Gaia Data Release 2: Observational Hertzsprung-Russell diagrams

We highlight the power of the Gaia DR2 in studying many fine structures of the Hertzsprung-Russell diagram (HRD). Gaia allows us to present many different HRDs, depending in particular on stellar population selections. We do not aim here for completeness in terms of types of stars or stellar evolutionary aspects. Instead, we have chosen several illustrative examples. We describe some of the selections that can be made in Gaia DR2 to highlight the main structures of the Gaia HRDs. We select both field and cluster (open and globular) stars, compare the observations with previous classifications and with stellar evolutionary tracks, and we present variations of the Gaia HRD with age, metallicity, and kinematics. Late stages of stellar evolution such as hot subdwarfs, post-AGB stars, planetary nebulae, and white dwarfs are also analysed, as well as low-mass brown dwarf objects. The Gaia HRDs are unprecedented in both precision and coverage of the various Milky Way stellar populations and stellar evolutionary phases. Many fine structures of the HRDs are presented. The clear split of the white dwarf sequence into hydrogen and helium white dwarfs is presented for the first time in an HRD. The relation between kinematics and the HRD is nicely illustrated. Two different populations in a classical kinematic selection of the halo are unambiguously identified in the HRD. Membership and mean parameters for a selected list of open clusters are provided. They allow drawing very detailed cluster sequences, highlighting fine structures, and providing extremely precise empirical isochrones that will lead to more insight in stellar physics. Gaia DR2 demonstrates the potential of combining precise astrometry and photometry for large samples for studies in stellar evolution and stellar population and opens an entire new area for HRD-based studies.


Introduction
The Hertzsprung-Russell diagram (HRD) is one of the most important tools in stellar studies.It illustrates empirically the relationship between stellar spectral type (or temperature or colour index) and luminosity (or absolute magnitude).The position of a star in the HRD is mainly given by its initial mass, chemical composition, and age, but effects such as rotation, stellar wind, magnetic field, detailed chemical abundance, over-shooting, and non-local thermal equilibrium also play a role.Therefore, the detailed HRD features are important to constrain stellar structure and evolutionary studies as well as stellar atmosphere modelling.Up to now, a proper understanding of the physical process in the stellar interior and the exact contribution of each of the effects mentioned are missing because we lack large precise and homogeneous samples that cover the full HRD.Moreover, a precise HRD provides a great framework for exploring stellar populations and stellar systems.
Up to now, the most complete solar neighbourhood empirical HRD could be obtained by combining the Hipparcos data (Perryman et al. 1995) with nearby stellar catalogues to provide the faint end (e.g.Gliese & Jahreiß 1991;Henry & Jao 2015).Clusters provide empirical HRDs for a range of ages and metal contents and are therefore widely used in stellar evolution studies.To be conclusive, they need homogeneous photometry for inter-comparisons and astrometry for good memberships.
With its global census of the whole sky, homogeneous astrometry, and photometry of unprecedented accuracy, Gaia DR2 is setting a new major step in stellar, galactic, and extragalactic studies.It provides position, trigonometric parallax, and proper motion as well as three broad-band magnitudes (G, G BP , and G RP ) for more than a billion objects brighter than G∼20, plus radial velocity for sources brighter than G RVS ∼12 mag and photometry for variable stars (Gaia Collaboration et al. 2018a).The amount, exquisite quality, and homogeneity of the data allows reaching a level of detail in the HRDs that has never been Article number, page 2 of 28 reached before.The number of open clusters with accurate parallax information is unprecedented, and new open clusters or associations will be discovered.Gaia DR2 provides absolute parallax for faint red dwarfs and the faintest white dwarfs for the first time.
This paper is one of the papers accompanying the Gaia DR2 release.The following papers describe the data used here : Gaia Collaboration et al. (2018a) for an overview, Lindegren et al. (2018) for the astrometry, Evans et al. (2018) for the photometry, and Arenou et al. (2018) for the global validation.Someone interested in this HRD paper may also be interested in the variability in the HRD described in Gaia Collaboration et al. (2018b), in the first attempt to derive an HRD using temperatures and luminosities from the Gaia DR2 data of Andrae et al. (2018), in the kinematics of the globular clusters discussed in Gaia Collaboration et al. (2018c), and in the field kinematics presented in Gaia Collaboration et al. (2018d).
In this paper, Sect. 2 presents a global description of how we built the Gaia HRDs of both field and cluster stars, the filters that we applied, and the handling of the extinction.In Sect. 3 we present our selection of cluster data; the handling of the globular clusters is detailed in Gaia Collaboration et al. (2018c) and the handling of the open clusters is detailed in Appendix A. Section 4 discusses the main structures of the Gaia DR2 HRD.The level of the details of the white dwarf sequence is so new that it leads to a more intense discussion, which we present in a separate Sect. 5.In Sect.6 we compare clusters with a set of isochrones.In Sect.7 we study the variation of the Gaia HRDs with kinematics.We finally conclude in Sect.8.

Building the Gaia HRDs
This paper presents the power of the Gaia DR2 astrometry and photometry in studying fine structures of the HRD.For this, we selected the most precise data, without trying to reach completeness.In practice, this means selecting the most precise parallax and photometry, but also handling the extinction rigorously.This can no longer be neglected with the depth of the Gaia precise data in this release.

