Globular clusters with Gaia

TL;DR

This paper assesses Gaia's capabilities for studying globular clusters, modeling crowding errors, and predicting the quality of astrometric, photometric, and kinematic data for various cluster types and distances.

Contribution

It provides a detailed simulation-based analysis of Gaia's expected performance on globular clusters, considering crowding effects and instrument limitations.

Findings

103-104 stars with minimal crowding effects will be measurable in most clusters.

Systemic proper motions and parallaxes will be accurate to 1% up to 15 kpc.

Internal kinematics and cluster masses can be determined with high precision.

Abstract

The treatment of crowded fields in Gaia data will only be a reality in a few years from now. In particular, for globular clusters, only the end-of-mission data (public in 2022-2023) will have the necessary full crowding treatment and will reach sufficient quality for the faintest stars. As a consequence, the work on the deblending and decontamination pipelines is still ongoing. We describe the present status of the pipelines for different Gaia instruments, and we model the end-of-mission crowding errors on the basis of available information. We then apply the nominal post-launch Gaia performances, appropriately worsened by the estimated crowding errors, to a set of 18 simulated globular clusters with different concentration, distance, and field contamination. We conclude that there will be 103-104 stars with astrometric performances virtually untouched by crowding (contaminated by <1 mmag) in the majority of clusters. The most limiting factor will be field crowding, not cluster crowding: the most contaminated clusters will only contain 10-100 clean stars. We also conclude that: (i) the systemic proper motions and parallaxes will be determined to 1% or better up to 15 kpc, and the nearby clusters will have radial velocities to a few km/s ; (ii) internal kinematics will be of unprecendented quality, cluster masses will be determined to 10% up to 15 kpc and beyond, and it will be possible to identify differences of a few km/s or less in the kinematics (if any) of cluster sub-populations up to 10 kpc and beyond; (iii) the brightest stars (V<17 mag) will have space-quality, wide-field photometry (mmag errors), and all Gaia photometry will have 1-3% errors on the absolute photometric calibration.

Tables

Table 1. Table 1: Adopted Gaia relevant quantities. We note that the AF window sizes are relevant for the astrometry; the BP/RP sizes for the photometry, chromaticity correction, and object classification and parametrization; the RVS window sizes are relevant for radial velocity, object parametrization and abundance analysis.

Size	Size	Description
(”)	(pix)
0.176789	1 (AC)	Across scan (AC) pixel size
0.058933	1 (AL)	Along scan (AL) pixel size
0.176789	3 (AL)	Gaia PSF
2.121468	12 (AC)	AC window size (AF, BP, and RP)
0.070720	12 (AL)	AL window size (AF)a
1.767890	10 (AC)	AC window size (RVS)
3.535980	60 (AL)	AL window size (BP and RP)
74.785977	1269 (AL)	AL window size (RVS)

Table 2. Table 2: Simulated clusters properties and crowding evaluation results. Fore each of the 18 simulated GCs we list (see text for more details): (1) the GC ID number; (2) the GC concentration parameter, c=log(r t /r c ); (3) the GC projected distance; (4) the type of simulated background; (5) the total number of simulated stars (GC and background) above Gaia detection limit; (6) the number of GC members; (7) the number of classic blends; (8) the number of Gaia blends; (9) the number of contaminated stars; (10) the number of clean stars, i.e., contaminated by less than 0.1% in flux (roughly 1 mmag); (11) the quick GC designation used in the paper; and (12) some examples of GCs with similar distance, concentration, and background field contamination.

