Author(s): Lennart Lindegren
The astrometric results in Gaia DR2 were not produced in a single large least-squares process, but were the end result of a long series of solutions using different versions of the input data and testing different calibration models and solution strategies. A complete astrometric solution consists of two parts, known as the primary solution and the secondary solution.
In the primary solution, which involves only a small fraction of the sources known as primary sources, the attitude and calibration parameters (and optionally the global parameters) are adjusted simultaneously with the astrometric parameters of the primary sources using an iterative algorithm. The reference frame is also adjusted using a subset of the primary sources identified as quasars.
In the secondary solutions the five astrometric parameters of every star are adjusted using fixed attitude, calibration, and global parameters from the preceding primary solution. The restriction on the number of primary sources comes mainly from practical considerations, as the primary solution is computationally and numerically demanding due to the large systems of equations that need to be solved. By contrast, the secondary solutions can be made one source at a time essentially by solving a system with only five unknowns (or six if pseudo-colour is also estimated). For consistency, the astrometric parameters of the primary sources are re-computed in the secondary solutions.
The primary solution consists of about 16 million primary sources for which all five astrometric parameters (position at the reference epoch J2015.5, parallaxes, and proper motion components) are provided, along with their standard uncertainties, correlation coefficients, and other statistics. The primary sources were selected based on the results of preliminary runs. The criteria for the selection were: (i) sources must have , , and magnitudes from the photometric processing; (ii) there should be a roughly equal number of sources with observations in each of the three window classes; (iii) for each window class there should be a roughly homogeneous coverage of the whole sky, and a good distribution in magnitude and colour; (iv) within the constraints set by the previous criteria, sources with high astrometric weight (bright, with small excess noise and a good number of observations) were preferentially selected. To this were added some 490 000 probable quasars for the reference frame alignment.
The secondary solution was generated using the final attitude, calibration, and global parameters from the primary solution, including a re-computation of the pseudo-colours for all sources using the final chromaticity calibration. Sources failing to meet the acceptance criteria for a five-parameter solution obtained a 2-parameter fall-back solution at this stage. This resulted in 1335 million sources with a five-parameter solution and 400 million with a fall-back solution, i.e. without parallax and proper motion. About 18 million sources were subsequently removed as duplicates, i.e. where the observations of the same physical source had been split between two or more different source identifiers. Duplicates were identified by positional coincidence, using a maximum separation of 0.4 arcsec.
|Median value at magnitude|
|Fraction of sources with 5-param. solution||99.1||99.0||99.0||99.0||98.9||98.6||97.6||94.5||82.9||15.9||%|
|Standard uncertainty in () at J2015.5||0.033||0.023||0.023||0.031||0.047||0.077||0.137||0.268||0.548||1.457||mas|
|Standard uncertainty in () at J2015.5||0.030||0.022||0.020||0.027||0.041||0.069||0.123||0.242||0.490||1.559||mas|
|Standard uncertainty in ()||0.041||0.029||0.028||0.038||0.057||0.094||0.165||0.317||0.651||2.104||mas|
|Standard uncertainty in ()||0.068||0.047||0.047||0.063||0.096||0.158||0.280||0.550||1.164||3.114||mas yr|
|Standard uncertainty in ()||0.059||0.042||0.040||0.054||0.082||0.137||0.243||0.479||1.011||3.374||mas yr|
|Fraction with significant excess noise||20.6||21.0||17.8||17.9||18.4||19.2||20.6||21.2||18.2||10.6||%|
|Excess source noise (when significant)||0.183||0.249||0.311||0.331||0.367||0.474||0.701||1.226||2.235||4.563||mas|
|Number of visibility periods used||13||13||13||13||13||12||12||12||12||9|
|Number of field-of-view transits used||26||26||26||26||25||25||24||23||22||12|
|Number of good CCD observations AL||220||227||226||223||218||215||212||199||194||102|
|Fraction of bad CCD observations AL||2.7||0.8||0.0||0.4||0.4||0.4||0.4||0.5||0.4||0.5||%|
|Median value at magnitude|
|Fraction of sources with fall-back solution||0.9||1.0||1.0||1.0||1.1||1.4||2.4||5.5||17.1||84.1||%|
|Standard uncertainty in () at J2015.5||0.905||0.968||0.972||0.970||0.989||1.018||1.036||1.518||2.204||3.623||mas|
|Standard uncertainty in () at J2015.5||0.876||0.924||0.931||0.921||0.936||0.956||0.971||1.399||1.897||3.387||mas|
|Number of visibility periods used||10||11||11||10||9||8||7||6||6||6|
|Number of field-of-view transits used||16||19||19||18||15||13||11||9||9||8|
|Number of good CCD observations AL||133||161||158||149||130||107||96||79||78||62|
|Fraction of bad CCD observations AL||2.7||0.6||0.0||0.0||0.0||0.0||0.0||0.0||0.0||0.0||%|
Gaia DR2 finally gives five-parameter solutions for 1332 million sources, with formal uncertainties ranging from about 0.02 mas to 2 mas in parallax and twice that in annual proper motion. For the 385 million sources with fall-back solutions the positional uncertainty at J2015.5 is about 1 to 4 mas. Basic statistics are given in Table 3.5 for source with full five parameter solutions and in Table 3.6 for source with 2-parameter fallback solutions.