A Gaia Early DR3 Mock Stellar Catalog: Galactic Prior and Selection Function

The underlying Galaxy model of galaxia is based on the Besançon (Robin et al. 2003) model. Since 2003 the Besançon model has seen many updates for various Galactic components. We have implemented a selection of these changes and list them in the following subsections. For each Galactic component we indicate the population ID (popid) which can be used to only select stars of a specific component. Basic information on age and local mass normalization of the thin- and thick-disk components can be inspected in Table 4.

2.1.1. Thin Disk—Popid = 0–6

2.1.2. Thick Disk—Popid = 7

2.1.3. Halo—Popid = 8

2.1.4. Bulge—Popid = 9

2.1.5. Magellanic Clouds—Popid = 10

2.1.6. Open Cluster—Popid = 11

Our underlying Milky Way model is smooth, but we know that the real Galaxy has many localized overdensities in phase-space, like moving groups, and open and globular cluster. Unraveling and cataloging such structures with the help of Gaia data is an active topic of research (e.g., Liu & Pang 2019; Castro-Ginard et al. 2020). We add mock open star clusters to our catalog, so that the astronomical community can train their algorithms to detect them and to extract their underlying astrophysical parameters.

As an input catalog we use 1118 real clusters from Cantat-Gaudin et al. (2018) and Kharchenko et al. (2013). We mock up the unknown astrophysical parameters of these in order to create an underlying truth, from which we can sample stars. The exact procedure can be inspected in notebook 7a of galaxia_wrap (where also a fits file with the exact values can be found), but in brief, the procedure for assigning parameters to individual objects is as follows.

• 1.  
  The metallicity, [Fe/H], is forced to be 0.1 dex in the inner disk, −0.35 dex in the outer disk with a linear transition in between 8 and 12 kpc galactocentric radius. We add Gaussian noise of ±0.1 dex to these [Fe/H] values.
• 2.  
  Mass values of the clusters are picked from a truncated normal distribution (300 < M_⊙ < 2050, most clusters have low masses) and were sorted and assigned according to the number of member stars in GDR2. We chose the mass distribution in order to roughly reproduce the overall number of all cluster members, which is of order of 400 K stars.
• 3.  
  We assume a solid body rotation for the stellar clusters with random spin axis. Rotational velocity is also correlated with the number of member stars (more stars mean higher rotational velocity). Velocities range from 0.1 to 0.7 km s⁻¹ and are given at the cluster radius.
• 4.  
  cluster center-of-mass positions and velocities were directly taken from the input catalog of 1118 clusters.

The mock data was generated using notebook 7. The particles contained in each cluster were distributed in a Plummer sphere using amuse (Portegies Zwart et al. 2009). To the resulting self-consistent velocity distribution we added the internal rotation depending on the position of each stellar particle with respect to the spin axis. The open cluster population can be easily queried¹² via:

SELECT GAVO_NORMAL_RANDOM(pmra,pmra_error) AS

pmra_obs, - - noise added values

GAVO_NORMAL_RANDOM(pmdec,pmdec_error) AS pmdec_obs

FROM gedr3mock.main

WHERE popid = 11 - - selects only open cluster stars

- - takes about 10 minutes

Download table as:  ASCIITypeset image

This query was used to generate the data for Figure 1, where observational noise has already been added via the GAVO_NORMAL_RANDOM function.¹³ We show the proper motions for mock and GDR2 cluster members (Cantat-Gaudin & Anders 2020) in orange and blue, respectively. Although the real clusters and their mock counterparts differ on a star-by-star basis, their statistical properties are (by design) in overall agreement.

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Finding and characterizing the mock clusters might be a good exercise to test the capabilities of detection methods to be used on the Gaia EDR3 data. If the user is not interested in those mock clusters, they can be excluded from a query via the statement:

WHERE popid! = 11 - - de-selects the open clusters

Download table as:  ASCIITypeset image

If users would like to mock up their own N-body data, e.g., clusters including tidal tails, streams or whole galaxies, they can adjust the procedure used in galaxia_wrap notebook 6 and 7.