Cluster	$c$	distance	background	$n_{tot}$	$n_{GC}$	$n_{classic}$	$n_{blends}$	$n_{contam}$	$n_{clean}$	Designation	Similar to
	(dex)	(kpc)
# 1	1.0	5	halo	73385	72510	4621	45101	52142	16093	Easy case	M13, M92
# 2	1.0	10	halo	30200	29325	3521	21550	23754	4275		M92
# 3	1.0	15	halo	14027	13152	2203	10312	11203	1495		NGC 5053
# 4	1.0	5	disk	54923	26816	1028	14115	17289	7379		M71
# 5	1.0	10	disk	33435	5328	326	3302	3812	1164	Intermediate case	M56, NGC 2298
# 6	1.0	15	disk	29737	1630	123	1048	1208	311		M79
# 7	1.0	5	bulge	1537592	71996	9833	69887	71600	218		M22, NGC 6553
# 8	1.0	10	bulge	1494601	29005	5620	28497	28919	36		M9, NGC 6638
# 9	1.0	15	bulge	1478538	12942	2998	12762	12911	15		Pal 11
# 10	2.5	5	halo	73385	72510	11902	47043	53029	15623		M5
# 11	2.5	10	halo	30200	29325	6914	21977	23944	4117		M3
# 12	2.5	15	halo	14027	13152	3663	10407	11176	1525		NGC 5466
# 13	2.5	5	disk	54923	26816	3236	15372	18085	6946		M92, Pal 10
# 14	2.5	10	disk	33435	5328	906	3491	3968	1055		M79, NGC 1851
# 15	2.5	15	disk	29737	1630	292	1097	1250	300		M15
# 16	2.5	5	bulge	1537592	71996	16564	70125	71648	190		NGC 6540, NGC 6558
# 17	2.5	10	bulge	1494601	29005	8726	28556	28924	40		NGC 6325, NGC 6342
# 18	2.5	15	bulge	1478538	12942	4378	12770	12914	13	Difficult case	M54, NGC 6517

Table 3. Table 3: Column-by-column description of the final simulated stars, that will only be available in the electronic edition of the journal, and at CDS.

Content	Column	Units	Description
Cluster	(1)		Cluster number
Star	(2)		Star ID
RA′	(3)	(deg)	Position along the RA direction
Dec′	(4)	(deg)	Position along the Dec direction
$\delta$coord	(5)	(deg)	Error on RA′ and Dec′
${\mu }_{{\mathrm{RA}}^{\prime }}$	(6)	(mas yr-1)	RA′ proper motion
${\mu }_{{\mathrm{Dec}}^{\prime }}$	(7)	(mas yr-1)	Dec′ proper motion
$\delta \mu$	(8)	(mas yr-1)	Error on proper motion
$\varpi$	(9)	(mas)	Parallax
$\delta \varpi$	(10)	(mas)	Parallax error
G	(11)	(mag)	G-band integrated magnitude
$\delta$G	(12)	(mag)	G magnitude error
GBP	(13)	(mag)	GBP integrated magnitude
$\delta$GBP	(14)	(mag)	GBP magnitude error
GRP	(15)	(mag)	GRP integrated magnitude
$\delta$GRP	(16)	(mag)	GRP magnitude error
Membership	(17)		True membership

Table 4. Table 4: Systemic parallax for the simulated clusters, based on members selected with the strict and loose criteria (see text for more details). The columns contain: (1) the cluster number; (2) concentration parameter; (3) projected cluster distance and (4) parallax; (5) background type; (6) systemic parallax and error for members selected with the strict criterium and (7) with the loose criterium.

Cluster	c	D0	${\varpi }_0$	field	${\varpi }_{\mathrm{strict}}$	${\varpi }_{\mathrm{loose}}$
		(kpc)	($\mu$as)		($\mu$as)	($\mu$as)
# 1	1.0	5	200.0	halo	200.2$\pm$2.6	200.2$\pm$0.6
# 2	1.0	10	100.0	halo	101.6$\pm$2.1	99.3$\pm$0.8
# 3	1.0	15	66.7	halo	69.2$\pm$2.6	69.1$\pm$1.0
# 4	1.0	5	200.0	disk	203.9$\pm$6.1	197.4$\pm$1.3
# 5	1.0	10	100.0	disk	95.6$\pm$4.4	98.5$\pm$1.5
# 6	1.0	15	66.7	disk	74.0$\pm$5.6	65.8$\pm$1.9
# 7	1.0	5	200.0	bulge	206.8$\pm$2.3	200.8$\pm$0.6
# 8	1.0	10	100.0	bulge	100.1$\pm$1.9	99.1$\pm$0.6
# 9	1.0	15	66.7	bulge	63.9$\pm$2.3	67.9$\pm$0.7
# 10	2.5	5	200.0	halo	197.5$\pm$0.7	198.4$\pm$0.4
# 11	2.5	10	100.0	halo	101.4$\pm$1.3	101.2$\pm$0.6
# 12	2.5	15	66.7	halo	62.2$\pm$1.5	66.4$\pm$0.9
# 13	2.5	5	200.0	disk	200.0$\pm$1.6	200.2$\pm$0.8
# 14	2.5	10	100.0	disk	100.0$\pm$3.1	102.8$\pm$1.3
# 15	2.5	15	66.7	disk	74.3$\pm$3.2	70.5$\pm$1.8
# 16	2.5	5	200.0	bulge	199.3$\pm$0.7	198.6$\pm$0.4
# 17	2.5	10	100.0	bulge	101.6$\pm$1.3	99.5$\pm$0.5
# 18	2.5	15	66.7	bulge	65.8$\pm$1.4	67.0$\pm$0.7

Table 5. Table 5: List of acronyms used in this paper.

