7.7 Combined solutions and post-treatment 7.7.1 Introduction 7.7.3 Processing steps

7.7.2 Properties of the input data

The combined solutions pipeline is fed with the solutions of all upstream development units. In the case a source is common in the results of more than one modules then they are ordered by their period, if the model contains one, or by model if not. In the simplest case that a source is identified by only one module then this solution is copied to the output. This is the treatment that is performed also in the case a source belongs to more than one model which are not supposed to be combined or when the consistency of the two solutions is not convincing.

In the case of EclipsingSpectro only EclipsingBinaries were combined with SB1 or SB2 spectroscopic binaries. Concerning the AstroSpectroSB1 model, Table 7.5 shows the models used for combination. One may notice two astrometric models that do not exist in the output of astrometric binaries, the OrbitalPoorlyConstrained and StochasticAstro are lower quality solutions produced internally and were kept for combination only when their existence was confirmed by the existence of another, compatible orbital solution. The same applies for about 12 000 StochasticSB1, i.e. where no satisfactory model had been found upstream to model the RV variations, and where the combination provides the spectroscopic orbital information (some may be ternary systems, though). No combination can imply SB1C as they have a too short period to hope for an Orbital counterpart. Acceleration solutions have not been used either as it was initially thought that the long periods that they represent would not be compatible with the shorter period spectroscopic solutions. However it happened that acceleration solutions have been adopted while orbital solutions could have been also acceptable, reducing the number of potential combinations. In clear, multiple NSS solutions for a given source do not imply that the source pertain to a ternary or higher order system: many combinations are also possible.

Table 7.5: Models used to produce AstroSpectroSB1 binaries. StochasticAstro were only combined with SB1 binaries.

Model 1	Model 2	Output
	47.3% SB1	AstroSpectroSB1
92.2% Orbital	5.4% FirstDegreeTrendSB1
7.6% OrbitalPoorlyConstrained	12.4% SecondDegreeTrendSB1
0.1% OrbitalAlternative	0.2% ThirdDegreeTrendSB1
	34.6% StochasticSB1

Before trying a combination the pipeline uses the criterion (7.46) to decide if the two input solutions are compatible for combination:

		$\displaystyle[(P_{2}\ \mathrm{mod}\ P_{1})<5\sigma_{\mathrm{max}}\ \mathrm{OR~% {}}(P_{2}\ \mathrm{mod}\ P_{1})<0.1P_{1}\ \mathrm{OR~{}}(P_{2}\ \mathrm{mod}\ % P_{1})>0.9P_{1}]\ \mathrm{AND~{}}$		(7.46)
		$\displaystyle(P_{2}/P_{1}<1.1)\ \mathrm{AND~{}}\mathrm{axisCriterion}=\mathrm{true}$		(7.46)

where $P_{1}$ is the model with the smallest period, $P_{2}$ is the largest and $\sigma_{\mathrm{max}}$ is the largest of the provided uncertainties. The axisCriterion is defined empirically and is presented in Equation 7.47. It has effectively been applied to filter out only the AstroSpectroSB1 cases that involve a spectroscopic solution of SB1 or SB1C model. In the EclipsingSpectro case this is not applicable.

K_{\mathrm{astro}}\geq K_{\mathrm{spectro}}-2.8\ \mathrm{OR~{}}0.7*K_{\mathrm{% astro}}-12\leq K_{\mathrm{spectro}}

(7.47)

where $K_{\mathrm{astro}}$ is the semi-amplitude of the radial velocity derived from the elements of the astrometric solution as defined in Equation 7.50 using $a_{0}$ instead of $a_{1}$ while $K_{\mathrm{spectro}}$ is the semi-amplitude as calculated using the spectroscopic solution.

Note that during the verification phase (Section 7.7.4) a supplementary filtering has been done, which reduced further the number of combinations.

gaia data release 3 documentation

7.7.2 Properties of the input data