20.6.1 nss_two_body_orbit

This table contains non-single-star orbital models for sources compatible with an orbital two-body solution. This covers astrometric binaries, spectroscopic binaries, eclipsing binaries and certain combinations thereof. Several possible models are hosted within the same table and they are indicated by the field nss_solution_type. The description of this latter lists all possible solution types considered for this release. Only a selection of parameters hosted in this table are provided here, depending on the solution. The details of those is given in the description of field bit_index, which can also be used to extract the relevant elements of the correlation vector corr_vec.
Details about the formalism used to derive the parameters in this table are given in the on-line documentation, see Chapter 7. Warning: as a source may receive independent astrometric, spectroscopic or photometric orbits, a query using a given source_id may return several solutions. This has to be accounted for when doing a crossmatch by source_id.

Columns description:

solution_id : Solution Identifier (long)

All Gaia data processed by the Data Processing and Analysis Consortium comes tagged with a solution identifier. This is a numeric field attached to each table row that can be used to unequivocally identify the version of all the subsystems that were used in the generation of the data as well as the input data used. It is mainly for internal DPAC use but is included in the published data releases to enable end users to examine the provenance of processed data products. To decode a given solution ID visit https://gaia.esac.esa.int/decoder/solnDecoder.jsp

source_id : Source Identifier (long)

A unique single numerical identifier of the source obtained from gaia_source (for a detailed description see gaia_source.source_id).

nss_solution_type : NSS model adopted (string)

This is the non-single star model which has been adopted for the published solution, see online documentation, Chapter 7, for details.

The solution types covered in table nss_two_body_orbit are:

• •

  Orbital: Orbital model for an astrometric binary

• •

  OrbitalAlternative[Validated]: Alternative orbital model mainly for low S/N systems, with a subset containing suffix ‘Validated’

• •

  OrbitalTargetedSearch[Validated]: Orbital model for a priori known systems, with a subset containing suffix ‘Validated’

• •

  EclipsingBinary: Eclipsing binary model

• •

  EclipsingSpectro: Combined eclipsing binary + spectroscopic orbital model

• •

  SB1: Single Lined Spectroscopic binary model

• •

  SB2: Double Lined Spectroscopic binary model

• •

  SB1C: Single Lined Spectroscopic binary model with circular orbit

• •

  SB2C: Double Lined Spectroscopic binary model with circular orbit

• •

  AstroSpectroSB1: Combined astrometric + single lined spectroscopic orbital model

ra : Right ascension (double, Angle[deg])

Barycentric right ascension $\alpha$ of the source in ICRS at the reference epoch gaia_source.ref_epoch

ra_error : Standard error of right ascension (float, Angle[mas])

Standard error ${\sigma }_{\alpha *}\equiv {\sigma }_{\alpha }\cos \delta$ of the right ascension of the source in ICRS at the reference epoch gaia_source.ref_epoch.

dec : Declination (double, Angle[deg])

Barycentric declination $\delta$ of the source in ICRS at the reference epoch gaia_source.ref_epoch

dec_error : Standard error of declination (float, Angle[mas])

Standard error ${\sigma }_{\delta }$ of the declination of the source in ICRS at the reference epoch gaia_source.ref_epoch

parallax : Parallax (double, Angle[mas] )

Absolute stellar parallax $\varpi$ of the source at the reference epoch gaia_source.ref_epoch

parallax_error : Standard error of parallax (float, Angle[mas] )

Standard error ${\sigma }_{\varpi }$ of the stellar parallax at the reference epoch gaia_source.ref_epoch

pmra : Proper motion in right ascension direction (double, Angular Velocity[mas yr${}^{-1}$])

Proper motion in right ascension ${\mu }_{\alpha *}\equiv {\mu }_{\alpha }\cos \delta$ of the source in ICRS at the reference epoch gaia_source.ref_epoch. This is the local tangent plane projection of the proper motion vector in the direction of increasing right ascension.