Data filtering
The Gaia DR2 is unprecedented in both the quality and the quantity of its astrometric and photometric data.Still, this is an intermediate data release without a full implementation of the complexity of the processing for an optimal usage of the data.A detailed description of the astrometric and photometric features is given in Lindegren et al. (2018) and Evans et al. (2018), respectively, and Arenou et al. (2018) provides a global validation of them.Here we highlight the features that are important to be taken into account in building Gaia DR2 HRDs and present the filters we applied in this paper.
Concerning the astrometric content (Lindegren et al. 2018), the median uncertainty for the bright source (G<14 mag) parallax is 0.03 mas.The systematics are lower than 0.1 mas, and the parallax zeropoint error is about 0.03 mas.Significant correlations at small spatial scale between the astrometric parameters are also observed.Concerning the photometric content (Evans et al. 2018), the precision at G=12 is around 1 mmag in the three passbands, with systematics at the level of 10 mmag.Lindegren et al. (2018) described that a five-parameter solution is accepted only if at least six visibility periods are used (e.g. the number of groups of observations separated from other groups by a gap of at least four days, the parameter is named visibility_periods_used in the Gaia archive).The observations need to be well spread out in time to provide reliable fiveparameter solutions.Here we applied a stronger filter on this parameter: visibility_periods_used>8.This removes strong outliers, in particular at the faint end of the local HRD (Arenou et al. 2018).It also leads to more incompleteness, but this is not an issue for this paper.
The astrometric excess noise is the extra noise that must be postulated to explain the scatter of residuals in the astrometric solution.When it is high, it either means that the astrometric solution has failed and/or that the studied object is in a multiple system for which the single-star solution is not reliable.Without filtering on the astrometric excess noise, artefacts are present in particular between the white dwarf and the main sequence in the Gaia HRDs.Some of those stars are genuine binaries, but the majority are artefacts (Arenou et al. 2018).To still see the imprint of genuine binaries on the HRD while removing most of the artefacts, we adopted the filter proposed in Appendix C of Lindegren et al. (2018): χ 2 /(ν − 5) < 1.2 max(1, exp(−0.2(G− 19.5)) with χ 2 and ν given as astrometric_chi2_al and astrometric_n_good_obs_al, respectively, in the Gaia archive.A similar clean-up of the HRD is obtained by the astrometric_excess_noise<1 criterion, but this is less optimised for the bright stars because of the degrees of freedom (DOF) issue (Lindegren et al. 2018, Appendix A).
We built the Gaia HRDs by simply estimating the absolute Gaia magnitude in the G band for individual stars using M G = G + 5 + 5 log 10 ( /1000.), with the parallax in milliarcseconds (plus the extinction, see next section).This is valid only when the relative precision on the parallax is lower than about 20% (Luri et al. 2018).We aim here to examine the fine structures in the HRD revealed by Gaia and therefore adopt a 10% relative precision criterion, which corresponds to an uncertainty on M G smaller than 0.22 mag: parallax_over_error>10.
The processing of the photometric data in DR2 has not treated blends in the windows of the blue and red photometers (BP and RP).As a consequence, the measured BP and RP fluxes may include the contribution of flux from nearby sources, the highest impact being in sky areas of high stellar density, such as the inner regions of globular clusters, the Magellanic Clouds, or the Galactic Bulge.During the validation process, misdeterminations of the local background have also been identified.In some cases, this background is due to nearby bright sources with long wings of the point spread function that have not been properly subtracted.In other cases, the background has a solar type spectrum, which indicates that the modelling of the background flux is not good enough.The faint sources are most strongly affected.For details, see Evans et al. (2018) and Arenou et al. (2018).Here, we have limited our analysis to the sources within the empirically defined locus of the (I BP + I RP )/I G fluxes ratio as a function of G BP − G RP colour: phot_bp_rp_excess_factor> 1.0+0.015(G BP −G RP ) 2 and phot_bp_rp_excess_factor< 1.3 + 0.06 (G BP − G RP ) 2 .The Gaia archive query combining all the filters presented here is provided in Appendix B.

Extinction
The dust that is present along the line of sight towards the stars leads to a dimming and reddening of their observed light.In the full colour -absolute magnitude diagram presented in Fig. 1, the effect of the extinction is particularly striking for the red clump.The de-reddened HRD using the extinction provided together with DR2 is presented in Andrae et al. (2018).To study the fine structures of the Gaia HRD for field stars, we selected here only low-extinction stars.High galactic latitude and close-by stars located within the local bubble (the reddening is almost negligible within ∼60 pc of the Sun (Lallement et al. 2003)) are affected less from the extinction, and we did not apply further selection for them.To select low-extinction stars away from these simple cases, we followed Ruiz-Dern et al. ( 2018) and used the 3D extinction map of Capitanio et al. (2017) 1 , which is particularly well adapted to finding holes in the interstellar medium and to select field stars with E(B − V) < 0.015.
For globular clusters we used literature extinction values (Sect.3.3), while for open clusters, they are derived together with the ages (Sect.3.2).Detailed comparisons of these global cluster extinctions with those that can be derived from the extinctions provided by Gaia DR2 can be found in Arenou et al. (2018).To transform the global cluster extinction easily into the Gaia passbands while taking into account the extinction coefficients dependency on colour and extinction itself in these large passbands (e.g.Jordi et al. 2010), we used the same formulae as Danielski et al. (2018) to compute the extinction coefficients k X = A X /A 0 : 1 http://stilism.obspm.fr/As in Danielski et al. (2018), this formula was fitted on a grid of extinctions convolving the latest Gaia passbands presented in Evans et al. (2018) with Kurucz spectra (Castelli & Kurucz 2003) and the Fitzpatrick & Massa (2007) extinction law for 3500 K< T eff <10000 K by steps of 250 K, 0.01< A 0 < 5 mag by steps of 0.01 mag and two surfaces gravities: logg = 2.5 and 4. The resulting coefficients are provided in Table 1.We assume in the following A 0 = 3.1E(B − V).
Some clusters show high differential extinction across their field, which broadens their colour-magnitude diagrams.These clusters have been discarded from this analysis.

Cluster data
Star clusters can provide observational isochrones for a range of ages and chemical compositions.Most suitable are clusters with low and uniform reddening values and whose magnitude range is wide, which would limit our sample to the nearest clusters.Such a sample would, however, present a rather limited range in age and chemical composition.

Membership and astrometric solutions
Two types of astrometric solutions were applied.The first type is applicable to nearby clusters.For the second Gaia data release, the nearby 'limit' was set at 250 pc.Within this limit, the parallax and proper motion data for the individual cluster members are sufficiently accurate to reflect the effects of projection along the line of sight, thus enabling the 3D reconstruction of the cluster.This is further described in Appendix A.1.
For these nearby clusters, the size of the cluster relative to its distance will contribute a significant level of scatter to the HRD if parallaxes for individual cluster members are not taken into account.With a relative accuracy of about 1% in the parallax measurement, an error contribution of around 0.02 in the absolute magnitude is possible.For a large portion of the Gaia photometry, the uncertainties are about 5 to 10 times lower, making the parallax measurement still the main contributor to the uncertainty in the absolute magnitude.The range of differences in parallax between the cluster centre and an individual cluster member depends on the ratio of the cluster radius over the cluster distance.At a radius of 15 pc, the 1% level is found for a cluster at 1.5 kpc, or a parallax of 0.67 mas.In Gaia DR2, formal uncertainties on the parallaxes may reach levels of just lower than 10 µas, but the overall uncertainty from localised systematics is about 0.025 mas.If this value is considered the 1% uncertainty level, then a resolution of a cluster along the line of sight, using Gaia DR2, becomes possible for clusters within 400 pc, and realistic for clusters within about 250 pc.
For clusters at larger distances, the mean cluster proper motion and parallax are derived directly from the observed astrometric parameters for the individual cluster members.The details of this procedure are presented in Appendix A.2.

Selection of open clusters
Our sample of open clusters consists of the mostly well-defined and fairly rich clusters within 250 pc, and a selection of mainly rich clusters at larger distances, covering a wider range of ages, mostly up to 1.5 kpc, with a few additional clusters at larger distances where these might supply additional information at more extreme ages.For very young clusters, the definition of the cluster is not always clear, as the youngest systems are mostly found Article number, page 4 of 28  2).   2 shows the combined HRD of these clusters, coloured according to their ages as provided in Table 2.The main-sequence turn-off and red clump evolution with age is clearly visible.The age difference is also shown for lower mass stars, the youngest stars lie slightly above the main sequence of the others.The white dwarf sequence is also visible.

