# 8.4.2 Astrometric precision and accuracy

The comparison of Gaia results with external astrometric data is not straightforward as Gaia provides the most accurate astrometric data ever produced, at least in the optical domain. An additional difficulty, especially for the comparison of parallaxes, is that the numbers of targets is hugely different: a few tens to a maximum of one hundred thousands for existing data versus more than a billion for Gaia. However the consistency between Gaia data and carefully selected external astrometric data might be important in order to detect any statistical misbehaviour in one or the other source of data, including Gaia.

## Parallaxes and proper motions

For the validation using external astrometric data, the following astrometric catalogues have been considered: Hipparcos new reduction, High proper motion stars, VLBI compilation, HST compilation, RECONS.

well-behaved Hipparcos stars (van Leeuwen 2007b) have been selected using the five-parameter solution type with a good astrometric solution (goodness of fit $|F2|<5$), and without any binary flag indicated in the literature, mainly from WDS (Mason et al. 2001), CCDM (Catalogue of the Components of Double and Multiple Stars, Dommanget and Nys 2000), and SB9 (9th Catalogue of Spectroscopic Binary Orbits, Pourbaix et al. 2004). Stars also included in Tycho-2 were kept only if the proper motions from Hipparcos were consistent with those of Tycho-2 (rejection p-value: 0.001). The resulting sample includes 93 802 well-behaved stars, against which both the parallaxes and proper motions of Gaia are tested.

VLBI compilation: VLBI data have mainly been obtained from the USA VLBA, the Japanese VERA, and the European EVN: 90 proper motions and 44 parallaxes. Over the years, with increasing baseline length and better calibration of the ionospheric and tropospheric delays, astrometric accuracy using VLBI at centimetre wavelengths approaches ${\sim}$10 $\mu$as for parallaxes and ${\sim}$1  $\mu$as yr${}^{-1}$ for proper motions (Reid and Honma 2014, and references therein). For proper motions, only those with a mean epoch $>$ 2000 were considered, as calibration techniques improved drastically at that epoch, especially with new detailed maps of ionospheric delay. The compilation covers all stellar sources for which trigonometric parallaxes and proper motions have been obtained from VLBI astrometry (as quoted in the review of Reid and Honma 2014), but also stars with only proper motions obtained from VLBI positions (Boboltz et al. 2007) and VLBI proper motions of X-ray binaries (Miller-Jones 2014).

HST compilation: The Fine Guidance Sensors (FGS) on the Hubble Space Telescope have produced high accuracy trigonometric parallaxes of astrophysically interesting objects such as Cepheids, RR-Lyrae, novae, cataclysmic variables, or cluster members (Benedict and McArthur 2015; Benedict et al. 2007). The FGS field of view is small and the parallaxes of target stars have been measured with respect to reference stars which have their own parallaxes estimated by spectro-photometric measurements. The correction to absolute leads to a median error of absolute parallaxes estimated to be 0.2 mas. The present compilation covers 69 stars with parallaxes and, for about a third of them, proper motions published up to the end of 2015.

RECONS: The REsearch Consortium On Nearby Stars (RECONS; www.recons.org) has built a database of all systems estimated to be closer than 25 pc (parallaxes greater than 40 mas with errors smaller than 10 mas). We have used the database as published on 1 April 2015 (Henry and Jao 2015), leading to 348 stars with trigonometric parallaxes.

For the proper motions, comparison have been done also with Tycho-2 (selecting only stars with a normal astrometric treatment (no double star with Tycho-2 separate entries, no close known or suspected double star with photocentre treatment).

High proper motion stars (HPMs). Known SIMBAD HPMs are checked to be in the Gaia catalogue. Inversely, the properties of Gaia HPMs with PM$>$0.5${}^{\prime\prime}$not already known in SIMBAD are studied.

## Parallax accuracy tested with very distant stars

The zero point of the parallaxes and their precision can also be tested directly by using sources distant enough so that their measured parallaxes can be considered as null according to the catalogue’s expected accuracy. We use QSOs (those used for the reference frame tests, see below) as well as LMC/SMC and dSph stars for which we still have to take into account the mean distance of the systems.