pmra_error : Standard error of proper motion in right ascension direction (float, Angular Velocity[mas yr${}^{-1}$] )

Standard error ${\sigma }_{\mu \alpha *}$ of the local tangent plane projection of the proper motion vector in the direction of increasing right ascension at the reference epoch gaia_source.ref_epoch

pmdec : Proper motion in declination direction (double, Angular Velocity[mas yr${}^{-1}$] )

Proper motion in declination ${\mu }_{\delta }$ of the source at the reference epoch gaia_source.ref_epoch. This is the projection of the proper motion vector in the direction of increasing declination.

pmdec_error : Standard error of proper motion in declination direction (float, Angular Velocity[mas yr${}^{-1}$] )

Standard error ${\sigma }_{\mu \delta }$ of the proper motion component in declination at the reference epoch gaia_source.ref_epoch

a_thiele_innes : Thiele-Innes element A (double, Angle[mas] )

The Thiele-Innes element $A$ of the orbit of the photocentre (for the orbital model). This parameter is fitted for orbital models based on astrometry (nss_solution_type = Orbital, OrbitalAlternative[Validated], or OrbitalTargetedSearch[Validated])) or a combination of astrometry and radial velocities (nss_solution_type = AstroSpectroSB1). For other orbital models based on photometry or radial velocities, or their combination, the Campbell parameters are fitted instead. See more details, including the transformation from the $A,B,F,G$ Thiele-Innes elements to the $a_0$, $i$, $\omega$ and $\mathrm{\Omega }$ Campbell elements, in the on-line documentation (Chapter 7).

a_thiele_innes_error : Standard error of Thiele-Innes element A (float, Angle[mas] )

Standard error of the Thiele-Innes element $A$ of the orbit of the photocentre (for the orbital model). The standard errors are derived from the variance-covariance matrix of the solution, correcting the measurement uncertainties to obtain the goodness-of-fit F2=0.

b_thiele_innes : Thiele-Innes element B (double, Angle[mas] )

The Thiele-Innes element $B$ of the orbit of the photocentre (for the orbital model). This parameter is fitted for orbital models based on astrometry (nss_solution_type = Orbital, OrbitalAlternative[Validated], or OrbitalTargetedSearch[Validated])) or a combination of astrometry and radial velocities (nss_solution_type = AstroSpectroSB1). For other orbital models based on photometry or radial velocities, or their combination, the Campbell parameters are fitted instead. See more details, including the transformation from the $A,B,F,G$ Thiele-Innes elements to the $a_0$, $i$, $\omega$ and $\mathrm{\Omega }$ Campbell elements, in the on-line documentation (Chapter 7).

b_thiele_innes_error : Standard error of Thiele-Innes element B (float, Angle[mas] )

Standard error of the Thiele-Innes element $B$ of the orbit of the photocentre (for the orbital model). The standard errors are derived from the variance-covariance matrix of the solution, correcting the measurement uncertainties to obtain the goodness-of-fit F2=0.

f_thiele_innes : Thiele-Innes element F (double, Angle[mas] )

The Thiele-Innes element $F$ of the orbit of the photocentre (for the orbital model). This parameter is fitted for orbital models based on astrometry (nss_solution_type = Orbital, OrbitalAlternative[Validated], or OrbitalTargetedSearch[Validated])) or a combination of astrometry and radial velocities (nss_solution_type = AstroSpectroSB1). For other orbital models based on photometry or radial velocities, or their combination, the Campbell parameters are fitted instead. See more details, including the transformation from the $A,B,F,G$ Thiele-Innes elements to the $a_0$, $i$, $\omega$ and $\mathrm{\Omega }$ Campbell elements, in the on-line documentation (Chapter 7).

f_thiele_innes_error : Standard error of Thiele-Innes element F (float, Angle[mas] )

Standard error of the Thiele-Innes element $F$ of the orbit of the photocentre (for the orbital model). The standard errors are derived from the variance-covariance matrix of the solution, correcting the measurement uncertainties to obtain the goodness-of-fit F2=0.

g_thiele_innes : Thiele-Innes element G (double, Angle[mas] )

The Thiele-Innes element $G$ of the orbit of the photocentre is fitted for orbital models based on astrometry (nss_solution_type = Orbital, OrbitalAlternative[Validated], or OrbitalTargetedSearch[Validated])) or a combination of astrometry and radial velocities (nss_solution_type = AstroSpectroSB1). For other orbital models based on photometry or radial velocities, or their combination, the Campbell parameters are fitted instead.

