20.6.3 nss_non_linear_spectro

This table contains non-single-star orbital models for spectroscopic binaries compatible with a trend. 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.

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_non_linear_spectro are:

• •

  FirstDegreeTrendSB1: Single Lined first degree trend

• •

  FirstDegreeTrendSB2: Double Lined first degree trend

mean_velocity : Mean velocity (double, Velocity[km s${}^{-1}$])

The mean_velocity as calculated over the current mission.

mean_velocity_error : Standard error of Mean velocity (float, Velocity[km s${}^{-1}$])

Standard error of mean_velocity. The standard errors are derived from the variance-covariance matrix of the final solution in the standard way.

first_deriv_velocity : First order derivative of the velocity (double, Acceleration[km s${}^{-1}$ day${}^{-1}$])

The coefficient of the first degree term in the fitting polynomial (for solutions FirstDegreeTrendSB1, FirstDegreeTrendSB2, SecondDegreeTrendSB1, SecondDegreeTrendSB2, ThirdDegreeTrendSB1, ThirdDegreeTrendSB2, FourthDegreeTrendSB1, FourthDegreeTrendSB2).

first_deriv_velocity_error : Standard error of First order derivative of the velocity (float, Acceleration[km s${}^{-1}$ day${}^{-1}$])

Standard error of the first acceleration. The standard errors are derived from the variance-covariance matrix of the final solution in the standard way.

second_deriv_velocity : Second order derivative of the velocity (double, Acceleration[km s${}^{-1}$ day${}^{-2}$])

The coefficient of the second degree term in the fitting polynomial (SecondDegreeTrendSB1, SecondDegreeTrendSB2, ThirdDegreeTrendSB1, ThirdDegreeTrendSB2, FourthDegreeTrendSB1, FourthDegreeTrendSB2).

second_deriv_velocity_error : Standard error of Second order derivative of the velocity (float, Acceleration[km s${}^{-1}$ day${}^{-2}$])

Standard error of the second acceleration. The standard errors are derived from the variance-covariance matrix of the final solution in the standard way.

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

Total number of 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 radial velocities actually used for the primary.

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_non_linear_spectro, 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 = FirstDegreeTrendSB1: the following 2 parameters are fitted and the bit index consequently takes value 7:

  • –

    mean_velocity

  • –

    first_deriv_velocity

• •

  nss_solution_type = SecondDegreeTrendSB1: the following 3 parameters are fitted and the bit index consequently takes value 15:

  • –

    mean_velocity

  • –

    first_deriv_velocity

  • –

    second_deriv_velocity

corr_vec : Vector form of the upper triangle of the correlation matrix (float[36] 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.

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)

Non-normalised chi-square of the trend solution.

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.

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.