Bayesian analysis of exoplanet and binary orbits - Demonstrated using astrometric and radial-velocity data of Mizar A

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Volume 545 (September 2012)

A&A, 545 (2012) A79

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Table 1

Model parameters used by BASE.

			Widest			Data types ^b


Symbol	Designation	Unit	Prior Support	Cyclic ^a	Prior type	AM	RV	AM+RV

e	eccentricity	1	[0, 1)		uniform	×	×	×
f	orbital frequency	d^-1	(0, 1]		Jeffreys	×	×	×
χ	mean anomaly at t₁ over 2π	1	[0, 1)	×	uniform	×	×	×
ω, ω ₂	argument of periapsis ^c	rad	[0, 2π)	×	uniform	×	×	×
i	inclination	rad	[0, π)		uniform	×		×
Ω	position angle of the ascending node^e	rad	[0, 2π)	×	uniform	×		×
	semi-major axis of orbit of secondary around primary over distance	mas	[10^-3, 10^-5] ^f		Jeffreys	×
ϖ	parallax	arcsec	(0, 0.77] ^g		Jeffreys			×
V	RV offset	ms^-1	—		uniform		×	×
K, K _i	RV semi-amplitude ^d	ms^-1	≥0		mod. Jeffreys		×	×
τ ₊	standard deviation of additional AM noise	mas	≥0		mod. Jeffreys	×		×
σ ₊	standard deviation of additional RV noise	ms^-1	≥0		mod. Jeffreys		×	×

Notes.

^(a)

For cyclic parameters θ, the indicated lower and upper bounds are treated as equivalent by BASE (see Sect. 2.3).

^(b)

The types of data for which each parameter is relevant. Abbreviations: AM (astrometry), RV (radial velocities).

^(c)

Normal mode employs ω, while binary mode employs ω₂.

^(d)

Normal mode employs K, while binary mode employs K₁ and K₂.

^(e)

The widest prior range of Ω reduces to [0,π) if no RV data are provided, in which case it cannot be determined whether a given node is ascending or descending; then, Ω is defined to be the position angle of the first node.

^(f)

Lower bound corresponds to AM measurement uncertainty of 1 μas; upper bound according to wide-binary observations by Tolbert (1964).

^(g)

Interval includes trigonometric parallax of the nearest star, Proxima Centauri (Perryman et al. 1997).

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