For orbits with small eccentricities (eccentricity and eccentricity_error is absent, see Section 7.2.5), g_thiele_innes is not an unknown in the model but is deduced from the $A,B,F$ Thiele-Innes elements, the whole set of which must yield $\omega =0$.

For more details, including the transformation from the $A,B,F,G$ Thiele-Innes elements to the $a_0$, $i$, $\omega$ and $\mathrm{\Omega }$ Campbell elements see Chapter 7 in the on-line documentation.

g_thiele_innes_error : Standard error of Thiele-Innes element G (float, Angle[mas])

Standard error of the Thiele-Innes element $G$ of the orbit of the photocentre (for the orbital model). The standard errors are derived from the variance-covariance matrix of the solution, correcting the measurement uncertainties to obtain the goodness-of-fit F2=0.

For orbits with small eccentricities (eccentricity and eccentricity_error is absent, see Section 7.2.5), g_thiele_innes is not an unknown in the model, being computed from $A,B,F$. g_thiele_innes_error is then set as unknown but it may be estimated applying the relations given in the documentation.

c_thiele_innes : C element of Thiele-Innes (double, Length & Distance[AU])

The Thiele-Innes element C representing the radial coordinate of the orbit of the primary around the barycentre, $C=a_1\sin \omega \sin i$, see Heintz (1978). This parameter is fitted for orbital models based on the combination of astrometry and radial velocities (nss_solution_type = AstroSpectroSB1). See more details in the on-line documentation (Chapter 7).

c_thiele_innes_error : Standard error of C element of Thiele-Innes (float, Length & Distance[AU])

Standard error of the Thiele-Innes element C.

h_thiele_innes : H element of Thiele-Innes (double, Length & Distance[AU])

The Thiele-Innes element H representing the radial coordinate of the orbit of the primary around the barycentre, $H=a_1\cos \omega \sin i$, see Heintz (1978). This parameter is fitted for orbital models based on the combination of astrometry and radial velocities (nss_solution_type = AstroSpectroSB1). See more details in the on-line documentation (Chapter 7).

h_thiele_innes_error : Standard error of H element of Thiele-Innes (float, Length & Distance[AU])

Standard error of the Thiele-Innes element H.

period : Orbital Period (double, Time[day])

Period of the orbital motion around the barycentre. For Eclipsing Binary solutions, it is the period obtained from the photometric variability analysis reported in field vari_eclipsing_binary.frequency. For EclipsingSpectro combined solution, it is either the aforementioned period, or the one stemming from the Spectroscopic binary model, in which case the bit 57 for nss_two_body_orbit.flags will be set to 1.

period_error : Standard error of Orbital Period (float, Time[day])

Standard error of the period of the orbit of the photocentre around the barycentre. The standard errors are derived from the variance-covariance matrix of the solution, correcting the measurement uncertainties to obtain the goodness-of-fit F2=0.

For Eclipsing Binary solutions, this error is provided in nss_two_body_orbit.input_period_error. For EclipsingSpectro combined solution, it is either the aforementioned period, or the one stemming from the Spectroscopic binary model, in which case the bit 57 for nss_two_body_orbit.flags will be set to 1.

t_periastron : Periastron epoch (double, Time[day])

The epoch at periastron is given relative to gaia_source.ref_epoch, in the range [–period/2, +period/2].

In case the eccentricity is not null, t_periastron is the time of periastron passage, whatever the input solution: astrometric, spectroscopic or eclipsing binary.

