint for the planet. The astrometric acceleration of 51 Eri derived from a comparison of the Hipparcos and Gaia catalogs was found to be inconsistent at the 2σ–3σ level with the predicted reflex motion induced by the orbiting planet. Potential sources of this inconsistency include a combination of random and systematic errors between the two astrometric catalogs and the signature of an additional companion within the system interior to current detection limits. We also explored the potential of using Gaia astrometry alone for a dynamical mass measurement of the planet by simulating Gaia measurements of the motion of the photocenter of the system over the course of the extended 8 yr mission. We find that such a measurement is only possible (&gt;98% probability) given the most optimistic predictions for the Gaia scan astrometric uncertainties for bright stars and a high mass for the planet (≳3.6 M Jup).