4.5 Quality assessment and validation 4.5.1 Overview 4.5.3 Source verification

4.5.2 Properties of the astrometric data

Author(s): Lennart Lindegren

The astrometric results in Gaia EDR3 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.

Gaia EDR3 finally gives full astrometric solutions (that is, positions, parallaxes, and proper motions) for about 1468 million sources (of which 882 million had six-parameter solutions, that is including the pseudocolour), with formal uncertainties ranging from about 0.015 mas to 2 mas in position at J2016.0, parallax, annual proper motion. For about 344 million sources with fall-back solutions the positional uncertainty at J2016 is about 1 to 4 mas. Basic statistics are given in Table 4.4 and Table 4.5 for sources with five- and six-parameter solutions, and in Table 4.6 for source with two-parameter (fallback) solutions.

Table 4.4: Summary statistics for the 585 million sources in Gaia EDR3 with five-parameter solutions.

	Value at $G=$
Quantity	$9$ – $12$	$13$	$14$	$15$	$16$	$17$	$18$	$19$	$20$	$21$	Unit
Frac. with 5p solution	92.9	97.0	97.1	96.7	93.8	87.5	76.7	49.7	14.5	1.4	%
Median $\sigma_{\alpha*}$ at J2016.0	0.014	0.012	0.015	0.022	0.034	0.054	0.094	0.175	0.374	1.006	mas
Median $\sigma_{\delta}$ at J2016.0	0.013	0.011	0.013	0.019	0.030	0.049	0.086	0.161	0.335	0.977	mas
Median $\sigma_{\varpi}$	0.018	0.015	0.019	0.027	0.042	0.069	0.120	0.221	0.459	1.320	mas
Median $\sigma_{\mu\alpha*}$	0.018	0.016	0.019	0.028	0.044	0.071	0.123	0.229	0.487	1.445	mas yr ${}^{-1}$
Median $\sigma_{\mu\delta}$	0.016	0.014	0.017	0.024	0.038	0.063	0.111	0.208	0.428	1.401	mas yr ${}^{-1}$
Median RUWE	1.039	1.023	1.016	1.013	1.012	1.011	1.010	1.010	1.010	1.016
Frac. with excess noise	97.3	59.4	19.2	16.8	13.8	10.6	7.5	5.0	5.0	11.7	%
Median excess noise	0.113	0.089	0.188	0.224	0.285	0.409	0.606	0.976	1.801	3.668	mas
Mean visibility periods used	20.9	21.0	20.9	20.8	20.7	20.7	20.7	20.5	19.2	13.1
Mean no. of FoV transits used	43.7	43.7	43.6	43.4	43.2	43.2	43.4	42.6	38.7	20.5
Mean no. of good AL obs.	378	378	377	376	374	374	376	368	334	175
Mean frac. of bad AL obs.	1.2	0.4	0.5	0.5	0.5	0.4	0.4	0.4	0.5	0.6	%
Median IPD GoF harm. ampl.	0.018	0.021	0.020	0.020	0.020	0.020	0.020	0.022	0.029	0.073
Mean IPD frac. multipeak	1.9	1.5	1.5	1.7	0.9	0.6	0.3	0.2	0.1	0.9	%
Mean IPD frac. odd win.	0.0	0.0	0.0	0.0	0.0	0.0	0.1	0.1	0.2	0.8	%

Notes. RUWE = renormalised unit weight error (ruwe). Frac. with excess noise = fraction of sources for which the astrometric excess noise is significant (astrometric_excess_noise_sig

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2). The median excess noise is calculated for the sources with significant excess noise. Statistics for the good and bad AL observations refer to the individual CCD observations. IPD GoF Harm. ampl. = ipd_gof_harm_amplitude. IPD frac. multipeak = ipd_frac_multi_peak. IPD frac. odd win. = ipd_frac_odd_win.

Table 4.5: Summary statistics for the 882 million sources in Gaia EDR3 with six-parameter solutions.