If the eccentricity is null, then the periastron has no meaning and the following convention is adopted:

• •

  for astrometric binaries the periastron is positioned on the ascending node and in the absence of radial velocity measurements, the ascending node is the node whose position angle is between 0 and 180 degrees;

• •

  for spectroscopic binaries the periastron is positioned on the ascending node, the definition of which is specified by the knowledge of the radial velocity curve and is the maximum of the radial velocity curve;

• •

  for eclipsing binaries it is the time of primary eclipse;

• •

  for combined eclipsing/spectroscopic binaries, it is the time of primary eclipse.

t_periastron_error : Standard error of Periastron epoch (float, Time[day])

Standard error of the periastron epoch, t_periastron, defined above. The standard errors are derived from the variance-covariance matrix of the solution, correcting the measurement uncertainties to obtain the goodness-of-fit F2=0.

eccentricity : eccentricity (double)

Eccentricity of the orbit.

eccentricity_error : Standard error of eccentricity (float)

Standard error of the eccentricity of the orbit. The standard errors are derived from the variance-covariance matrix of the solution, correcting the measurement uncertainties to obtain the goodness-of-fit F2=0.

If the eccentricity is null, a special circular or a pseudo-circular solution is implemented (see Section 7.2.5) and the standard error will be null.

For orbits with small eccentricities (eccentricity and eccentricity_error is absent, see Section 7.2.5), the standard error will be null to indicate that the orbit has been made pseudo-circular.

center_of_mass_velocity : The velocity of the centre of mass (double, Velocity[km s${}^{-1}$])

The radial velocity of the centre of mass for SB1, SB1C, SB2 and SB2C solutions.

center_of_mass_velocity_error : Standard error of The velocity of the centre of mass (float, Velocity[km s${}^{-1}$])

Standard error of the center_of_mass_velocity as defined above. The standard errors are derived from the variance-covariance matrix of the final solution in the standard way.

semi_amplitude_primary : Semi-amplitude of the centre of mass (double, Velocity[km s${}^{-1}$])

The semi-amplitude of the radial velocity curve related to the first component: K1. The first component is either the only visible one (concerns SB1, SB1C solutions) or is expected to be any of the two stars (concerns SB2, SB2C solutions).

semi_amplitude_primary_error : Standard error of Semi-amplitude of the centre of mass (float, Velocity[km s${}^{-1}$])

Standard error of the semi_amplitude_primary as defined above. The standard errors are derived from the variance-covariance matrix of the final solution in the standard way.

semi_amplitude_secondary : The semiamplitude of the radial velocity curve for second component (double, Velocity[km s${}^{-1}$] )

The semi-amplitude of the radial velocity curve related to the second component: K2 (concerns SB2, SB2C solutions).

semi_amplitude_secondary_error : Standard error of The semiamplitude of the radial velocity curve for second component (float, Velocity[km s${}^{-1}$] )

Standard error of the semi_amplitude_secondary as defined above. The standard errors are derived from the variance-covariance matrix of the final solution in the standard way.

mass_ratio : Mass ratio (double)

The mass ratio $q=M_S/M_P$ is given only for EclipsingSpectro solutions.

mass_ratio_error : Standard error of Mass ratio (float)

Standard error of the mass_ratio as defined above. In the pure spectroscopic (concerns SB2 and SB2C), the pure eclipsing, and the combined spectroscopic-eclipsing cases, the standard errors are derived from the variance-covariance matrix of the final solution in the standard way. In all the other cases, the standard errors are derived from the variance-covariance matrix of the solution, correcting the measurement uncertainties to obtain the goodness-of-fit F2=0.

fill_factor_primary : Fill factor of primary (double)

The fill factor of the primary component, as determined from the eclipsing case. When $s_1\in [0,1)$ the component does not fill its Roche lobe. When $s_1=1$ the component fills its Roche lobe exactly (semi-detached system). When $s_1>1$ then $s_2>1$ as well, and the binary system is over-contact (common envelope system).

