20.6.3 nss_non_linear_spectro
This table contains nonsinglestar 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 online documentation, see Chapter 7.
Columns description:
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
A unique single numerical identifier of the source obtained from gaia_source (for a detailed description see gaia_source.source_id).
This is the nonsingle 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
The mean_velocity as calculated over the current mission.
Standard error of mean_velocity. The standard errors are derived from the variancecovariance 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 variancecovariance 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 variancecovariance matrix of the final solution in the standard way.
Total number of radial velocities considered for the primary.
Total number of radial velocities actually used for the primary.
The bit_index field corresponds to a boolean mask indicating which of the parameters have been fitted by the model applicable to the nonsinglestar 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 nonsingle 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

–
Correlation matrix of the fitted profile parameters for the applicable nonsingle 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 nonzero, nonunity, correlation coefficients from the correlation matrix M are provided here. They are served as a linear array of constant size $S=n(n1)/2$ corresponding to the full normal matrix of dimension $n\times n$. The ordering of the elements in the linear array follows a columnmajor storage scheme, i.e.:
$\mathbf{M}=\left[\begin{array}{ccccccc}\hfill 1\hfill & \hfill C[0]\hfill & \hfill C[1]\hfill & \hfill C[3]\hfill & \hfill C[6]\hfill & \hfill \mathrm{\cdots}\hfill & \hfill C[S(n1)]\hfill \\ \hfill \hfill & \hfill 1\hfill & \hfill C[2]\hfill & \hfill C[4]\hfill & \hfill C[7]\hfill & \hfill \mathrm{\cdots}\hfill & \hfill C[S(n2)]\hfill \\ \hfill \hfill & \hfill \hfill & \hfill 1\hfill & \hfill C[5]\hfill & \hfill C[8]\hfill & \hfill \mathrm{\cdots}\hfill & \hfill C[S(n3)]\hfill \\ \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill 1\hfill & \hfill C[9]\hfill & \hfill \mathrm{\cdots}\hfill & \hfill C[S(n4)]\hfill \\ \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \mathrm{\ddots}\hfill & \hfill \mathrm{\ddots}\hfill & \hfill \mathrm{\vdots}\hfill \\ \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill 1\hfill & \hfill C[S1]\hfill \\ \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill 1\hfill \end{array}\right]$
Nonnormalised chisquare of the trend solution.
Goodnessoffit statistic of the solution. This is the ‘gaussianized chisquare’ (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:
$$F2=\sqrt{\frac{9\nu}{2}}(\sqrt[3]{\frac{obj\mathrm{\_}func}{\nu}}+\frac{2}{9\nu}1)$$ 
where obj_func is hopefully a ${\chi}^{2}$ and $\nu $ is the number of degrees of freedom.
Processing flag applicable to specific nonsinglestar solutions. The meaning of each of those is given in the table below.
Flags bit number  Flag Meaning  Comment  
8  BAD_UNCHECKED_NUMBER_OF_TRANSITS 


9  NO_MORE_VARIABLE_AFTER_FILTERING 


10  BAD_CHECKED_NUMBER_OF_TRANSITS 


11  SB2_REDIRECTED_TO_SB1_CHAIN_NOT_ENOUGH_COUPLE_MEASURES 


12  SB2_REDIRECTED_TO_SB1_CHAIN_PERIODS_NOT_COHERENT 


13  NO_SIGNIFICANT_PERIODS_CAN_BE_FOUND 


14  REFINED_SOLUTION_DOES_NOT_CONVERGE  The refined orbital solution does not converge (with 50 iterations)  
15  REFINED_SOLUTION_SINGULAR_VARIANCE_COVARIANCE_MATRIX 


16  CIRCULAR_SOLUTION_SINGULAR_VARIANCE_COVARIANCE_MATRIX 


17  TREND_SOLUTION_SINGULAR_VARIANCE_COVARIANCE_MATRIX 


18  REFINED_SOLUTION_NEGATIVE_DIAGONAL_OF_VARIANCE_COVARIANCE_MATRIX 


19  CIRCULAR_SOLUTION_NEGATIVE_DIAGONAL_OF_VARIANCE_COVARIANCE_MATRIX 


20  TREND_SOLUTION_NEGATIVE_DIAGONAL_OF_VARIANCE_COVARIANCE_MATRIX 


21  CIRCULAR_SOLUTION_DOES_NOT_CONVERGE 


22  LUCY_TEST_APPLIED  The Lucy test has been applied  
23  TREND_SOLUTION_NOT_APPLIED 


24  SOLUTION_OUTSIDE_E_LOGP_ENVELOP  The orbital solution (SB1 or SB2) is outside the elog(P) envelop.  
25  PERIOD_FOUND_IN_CU7_PERIODICITY 


26  FORTUITOUS_SB2  V1 and V2 seem to be uncorrelated 