The LMC/SMC catalogue is a compilation from Hipparcos (Annex 4 of Turon et al. 1992), Prévot (1989), Evans et al. (2004), Soszynski et al. (2008), Bonanos et al. (2009), Gruendl and Chu (2009), Bonanos et al. (2010), Neugent et al. (2010), Soszyński et al. (2010), Neugent et al. (2012). It contains 60344 LMC and 33922 SMC member stars. A sub-test is performed for stars with radial velocity membership from the Gaia data assuming a mean radial velocity and a dispersion of $RV$=262.2 km s${}^{-1}$ and $\sigma_{RV}$=20.2 km s${}^{-1}$ for the LMC and $RV$=145.6 km s${}^{-1}$ and $\sigma_{RV}$=27.66 km s${}^{-1}$ for the SMC (values from McConnachie 2012).

dSph members were compiled for several dSph with secure membership, mostly by RV measurements: Segue 1 (71 members , Simon et al. 2011), TucanaIII (52 members , Simon et al. 2017; Li et al. 2018a), HydrusI (33 members , Koposov et al. 2018), CarinaIII (4 members , Li et al. 2018b), Triangulum II (13 members , Kirby et al. 2017), ReticulumII (28 members , Simon et al. 2015), UrsaMajorII (11 members , Martin et al. 2007), Segue 2 (26 members , Kirby et al. 2013), CarinaII (18 members , Li et al. 2018b), Willman1 (14 members , Martin et al. 2007), TucIV (39 members , Simon et al. 2020), TucV (6 members , Simon et al. 2020), GruII (49 members , Simon et al. 2020), TucanaII (15 members , Walker et al. 2016), Bootes I (42 members , Martin et al. 2007; Koposov et al. 2011), Sagittarius II (21 members , Longeard et al. 2020), Draco (581 members , Kleyna et al. 2002; Walker et al. 2015; Armandroff et al. 1995), Ursa Minor (94 members , Armandroff et al. 1995), Sculptor (1415 members , Walker et al. 2009; Hill et al. 2019), Sextans (533 members , Walker et al. 2009; Battaglia et al. 2011), UrsaMajorI (17 members , Martin et al. 2007), Carina (939 members , Walker et al. 2009; Muñoz et al. 2006), Crater II (63 members , Caldwell et al. 2017), GrusI (8 members , Walker et al. 2016), Antlia II (159 members , Torrealba et al. 2019), HerculesI (47 members , Adén et al. 2009), Fornax (2777 members , Walker et al. 2009; Battaglia et al. 2006), Crater I (10 members , Kirby et al. 2015; Voggel et al. 2016), Hydra II (13 members , Kirby et al. 2015), Pisces II (7 members , Kirby et al. 2015), CVnI (101 members , Ural et al. 2010; Martin et al. 2007), Leo II (239 members , Spencer et al. 2017; Koch et al. 2007), Leo I (400 members , Mateo et al. 2008; Sohn et al. 2007), EridanusII (28 members , Li et al. 2017), Phoenix (194 members , Kacharov et al. 2017). A cross-match with a radius of 1${}^{\prime\prime}$is done between catalogues to removed duplicated entries and stars in common between 2 catalogues are flagged as members only if they are members in both catalogues. We use the distances provided by Fritz et al. (2018).

## Parallax accuracy tested with distant stars

An estimation of the parallax accuracy has also been obtained with stars distant enough so that their estimated distance through period-luminosity relation or spectro-photometry is known accurately enough. We are using the period-luminosity relation for Cepheids and RRLyrae, and we use the APOGEE DR16 for which we compute spectro-photometric distance modulus, as well as the SEGUE K Giant Survey (Xue et al. 2014). For all those catalogues for which we derive the distance modulus, we use 2MASS stars with quality flags AAA and the magnitude independent of extinction $K_{J-K}=K-\frac{k_{K}}{k_{J}-k_{K}}(J-K)$ to derive the distance modulus, as in Arenou et al. (2017), with the extinction coefficients $k$ computed using the Fitzpatrick and Massa (2007) extinction law. To avoid being dominated by potential systematics in those estimates, we select only stars distant enough so that the error on their parallax is 10 times smaller than the Gaia one.