Acronym	Description
AC	ACross scan
AF	Astrometric field
AL	ALong scan
BP	Blue spectro-Photometer
CCD	Charge Coupled Device
CDS	Centre de Données astronomiques de Strasbourg
CMD	Color Magnitude Diagram
CNES	Centre National d’Études Spatiales
DPAC	Data Processing and Analysis Consortium
ESA	European Space Agency
FWHM	Full Width at Half Maximum
GIBIS	Gaia Instrument and Basic Angle Simulator
GC	Globular Cluster
HB	Horizontal Branch
HST	Hubble Space Telescope
IMF	Initial Mass Function
LSF	Line Spread Function
MLE	Maximum Likelihood Estimator
MW	Milky Way
NSS	Non Single Stars
PSF	Point Spread Function
RAVE	RAdial Velocity Experiment
RP	Red spectro-Photometer
RV	Radial Velocity
RVS	Radial Velocity Spectrometer
SEA	source Environment Analysis
SM	Sky Mapper
TDI	Time Delayed Integration

Full text

††pagerange: Globular clusters with Gaia–A††pubyear: 2013

1 Introduction

The ESA111A list of the acronyms used in this paper (Table 5) can be found in Appendix A. (European Space Agency) space mission Gaia222http://www.cosmos.esa.int/web/gaia (Perryman et al., 2001; Mignard, 2005; Gaia Collaboration, 2016a; Gaia Collaboration et al., 2016b) is the successor of Hipparcos (Perryman et al., 1997), with the goal of providing astrometry for billions of point-like sources across the whole sky, with an error of 24 $\mu$as-level for stars of G$\simeq$15 mag. Gaia will also provide broadband magnitudes and colours for all sources, down to the Gaia white-light magnitude of G=20.7 mag (V$\simeq$21 mag). Low-dispersion spectra will also be obtained in two broad bands with the red and blue spectrophotometers (BP and RP). Finally, Gaia will produce spectra in the calcium triplet region with the RVS (the Radial Velocity spectrometer) down to G$\simeq$17 mag, from which radial velocities (RVs). Object classification and parametrization will be possible for all sources. Gaia was launched in December 2013 (de Bruijne, Rygl, & Antoja, 2014), and the first data release was in September 2016 (Gaia Collaboration et al., 2016b), containing positions and white-light magnitudes for the best behaved stars, and additional information like parallaxes and proper motions for $\simeq$2 million stars observed previously with Tycho-2 (Høg et al., 2000; Michalik, Lindegren, & Hobbs, 2015; Lindegren et al., 2016).

Gaia will observe not only stars, but also tens of thousands of quasars, unresolved galaxies, Solar system objects, many transient and variable objects like supernovae, and finally the interstellar medium (Altavilla et al., 2012; Ducourant et al., 2014; Eyer et al., 2014; de Bruijne et al., 2015; Proft & Wambsganss, 2015; Zwitter & Kos, 2015; Bachchan, Hobbs, & Lindegren, 2016; Tanga et al., 2016). Gaia will also pose a challenge because of its data amount and complexity, pushing the astrophysical community farther into the path of big data and data mining (Gaia Collaboration, 2016a).

Gaia is limited in dense stellar fields, owing to the on-board and downstream telemetry bandwidth. For spectroscopy, an additional limitation is provided by the large physical size of the dispersed images and spectra on the focal plane. This has particular relevance for studies of the Galactic plane, the bulge, and globular clusters (hereafter, GCs). In the first few Gaia data releases, disturbed sources like binaries, multiple stars, and stars in crowded fields will likely not be part of the released material (Gaia Collaboration et al., 2016b). In any case, the inclusion of a sufficient sample of stars at the main sequence turn-off point or fainter – with good quality measurements – is very important for GC research. Therefore, only the latest few Gaia releases (2020–2023) are expected to provide a significant breakthrough in GC research. To prepare the work, we explore in this paper the expected behaviour of Gaia data in several simulated Galactic GCs, adopting the official post-launch Gaia science performances and some simplified recipes to describe additional deblending error components, based on the Gaia deblending pipelines. A very preliminary – and now outdated – version of this work was presented by Pancino, Bellazzini, & Marinoni (2013).

