20.6.2 nss_acceleration_astro
This table contains nonsinglestar astrometric models for sources having a nonlinear proper motion which is compatible with an acceleration solution. 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_acceleration_astro are:

•
Acceleration7: Acceleration model with 7 parameters

•
Acceleration9: Acceleration model with 9 parameters
Right ascension $\alpha $ of the source in ICRS at the reference epoch gaia_source.ref_epoch, compensated for the trajectory assumed by the model in order to be an average estimate.
Standard error ${\sigma}_{\alpha *}\equiv {\sigma}_{\alpha}\mathrm{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 variancecovariance matrix of the solution, correcting the measurement uncertainties to obtain the goodnessoffit F2=0.
Declination $\delta $ of the source in ICRS at the reference epoch gaia_source.ref_epoch, compensated for the trajectory assumed by the model in order to be an average estimate.
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 variancecovariance matrix of the solution, correcting the measurement uncertainties to obtain the goodnessoffit F2=0.
Absolute stellar parallax $\varpi $ of the source at the reference epoch gaia_source.ref_epoch
Standard error ${\sigma}_{\varpi}$ of the stellar parallax at the reference epoch gaia_source.ref_epoch. The standard errors are derived from the variancecovariance matrix of the solution, correcting the measurement uncertainties to obtain the goodnessoffit F2=0.
Proper motion in right ascension ${\mu}_{\alpha *}\equiv {\mu}_{\alpha}\mathrm{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. As for the position, the effect of the motion assumed in the model is compensated in order to be an average estimate.
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 variancecovariance matrix of the solution, correcting the measurement uncertainties to obtain the goodnessoffit F2=0.
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. As for the position, the effect of the motion assumed in the model is compensated in order to be an average estimate.
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 variancecovariance matrix of the solution, correcting the measurement uncertainties to obtain the goodnessoffit F2=0.
Acceleration along the RA axis. This is the time derivative of pmra.
Standard error of the acceleration along the RA axis. The standard errors are derived from the variancecovariance matrix of the solution, correcting the measurement uncertainties to obtain the goodnessoffit F2=0.
Acceleration along the declination axis. This is the time derivative of pmdec.
Standard error of the acceleration along the declination axis. The standard errors are derived from the variancecovariance matrix of the solution, correcting the measurement uncertainties to obtain the goodnessoffit F2=0.
Time derivative of the acceleration along the RA axis, accel_ra.
deriv_accel_ra_error : Standard error of Time derivative of the acceleration in RA (float, Misc[mas yr${}^{3}$])
Standard error of the time derivative of the acceleration along the RA axis. The standard errors are derived from the variancecovariance matrix of the solution, correcting the measurement uncertainties to obtain the goodnessoffit F2=0.
Time derivative of the acceleration along the declination axis, accel_dec.
deriv_accel_dec_error : Standard error of Time derivative of the acceleration in DEC (float, Misc[mas yr${}^{3}$])
Standard error of the time derivative of the acceleration along the declination axis. The standard errors are derived from the variancecovariance matrix of the solution, correcting the measurement uncertainties to obtain the goodnessoffit F2=0.
Total astrometric CCD observations considered in the alongscan direction.
Dimension : Number of sources
Total astrometric along–scan CCD observations that may have been used in the calculation of the solution.
For the acceleration solutions, up to 5% of these transits may have been discarded as being outliers.
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_acceleration_astro, all parameters of a given nonsingle 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:

•
nss_solution_type = Acceleration7: the following 7 parameters are fitted and the bit index consequently takes value 255:

–
ra

–
dec

–
parallax

–
pmra

–
pmdec

–
accel_ra

–
accel_dec

–

•
nss_solution_type = Acceleration9: the following 9 parameters are fitted and the bit index consequently takes value 1023:

–
ra

–
dec

–
parallax

–
pmra

–
pmdec

–
accel_ra

–
accel_dec

–
deriv_accel_ra

–
deriv_accel_dec

–
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.
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 goodnessoffit ${F}_{2}$ is zero.
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.:
$\mathbf{M}=\left[\begin{array}{ccccccc}\hfill 1\hfill & \hfill C[0]\hfill & \hfill C[1]\hfill & \hfill C[3]\hfill & \hfill C[6]\hfill & \hfill \mathrm{\cdots}\hfill & \hfill C[S(n1)]\hfill \\ \hfill \hfill & \hfill 1\hfill & \hfill C[2]\hfill & \hfill C[4]\hfill & \hfill C[7]\hfill & \hfill \mathrm{\cdots}\hfill & \hfill C[S(n2)]\hfill \\ \hfill \hfill & \hfill \hfill & \hfill 1\hfill & \hfill C[5]\hfill & \hfill C[8]\hfill & \hfill \mathrm{\cdots}\hfill & \hfill C[S(n3)]\hfill \\ \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill 1\hfill & \hfill C[9]\hfill & \hfill \mathrm{\cdots}\hfill & \hfill C[S(n4)]\hfill \\ \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \mathrm{\ddots}\hfill & \hfill \mathrm{\ddots}\hfill & \hfill \mathrm{\vdots}\hfill \\ \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill 1\hfill & \hfill C[S1]\hfill \\ \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill 1\hfill \end{array}\right]$
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.
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.
It turns out that goodness_of_fit 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 uncertainty. This uncertainty is derived from the solution covariance matrix, where the uncertainties are corrected in order to obtain the corrected goodnessoffit ${F}_{2corrected}=0$. The function characterising the model is as follows: (a) for the acceleration 7 model, it is the norm of the acceleration vector; (b) for the acceleration 9 model, it is the norm of the time derivative of the acceleration vector.
Processing flag applicable to specific nonsinglestar solutions. The meaning of each of those is given in the table below.
Flags bit number  Flag Meaning 
6  RV available 
7  RV used for perspective acceleration correction 