APOGEE DR16. Distance moduli were computed using a Bayesian method on the Padova isochrones (Bressan et al. 2012, CMD 2.7) and using the magnitude independent of extinction $K_{J-K}$. The prior on the mass distribution used the IMF of Chabrier (2001), while the prior on age was chosen flat. Stars too far from the isochrones were rejected using the $\chi^{2}_{0.99}$ criterion. It led to 135 898 stars with $\sigma_{\varpi_{\mathrm{E}}}<0.1$ mas.

Gaia DR2 RR Lyrae. We selected Gaia DR2 RR Lyrae classified as RRab by both the supervised classification and the SOS. We used the period luminosity relation of Muraveva et al. (2015), assuming a mean metallicity of -1 dex with a dispersion of 0.6 dex or the metallicity information provided together with the Gaia DR2 RR Lyrae when available. An increase in the $M_{K}$ uncertainty of 0.15 mag is added to take into account the fact that we use here the observed and not the mean $K$ magnitude. As above, we use the magnitude independent of extinction $K_{J-K}$. The J-K colour is derived from Catelan (2004) transformed in the 2MASS system using the transformations of Carpenter (2001). The catalogue contains 14 587 stars with $\sigma_{\varpi_{E}}<0.1$ mas.

Gaia DR2 Cepheids. We select Gaia DR2 Cepheids classified as fundamental mode CEP by both the supervised classification and the SOS. We use the period luminosity relation of Fouqué et al. (2007). The catalogue contains 1 620 stars with $\sigma_{\varpi_{E}}<0.1$ mas.

## Positions and reference frame

The validation of the positions and reference frame was done using different QSO catalogues: ICRF3 (https://www.iers.org/IERS/EN/DataProducts/ICRF/ICRF3/icrf3.html), RFC2016c (http://astrogeo.org/vlbi/solutions/rfc_2016c/) removing sources with the unreliable coordinate flag, LQRF (Andrei et al. 2009). Those were also used to test the parallax zero point and uncertainties as well as the proper motions.

## Astrometry of known double and multiple systems

In addition to the above general tests, specific tests have also been done on known double and multiple systems from Hipparcos (HIP2 van Leeuwen 2007b) and Tycho-2 (TDSC, Fabricius et al. 2002) in order to detect any possible bias between single and non-single stars. For non-Hipparcos systems, we use the component designation given in the TDSC (m_TDSC) to distinguish between primary components (A or Aa), unresolved systems (AB), and secondary components (all other entries in TDSC). For Hipparcos systems, four categories with increasing periods were distinguished: stochastic solutions (short period, solution type Sn = 1 modulo 10 in HIP2), acceleration stars with seven- or nine-parameter solutions (intermediate period, Sn = 7 or 9 modulo 10 in HIP2), secondary components (long period, separation $\rho>0$ as provided in the original Hipparcos Catalogue), and other double stars (the remaining non-single stars). The characteristics of these Hipparcos and Tycho systems were compared to those of the well-behaved Hipparcos sample described above, adding the extra criterion of passing the $\chi^{2}$ test comparing the parallax and proper motion between Hipparcos and Gaia. Of course, many unknown unresolved binaries may hide within these single-star samples. A difference in behaviour between those different subsets with respect to the single-star samples is looked for, using various parameters: the parallax and proper motion residuals, and the Gaia errors, goodness of fit, and excess noise (source modelling errors). Mainly acceleration solutions are expected to show large discrepancies between their proper motions in Gaia and those from Hipparcos or TDSC. Another source of discrepancy may be the fictitious difference created by the comparison of Gaia and Hipparcos proper motions for close systems for which only the photocentre was observed by Hipparcos. Several other tests are done on secondary components, checking whether the separation or position angle with respect to the primary component had no adverse effect.

We also used wide physical binaries from the Washington Visual Double Star Catalogue (WDS; Mason et al. 2001, with flag $V$) and the companions of Cepheids and RRLyrae from Kervella et al. (2019) to test the compatibility of their parallaxes.