2.1.7. Galactic Warp and Flare

We update the parameterization of the warp, based on Gyuk et al. (1999), following Reylé et al. (2009). Their comparison to 2MASS starcounts reveals that the displacement of the mid plane, characterized by the term γ_warp in the expression

$$\begin{eqnarray}&&{z}_{\mathrm{warp}}(R)={\gamma }_{\mathrm{warp}}\times (R-{R}_{\mathrm{warp}})\times \sin (\phi -{\phi }_{\mathrm{warp}})\end{eqnarray} \tag{ 1 }$$

needs to be lowered from 0.18 to 0.09. ${z}_{\mathrm{warp}}(R)$ denotes the height of the warp above the plane. The starting galactocentric radius of the warp, R_warp is left at 8.4 kpc. For the warp angle, ϕ_warp, we change the value from 0° to 15° in line with Yusifov (2004), which had no major effect on the fitting in Reylé et al. (2009).

2.1.8. Thin- and Thick-disk Normalization

The set of isochrones is the main astrophysical input that turns the underlying density distribution into mock stellar observations. Therefore we included the latest updates on these, as well as white dwarf tracks.¹⁸ The basic isochrones come from Marigo et al. (2017), and are built joining the PARSEC evolutionary tracks from Bressan et al. (2012) with the thermally pulsing asymptotic giant branch (AGB) from Pastorelli et al. (2019).¹⁹ To these tracks, we add WD tracks from Miller Bertolami (2016), using cooling sequences of initial metallicity Z = 0.01 from Renedo et al. (2010). These grids of white dwarfs have been extrapolated up to a final WD mass of 1.1 M_⊙ by using fitting relations. The derived isochrones are converted into the Gaia DR2 magnitudes by means of synthetic photometry performed with the YBC software (Chen et al. 2019),²⁰ in this case using the Weiler (2018) filter transmission curves for Gaia, which provides two BP bands, i.e., one for bright and one for faint magnitudes with a limit of G = 10.87 mag.

For the generation of Gaia photometry galaxia uses the complete isochrone set. In order to calculate the extinction in all bands (Gaia, SDSS, 2MASS, UBV) and the photometry in other systems (SDSS, 2MASS, UBV) we use a gridded version of the isochrones, reducing the total number of model stars from 8102,858 to 243,238. We create a grid with the following number of bins (step-size in parentheses) [boundaries in brackets]: [Fe/H] 36 (0.05 dex)[−1.5, 0.34]; ${\mathrm{log}}_{10}({T}_{\mathrm{eff}})$ 162 (0.02) [2.45, 5.68]; ${\mathrm{log}}_{10}({L}_{\odot })$ 217 (0.05) [−4.60, 6.24]. A combination of those three-dimensions determines the index_parsec (LLLTTTFFF, L = lum, T = teff, F = feh). The median of all stars that fall into a specific gridpoint is taken and also the standard deviation inspected.²¹ We report here the 50 and 99 percentiles of the standard deviation for all bins of this grid for the other stellar parameters: log(age) [0.03, 1.22]; initial mass [0.10, 2.96]; current mass [0.03, 4.14]; log(g) [0.04, 0.51]; G [0.04, 0.78]; G_BP [0.04, 1.12]; G_RP [0.04, 0.68]; G_RVS [0.04, 0.63]. These photometric bands and extinctions can be queried via a separate table: gedr3mock.parsec_props. An example is given in Section 6.5. Due to the nonlinear scaling of extinction with dust column density (reddening of an already reddened spectrum is weaker), extinction values are given for 6 different A0 values: 1, 2, 3, 5, 10, 20 mag. For an extinction law we used Cardelli et al. (1989) plus O'Donnell (1994), with R_V = 3.1, and higher order bolometric corrections have been taken into account. Links to the raw and reduced isochrone data are given in galaxia_wrap. Notebooks on the generation of the grid can be found here.²²