Selection of globular clusters
The details of selecting globular clusters are presented in Gaia Collaboration et al. (2018c).A major issue for the globular cluster data is the uncertainties on the parallaxes that result from the systematics, which is in most cases about one order of magnitude larger than the standard uncertainties on the mean parallax determinations for the globular clusters.The implication of this is that the parallaxes as determined with the Gaia data cannot be used to derive the distance moduli needed to prepare the composite HRD for the globular clusters.Instead, we had to rely on distances as quoted in the literature, for which we used the tables (2010 edition) provided online by Harris (1996).The inevitable drawback is that these distances and reddening values have been obtained through isochrone fitting, and the application of these values to the Gaia data will provide only limited new information.The main advantage is the possibility of comparing the HRDs of all globular clusters within a single, accurate photometric system.The combined HRD for 14 globular clusters is shown in Fig. 3, the summary data for these clusters is presented in Table 3.The photometric data originate predominantly from the outskirts of the clusters, as in the cluster centres the crowding often affects the colour index determination.Figure 3 shows the blue horizontal branch populated with the metal-poor clusters and the move of the giant branch towards the blue with decreasing metallicity.
An interesting comparison can be made between the most metal-rich well-populated globular cluster of our sample, 47 Tuc (NGC 104), and one of the oldest open clusters, M67 (NGC 2682) (Fig. 4).This provides the closest comparison between the HRDs of an open and a globular cluster.Most open clusters are much younger, while most globular clusters are much less metal rich.

Details of the Gaia HRDs
In the following, several field star HRDs are presented.Unless otherwise stated, the filters presented in Sect.2.1, including the E(B−V) < 0.015 mag criteria, were applied.The HRDs use a red colour scale that represents the square root of the density of stars.The Gaia DR2 HRD of the low-extinction stars is represented in Fig. 5.The approximate equivalent temperature and luminosity to the G BP − G RP colour and the absolute Gaia M G magnitude provided in the figure were determined using the PARSEC isochrones (Marigo et al. 2017) for main-sequence stars.

Main sequence
The main sequence is very thin, both in fields and in clusters.This is very clearly visible in Fig. 7, which shows the HRDs of the Hyades and Praesepe clusters (ages ∼700 Myr), which accurately overlap, as has previously been noticed in van Leeuwen (2009) and confirmed in Gaia Collaboration et al. (2017).This figure shows the very narrow sequence described by the stars in both clusters, as well as the scattering of double stars up to 0.75 magnitudes above the main sequence.The remaining width of the main sequence is still largely explained as due to the uncertainties in the parallax of the individual stars, and the underlying main sequence is likely to be even narrower.
The binary sequence spread is visible throughout the main sequence (Figs. 5 and 6), and most clearly in open clusters (Fig. 7, see also Sect.6).It is most preeminent for field stars below M G = 13.Figure 8 shows the main-sequence fiducial of the local HRD shifted by 0.753 mag, which corresponds to two identical stars in an unresolved binary system observed with the same colour but twice the luminosity of the equivalent single star.See Hurley & Tout (1998), for instance, for a discussion of this strong sequence.Binaries with a main-sequence primary and a giant companion would lie much higher in the diagram, while binaries with a late-type main-sequence primary and a white dwarf companion lie between the white dwarf and the main sequence, as is shown in Fig. 5, for example.
The main sequence is thicker between 10 < M G < 13 (Figs.2, 5, 6).The youngest main-sequence stars lie on the upper part of the main sequence (in blue in Fig. 2).The subdwarfs, which are metal-poor stars associated with the halo, are visible in the lower part of the local HRD (in red in Fig. 2, see also Sect.7).
The main-sequence turn-off variation with age is clearly illustrated in Fig. 2, and the variation with metallicity is shown in Fig. 3. Blue stragglers are also visible over the main-sequence turn-off (Figs. 4).
Between the main sequence and the subgiants lies a tail of stars around M G = 4 and G BP − G RP =1.5.These stars shows variability and may be associated with RS Canum Venaticorum variables, which are close binary stars (Gaia Collaboration et al. 2018b).
Article number, page 7 of 28

Brown dwarfs
To study the location of the low-mass objects in the Gaia HRD, we used the Gaia ultracool dwarf sample (GUCDS) compiled by Smart et al. (2017).It includes 1886 brown dwarfs (BD) of L, T, and Y types, although a substantial fraction of them are too faint for Gaia.We note that the authors found 328 BDs in common with the Gaia DR1 catalogue (Gaia Collaboration et al. 2016).
The crossmatch between the 2MASS catalogue (Skrutskie et al. 2006) and Gaia DR2 provided within the Gaia archive (Marrese et al. 2018) has been used to identify GUCDS entries.The resulting sample includes 601 BDs.Of these, 527 have fiveparameter solutions (coordinates, proper motions, and parallax) and full photometry (G, G BP , and G RP ).Most of these BDs have parallaxes higher than 4 mas (equivalent to 250 pc in distance) and relative parallax errors smaller than 25%.They also have astrometric excess noise larger than 1 mas and a high (I BP +I RP )/I G flux ratio.They are faint red objects with very low flux in the BP wavelength range of their spectrum.Any background under- estimation causes the measured BP flux to increase to more than it should be, yielding high flux ratios, the highest ratios are derived for the faintest BDs.The filters presented in Sect.2.1 therefore did not allow us to retain them.
We accordingly adapted our filters for the background stars of Fig. 9.We plot the HRD using the G − G RP colour instead of G BP − G RP because of the poor quality of G BP for these faint red sources.We applied the same astrometric filters as for Fig. uncertainties.More dispersion is present in this diagram than in Fig. 6c because of this missing filter, but the faint red sources we study here are represented better.
The 470 BDs for which DR2 provides parallaxes better than 10%, and the G and G RP magnitudes are overlaid in Fig. 9 without any filtering.The sequence of BDs follows the sequence of low-mass stars.The absolute magnitudes of four stars are too bright, most probably because of a cross-match issue.In Fig. 9a the M-, L-and T-type BDs are sorted according to the classification in GUCDS.There are 21, 443, and 7 of each type, respectively.We also present in Fig. 9c the corresponding HRD using 2MASS colours with the 2MASS photometric quality flag AAA (applied to background and GUCDS stars).Figures 9b,d includes BT-Settl tracks2 (Baraffe et al. 2015) for masses < 0.08 M that were computed using the nominal Gaia passbands.With the Gaia G − G RP colour, the sequence of M, L, T types is continuous and relatively thin.Conversely, the spread in the near-infrared is larger and the L/T transition feature is strongly seen with a shift of J − K s to the blue, which is due to a drastic change in the brown dwarf cloud properties (e.g.Saumon & Marley 2008).Some GUCDS L-type stars with very blue 2MASS colours seem at first sight intriguing, but their location might be consistent with metal-poor tracks (Fig. 9d).Following Faherty et al. ( 2009), we studied their kinematics, which are indeed consistent with the halo kinematic cut of the tangential velocity V T >200 km s −1 (see Sect. 7).A kinematic selection of the global HRD as done in Sect.7 but using the 2MASS colours confirms the blue tail of the bottom of the main sequence in the near-infrared for the halo kinematic selection.