The paper is organized as follows: in Section 2 we describe the current status of crowding treatment in Gaia; in Section 3 we present our crowding errors modeling; in Section 4 we describe our simulated clusters and the computation of Gaia observed quantities and final errors; in Section 5 we explore the simulations and show the potential of Gaia data for GC studies; in Section 6 we summarize the main results and draw our conclusions.

2 Crowding in Gaia data

As mentioned in the previous section, Gaia is a complex space mission, with two different telescopes projecting their light on a large common focal plane, captured by 106 different CCDs (Charged-Coupled Devices), and passing through different instruments. Gaia scans the whole sky by precessing its spin axis, and describing great circles on the sky that slowly drift with its precession. Each region is scanned from a minimum of $\simeq$40 times, to a maximum of $\simeq$250 times, with an average number of $\simeq$70 passages for the AF, BP and RP, and $\simeq$40 passages for RVS. All the CCDs in the focal plane are read in TDI (Time-Delayed Integration) mode to closely follow Gaia’s movement across the sky. On the focal plane, stars “move” along the scanning direction, encountering different instruments:

• •

the first two columns of the CCD array are called Sky Mappers (SM), and they are used for the on-board detection of point-like sources; each of the SM columns sees only light from one of the two telescopes;

• •

the AF (Astrometric Field), provides astrometry and photometry of point-like sources in the G-band, a white-light passband defined by the telescope and instrument transmission and by the CCD quantum efficiency (Figure 1);

• •

the BP and RP provide low resolution spectra (R=$\lambda/\delta\lambda$=20-100) in the ranges shown in Figure 1, and the integrated GBP and GRP magnitudes; the spectra are necessary for the chromaticity displacement correction in astrometric measurements;

• •

the RVS, provides R$\simeq$11 700 spectra in the calcium triplet region, for stars down to G$\simeq$17 mag, depending on the object.

To save telemetry bandwidth, given the enormous amount of data produced daily by Gaia, observations in each instruments are only transmitted for pixels contained in rectangular windows, that follow the detected point-like objects along the focal plane. For the faint stars, data in the allocated windows are binned in the AC direction by the on-board processing software. The adopted window sizes and relevant quantities for our treatment of crowding are listed in Table 1. More information can be found in the Gaia mission paper (Gaia Collaboration, 2016a).

2.1 Gaia deblending and decontamination pipelines

Crowding treatment ideally requires a preliminary evaluation of the crowding conditions of each source and transit, based on knowledge of the scene, i.e., the distribution and characteristics of all the neighbouring sources, as collected before the current observation. Different pipelines are employed for different instruments and to treat different cases. Here below we describe the current status of the ones that are relevant for the present study.

2.1.1 AF deblending

Stars closer than the Gaia PSF width (which is assumed here333The value we adopted is a conservative estimate. The Gaia effective PSF varies across the field of view and has a median value of 0.103” (Fabricius et al., 2016). to be 0.177”, see also Table 1) can be recognized as blends already in the astrometric processing of AF data. These blends can be detected, for example, from the high errors in the centroid determination and its wobbling from one transit to another, or by photometric variability, radial velocity variability, or in general because the fits of the PSF or LSF to the data show large residuals or require more than one component.

Assessing whether a star is isolated or has detected or suspected companions is a crucial task. Multiple or blended objects are redirected to the NSS (Non-Single Stars) pipeline where an attempt to model them as binary systems is carried out (Gaia Collaboration, 2016a; Pourbaix, 2011). If none of the available binary models or configurations produces a good fit to the data, then a stochastic model is employed to derive preliminary parameters of the secondary (or tertiary and so on) source. Therefore we can assume that – considering also the small Gaia PSF – the vast majority of NSS will be known.

Stars that are further apart than the tiny Gaia PSF are easily deblended by the PSF fitting algorithms, with results much more similar to HST (Hubble Space Telescope) than to typical ground-based telescopes. This is the main reason why – as we will see in the following – astrometric measurement uncertainties (and G magnitudes) are in general less affected by crowding, unlike BP/RP and RVS measurements.

2.1.2 BP and RP deblending and decontamination pipelines

BP and RP transits of sources that are not isolated will be called here either blended or contaminated. The idea is that when the sources are so close that they occupy the same window or interfering windows in the vast majority of the transits (blends, with D$<$2.12”), they will require a different treatment than objects that will often be assigned well separated windows, or transits that are just altered by the flux of a bright source that is well outside of the window (contaminants, with D$<$3.54”). This is illustrated in Figure 2, where different cases are shown together with the background evaluation regions, and in Figure 3, showing how the differing orientation and AL projected distance between sources affects window assignment.