An integral part of a mock stellar catalog generation is the application of interstellar reddening due to dust, because most stars which would have a G magnitude brighter than 20.7 in the absence of dust have a fainter G magnitude after extinction has been added. We build upon our experience with the Bovy et al. (2016) combined dust map, which was put together using different 3D extinction maps (in order to get full-sky coverage). We replace the Bayestar 2015 map (Green et al. 2015) by Bayestar 2019 (Green et al. 2019) up to $| b| \lt 20^\circ$ and Bayestar 2017 Green et al. (2018) above (Bayestar 2017 has less clustering in low dust regions). Toward the Galactic center the combined map uses Marshall et al. (2006) which goes deeper since it is based on infrared data, whereas Bayestar requires photometric measurements in the optical as well. Parts that are not filled due to the Pan-STARRS (Chambers et al. 2016) footprint are filled with Drimmel et al. (2003). See Figure 1 of Bovy et al. (2016) for the footprint of each map. Resolution was increased to HEALpix level 9 (nside = 512, area of 47 arcmin²) from Healpix level 7 (nside = 128, 755 arcmin²) in GDR2mock and distance sampling is refined to 120 bins logarithmically sampled from 60 pc to 60 kpc.²³ The data cube is linked in galaxia_wrap and methods for application are present in the library/add_extinction.py file of galaxia_wrap. A₀ (monochromatic extinction at lambda = 547.7 nm in mag) values are interpolated linearly in distance while adjacent HEALpix values are not interpolated (HEALpix footprint is visible, as are the borders between the different extinction maps).

As reported before, the extinction in specific bands (G, BP_bright, BP_faint, RP and RVS; these two BP bands will be merged in a later step, described in Section 2.4) has been precalculated for 6 different values of A₀: 1, 2, 3, 5, 10, 20 mag. In order to calculate the extinction in a specific band for a specific value of A₀ (that comes from the 3D extinction map), we make a cubic fit to those 6 values onto a finer grid between 0 and 20 mag and then interpolate linearly to the exact A₀ (this two step interpolation is a compromise between accuracy and speed, when operating with large arrays of extinction).²⁴ For values of A₀ that are larger than 20 mag, we linearly scale the value for A₀ = 20 mag. The procedure outlined above illustrates the steps taken in library/util.py:apply_extinction_curves() and gives the extinction in the respective photometric band which we add to the apparent magnitude of the unreddened stars as generated by galaxia.

For GeDR3mock we compute all stars with G brighter than 20.7 mag using galaxia. Afterwards we apply our 3D extinction map and add absorption to each band. Thereafter we remove stars with G > 20.7 mag, which diminishes stars by a factor of 4. Until this point we have used BP bright and faint bands separately, but now we use either of these as BP depending on whether the source is brighter or fainter than G = 10.87 mag (Weiler 2018). Note that some of the sources in our catalog can have BP or RP magnitudes much fainter than 20.7 mag in their respective bands. Thus in order to retrieve sources from our catalog that would have BP and RP measurements in GDR2 (or Gaia EDR3), the user may want to apply cuts to our catalog on these magnitudes. We do not model BP or RP excess flux spilling over from nearby sources, which will brighten up those bands for faint stars in dense areas in the Gaia data.

In GDR2mock we used the pre-launch nominal sky-averaged error model. This underestimates uncertainties, especially in the bright regime. To simulate the Gaia measurement metrics (e.g., no. of observations, parallax or photometric uncertainties) more accurately for GeDR3mock, we use GDR2 data to fit a predictive model of a metric as a function of parameters that we can simulate from galaxia (e.g., magnitude, color, position). Specifically, we select 0.5% of GDR2 data at random and use this to train ExtraTree models (Geurts et al. 2006; Pedregosa et al. 2011). The first model uses Galactic longitude and latitude as inputs to predict the number of visibility_periods_used (VPU) and phot_g_n_obs (NOBS). These are mutliplied by 34/22 (the longer baseline of Gaia EDR3 compared to GDR2) and rounded to the nearest integer. We then train separate models with G, BP-RP, VPU and NOBS (all values are still coming from GDR2) as inputs to predict the parallax_error and phot_g_mean_mag_error (using approximate values computed from the symmetrized flux uncertainties). These are then scaled by $\sqrt{22/34}$ to account for the longer baseline. This scaling factor assumes that the dominant noise factor is source-noise rather than systematics, which is not actually the case at the bright end. The factor of $\sqrt{22/34}$ is the factor for flux uncertainties, not magnitude uncertainties. Similarly, the radial_velocity_error is predicted from G, BP-RP, and Teff and the same rescaling is applied. The procedure outlined above can be inspected in notebook 8.