Giant branch
The clusters clearly illustrate the change in global shape of the giant branch with age and metallicity (Figs. 2 and 3).For field stars, there are fewer giants than dwarfs in the first 100 pc.To observe the field giant branch in more detail, we therefore extended our selection to 500 pc with the low-extinction selection (E(B − V) < 0.015, see Sect.2.2) for Fig. 10.
The most prominent feature of the giant branch is the Red Clump (RC in Fig. 10, around G BP − G RP = 1.2, M G = 0.5 mag).
Article number, page 9 of 28 It corresponds to low-mass stars that burn helium in their core (e.g.Girardi 2016).The colour of core-helium burning stars is strongly dependent on metallicity and age.The more metal-rich, the redder, which leads to this red clump feature in the local HRD.For more metal-poor populations, these stars are bluer and lead to the horizontal-branch (HB) feature that is clearly visible in globular clusters (Fig. 11).
The secondary red clump (SRC in Fig. 10, around G BP − G RP = 1.1, M G = 0.6) is more extended in its bluest part to fainter magnitudes than the red clump.It corresponds to younger more massive red clump stars (Girardi 1999) and is therefore mostly visible in the local HRD (Fig. 6c).Core-helium burning stars that are even more massive are more luminous than the red clump and lie still on the blue part of it, leading to a vertical structure that is sometimes called the Vertical Red Clump (VRC in Fig. 10).
On the red side and fainter than the clump lies the RGB bump (RGBB in Fig. 10).This bump is caused by a brief interruption of the stellar luminosity increase as a star evolves on the red giant branch by burning its hydrogen shell, which creates an accumulation of stars at this HRD position (e.g.Christensen-Dalsgaard 2015).Its luminosity changes more with metallicity and age than the red clump.Brighter than the red clump, at M G ∼ −0.5, lies the AGB bump (AGBB in Fig. 10), which corresponds to the start of the asymptotic giant branch (AGB) where stars are burning their helium shell (e.g.Gallart 1998).The AGB bump is much less densely populated than the RGB bump.It is also clearly visible in the HRD of 47 Tuc (Fig. 11a).
The globular clusters in Fig. 11 clearly illustrate the diversity of the HB morphology.Some have predominantly blue HB (NGC 6397), some just red HB (NGC 104), and some a mixed HB showing bimodal distribution (NGC 5272 and NGC 6362).The HB morphology is explained in the framework of the multiple populations; it is regulated by age, metallicity, and first/second generation abundances (Carretta et al. 2009).NGC 6362 is the least massive globular that presents multiple populations.Mucciarelli et al. (2016) concluded that most of the stars that populate the red HB are Na poor and belong to the first generation, while the blue side of the HB is populated by the Na-rich stars belonging to the second generation.The same kind of correlation is shown in general by the globular clusters.We quote among others the studies of 47 Tuc (Gratton et al. 2013) and NGC 6397 (Carretta et al. 2009).The role of the He abundances is still under discussion (Valcarce et al. 2016;Marino et al. 2014).He-enhanced stars are indeed expected to populate the blue side of the instability strip because they are still O depleted and Na enhanced, as observed in the second-generation stars.How significant the He enhancement is is still unclear.
Figure 3 shows that the globular cluster HB can extend towards the extreme horizontal branch (EHB) region.They are in the same region of the HRD as the hot subdwarfs, which creates a clump at M G =4 and G BP −G RP =-0.5 that is well visible in Fig. 1 and Fig. 5.These stars are also nicely characterised in terms of variability, including binary-induced variability, in Gaia Collaboration et al. (2018b).These hot subdwarfs are considered to be red giants that lost their outer hydrogen layers before the core began to fuse helium, which might be due to the interaction with a low-mass companion, although other processes might be at play (e.g.Heber 2009).Gaia will allow detailed studies of the differences between cluster and field hot subdwarfs.

Planetary nebulae
At the end of the AGB phase, the star has lost most of its hydrogen envelope.The gas expands while the central star first grows hotter at constant luminosity, contracting and fusing hydrogen in the shell around its core (post-AGB phase), then it slowly cools when the hydrogen shell is exhausted, to reach the white dwarf phase.This planetary nebulae phase is very short, about 10,000 years, and is therefore quite difficult to observe in the HRD.The Gaia DR2 contains many observations of nearby planetary nebulae as their expanding gas create excess flux over the mean sky background that triggers the on-board detection.We here wish to follow the route of the central star in the HRD.While some central planetary nebula stars are visible in the Galactic Pole HRD (Fig. 12), post-AGB stars are too rare to appear in this diagram.We used catalogue compilations to highlight the position of the two types in the Gaia HRD.
We used the Kerber et al. (2003) catalogue of Galactic planetary nebulae, selecting only sources classified as central stars that are clearly separated from the nebula.With a cross-match radius of 1 and using all our filter criteria of Sect.2.1, only four stars remain.We therefore relaxed the extinction criteria to E(B − V) < 0.05 and the parallax relative uncertainty to σ / < 20%, leading to 23 stars.
For post-AGB stars, we used the catalogue of Szczerba et al. (2007) and the 2MASS identifier provided for the cross-match.We selected only stars that are classified as very likely post-AGB objects.Here we also relaxed the extinction criteria to E(B − V) < 0.05 and the parallax relative uncertainty to σ / < 20%, leading to 11 stars.
While some outliers are seen in Fig. 12, either due to crossmatch or misclassification issues, the global position of these stars in the HRD closely follows the expected track from the AGB to the white dwarf sequence.We note that this path crosses the hot subdwarf region we discussed in the previous section.

