# 20.12.3 xp_continuous_mean_spectrum

Table hosting the mean BP and RP spectra based on the continuous representation in basis functions (see Section 5.3.4).

Note this table is not available through the main archive TAP interface. Data are delivered via the Massive Data service indexed by the VO Datalink protocol and described in Chapter 18. For example this can be actioned in the archive user interface by querying the main source catalogue gaia_source and selecting has_xp_continuous = 't'.

Columns description:

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

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.

bp_basis_function_id : Identifier defining the set of basis functions for the BP spectrum representation (short)

Identifier defining the set of basis functions used for the continuous representation of this spectrum.

Number of degrees of freedom in the LSQ system.

Number of parameters in the LSQ system.

Number of measurements contributing to solution.

Number of measurements that have been rejected.

Standard deviation of the solution.

${\chi}^{2}$ of the solution.

bp_coefficients : Basis function coefficients for the BP spectrum representation (double[bp_n_parameters] array)

Array of basis function coefficients for the representation of the BP spectrum.

bp_coefficient_errors : Basis function coefficient errors for the BP spectrum representation (float[bp_n_parameters] array)

Errors on the basis function coefficients for BP

bp_coefficient_correlations : Correlation matrix for BP coefficients (float[bp_n_parameters*(bp_n_parameters-1)/2] array)

Upper-triangular (non-zero, non-unity) part of the correlation matrix M of the coefficients $C$ for the representation of the BP spectrum as basis functions. The matrix elements are stored 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.:

$\mathbf{M}=\left[\begin{array}{ccccccc}\hfill 1\hfill & \hfill C[0]\hfill & \hfill C[1]\hfill & \hfill C[3]\hfill & \hfill C[6]\hfill & \hfill \mathrm{\cdots}\hfill & \hfill C[S-(n-1)]\hfill \\ \hfill \hfill & \hfill 1\hfill & \hfill C[2]\hfill & \hfill C[4]\hfill & \hfill C[7]\hfill & \hfill \mathrm{\cdots}\hfill & \hfill C[S-(n-2)]\hfill \\ \hfill \hfill & \hfill \hfill & \hfill 1\hfill & \hfill C[5]\hfill & \hfill C[8]\hfill & \hfill \mathrm{\cdots}\hfill & \hfill C[S-(n-3)]\hfill \\ \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill 1\hfill & \hfill C[9]\hfill & \hfill \mathrm{\cdots}\hfill & \hfill C[S-(n-4)]\hfill \\ \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \mathrm{\ddots}\hfill & \hfill \mathrm{\ddots}\hfill & \hfill \mathrm{\vdots}\hfill \\ \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill 1\hfill & \hfill C[S-1]\hfill \\ \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill 1\hfill \end{array}\right]$

bp_n_relevant_bases : Number of bases that are relevant for the representation of this mean BP spectrum (short)

Although all bases defined in the set of bases associated with this mean BP spectrum have been used for the source update process, only the coefficients of the first bp_n_relevant_bases bases are significant.

The criterion adopted to estimate the number of relevant basis functions is based on the standard deviation of the coefficients, normalised to their corresponding square root of variance. All coefficients are divided by the square root of variances, and the standard deviation of the last n values is computed, where n is increasing from 2 onwards. The resulting standard deviation for the last n coefficients is then compared with the (idealised) theoretical expectation of 1, plus a configurable threshold times the standard error on the standard deviation. The largest index for which the standard deviation exceeds this limit is taken as the highest coefficient in the truncated representation and the number of relevant bases.

bp_relative_shrinking : Measure of the relative shrinking of the coefficient vector when truncation is applied for the mean BP spectrum (float)

This parameter is defined as the ratio between the lengths of the truncated and full BP spectrum defined by the array of coefficients to be applied to the basis functions.

rp_basis_function_id : Identifier defining the set of basis functions for the RP spectrum representation (short)

Identifier defining the set of basis functions used for the continuous representation of this spectrum.

Number of degrees of freedom in the LSQ system.

Number of parameters in the LSQ system.

Number of measurements contributing to solution.

Number of measurements that have been rejected.

Standard deviation of the solution.

${\chi}^{2}$ of the solution.

rp_coefficients : Basis function coefficients for the RP spectrum representation (double[rp_n_parameters] array)

Array of basis function coefficients for the representation of the RP spectrum.

rp_coefficient_errors : Basis function coefficient errors for the RP spectrum representation (float[rp_n_parameters] array)

Errors on the basis function coefficients for RP

rp_coefficient_correlations : Correlation matrix for RP coefficients (float[rp_n_parameters*(rp_n_parameters-1)/2] array)

Upper-triangular (non-zero, non-unity) part of the correlation matrix M of the coefficients $C$ for the representation of the RP spectrum as basis functions. The matrix elements are stored 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.:

$\mathbf{M}=\left[\begin{array}{ccccccc}\hfill 1\hfill & \hfill C[0]\hfill & \hfill C[1]\hfill & \hfill C[3]\hfill & \hfill C[6]\hfill & \hfill \mathrm{\cdots}\hfill & \hfill C[S-(n-1)]\hfill \\ \hfill \hfill & \hfill 1\hfill & \hfill C[2]\hfill & \hfill C[4]\hfill & \hfill C[7]\hfill & \hfill \mathrm{\cdots}\hfill & \hfill C[S-(n-2)]\hfill \\ \hfill \hfill & \hfill \hfill & \hfill 1\hfill & \hfill C[5]\hfill & \hfill C[8]\hfill & \hfill \mathrm{\cdots}\hfill & \hfill C[S-(n-3)]\hfill \\ \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill 1\hfill & \hfill C[9]\hfill & \hfill \mathrm{\cdots}\hfill & \hfill C[S-(n-4)]\hfill \\ \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \mathrm{\ddots}\hfill & \hfill \mathrm{\ddots}\hfill & \hfill \mathrm{\vdots}\hfill \\ \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill 1\hfill & \hfill C[S-1]\hfill \\ \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill 1\hfill \end{array}\right]$

rp_n_relevant_bases : Number of bases that are relevant for the representation of this mean RP spectrum (short)

Although all bases defined in the set of bases associated with this mean RP spectrum have been used for the source update process, only the coefficients of the first rp_n_relevant_bases bases are significant.

The criterion adopted to estimate the number of relevant basis functions is based on the standard deviation of the coefficients, normalised to their corresponding square root of variance. All coefficients are divided by the square root of variances, and the standard deviation of the last n values is computed, where n is increasing from 2 onwards. The resulting standard deviation for the last n coefficients is then compared with the (idealised) theoretical expectation of 1, plus a configurable threshold times the standard error on the standard deviation. The largest index for which the standard deviation exceeds this limit is taken as the highest coefficient in the truncated representation and the number of relevant bases.

rp_relative_shrinking : Measure of the relative shrinking of the coefficient vector when truncation is applied for the mean RP spectrum (float)

This parameter is defined as the ratio between the lengths of the truncated and full RP spectrum defined by the array of coefficients to be applied to the basis functions.