20.6.4 nss_vim_fl

This table contains non-single-star models for sources compatible with an Variability Induced Mover (VIM) solution. Several possible models are in principle 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.
For DR3, only VIMF solutions are provided here.
Details about the formalism used to derive the parameters in this table are given in the on-line documentation, see Chapter 7.

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_vim_fl are:

• •

  VIMF: Variability-Induced Mover with fixed configuration

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

Right ascension $\alpha$ of the source in ICRS at the reference epoch gaia_source.ref_epoch, if the total flux is then equal to the reference flux.

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. 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.

dec : Declination (double, Angle[deg])

Declination $\delta$ of the source in ICRS at the reference epoch gaia_source.ref_epoch, if the total flux is then equal to the reference flux.

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. 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.

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. 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.

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. 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.

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. 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.

ref_flux_g : Reference flux in the G band (float, Flux[e${}^{-}$ s${}^{-1}$])

The photocentre of a VIM object moves in relation to its total flux in the G band. In a VIMF solution, the position (ra, dec) is the mean position of the object when its total flux is the reference flux. In practice, the reference flux is close to (or is) the median flux of the object.

vim_d_ra : VIM coordinate in RA (double, Angle[mas] )

The coordinate, on the RA axis and measured from the variable component, of the position of the photocentre when the total flux is equal to the reference flux. The right ascension of the variable component is therefore: ra - vim_d_ra.

vim_d_ra_error : Standard error of VIM coordinate in RA (float, Angle[mas] )

Standard error of the coordinate of the photocentre on the RA axis. 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.

vim_d_dec : VIM coordinate in DEC (double, Angle[mas] )

The coordinate, on the declination axis and measured from the variable component, of the position of the photocentre when the total flux is equal to the reference flux. The declination of the variable component is therefore: dec - vim_d_dec.

vim_d_dec_error : Standard error of VIM coordinate in DEC (float, Angle[mas] )

Standard error of the coordinate of the photocentre on the declination axis. 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.

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.

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_vim_fl, all parameters of a given non-single star model are always fitted and all bits are set to 1. The parameters covered in each case and the value taken by bit_index are given by:

• •

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

  • –

    ra

  • –

    dec

  • –

    parallax

  • –

    pmra

  • –

    pmdec

  • –

    vim_d_ra

  • –

    vim_d_dec

corr_vec : Vector form of the upper triangle of the correlation matrix (float[50] 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.

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 abscissa of the i${}^{th}$ transit, $y_i$ is the value calculated from the model, and ${\sigma }_i$ is the uncertainty obtained from the astrometric reduction, without any correction.

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 addresses some these limitations.

For astrometric binaries, it is defined as a function of the parameters that characterise the model, divided by its revised 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 model is as follows: for the VIMF model, it is the norm of the position of the photocentre for the reference flux, measured from the variable component, i.e. the norm of the vector (vim_d_ra,vim_d_dec).

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.