White dwarfs
The Sloan Digital Sky Survey (SDSS, Ahn et al. 2012) has produced the largest spectroscopic catalogue of white dwarfs so far (e.g.Kleinman et al. 2013).This data set has greatly aided our understanding of white dwarf classification and evolution.For example, it has allowed determining the white dwarf mass distribution for large statistical samples of different white dwarf Article number, page 10 of 28  spectral types.However, much of this work is model dependent and relies upon theoretical mass-radius relationships and stellar atmosphere models, whose precision has only been tested in a limited way.These tests have been limited by the relatively small number of white dwarfs for which accurate parallaxes are available (e.g.Provencal et al. 1998) and by the precision of the parallaxes for these faint stars.This work was updated using the Gaia DR1 catalogue (Tremblay et al. 2017), which included more stars, but the uncertainties remain too large to constrain the theoretical mass-radius relations.Only in a few cases, where the white dwarf resides in a binary system, have mass radius measurements begun to approach the accuracy required to constrain the core composition and H layer mass of individual stars (e.g.Barstow et al. 2005;Parsons et al. 2017;Joyce et al. 2017).Even then, some of these white dwarfs may not be representative of the general population because common envelope evolution may have caused them to depart from the normal white dwarf evolutionary paths.
The publication of Gaia DR2 presents the opportunity to apply accurate parallaxes, with uncertainties of 1% or smaller, to the study of white dwarf stars.The availability of these data, coupled with the accurate Gaia photometry, yields the absolute magnitude, with which the white dwarfs can be clearly located in the expected region of the HRD (Figs. 5, 6). Figure 13 shows the white dwarf region of the HRD alone.This sample was selected with G BP −G RP < 2 and G−10+5 log 10 > 10+2.6 (G BP −G RP ) and by applying the filters described in Sect.2, including the low-extinction E(B − V) < 0.015 criterion, but with a stronger constraint on the parallax relative uncertainty of 5%.This yields a catalogue of 26,264 objects.We overplot in Fig. 14 white dwarf evolutionary models3 for C/O cores (Holberg & Bergeron 2006;Kowalski & Saumon 2006;Tremblay et al. 2011;Bergeron et al. 2011) with colours computed using the revised Gaia DR2 passbands (Evans et al. 2018).Several features are clearly visible in Fig. 13.First there is a clear main concentration of stars that is distributed continuously from left to right in the diagram (A) and coincides with the 0.6 M hydrogen evolutionary tracks (in magenta).This is expected because the white dwarf mass distribution peaks very strongly near 0.6 M (Kleinman et al. 2013).Interestingly, the concentration of white dwarfs departs from the cooling tracks towards the red end of the sequence.
Just below the main 0.6 M concentration of white dwarfs is a second, separate concentration (B) that seems to be separate from the 0.6 M peak at G BP − G RP ∼ −0.1 before again merging by G BP − G RP ∼ 0.8.At the maximum separation, this concentration is roughly aligned with the 0.8 M hydrogen white dwarf cooling track (in green), which is not expected.While the SDSS mass distribution (Kleinman et al. 2013) shows a significant upper tail that extends through 0.8 M and up to almost 1.2 M , there is no evidence for a minimum between 0.6 and 0.8 M like that seen in Fig. 14a.A mass difference should therefore not lead to this feature.However, for a given mass, the evolutionary tracks for different compositions (DA: hydrogen and DB: helium) and envelope masses are virtually coincident at the resolution of Fig. 14 in the theoretical tracks, leading to no direct interpretation from the tracks in the HRD alone, but we describe below a different view from the colour-colour relation and the SDSS comparison.
A third, weaker concentration of white dwarfs in Fig. 13 lies below the main groups (Q).It does not follow an obvious evolutionary constant mass curve, which would be parallel to those shown in the plot.Beginning at approximately M G = 13 and G BP − G RP = −0.3, it follows a shallower curve that converges with the other concentrations near G BP − G RP = 0.2.
White dwarfs are also seen to lie above the main concentration A. This can be explained as a mix between natural white dwarf mass distributions and binarity (see Fig. 8).
Selecting only the most precise G BP and G RP photometry (σ G BP < 0.01 and σ G RP < 0.01), we examined the colour-colour relation in Fig. 14b.The sequence is also split into two parts in this diagram.We verified that the two splits coincide, meaning that the stars in the lower part of Fig. 14a lie in the upper part of Fig. 14b.The mass is not expected to lead to significant differences in this colour-colour diagram, and the theoretical tracks coincide with the observed splits, pointing towards a difference between helium and hydrogen white dwarfs.It also recalls the split in the SDSS colour-colour diagram (Harris et al. 2003).
While Gaia identifies white dwarfs based on their location on the HRD, SDSS white dwarfs were identified spectroscopically, providing further information on the spectral type, T eff , and log g as well as a classification.Therefore we cross-matched the two data sets to better understand the features observed in Fig. 14.
We obtained a catalogue of spectroscopically identified SDSS white dwarfs from the Montreal White Dwarf Database4 (Dufour et al. 2017) by downloading the whole catalogue and then filtering for SDSS identifier, which yielded 28,797 objects.Using the SDSS cross-match provided in the Gaia archive (Marrese et al. 2018), we found that there are 22,802 objects in common and 5,237 satisfying all the filters described in Sect.2.1 and with single-star spectral type information.Figure 15 shows the SDSS u − g colour magnitude for the sample with the absolute u magnitude calculated using the Gaia parallax.The distribution is clearly bifurcated.Evolutionary tracks for H and He atmospheres (0.6 M ) are overplotted in the figure, indicating that this is due to the different atmospheric compositions.The Gaia counterparts of these SDSS white dwarfs are quite faint, and therefore the features seen in Fig. 14a are less well visible in this sample because of the larger noise in the parallaxes and the colours.Still, it allowed us to verify that the split of the SDSS white dwarfs corresponds to the location of the Gaia splits in Fig. 14.The narrower filter bands of SDSS are more sensitive to atmospheric compositions than the broad BP and RP Gaia bands.In particular, the u -band fluxes of H-rich DA white dwarfs are suppressed by the Balmer jump at 364.6 nm, which reddens the colours of these stars.The Balmer jump is in the wavelength range where the Gaia filters calibrated for DR2 differ most from the nominal filters (Evans et al. 2018), which explains the importance of using tracks that are updated to the DR2 filters for the white dwarf studies instead of the nominal tracks provided by Carrasco et al. (2014).
Figure 16 shows the colour-magnitude diagrams in the Gaia and SDSS photometry bands, overlaid with the white dwarfs for specific spectral types.The locations of the various spectral types correspond well to the expected colours arising from their effective temperatures.For example, DQ (carbon), DZ (metal rich), and DC (no strong lines) stars are confined to the red end of the colour-magnitude diagram, while the DO stars (ionised helium) all lie at the blue end.DAs cover the whole diagram.Interestingly, in Fig. 16b, a significant number of classified DA white dwarfs appears to occupy the He-rich atmosphere branch that is indicated by the evolutionary track in Fig. 15.The weaker Q concentration seems to include stars of all types except for DO and DZ.However, the most numerous components are the DA and DQs.