From NOBS we derive NOBS for BP and RP by fitting a linear relation that minimizes the least squares. We similarly derive the photometric uncertainties in the other bands from linear relations on phot_g_mean_mag_error, and uncertainties in positions and proper motions from linear relations²⁵ on parallax_error. The fitted relations are listed in Table 1 and the procedure to obtain those values can be inspected in notebook 8a. We account for the ${\left(22/34\right)}^{1.5}$ uncertainty scaling for the proper motions. We produce the mock errors this way in order to save storage in the ADQL database, because simple scaling relations with other columns do not require additional space.

All quantities that we report in GeDR3mock are noise-free. Noise can be added based on the uncertainty estimates derived in Section 2.5 from within ADQL: see the example in Section 6. As in the GDR2 data model, GeDR3mock contains the phase space distribution in the following observables: ra, dec, l, b, parallax, pmra, pmdec, radial_velocity and similarly for the photometry, though we add an extra G_RVS column. A few stellar parameters have been estimated in GDR2 (Andrae et al. 2018) and these are reported together with all the other known quantities in GeDR3mock: teff_val, ag_val, a_g_val, e_bp_min_rp_val, radius_val, lum_val, feh, a0, initial_mass, current_mass, age, logg, popid, a_bp_val, a_rp_val, a_rvs_val. The column descriptions can be inspected here.²⁶

When two sources in Gaia are close to each other, the fainter one might not get allocated an observational window by Gaia, depending on their separation and magnitude difference (de Bruijne et al. 2015). This effect, dubbed "contrast sensitivity," has been quantified to some degree for GDR2 by Brandeker & Cataldi (2019). We used their Table 1 to calculate, for each source in GeDR3mock, its probability to be seen, which we call "visibility." We compute and add to GeDR3mock a quantity d11y that gives an integer from 0 to 100, where 0 means no visibility. The ADQL query that pre-selects close pairs and calculates d11y is linked to the galaxia_wrap repository. As can be seen from Table 2, 69 million sources have issues with too bright and too near neighbors. When accounting for the magnitude limits from GDR2 this number drops to 33 million. GeDR3mock does not include binaries or globular clusters, which would otherwise increase those numbers.

The effective magnitude limit along a line of sight can be shifted toward brighter magnitudes by a combination of crowding (Gaia Collaboration et al. 2016) and a limited number of scans. The latter can, for faint sources, drop below the number of observations required for specific Gaia data products to be included in a release, e.g., parallax (Lindegren et al. 2018), G, BP, RP, or RVS. This magnitude limit can be approximated by the mode of the magnitude distribution within a specific HEALpix. When, in the following, we speak of the magnitude limit, we refer to the mode of the magnitude distribution binned in 0.1 mag bins. To illustrate how this manifests itself in the real data we show in Figure 2 such maps for GDR2 for G < 20.7. The top panel shows the magnitude limits when only requiring G measurements. We see that in the bulge and Magellanic Clouds the magnitude limits are brighter than everywhere else. Away from the disk the limit becomes rather noisy. In the middle panel we require that a parallax measurement be available. This makes the bulge limits brighter, and satellite scanning patterns become visible. In the bottom panel we show the same map again (requiring parallax measurement), but this time we only set the limit from the G-magnitude distribution for a HEALpix if it has more than 1e5 sources per deg². In all other HEALpix the limits are set to 20.7.

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As we can see the mode estimator—upper panel of Figure 2 has two main failure modes: (a) the starcount in a specific HEALpix is low, such that the magnitude distribution gets noisy due to Poisson sampling, and (b) a peak in the magnitude distribution is produced by some localized stellar population in a distant overdensity, e.g., red clump stars in the Magellanic Clouds, that is not characteristic of the crowding limit. An easy fix for (a) is to only apply the magnitude limits in dense areas and to set the magnitude limit to 20.7 in all HEALpix that have a small stellar density. This is what we do in the bottom panel of Figure 2 for a density threshold of 1e5 sources per deg².²⁷