	Value at $G=$
Quantity	$9$ – $12$	$13$	$14$	$15$	$16$	$17$	$18$	$19$	$20$	$21$	Unit
Frac. with 6p solution	6.2	2.4	2.2	2.7	5.6	11.9	22.4	48.6	77.7	27.5	%
Median $\sigma_{\alpha*}$ at J2016.0	0.017	0.026	0.025	0.033	0.052	0.081	0.131	0.225	0.430	1.031	mas
Median $\sigma_{\delta}$ at J2016.0	0.016	0.024	0.023	0.030	0.045	0.069	0.112	0.194	0.382	1.025	mas
Median $\sigma_{\varpi}$	0.023	0.033	0.031	0.040	0.061	0.093	0.151	0.266	0.526	1.390	mas
Median $\sigma_{\mu\alpha*}$	0.023	0.034	0.033	0.042	0.065	0.102	0.167	0.291	0.565	1.469	mas yr ${}^{-1}$
Median $\sigma_{\mu\delta}$	0.021	0.031	0.029	0.036	0.051	0.078	0.132	0.240	0.490	1.470	mas yr ${}^{-1}$
Median $\sigma(\hat{\nu}_{\text{eff}})$	0.004	0.006	0.006	0.008	0.012	0.019	0.031	0.055	0.109	0.281	$\mu$ m ${}^{-1}$
Median RUWE	1.127	1.362	1.167	1.104	1.102	1.085	1.053	1.033	1.029	1.048
Frac. with excess noise	99.6	95.1	75.4	68.3	64.0	58.3	45.5	27.8	17.7	19.6	%
Median excess noise	0.169	0.275	0.387	0.405	0.471	0.569	0.809	1.343	2.153	3.838	mas
Mean visibility periods used	21.4	21.1	20.7	20.1	18.9	18.2	18.4	18.5	18.1	13.3
Mean no. of FoV transits used	46.1	44.6	44.0	42.6	39.3	38.2	37.9	37.8	36.6	21.1
Mean no. of good AL obs.	400	384	379	366	339	331	328	327	315	181
Mean frac. of bad AL obs.	1.3	1.5	1.9	2.1	1.5	1.0	0.7	0.6	0.6	0.6	%
Median IPD GoF harm. ampl.	0.020	0.033	0.032	0.030	0.035	0.034	0.032	0.030	0.031	0.071
Mean IPD frac. multipeak	9.4	25.4	21.6	18.3	10.7	7.0	5.5	3.2	1.0	0.5	%
Mean IPD frac. off win.	0.0	4.8	7.9	8.1	6.3	5.2	4.4	4.2	3.8	2.1	%

Notes. RUWE = renormalised unit weight error (ruwe). Frac. with excess noise = fraction of sources for which the astrometric excess noise is significant (astrometric_excess_noise_sig

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Table 4.6: Summary statistics for the 344 million sources in Gaia EDR3 with two-parameter solutions.

	Value at $G=$
Quantity	$9$ – $12$	$13$	$14$	$15$	$16$	$17$	$18$	$19$	$20$	$21$	Unit
Frac. with 2p solution	0.8	0.7	0.7	0.6	0.6	0.6	0.9	1.7	7.8	71.1	%
Median $\sigma_{\alpha*}$ at J2016.0	1.771	1.260	1.127	1.116	1.060	1.008	0.979	1.436	2.579	3.250	mas
Median $\sigma_{\delta}$ at J2016.0	1.703	1.211	1.078	1.067	0.994	0.925	0.888	1.252	2.106	2.847	mas
Mean visibility periods used	17.9	18.4	18.2	18.0	17.7	17.0	15.7	10.9	8.0	6.9
Mean no. of FoV transits used	35.2	36.3	35.9	35.4	34.7	33.6	30.7	19.7	13.3	10.0
Mean no. of good AL obs.	299	306	304	300	294	285	261	167	113	85
Mean frac. of bad AL obs.	4.3	3.5	3.5	3.5	3.5	3.4	3.1	2.5	1.6	0.9	%
Median IPD GoF harm. ampl.	0.217	0.251	0.258	0.261	0.279	0.273	0.256	0.259	0.175	0.096
Mean IPD frac. multipeak	59.2	53.0	44.8	43.6	36.0	27.8	20.8	14.2	6.8	0.3	%
Mean IPD frac. odd win.	0.0	12.5	19.2	19.8	27.2	31.1	33.3	35.6	25.2	3.1	%

Notes. Statistics for the good and bad AL observations refer to the individual CCD observations. IPD GoF Harm. ampl. = ipd_gof_harm_amplitude. IPD frac. multipeak = ipd_frac_multi_peak. IPD frac. odd win. = ipd_frac_odd_win.

gaia early data release 3 documentation

4.5.2 Properties of the astrometric data