Cluster as stellar parameter templates
Clusters have long been considered as benchmarks with regard to the determination of the stellar properties.Open cluster stars share common properties, such as age and chemical abundances.The level of homogeneity of open clusters has been assessed in several papers (Cantat-Gaudin et al. 2014;Bovy 2016).By means of a high-precision differential abundance analysis, the Hyades have been proved to be chemically in-homogeneous at the 0.02 dex level (Liu et al. 2016) at maximum.Until now, the study of clusters was hampered by the disk field contamination.This in turn results in difficult membership determination, and in highly uncertain parameters (Netopil et al. 2015).Distance and age, together with chemical abundances, are the fundamental properties for a meaningful description of the disk characteristics.Their study complements the field population studies that are based on Galactic surveys.Globular clusters are fundamental tools for studying the properties of low-mass stars and the early chemical evolution of the Galaxy.Now Gaia DR2 data bring us into a completely new domain.High-accuracy parallaxes and exquisite photometry make the comparison with theoretical isochrones very fruitful, based on which, stellar properties can be defined.A detailed discussion of the uncertainties of stellar models is beyond the scope of this paper.Here we would like to recall that effects such as convection in the stellar core, mass loss, rotation, and magnetic fields are still poorly constrained and are often only parametrised in stellar models (Bell 2016;Pasetto et al. 2016;Weiss & Heners 2013).Although very significant, seismic predictions depend on our poor knowledge of the relevant physics (Miglio et al. 2015).A calibration of these effects on star cluster photometry is mandatory and will complement asteroseismology as a tool for testing stellar physics and will ultimately improve stellar models.In Table 2 we present the ages and the extinction values derived by isochrone fitting for the sample of open clusters discussed in this paper.The uncertainties are ∆(log(age)) +0.14 −0.22 , +0.11 −0.13 , +0.08 −0.06 for 6 < log(age) ≤ 7, 7 < log(age) ≤ 8, log(age) > 8, respectively, and ∆E(B − R) = 0.04.Here we made use of PARSEC isochrones (Chen et al. 2014) for metallicities Z = 0.017 and Z = 0.020 updated to the latest transmission curve calibrated on Gaia DR2 data (Evans et al. 2018)  5 .Praesepe, Hyades, Alpha Per, and NGC 6475 were fitted with Z = 0.02 (Gaia Collaboration et al. 2017;Kharchenko et al. 2015), while the others were reproduced using Z = 0.017.This gave a relatively poor fit for clusters that are known to have sub-solar metallicity, such as NGC 2158, which has [Fe/H]=-0.25(Kharchenko et al. 2015). 5PARSEC isochrones in Gaia DR2 passbands are available at http: //stev.oapd.inaf.it/cgi-bin/cmdArticle number, page 13 of 28   was used, and the extinction was not corrected in the photometry, but was applied on the isochrones.
The fits are remarkably good in the upper and lower main sequence.The high quality of Gaia photometry produces welldefined features, very clean main sequences, and a clear definition of the binary sequence.The agreement for the Pleiades is particularly remarkable.In spite of the impressively good agreement across a range of several magnitudes, at about M G ∼ 10, the model predictions and the observed main sequence still disagree.The slope of the theoretical main sequence initially seems to be slightly steeper than the observed main sequence, while at even lower magnitudes, the slope of the observed main sequence becomes steeper than the predicted main sequence.The latter effect might be due to the background subtraction, which becomes challenging at these faint magnitudes (Evans et al. 2018;Arenou et al. 2018).Instead, the initial steepening of the isochrones, which is also observed in other clusters in Fig. 17, might indicate that the adopted boundary conditions in the domain of very low mass stars in PARSEC need a further small revision.It is well known that current models and the colour transformations fail to reproduce the main sequence in the very low mass regime (Bell 2016), and the data gathered by Gaia will certainly help to overcome this long-standing problem.
The age determination of Blanco 1 deserves further comments.Blanco 1 has a slightly super-solar metallicity [Fe/H] = +0.04 ± 0.04 (Ford et al. 2005).Previous age determination placed Blanco 1 in the age range log(age) = 8.0 − 8.17 (Moraux et al. 2007).A determination of the lithium depletion boundary on very low mass stars gives log(age) = 8.06 ± 0.13 when a correction for magnetic activity is applied (Juarez et al. 2014).From the main-sequence turnoff, we obtain log(age) = 8.30.However, fitting the main-sequence turnoff in such an inconspicuous cluster might not lead to correct results, since the initial mass function disfavours higher mass stars.Using the lithium depletion boundary age of log(age) of 8.06 ± 0.04, we reproduce the lower main sequence, with a marginal fit to the upper main sequence.Similar considerations apply to the Pleiades, whose log(age) is in the range 8.04 ± 0.03 -8.10 ± 0.06 and is derived from the lithium depletion boundary or from eclipsing binaries (for a recent discussion, see David et al. 2016).Using the lithium depletion boundary age of 8.04 ± 0.06, we can reproduce the main sequence with PARSEC isochrones.
Figure 18 presents the comparison of two distant clusters, NGC 2682 (M67) and NGC 2447, with PARSEC isochrones.M 67 is one of the best-studied star clusters.It has a metallicity near solar, an accessible distance of about 1028 pc with low reddening (Taylor 2007), and an age close to solar (∼ 4 Gyr).It is a very highly populated object that includes over 1000 members from main-sequence dwarfs, a well-populated subgiant and red giant branch, white dwarfs, blue stragglers, sub-subgiants, X-ray sources, and cataclysmic variables.Gaia identifies 1526 members.It was observed by almost all the most relevant spectroscopic surveys (Gaia-ESO, APOGEE, WIYN, etc.).Asteroseismologic data are available from the Kepler 2 mission (Stello et al. 2016).M67 is a cornerstone of stellar astrophysics, and it is a calibrator of age determination via gyrochronology (Barnes et al. 2016).Its turn-off mass is very close to the critical mass for the onset of core convection.For this reason, the cluster is especially interesting for this specific regime of stellar models and their dependence on different parameters such as nuclear reaction rate and solar abundances.The main-sequence termination presents a distinctive hook and a gap just above it.These fea-tures are used to distinguish between diffusive and non-diffusive evolutionary models.Atomic diffusion is very important for the morphology of isochrones in the vicinity of the turn-off.The hook feature traces the rapid contraction phase that occurs at central H exhaustion in those stars that have convective cores during their main-sequence phase.This hook is located at somewhat higher luminosities and cooler temperatures when diffusive processes are included (Michaud et al. 2004).Gaia photometry and parallax place the location of these features very precisely in the HRD.PARSEC isochrones, including overshoot and diffusion, reproduce the main-sequence slope and termination point reasonably well, although additional overshoot calibration might be necessary.A population of blue stragglers, a few yellow giants, and two sub-subgiants are clearly visible among the members.The binary star sequence in M67 is clearly defined as well.
NGC 2447 is a younger object with an age of 0.55 Gyr and almost solar metallicity.Previous photometry is relatively poor (Clariá et al. 2005).In Gaia DR2, photometry and membership of the cluster stand out very clearly.PARSEC isochrones reproduce the main sequence very well, while the red clump colour is slightly redder.
Figure 19 presents the HRD of the globular cluster 47 Tuc (see Table 3), which is one prominent example of multiple populations in globular clusters.Hubble Space Telescope (HST) photometry in the blue passbands has revealed a double main sequence (Milone et al. 2012) and distinct subgiant branches (Anderson et al. 2009).These components are not visible in the highaccuracy Gaia photometry, since bluer colours would be necessary.47 Tuc has a relatively high average metallicity of [Fe/H]=-0.72.We fit it with PARSEC isochrones with Z = 0.0056, Y = 0.25.Since no alpha-enhanced tracks are available in the PARSEC data set, we use the Salaris et al. (1993) relation to account for the enhancement.