To illustrate those failure modes further we plot in Figure 3 the G magnitude distributions for three different HEALpix at level 6, namely toward Baades window, the LMC and a low density field at l = 20 and b = 30. The following query exemplifies the data acquisition for Figure 3:

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We can see how the red clump peak (blue points) in the LMC at around G = 19 mag can yield an incorrect magnitude limit estimate. The low density field (red points) is not yet too noisy such that the mode of the distribution is still a good estimator for the magnitude limit but one can see how the Poisson noise in the magnitude distribution can produce modes at brighter magnitude limits if the stellar density gets even lower or the HEALpix level increases. In Baades window (green points) it can be seen that a brighter magnitude limit of about G = 19 mag is reached and sources are petering out beyond that. The red clump peak in the luminosity function of Baades window at G = 16 mag is well visible, but does not bias our magnitude limit estimation in this particular case, since the mode is at fainter magnitudes still.

We provide both variants, i.e., with and without a density threshold applied in the tables where the latter has no suffix and the former has _density_thresholdadded. We also provide magnitude limits for BP (also under the condition that G < 20.7). For each band the magnitude limit comes for four flavors (and each flavor has one with and without density threshold applied):

• (1)  
  G < 20.7 mag (applies to all variants)
• (2)  
  parallax measurement is available
• (3)  
  BP and RP measurement is available
• (4)  
  parallax, BP and RP are available.

In Table 3 we list the number of sources that are included in the G magnitude limits for both GeDR3mock and GDR2. In total, GeDR3mock has 1573 M sources compared to 1451 M in GDR2.²⁸ When considering only sources that are brighter than the HEALpix dependent magnitude limit the numbers are more similar. The reason why the mock catalog has more sources than GDR2 is because of the density limit of the Gaia instrument of about 1.05 M sources deg⁻² (Gaia Collaboration et al. 2016). The highest density area in GeDR3mock has 5.6 M sources deg⁻². An illustration of this can be seen in Figure 8, the CMD of Baade's window, where the magnitude limit that also requires the existence of color and parallax measurements is depicted too.

We generated HEALpix maps of those magnitude limits for HEALpix levels 5, 6, and 7 (nside = 32, 64, and 128, have areas of 3.36, 0.84, and 0.21 deg², respectively) using the gdr2_completeness package²⁹ (Rybizki & Drimmel 2018). They can be accessed via gedr3mock.maglim_X, where X is the HEALpix level.

Notebook 3 and 4 of gdr2_completeness illustrate how to generate those maps. We encourage the user to produce maps for their specific use-cases, e.g., accounting for quality cuts or the existence of measurements, for example radial velocity.

We did not provide RP magnitude limits because those are mainly governed by the condition that G is brighter than 20.7 mag. Since RP is usually brighter than G, sources are usually lost because they get too faint in G not because they get too faint in RP.

We also caution the use of the BP magnitude limit, because in dense areas, faint sources can acquire very bright BP (and RP) magnitudes due to flux contamination from neighboring sources, something that is not modeled in GeDR3mock. BP maps might still be useful when comparing to other data or when modeling the BP and RP flux excess.

More details on all bands and a comparison to GeDR3mock magnitude limits can be found in Appendix A.

Once the real data, Gaia EDR3, comes out we will provide updated magnitude limit maps in the TAP service.

An example of how to query all stars in GDR2 that are below the maglim_g magnitude limit for HEALpix level 6 is given below.

A python package with a more rigorous method providing completeness as a function of magnitude per HEALpix (Boubert & Everall 2020) can be found here.³⁰ One drawback of this is that the magnitude limits seem to depend on the authors' all-sky partition into equal density areas.

In order to compare the source density over the sky between GeDR3mock and GDR2, we apply the contrast sensitivity and the magnitude limits from the previous section to GeDR3mock:

In Figure 4 we show the stellar densities in HEALpix level 6 for GeDR3mock and GDR2 and a comparison map at the bottom. GDR2 has more sources toward the poles, but overall the agreement is reasonably good. Globular clusters and the Sagittarius stream are visible, and the Magellanic Clouds show more structure in GDR2. When looking at the comparison map, we see the footprint of the Marshall et al. (2006) extinction map transitioning into Drimmel et al. (2003) (see Figure 1 of Bovy et al. 2016), where there is a discrete jump in the model starcounts (color getting redder) toward the right in the galactic plane. The warp is more prominent in the model, and the bulge structure is not well reproduced. The fit to the Magellanic clouds is poor, owing to the simplistic Gaussian distribution in GeDR3mock.