fill_factor_primary_error : Standard error of Fill factor of primary (float)

Standard error of the fill factor of the primary as defined above, derived from the variance-covariance matrix of the final solution in the standard way.

fill_factor_secondary : Fill factor of secondary (double)

The fill factor of the secondary component as determined from the eclipsing case. When $s_2\in [0,1)$ the component does not fill its Roche lobe. When $s_2=1$ the component fills its Roche lobe exactly (semi-detached system). When $s_2>1$ then $s_1>1$ as well, and the binary system is over-contact (common envelope system).

fill_factor_secondary_error : Standard error of Fill factor of secondary (float)

Standard error of the fill factor of the secondary as defined above, derived from the variance-covariance matrix of the final solution in the standard way.

inclination : Orbital inclination (double, Angle[deg])

Inclination of the orbital plane with respect to the sky. The angle is estimated for eclipsing binary solutions only, and given between 0 and 90${}^{\circ }$ within uncertainties. For astrometric binaries, the inclination is not an estimated parameter, as it is already represented by the $A,B,F,G$ Thiele Innes elements, and should be derived from them.

inclination_error : Standard error of Orbital inclination (float, Angle[deg])

Standard error on the orbital inclination as derived from the eclipsing binary solution.

arg_periastron : Argument of periastron (double, Angle[deg])

The argument of periastron is the angular position of the periastron as measured in the plane of the orbit in the sense of the object motion. When the spectroscopic orbit is established, the zero point of the angle is the ascending node (node on the line of nodes where the objects are moving away from the observer). In the absence of spectroscopic constraints, the zero point is the node whose position angle is between 0 and 180 degrees, the position angle being measured in the trigonometric direction. The argument of periastron is considered as fixed (no precession of the apsides). In the case of circular orbits, $\omega$ is undefined and set up arbitrarily to zero.

arg_periastron_error : Standard error of Argument of periastron (float, Angle[deg])

Standard error of the arg_periastron as defined above. In the pure spectroscopic case, the standard errors are derived from the variance-covariance matrix of the final solution in the standard way (concerns SB1, SB1C, SB2 and SB2C solutions). In all the other cases, the standard errors are derived from the variance-covariance matrix of the solution, correcting the measurement uncertainties to obtain the goodness-of-fit F2=0.

temperature_ratio : Ratio of the effective temperatures (double)

Ratio of the fitted effective temperature over that of the unfitted effective temperature.

See temperature_ratio_definition for a description of the fitting scenario.

temperature_ratio_error : Standard error of the ratio of the effective temperatures (double)

Standard error of the ratio of the effective temperatures, temperature_ratio.

temperature_ratio_definition : Code defining which fitting scenario did apply to the effective temperature (byte)

Code defining temperature_ratio:

1: temperature of the primary (fitted parameter) over temperature of the secondary (fixed parameter)

2: temperature of the secondary (fitted parameter) over temperature of the primary (fixed parameter)

with the convention that the primary component is always the one which is the more luminous in the $G$ band.

astrometric_n_obs_al : Total astrometric CCD observations in AL considered (int)

Total astrometric CCD observations considered in the along-scan direction.

astrometric_n_good_obs_al : Total astrometric CCD observations in AL actually used (int)

Total astrometric CCD observations actually used in the along-scan direction.

rv_n_obs_primary : Total number of radial velocities considered for the primary (int)

Total number of epoch radial velocities considered for the primary.

rv_n_good_obs_primary : Total number of radial velocities actually used for the primary (int)

Total number of epoch radial velocities actually used for the primary.

rv_n_obs_secondary : Total number of radial velocities considered for the secondary in the case of SB2 (int)

Total number of epoch radial velocities considered for the secondary in the case of SB2.

rv_n_good_obs_secondary : Total number of radial velocities actually used for the secondary in the case of SB2 (int)

Total number of epoch radial velocities actually used for the secondary in the case of SB2.

phot_g_n_obs : Total number of G photometry measurements considered (int)

Total number of G epoch photometry measurements considered.

phot_g_n_good_obs : Total number of G photometry measurements actually used (int)

Total number of G epoch photometry measurements actually used.

bit_index : boolean mask for the fields above in the corr_vec matrix (long)

The bit_index field corresponds to a boolean mask indicating which of the parameters have been fitted by the model applicable to the non-single-star solution type labelled in nss_solution_type. This bit index can then be used in order to identify the fields corresponding to each element of the correlation matrix served through corr_vec. When a given parameter has not been fitted, the corresponding elements are empty in the correlation matrix.

bit_index contains N+1 bits, where the leading bit (MSB) is always 1, and the other N bits correspond to the possible parameters of a given model.

For solution types hosted in table nss_two_body_orbit, not all parameters of a given non-single star model are always fitted and the parameters covered in each case and the value taken by bit_index are given by:

• •

  nss_solution_type = Orbital: these solutions have either all 12 parameters filled (bit index at 8191) or only 10 (bit index at 8179). The 12 parameters are the following:

  • –

    ra

  • –

    dec

  • –

    parallax

  • –

    pmra

  • –

    pmdec

  • –

    a_thiele_innes

  • –

    b_thiele_innes

  • –

    f_thiele_innes

  • –

    g_thiele_innes (not fitted if bit_index = 8179)

  • –

    eccentricity (not fitted if bit_index = 8179)

  • –

    period

  • –

    t_periastron

• •

  nss_solution_type = OrbitalAlternative[Validated] and OrbitalTargetedSearch[Validated]: the following 13 parameters are fitted though the bit index takes value 8191 (i.e., the same as the 12 parameter fields in nss_solution_type = Orbital ) as the astrometric_jitter term is not separately indexed in the bit representation.:

  • –

    ra

  • –

    dec

  • –

    parallax

  • –

    pmra

  • –

    pmdec

  • –

    a_thiele_innes

  • –

    b_thiele_innes

  • –

    f_thiele_innes

  • –

    g_thiele_innes

  • –

    period

  • –

    eccentricity

  • –

    t_periastron

• •

  nss_solution_type = SB1: the following 6 parameters are fitted and the bit index consequently takes value 127:

  • –

    period

  • –

    center_of_mass_velocity

  • –

    semi_amplitude_primary

  • –

    eccentricity

  • –

    arg_periastron

  • –

    t_periastron

• •

  nss_solution_type = SB1C: the following 4 parameters are fitted and the bit index consequently takes value 31:

  • –

    period

  • –

    center_of_mass_velocity

  • –

    semi_amplitude_primary

  • –

    t_periastron

• •

  nss_solution_type = SB2: the following 7 parameters are fitted and the bit index consequently takes value 255:

  • –

    period

  • –

    center_of_mass_velocity

  • –

    semi_amplitude_primary

  • –

    semi_amplitude_secondary

  • –

    eccentricity

  • –

    arg_periastron

  • –

    t_periastron

• •

  nss_solution_type = SB2C: the following 5 parameters are fitted and the bit index consequently takes value 63:

  • –

    period

  • –

    center_of_mass_velocity

  • –

    semi_amplitude_primary

  • –

    semi_amplitude_secondary

  • –

    t_periastron

• •

  nss_solution_type = AstroSpectroSB1: these solutions have either all 15 parameters filled (bit index at 65535) or only 12 (bit index at 65435). The 15 parameters are the following:

  • –

    ra

  • –

    dec

  • –

    parallax

  • –

    pmra

  • –

    pmdec

  • –

    a_thiele_innes

  • –

    b_thiele_innes

  • –

    f_thiele_innes

  • –

    g_thiele_innes (not fitted if bit_index = 65435)

  • –

    c_thiele_innes (not fitted if bit_index = 65435)

  • –

    h_thiele_innes

  • –

    center_of_mass_velocity

  • –

    eccentricity (not fitted if bit_index = 65435)