Variation of the HRD with kinematics
Thin disk, thick disk, and halo have different age and metallicity distributions as well as kinematics.The Gaia HRD is therefore expected to vary with the kinematics properties.For stars with radial velocities, we apply classical cuts to broadly kinematically select thin-disk (V tot <50 km s −1 ), thickdisk (70<V tot <180 km s −1 ), and halo stars (V tot >200 km s −1 ) (e.g.Bensby et al. 2014), using U,V,W computed within the framework of Gaia Collaboration et al. (2018d), in which a global Toomre diagram is presented.This sample with radial velocities is limited to bright stars.To probe deeper into the HRD, we also made a selection using only tangential velocities, which we computed with V T =4.74/ µ 2 α * + µ 2 δ .We roughly adapted our kinematic cut to the fact that we now only have two components of the velocity instead of three: we used V T <40 km s −1 for the thin disk and 60<V T <150 km s −1 for the thick disk, but still V T >200 km s −1 for the halo.To all our samples we also applied the E(B − V) < 0.015 selection criterion.The results are presented in Fig. 20 and Fig. 21.We note that hot star radial velocities are not included in Gaia DR2 (Sartoretti et al. 2018), which explains why they are missing in Fig. 20.
The left figures associated with the thin disk show the same main features typical of a young population as the local HRD of Fig. 6: young hot main-sequence stars are present (Fig. 21a), the secondary red clump as well as the AGB bump is visible (Fig. 20a), and the turn-off region is diffusely populated.The middle figures associated with the thick disk show a more localised turn-off typical of an intermediate to old population.The median locus of the main sequence is similar to the thin-disk selection.The right figures associated with the halo show an extended horizontal branch, typical of old metal-poor populations, but also two very distinct main sequences and turn-offs.We note the presence of the halo white dwarfs.
We study the kinematic selection associated with the halo in Fig. 22 in more detail.The two main-sequence turn-offs are shifted by ∼0.1 mag in colour.The red main-sequence turn-off is shifted by ∼0.05 mag from the thick-disk kinematic selection main sequence (green line in Fig. 22a).Comparison with isochrones clearly identifies the distinct main sequences as being driven by a metallicity difference of about 1 dex.To further confirm this, we cross-matched our selection with the APOGEE DR14 catalogue (Holtzman et al. 2015) using their 2MASS ID and the 2MASS cross-match provided in the Gaia archive (Marrese et al. 2018).There are 184 stars in common, 1168 if we relax the low-extinction criteria that mostly confine our HRD selection to the galactic poles.The metallicity distribution is indeed double-peaked, with peak metallicities of -1.3 and -0.5 dex.We superimpose in Fig. 22 the corresponding PARSEC isochrones using the Salaris et al. (1993) formula for the mean α enhancement of 0.23 for [M/H]=-1.3and -0.5 and ages of 13 and 11 Gyr, respectively.While the extent of the horizontal branch does not correspond to the isochrones used here, it can be compared to the empirical horizontal branches of the globular clusters presented in Fig. 11.
This bimodal metallicity distribution in the kinematic selection of the halo may recall the globular cluster bimodal metallicity distribution with the same peaks at [Fe/H]∼-0.5 and [Fe/H]∼-1.5 (e.g. Zinn 1985), the more metal-rich part being associated with the thick disk and bulge.We verified with the globular cluster kinematics provided in Gaia Collaboration et al. (2018c) that 80% of these globular clusters indeed fall into our halo kinematic selection, independently of their metallicity.The -0.5 dex peak also recalls the bulge metal-poor component (e.g.Hill et al. 2011).However, it seems to be different from the double halo found at larger distances (Carollo et al. 2007;de Jong et al. 2010): while their inner-halo component at ∼-1.6 could correspond to our metal-poor component, their metal-poor component is at metallicity ∼-2.2 and is found in the outer Galaxy.This duality in the metallicity distribution of the kinematically selected halo stars has also been found using TGAS data with RAVE and APOGEE (Bonaca et al. 2017).Half of the stars are also found to have [M/H]>-1 dex with a dynamically selected halo sample in TGAS/RAVE by Posti et al. (2017).
The α abundances of this APOGEE sample (Fig. 22b) let us recover the two sequences described by Nissen & Schuster (2010) using an equivalent kinematic selection.We adjusted a median spline to the main sequence of the high-velocity HRD and present the velocity distribution of the stars on either side of this median spline in Fig. 22c.The magenta sequence looks like a velocity distribution tail towards high velocities, while the blue sequence has a flat velocity distribution.We do not see any difference in the sky distribution of these components, most probably because the sky distribution is fully dominated by our sample selection criteria.All these tests and comparisons with the literature seem to indicate a very different formation scenario for the two components of this kinematic selection of the halo.

Summary
The unprecedented all-sky precise and homogeneous astrometric and photometric content of Gaia DR2 allows us to see fine structures in both field star and cluster Hertzsprung-Russell dia-Article number, page 16 of 28  grams to an extent that has never been reached before.We have described the main filtering of the data that is required for this purpose and provided membership for a selection of open clusters covering a wide range of ages.
The variations with age and metallicity are clearly illustrated by the main sequence and the giant branches of a large set of open and globular clusters and kinematically selected stellar populations.The main sequence for nearby stars is extremely thin, for field and cluster stars both, with a clear scattering of double stars up to 0.75 magnitude visible above the main sequence.Gaia DR2 provides a very unique view of the bottom of the main sequence down to the brown dwarf regime, including L-type and halo BDs.We also see the post-AGB stars and the central stars of planetary nebulae, which follow the expected tracks down to the white dwarf sequence, as well as hot subdwarfs.
The split in the white dwarf sequence between hydrogen and helium white dwarfs, which was first detected in the SDSS colour-colour diagrams, is visible for the first time in an HRD, with very thin sequences that agree with the strong peak of their mass distribution around 0.6 M .
Kinematic selections clearly show the change in HRDs with stellar populations.It highlights the strong bimodality of the HRD of the classical halo kinematic selection, and gives evidence of two very different populations within this selection.
All the features in the Gaia HRDs chiefly agree in general with the theoretical stellar evolution models.The differences that are observed for the faintest brown dwarfs, the white dwarf hydrogen/helium split, or the very fine structures of the open cluster main sequences, for example, are expected to bring new insight into stellar physics.
Numerous studies by the community are expected on the Gaia HRD.For example, rare stages of evolution will be extracted from the archive, together with more clusters, and detailed comparisons with different stellar evolution models will be made.The completeness of the data is a difficult question that Article number, page 17 of 28 we did not discuss here, but that will be studied by the community as it is a very important issue, in particular for determining the local volume density and all the studies of the initial mass function and stellar evolution lifetimes.
The next Gaia release, DR3, will again be a new step for stellar studies.This will be achieved not only by the increase in completeness, precision, and accuracy of the data, but also by the additional spectrophotometry and spectroscopy, together with the binarity information that will be provided.
(CITIC), the Red Española de Supercomputación (RES) computer resources at MareNostrum, and the Barcelona Supercomputing Centre -Centro Nacional de Supercomputación (BSC-CNS) through activities AECT-2016-1-0006, AECT-2016-2-0013, AECT-2016-3-0011, and AECT-2017-1-0020; the Swedish National Space Board (SNSB/Rymdstyrelsen); the Swiss State Secretariat for Education, Research, and Innovation through the ESA PRODEX programme, the Mesures d'Accompagnement, the Swiss Activités Nationales Complémentaires, and the Swiss National Science Foundation; the United Kingdom Rutherford Appleton Laboratory, the United Kingdom Science and Technology Facilities Council (STFC) through grant ST/L006553/1, the United Kingdom Space Agency (UKSA) through grant ST/N000641/1 and ST/N001117/1, as well as a Particle Physics and Astronomy Research Council Grant PP/C503703/1.This publication has made use of SIMBAD and VizieR, both operated at the Centre de Données astronomiques de Strasbourg (CDS, http://cds.u-strasbg.fr/).This publication has made use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation.This publication has made use of data products from SDSS-III.The Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science.The SDSS-III web site is http://www.sdss3.org/.SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration.Nine clusters within 250 pc from the Sun were analysed as nearby clusters.The analysis is iterative, and consists of two elements: 1. determinations of the space velocity vector at the cluster centre, and 2. determination of the cluster centre.A first selection is made of stars contained in a sphere with a radius of around 15 pc around the assumed centre of the cluster.A summary of the observed radii for the nearby and more distant clusters is shown in , where the outermost radius is set at the point beyond which the density of contaminating field stars starts to dominate.The selected stars are further filtered on their agreement between the observed proper motion and the predicted projection of the assumed space motion at the 3D position of the star, using the measured stellar parallax, and taking into account the uncertainties on the observed proper motion and parallax.The solution for the space motion follows Eq.A13 in Gaia Collaboration et al. (2017).Although it is in principle possible to solve also for the radial velocity using only the astrometric data, this effectively only works for the Hyades cluster.Instead, a single equation for the observed radial velocity of the cluster was added, where the observed radial velocity is based on the weighted mean of the Gaia radial velocities of cluster members for which these data are available.
To stabilise the solution, it is important to align the coordinate system with the line of sight towards the cluster centre, minimising the mixing of the contributions from the proper motions and the additional information from the radial velocity.The solution for the space motion does provide an estimate of the radial velocity component, but except for the Hyades and Coma Ber, this is largely dominated by the radial velocity value and its accuracy that is used as input to the solution.Small differences are therefore seen between the radial velocities as presented in Table A.2 (as directly derived from the Gaia spectroscopic data) and in Table A.3 (the summary data for the nine clusters in this selection), where the astrometric information on the radial velocity is also taken into account.show an example of the 3D distribution maps for this cluster; maps like this were prepared for all nearby clusters.Next to the astrometric data, the second Gaia data release also presents radial velocity measurements for a magnitudelimited sample.The radial velocities were compared with the projection of the cluster space velocity at the position of each star for which these data are available.This is particularly relevant for stars in the Hyades cluster, where the projection effects of the radial velocity can be of the order of several km s −1 .Table A.2 presents the results for the nine nearby clusters.