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Another insightful test is the CMD comparison. Here we do not apply HEALpix-dependent magnitude limits to either catalog, as those do not change the basic structure of the distributions. The query is:

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Our catalog, by design, mimicks the GDR2 data model, which will be similar in Gaia EDR3. Some fields are filled with NULLs rather than omitted in order for GDR2 ADQL queries not to throw errors. Values like phot_bp_rp_excess_factor or ruwe are not easy to model because they depend on the actual measurement, but one could train models on the real data to predict those values for the mock catalog, using the method presented in Section 2.5 (notebook 8).

Entries in GeDR3mock that have no counterpart in the GDR2 data model are now explained:

• 1.  
  phot_g_mean_mag_error For convenience we provide magnitude errors for all photometric bands. These are only good approximations of the flux error for small values.
• 2.  
  phot_rvs_mean_mag Since we have the isochrone models with an approximate RVS band³⁶ we also provide RVS mag (simply computed assuming a Vegamag zero-point) because it is useful to select magnitude complete RVS samples.
• 3.  
  popid The popid from the Besançon model (see Table 4; halo = 8 and bulge = 9), additionally having the Magellanic clouds = 10 and the open clusters = 11.
• 4.  
  d11y The visibility is given in percentage. Can be lower than 100 due to bright sources in the near vicinity (see Section 3.1).
• 5.  
  index_parsec Is an index for joining the main mock catalog to other photometric bands/extinctions in the gedr3mock.parsec_props table.
• 6.  
  a_bp_val, a_rp_val, a_rvs_val These are extinctions in the specified bands, in analogy to a_g_val in the G band.
• 7.  
  source_id The most significant bits identify the HEALpix number as with Gaia source_id. The rest of the source_id is a running number. The source_id can be easily turned into HEALpix number for any arbitrary HEALpix level, n, smaller than or equal to 12 (level 12 corresponding to Nside = 4096) via division:

  $$\begin{eqnarray}&&\mathrm{Healpix}(\mathrm{level}=n)=\mathrm{FLOOR}\left(\displaystyle \frac{{\mathtt{source}}\_{\mathtt{id}}}{{2}^{35}\times {4}^{(12-n)}}\right).\end{eqnarray} \tag{ 2 }$$

Few additional stellar parameters not listed above but can be found in Section 2.6. General information on the catalog and its columns can be inspected here.³⁷

The underlying Galaxy model is a simple approximation of reality with know shortcomings, see lower panel of Figure 4 and discussion thereof in Section 4. There have been improvements in the thick disk, halo (e.g., Robin et al. 2014) and bulge (Robin et al. 2012b) components of the Milky Way model, but these updates did not build on each other, so we decided to stay with the basic model update from Czekaj et al. (2014). LMC and SMC have only Gaussian distributions with inconsistent velocity prescription. We only simulate single stars. The star formation in GeDR3mock is smooth (not clumpy) and independent of the 3D extinction model, therefore the two do not show the correlations one observes in the real MW. The all-sky 3D extinction map is up-to-date but not perfect, especially where different maps have been joined together.

We plan to update our mock catalog after the release of GaiaEDR3, foreseen for late 2020. This will contain magnitude limit maps as well as error, nobs, ruwe and contrast sensitivity columns based on GaiaEDR3 data. As some of those already exist, we will add abbreviations indicating that these were derived using Gaia EDR3 data. Updates to GeDR3mock will be announced here.³⁸

The "full" GaiaDR3 currently planned for late 2021 will include many more data products. To assist the use and analysis of that catalog, we plan to augment GeDR3mock in a follow-up study with:

• 1.  
  binaries
• 2.  
  galaxies and quasars
• 3.  
  models of BPRP and RVS spectra (if publicly available)
• 4.  
  chemical abundances using chemical evolution models.

