# 8.7.1 Astrometry

When we use clusters located farther than 1000 pc, we derive an average zero point difference with MSWC ($\varpi$${}_{\rm Gaia}-$$\varpi$${}_{\rm reference})=$ -0.059, -0.091 mas for MWSC and DAML respectively, but with a large $\sigma\sim 0.2$. However, looking at the trends with color and magnitude, we find a complex pattern. This is also evident looking at individual clusters, whose members are selected on the basis of the proper motions (see for instance Figure 8.30).

Looking at differential parallax to the cluster median $\Delta_{par}$, for the whole sample of clusters located farther than 1000 pc, we get indication about zero point changes. When plotted versus $G$ jumps in the zero point at G=11.5,13,14 are evident. Strong variations are evident for stars bluer and redder than $G_{\mathrm{BP}}-G_{\mathrm{RP}}$ $\sim 0.8$. When divided by the nominal uncertainty, these patterns are still present, with reduced amplitude, implying that nominal uncertainties on the parallax do not account for the zero point variation, i.e. nominal uncertainties are underestimated. More detail can be found in Fabricius et al. (2021).

Finally, we compare the parallaxes of single stars in Gaia DR2 and Gaia DR3. The median difference is ($\varpi$${}_{\rm Gaia~{}DR3}$-$\varpi$${}_{\rm Gaia~{}DR3})=0.017$ mas, ( with 16%= 0.047 mas; 84%=0.082 mas) on the whole sample, with a dependence on the magnitude.

## Astrometric precision of parallaxes

In Figure 8.31 we analysed the uncertainties on the parallax for clusters more distant than 1000 pc. We analyse the difference between Gaia EDR3 parallaxes for single stars and the median parallax of the cluster normalised to the Gaia EDR3 nominal error. The sigma of the distribution is larger than 1 ($\sim 1.2$) i.e. the uncertainties are underestimated. In particular, formal uncertainties underestimate the errors mainly for stars brighter than G=14. The distribution shows a bump at $G$ $\sim 13$.

## Proper motions

Figure 8.32 shows the case of NGC 7099 compared with literature values. The zero point of proper motions presents a complex dependence on magnitude and color. Similar patterns are evident for all the clusters. The dispersion of the proper motions is not accounted by the nominal uncertainties, i.e. nominal uncertainties are underestimated, mainly at the bright end ($G$ $<14$). More detail can be found in Fabricius et al. (2021).

We calculate the proper motion differences (median) between Gaia EDR3 and Gaia DR2 for the whole cluster sample. The zero point median difference is $-0.006$ mas yr${}^{-1}$(3-Quartile 0.06) in right ascension and in declination.

## Proper motion precision in crowded areas

We compare the proper motions in the centre of M4 with external HST data (Nascimbeni et al. 2014) , where high quality relative proper motions are available. The precision of HST proper motions is of the order of 0.33  mas yr${}^{-1}$. M4 stars are affected by crowding already at bright magnitudes ($G$ $>$ 16-17) (see Figure 8.33) In Figure 8.34 we present the scaled dispersion of the difference between Gaia and HST proper motions for the stars having different Gaia nominal uncertainties, and a moderate (c=2) to high ($c>5$) flux excess parameter. This flux excess parameter is taken as a proxy for the level of contamination. The scaled dispersion is very close to 1 for both $\mu_{\alpha}$ and $\mu_{\delta}$ for bright stars with little contamination, but it gets to 1.6-1.8 for faint stars with a high contamination level. This indicated that the nominal uncertainties are correctly estimated only for bright stars.

## Photometry

CMD features

In Figure 8.35 we show the CMD of NGC2516 where stars are selected on the basis of the pms. A hook is visible from $G$ $\sim 19$ and ($G_{\rm BP}$-$G_{\rm RP}$)$\sim$ 3 where a number of stars have a too blue color for their location in the main sequence. This behaviour is found in all the clusters where the photometry reaches this magnitude. Looking at the uncertainties on the magnitude,

Photometry in crowded clusters

Photometry in crowded areas is still worse than in non-crowded regions. This is the case of all the globulars, where the photometry in the inner regions is shifted in color and magnitude as an effect of crowding, with a large dispersion. See for instance Figure 8.36 showing the quality of the photometry in NGC5986.

Comparison with Gaia DR2 photometry The photometry of Gaia DR2 and Gaia DR3 are on different photometric systems. Median differences are very small, i.e. -0.0087 (G),0.0027 (BP), 0.0074 (RP), 0.0074(BP-RP) with dispersions of the order of 0.01-0.02 in G, BP, (BP-RP), and lower in RP. However, for a small sample of stars differences can be higher than 1.5-1.7 mag in BP and G, possibly related with the small number of observations ($<30$). The (BP-RP) difference shows a bump at BP$\sim 11.5$ as an effect of the different calibrations (see Figure 8.37)

## Completeness in crowded areas

We derive the completeness for 26 globular clusters comparing Gaia DR3 data with HST completeness Sarajedini et al. (2007). The procedure and the sample are the same already used for Gaia DR2. We remember that the completeness of HST data is derived using crowding experiments and is higher than 90% in the whole Gaia range. Completeness table for all the clusters can be found in Fabricius et al. (2021). In Figure 8.38 we present the completeness as function of $G$.

A few significant cases are shown in Figure 8.39, Figure 8.40, Figure 8.41. In NGC 5053, the completeness in the inner and outer regions are very similar an quite high (60% at G=20), in NGC 2298 the inner and outer regions have very different level of completeness. In the inner region, the completeness is about 10% at G=20, and 60% in the outer region. In NGC 5286 the completeness in the inner region is 20% at G$\sim$17.

It should be mentioned that the completeness of the astrometry only is generally higher. This is not an issue, but a feature of the data that depends on the processing. In globular clusters a percentage of about 20%-30% of stars with astrometry (5p and 6p solutions), do not have $G_{\mathrm{BP}}-G_{\mathrm{RP}}$ color. In NGC 6809 the percentage if of 37% (see Figure 8.42). Open clusters are more favourable cases. In general the percentage of stars missing $G_{\mathrm{BP}}-G_{\mathrm{RP}}$ is of the order of 1%-3% (see Figure 8.43). Some artifacts on the completeness showing the effect of the scanning law are visible (see Figure 8.43), but the number of cases is reduced in comparison to Gaia DR2.