  • –

    period

  • –

    t_periastron

• •

  nss_solution_type = EclipsingBinary: the bit index can take different values and the following table indicates which of the possible 20 parameters are being fitted in each of the cases contemplated thereafter. In the case of temperature_ratio, the applicable index depends on the fitting scenario (see temperature_ratio_definition):
  BitIndex period t_periastron center_of_mass_velocity semi_amplitude_primary mass_ratio fill_factor_primary fill_factor_secondary eccentricity inclination arg_periastron temperature_ratio temperature_ratio 1329216 X X X X 1321088 X X X X 1342528 X X X X X X X 1337472 X X X X X 1337408 X X X X X 1342592 X X X X X X X 1329280 X X X X 1321024 X X X X

• •

  nss_solution_type = EclipsingSpectro: the bit index can take different values and the following table indicates which of the possible 20 parameters are being fitted in each of the cases contemplated thereafter. In the case of temperature_ratio, the applicable index depends on the fitting scenario (see temperature_ratio_definition):
  BitIndex period tperiastron center_of_mass_velocity semi_amplitude_primary mass_ratio fill_factor_primary fill_factor_secondary eccentricity inclination arg_periastron temperature_ratio temperature_ratio 1566784 X X X X X X X X 1517632 X X X X X X 1566848 X X X X X X X X 1517696 X X X X X X 1539200 X X X X X X X X X 1534080 X X X X X X X 1534016 X X X X X X X

corr_vec : Vector form of the upper triangle of the correlation matrix (column-major ordered) (float[231] array)

Correlation matrix of the fitted profile parameters for the applicable non-single star solution. The parameters stored in this matrix and their order is given in the description of field bit_index. Since not all parameters of a given solution model are systematically fitted, the matrix can contain empty elements at the corresponding indices.

For astrometric binaries, contrary to the fields obj_func and goodness_of_fit, the matrix corresponds to a solution calculated by correcting the uncertainties of the astrometric transits so that the goodness-of-fit $F_2$ is zero.

Only non-zero, non-unity, correlation coefficients from the correlation matrix M are provided here. They are served as a linear array of constant size $S=n(n-1)/2$ corresponding to the full normal matrix of dimension $n\times n$. The ordering of the elements in the linear array follows a column-major storage scheme, i.e.:

obj_func : value of the objective function at the solution (float)

The ${\chi }^2$, defined as ${\sum }_{i=1}^n{(x_i-y_i)}^2/{\sigma }_i^2$, where $x_i$ is the observation of the i${}^{th}$ transit, $y_i$ is the value calculated from the model, and ${\sigma }_i$ is the uncertainty associated with the observation.

goodness_of_fit : goodness of fit in the Hipparcos sense (float)

Goodness-of-fit statistic of the solution. This is the ‘gaussianized chi-square’ (Wilson and Hilferty (1931)’s cube root transformation), which for good fits should approximately follow a normal distribution with zero mean value and unit standard deviation.

This statistic is computed according to the formula:

where obj_func is hopefully a ${\chi }^2$ and $\nu$ is the number of degrees of freedom.

efficiency : Efficiency of the solution (float)

The efficiency expresses the level of correlation between the parameters of a model. A value of 1 means a total absence of correlation whereas it falls to 0 as the correlation increases. It is defined as the n-th root of the ratio of the product of the diagonal elements of the covariance matrix and the product of the eigen value of that matrix. When all the covariances are 0, the matrix is diagonal and the ratio is exactly 1. See also Eichhorn (1989).

significance : The significance of the solution (i.e. how worth keeping a model is) (float)

It turns out that F2 is not always enough to decide whether a model is worth keeping or not. The significance, equivalent to a signal-to-noise ratio, addresses some of these limitations.

For astrometric binaries, it is defined as a function of the parameters that characterise the model, divided by its uncertainty. This uncertainty is derived from the solution covariance matrix, where the uncertainties are corrected in order to obtain the corrected goodness-of-fit $F{2}_{\mathrm{corrected}}=0$. The function characterising the orbital model is the semi-major axis, derived from the Thiele-Innes elements.