The user might be interested in producing a distance prior for the GDR2 RVS sample to be used in a Bayesian parameter estimation similar to the distance estimation in Bailer-Jones et al. (2018b) (see also McMillan 2018). Following is a query that would mimick the GDR2 RVS sample selection and returns the mean distance per HEALpix:

$\left({2}^{35}\times {4}^{(12-5)}\right)$

We can not use the statement "WHERE radial_velocity IS NOT NULL" because in GeDR3mock all radial velocities are known. Therefore the selection function needs to be approximated.

Figure 6 shows the mean distance per HEALpix which could be directly used as a prior parameterization. 7.1 M sources are returned by GeDR3mock which is more than the 5.3 M that GDR2 has below G_RVS = 12 (G_RVS needs to be approximated using Equations (2) and (3) from Gaia Collaboration et al. 2018). The reason of course is that the effective magnitude limit is brighter in the dense parts of the sky. Cutting on G_RVS < 12 is only a first order approximation. For refinement we recommend to produce a custom magnitude limit map for the RVS sample using the gdr2_completeness package.

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Because measured parallaxes can have very large uncertainties, the distribution of measured parallaxes can be quite different than for mock (true) parallaxes. We show this for the HEALpix 7876 (at level 5) which is a low density out-off-plane field at l = 20, b = 30. GDR2 contains 46k sources (G  < 20.7) and GeDR3mock has 39k sources in that HEALpix. Figure 7 shows, from left to right, the inverted parallax versus the G for: GeDR3mock; the same with parallax noise added; GDR2. In the absence of measurement uncertainty on the left we see a bimodal distribution in parallax at G = 20.7, the peak at 1 kpc consists mainly of lower main sequence stars while the one at about 8 kpc consists mainly of upper main sequence and turn-off stars. These two sequences merge when the parallax uncertainty is added (the G magnitude error is negligible in this diagram). Similarly, the diagonal line in the top right of the three CMDs, which corresponds to the red clump, becomes blurred once noise is added. Noise can be added from within ADQL using:

${2}^{35}\times {4}^{(12-5)}\,\times 7876$

${2}^{35}\times {4}^{(12-5)}\times 7877-1$

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Here we look at a CMD in a high density area, namely Baade's window. This time we add noise to the mock photometry and compare to GDR2 data. The G magnitude limit, when parallax and BP and RP measurement are required, is 18.9 mag. We only query in a circle of radius 0.1° to keep the runtime short (query runs in synchronous mode). GDR2 contains 13k sources, whereas GeDR3mock contains 134k sources. When applying the magnitude cut, these numbers change to 12k and 18k, respectively. The GeDR3mock data for Figure 8 comes from the following query:

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The local normalization, i.e., the local stellar mass density, is a common benchmark for Galaxy models, we query the 50 pc sample using:

In Table 4 we compare our local mass density to Model B of Czekaj et al. (2014), their Table 7. The mass values agree pretty well, just the thick disk is only about 5% of the local mass density, compared to their 9%. Figure 9 shows the age distribution of the local 50 pc sample. The piecewise flat, but exponentially decreasing SFR (for thin-disk popid 0 to 6) is visible, as well as a local overdensity of very young (dynamically cold) stars. All stars of the 50 pc sample are depicted in Figure 10 together with their respective metallicities (color coded). The sample contains 4162 white dwarfs (WD) for which the current mass is much lower than the initial mass. Extrapolating to a 100 pc sample 10,856 of these WDs would be within the completeness range of Jiménez-Esteban et al. (2018). They find 8555 stars, which is only a 20% difference.

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The stellar distribution in the CMD looks reasonably well but the pre-main sequence might be a bit too pronounced, as it was in GDR2mock (Rybizki et al. 2018). We find that 214 (0.4%) mainly faint sources would have scattered out of our 50 pc sample if cutting on observed parallax. Vice versa 236 that are truly outside of 50 pc would have scattered in when cutting on observed parallax. The 10% increase for the in-scattering stars is due to the assymetric volume at the border of the 50 pc sphere, given that the stellar density is almost isotropic.

It is possible to query the absolute magnitudes and extinctions in other bands (UBV, 2MASS, SDSS) for specific values of A₀ via the gedr3mock.parsec_props table. An example query for apparent magnitudes in 2MASS bands could be: