2014
DOI: 10.1051/0004-6361/201322649
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Mass estimates for visual binaries with incomplete orbits

Abstract: The problem of estimating the total mass of a visual binary when its orbit is incomplete is treated with Bayesian methods. The posterior mean of a mass estimator is approximated by a triple integral over orbital period, orbital eccentricity and time of periastron. This reduction to 3D from the 7D space defined by the conventional Campbell parameters is achieved by adopting the Thiele-Innes elements and exploiting the linearity with respect to the four Thiele-Innes constants. The formalism is tested on syntheti… Show more

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Cited by 40 publications
(49 citation statements)
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“…For the relative orbit parameters, we performed a grid search over the parameters P , e, and T 0 . Once these three parameters are specified, then the eccentric anomaly can be computed and the best-fit orbit can be directly analytically determined, as described in detail by Lucy (2014). We searched across 10 4 randomly drawn values between 0 ≤ e < 1, 0 ≤ T 0 /P < 1, and log(P ) initially from 10 3 to 10 6 days.…”
Section: Joint Orbit and Parallax Analysismentioning
confidence: 99%
“…For the relative orbit parameters, we performed a grid search over the parameters P , e, and T 0 . Once these three parameters are specified, then the eccentric anomaly can be computed and the best-fit orbit can be directly analytically determined, as described in detail by Lucy (2014). We searched across 10 4 randomly drawn values between 0 ≤ e < 1, 0 ≤ T 0 /P < 1, and log(P ) initially from 10 3 to 10 6 days.…”
Section: Joint Orbit and Parallax Analysismentioning
confidence: 99%
“…To estimate the orbits of the G objects, we use uniform priors on all eight fitted parameters (six orbital parameters and two systematic uncertainty parameters). While uniform priors are commonly assumed in orbit fitting, this choice has been shown to cause potential biases in estimated parameters when orbital periods are much longer than the time baseline of observations 39,40 . To assess the impact of our fitting procedure in this context, we ran simulations to assess possible biases in the estimated parameters and to test the accuracy of confidence intervals obtained in our analysis 40 .…”
Section: Dependence On Priorsmentioning
confidence: 99%
“…However exoplanets are not the only objects to perturb the positions of stars; it has also been suggested that precise astrometric observations also have the potential to detect and characterize otherwise unseen black hole (BH) and neutron star (NS) companions to main sequence stars (Gould & Salim 2002;Tomsick & Muterspaugh 2010;Barstow et al 2014). Pioneering studies with ground-based interferometry have proven that precise tracking of the sky position of stars can afford some of the best measurements of binary star orbits, particularly when combined with spectroscopic radial velocities (Hartkopf et al 1996;Mason et al 1999;Bowler et al 2018;Gardner et al 2018;Lucy 2018). Extensions to space-based observatories have so far been limited to a handful of binaries observed using the Hubble Space Telescope's Fine Guidance Sensor (Franz et al 1998;Hershey & Taff 1998;Benedict et al 2000) and with Hipparcos (Pourbaix & Jorissen 2000;Halbwachs et al 2000;Pourbaix & Boffin 2003;Goldin & Makarov 2007).…”
Section: Introductionmentioning
confidence: 99%