Two New Close Binary Stars

Aitken, R. G.

doi:10.1086/122696

Cited by 15 publications

(18 citation statements)

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“…As noted already by Aitken (1918), when an orbit is incomplete, several theoretical orbits will provide satisfactory fits. Two possible responses to this circumstance are: 1) scan parameter space to find the global minimum (e.g., Hartkopf et al 1989) and assume that this orbit is the closest achievable approximation to the truth; or 2) scan parameter space to make a complete census of acceptable orbits and then compute an appropriate average of the individual mass determinations (e.g., Schaefer et al 2006).…”

Section: Bayesian Estimationmentioning

confidence: 73%

Mass estimates for visual binaries with incomplete orbits

Lucy

2014

A&A

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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 synthetic observational data covering a variable fraction of a model binary's orbit. The posterior mean of the mass estimator is numerically found to be unbiased when the data cover > ∼ 40% of the orbit.

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Section: Bayesian Estimationmentioning

confidence: 73%

Mass estimates for visual binaries with incomplete orbits

Lucy

2014

A&A

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“…(1) is easy to calculate, statistical tests indicate that the resulting ellipse seems inferior to that calculated from SDP. Despite what Aitken (1964), and others, have stated, it seems worthwhile to pay the computational price for a method such as SDP, where the minimization criterion bears a strict relationship to the fitted ellipse and convergence, unlike what may occur with nonlinear least squares, is guaranteed.…”

Section: Discussionmentioning

confidence: 96%

Double star orbits with semi-definite programming and alternatives

Branham¹

2009

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Many methods have been proposed to calculate the apparent orbit of a double star. Semi-definite programming (SDP) offers numerous advantages, but is mathematically and computationally demanding. Aitken suggested seventy years ago a simpler method that uses ordinary least squares to calculate the coefficients of a conic section to represent the apparent ellipse. But although simpler, this approach obfuscates what is being minimized geometrically, and the calculated ellipse appears inferior to that found from SDP. An alternative, proposed in various investigations, uses nonlinear least squares to minimize the square of the deviations in distance and position angle. This method can suffer from divergence or convergence, if it occurs, to a local rather than to a global minimum. All three methods are applied to three binary systems RST 4816, Wolf 424, and HR 466.

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“…Interpolating curves were drawn for the P.A. (t) and the separation (t) (Aitken 1964). These curves were constructed to vary smoothly with time and to yield a consistent value for the constant of areas, 2 ave ½DðP:A:Þ=Dt, across equally spaced time intervals.…”

Section: Computation Of Orbital Elementsmentioning

confidence: 99%

Dynamical Masses of Young Stars in Multiple Systems

et al. 2003

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We present recent measurements of the orbital motion in the young binaries DF Tau and ZZ Tau and the hierarchical triple Elias 12 that were obtained with the Fine Guidance Sensors on the Hubble Space Telescope and at the Keck Observatory using adaptive optics. Combining these observations with previous measurements from the literature, we compute preliminary orbital parameters for DF Tau and ZZ Tau. We find that the orbital elements cannot yet be determined precisely because the orbital coverage spans only $90 in position angle. Nonetheless, the range of possible values for the period and semimajor axis already defines a useful estimate for the total mass in DF Tau

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Two New Close Binary Stars

Cited by 15 publications

References 0 publications

Mass estimates for visual binaries with incomplete orbits

Mass estimates for visual binaries with incomplete orbits

Double star orbits with semi-definite programming and alternatives

Dynamical Masses of Young Stars in Multiple Systems

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