For spectroscopic binaries, this is the ratio of the semi-amplitude of the primary over its uncertainty.

For astroSpectroSB1, the significance is the one of the astrometric semi-major axis, before the uncertainties are corrected. For eclipsingSpectro, it is the significance of the semi-amplitude of the primary.

flags : Quality flag for the achieved NSS solution (long)

Processing flag applicable to specific non-single-star solutions. The meaning of each of those is given in the table below.

conf_spectro_period : The probability of the period for not being due to (gaussian white) noise. Relevant for SB1, SB1C, SB2 and SB2C models. To be ignored otherwise. (float)

One of the first important step in the analysis of the RV time series suspected to present variations is the computation of a Fourier periodogram and the search for a period. A probability can be associated with the selected period. This probability is 1 - SL (significance level) where the SL is the probability to observe at least such a peak under the null-hypothesis of white noise. A probability of 1 indicates a very significant periodicity.

This field is only relevant for SB1, SB1C, SB2 and SB2C models and can be ignored otherwise.

r_pole_sum : Sum of the polar radii of primary and secondary (in units of the semi-major axis) (double)

The sum of the polar radii of the primary and secondary in the Roche model corresponding to the eclipsing solution. Provided as a convenience.

r_l1_point_sum : L1-pointing radii of primary and secondary (in units of the semi-major axis) (double)

The sum of the radii of the primary and secondary that points towards the first Lagrange point ($L_1$) in the Roche model corresponding to the eclipsing solution. Provided as a convenience.

r_spher_sum : Sum of the radii of sphere having the same volume as the primary and secondary (in units of the semi-major axis (double)

The sum of the radii of a sphere having the same volume as that of the Roche model for the primary and secondary. Provided as a convenience.

ecl_time_primary : Time of mid-eclipse of the primary by the secondary (double, Time[Julian Date (day)])

Time of mid-eclipse of the primary by the secondary, expressed relative to the same reference epoch as the periastron epoch, i.e., gaia_source.ref_epoch.

ecl_time_secondary : Time of mid-eclipse of the secondary by the primary (double, Time[Julian Date (day)])

Time of mid-eclipse of the secondary by the primary, expressed relative to the same reference epoch as the periastron epoch, i.e., gaia_source.ref_epoch.

ecl_dur_primary : Duration of primary eclipse assuming spherical components (double, Time[day])

An estimation of primary eclipse duration assuming spherical components with radii equal to the polar radii of the Roche model. This is generally accurate for detached systems but an underestimate for overcontact ones.

ecl_dur_secondary : Duration of secondary eclipse assuming spherical components (double, Time[day])

An estimation of secondary eclipse duration assuming spherical components with radii equal to the polar radii of the Roche model. This is generally accurate for detached systems but an underestimate for overcontact ones.

g_luminosity_ratio : Ratio of the G-band luminosity of the secondary over the primary (double)

Ratio of the G-band luminosity of the secondary over the primary.

input_period_error : Standard error of the period taken from vari_eclipsing_binary.frequency_error (float, Time[day])

For Eclipsing Binary models, the period is not fitted but taken instead from the variability analysis published in table vari_eclipsing_binary. This input period is tabulated in nss_two_body_orbit.period, but its standard error is not indicated in nss_two_body_orbit.period_error. It is registered in nss_two_body_orbit.input_period_error instead.

g_rank : Rank of the G-band solution (double)

An estimate of the quality of the fit based on the ‘fraction of variance unexplained’ (FVU) of the Eclipsing Binary model.

astrometric_jitter : Uncorrelated astrometric jitter term (double, Angle[mas])

In order to account for some poorly calibrated effects, this is an excess astrometric noise quadratically added to the uncertainty on the observations such that the resulting gaussianised Goodness of Fit is null. This applies to OrbitalAlternative[Validated] and OrbitalTargetedSearch[Validated] solutions only.