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Table 15

Initial osculating orbital elements aj,ej,ijj,ωj,Mj of the ξ Tau system as derived by our N-body model.

Parameter Value Unit Note

a 1 a 2 a 3 au
e 1 e 2 e 3
i 1 i 2 i 3 deg
Ω1 Ω2 Ω3 deg
ω 1 ω 2 ω 3 deg
M 1 M 2 M 3 deg
γ km s-1

deg mirror solution with χ2 = 2545,
Aa+Ab eclipses partially disappear
deg mirror solution with χ2 = 2749,
Aa+Ab eclipses partially disappear,
orbit 1 is retrograde w.r.t. orbit 2
deg mirror solution with χ2 = 2678

Notes. The epoch is T0 = 2 456 224.724705. The values below correspond to that of best-fit solutions with χ2 = 2578, with individual contributions: , , and . The masses of components in M units were , , and . Component B is on its lower limit . The mass of component C is very poorly constrained, it is more of a distant test mass compared to the others. The 3σ uncertainties of the elements were determined by a simplified one-dimensional χ2 mapping, assuming a relative increase of χ2 by a factor of 1.13, i.e. suitable for the number of degrees of freedom we have (ν = 908). The uncertainty values were verified using the bootstrap method with 100 random selections of datasets and corresponding simplex optimisation, but realistic uncertainties are likely to be larger than that because there are a number of local minima with statistically equivalent χ2 values. We do not report a full correlation matrix of our solution here. Its non-diagonal terms indicate higher values of uncertainties for those elements that are strongly correlated or anti-correlated with others (e.g. rmAa,ω2 = 0.74, ra12 = −0.77, ra1,ω2 = −0.80, ra3,i3 = −0.79).

(†)

The value is expressed in hierarchical Jacobian elements, with respect to Aa+Ab barycentre because this pair is the most compact and massive. If the reference point were the photocentre of the brightest component B instead, then the longitude of the ascending node would be shifted by − 180°.

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