Fig. 1 .
Fig. 1.Full Gaia colour-magnitude diagram of sources with the filters described in Sect.2.1 applied (65,921,112 stars).The colour scale represents the square root of the relative density of stars.

Gaia
Fig. 2. Composite HRD for 32 open clusters, coloured according to log(age), using the extinction and distance moduli as determined from the Gaia data (Table2).

Fig. 5 .
Fig. 5. Gaia HRD of sources with low extinction (E(B − V) < 0.015 mag) satisfying the filters described in Sect.2.1 (4,276,690 stars).The colour scale represents the square root of the density of stars.Approximate temperature and luminosity equivalents for main-sequence stars are provided at the top and right axis, respectively, to guide the eye.

Fig. 7 .
Fig. 7. Extract of the HRD for the Hyades and Praesepe clusters, showing the detailed agreement between the main sequences of the two clusters, the narrowness of the combined main sequence, and a scattering of double stars up to 0.75 mag above the main sequence.

Fig. 8 .
Fig.8.Same as Fig.6c, overlaid in blue with the median fiducial and in green with the same fiducial shifted by -0.753 mag, corresponding to an unresolved binary system of two identical stars.
Fig. 9. a): Gaia HRD of the stars with > 10 mas with adapted photometric filters (see text, 240,703 stars) overlaid with all cross-matched GUCDS (Smart et al. 2017) stars with σ / < 10% in blue (M type), green (L type), and red (T type).Pink squares are added around stars with tangential velocity V T >200 km s −1 .b) BT-Settl tracks (Baraffe et al. 2015) of solar metallicity for masses from 0.01 M to 0.08 M in steps of 0.01 (the upper tracks correspond to lower masses) plus in pink the same tracks for [M/H]= -1.0.Panels c) and d): Same diagrams using the 2MASS colours.

Fig. 13 .
Fig. 13.Gaia HRD of white dwarfs with σ / < 5% (26,264 stars), with letter labels to the features discussed in the text.

Fig. 15 .
Fig. 15.SDSS white dwarfs (5,237 stars) with evolutionary models.M u is computed using the SDSS u magnitude and the Gaia parallax.Magenta: 0.6 M pure H; green dashed: 0.8 M pure H; and blue : 0.6 M pure He.

Figure 17
Figure17shows the HRD of a few nearby open clusters compared with PARSEC isochrones.The distance modulus (Table2)

Fig. 19 .
Fig. 19.HRD of the globular cluster 47 Tuc compared with PARSEC isochrones (see text for details).The inner region (radius < 10 arcmin, e.g. three times the half-light radius) is shown in green, while the external regions are plotted in blue.A maximum radius of 1.1 degrees was used.

Fig. A. 1 .
Fig. A.1.Maximum radius in degrees in DR2 for the 46 open clusters as a function of parallax.The two diagonal lines represent maximum radii of 10 (bottom) and 20 (top) pc.

Fig
Fig. A.2. Surface-density profile for the Pleiades cluster, based on 1332 identified cluster members.
Fig. A.1.The radius can be adjusted based on the derived surface density distribution (Fig. A.2) Figure A.3 shows an example of the level of agreement between the differential parallax and proper motion values in the cluster IC 2602.In Fig. A.4 we also

Fig
Fig. A.3.Comparison between the directly measured parallaxes and the parallaxes obtained by including the relative proper motion data, for the cluster IC 2602.The clear linear relation shows the good agreement between proper motion and parallax offsets from the mean cluster values.

Figure A. 5
shows the differences (observed − predicted, where the predicted value is based on the local projection of the space velocity of the cluster) in the radial velocities for 191 stars in the Hyades cluster.Only stars for which the colour index G BP − G RP is greater than 0.4 mag were used.The results for all 9 nearby clusters are shown in TableA.2.

Table 1 .
Parameters used to derive the Gaia extinction coefficients as a function of colour and extinction (Eq.1).

Table 2 .
Overview of reference values used in constructing the composite HRD for open clusters (Figure2).
Netopil et al. (2016) (DM) as derived from the Gaia astrometry; ages and reddening values as derived from Gaia photometry (see Sect. 6), with distances fixed on astrometric determinations; metallicities fromNetopil et al. (2016); Memb: the number of members with Gaia photometric data after application of the photometric filters.

Table 3 .
Gaia Collaboration et al.: Gaia Data Release 2: Observational Hertzsprung-Russell diagrams Reference data for 14 globular clusters used in the construction of the combined HRD (Figure3).

Table A .
1. Membership data for the open clusters.Only the first three lines with data for members of the Praesepe cluster are presented here.For the more distant clusters, the last two columns are not included.The astrometric and photometric extra filters presented in Sect.2.1 and used in the figures of this paper are not applied in this table.The full table will be available in electronic form at the CDS.

Table A .
2. Mean radial velocity values as derived from the Gaia spectroscopic data for nearby clusters.Notes.Columns: 1. Cluster name; 2: weighted-mean radial velocity in km s −1 ; 3. standard uncertainty on radial velocity; 4. unit-weight standard deviation of mean velocity solution; and 5. number of observations in mean velocity solution.