For blended sources, there are different pipelines that can be used in different phases of the mission. Blind pipelines (without knowledge of the scene) can be applied in the initial phases, when the history of each source in different instruments has not built up to a sufficient level. The two (or more) blended sources can be roughly modeled without a priori knowledge of their exact positions, astrophysical parameters, and fluxes, just by modeling them with two overlapping spectral energy distributions. This approach was successfully applied to Gaia commissioning data444http://www.cosmos.esa.int/web/gaia/iow_20150226 of bright stars, recovering the vast majority of the Ticho-2 binary and double stars. Once a few transits are accumulated, they can be better disentangled if they are modeled simultaneously (per source rather than per transit), even if there is still not enough information on the scene, improving the quality of the reconstruction. Finally, once the scene is well characterized and the history of the source is well developed, other parameters of the modeling like the spectral type, the projected distance of the sources along scan, and the relative fluxes, can be used to further improve the involved sources reconstruction.

For contaminated sources, it is necessary to know well the flux of the contaminating sources around, thus knowledge of the scene is necessary. Each known source is modeled to reconstruct the flux even at large distances from the window (especially for bright stars). The amount of reconstructed contaminating flux from neighboring sources is computed in each pixel of the contaminated source window, and subtracted. For all these reasons, decontamination will have to be performed contextually with the scene reconstruction and crowding evaluation.

2.1.3 RVS deblending and decontamination pipelines

The deblending phylosophy adopted by RVS is slightly different from the one adopted in AF, or BP and RP. The deblending pipelines are being adapted and reweitten to mitigate the stray light issues found after launch555http://www.cosmos.esa.int/web/gaia/news_20141217 (Mora et al., 2016) that impact mostly on RVS spectra, with an expected loss of $\simeq$1.4 mag in sensitivity (Seabroke et al., 2016). We therefore based our modeling of deblending errors on a previous algorithm that was based on general geometrical considerations (Allende Prieto, 2008).

The treatment of contamination is instead part of the background treatment, that is a vital part of RVS processing, because of the length of the spectra (see Table 1). The background is divided in diffused and point-like, and treated separately. In both cases, a modeling takes place based on knowledge of the scene and all available data on stray light and nearby objects. The model produces an estimate of the total background in the RVS windows that is subtracted from the source signal. Clearly, the model becomes more and more accurate as Gaia data are progressively accumulated and therefore the best results will be obtained towards the end of the mission (K. Janssen, H. E. Huckle, and G. Seabroke, 2015, private communication).

2.1.4 Image reconstruction and future possibilities

To facilitate the study of crowded areas, two paths are being followed. On the one hand, some crowded regions like the center of $\omega$ Centauri or NGC 1818 in the Magellanic Cloud were imaged and transmitted to the ground in 2D mode in the SM666http://www.cosmos.esa.int/web/gaia/iow_20140206, during commissioning, and further regions might be observed in 2D during the mission lifetime. The goal of these 2D images is to fully reconstruct the scene around each Gaia source to help improving and testing the deblending algorithms in crowded areas.

On the other hand, pipelines for the 2D image reconstruction from individual Gaia transits are being developed. One such pipeline, called Source Environment Analysis (SEA) pipeline, is based on the FastStack image reconstruction (Harrison, 2011; Gaia Collaboration, 2016a). The initial tests are promising and the reconstructed images could be useful, among other things, to test and improve the deblending and decontamination pipelines as well.

Therefore, the simulations presented in this paper, being based on the current status of the deblending and decontamination pipelines, have to be seen as generally pessimistic.

2.2 A note about completeness in Gaia data

A particular limitation of the Gaia design is related to the number of simultaneous object and background (virtual object) windows that can be allocated by the on-board detection algorithm in each CCD and in any given moment. This number varies from $\simeq$35 000 to 1 050 000 objects per square degree, depending on the instrument (see Gaia Collaboration, 2016a, for more details). Areas of the sky that can suffer from this limitation are clearly the Galactic bulge and plane, and all other fields of view that happen to overlap them on the Gaia focal plane777We recall that to obtain absolute astrometric measurements, Gaia projects two different lines of sight on a common focal plane. To disentangle sources coming from the two projected lines of sight, each of the SM (Sky Mapper) CCD columns sees only one of the lines of sight. Therefore, there will be some fields that – even with low stellar background – will happen to overap crowded areas in some fraction of their transits.. More relevant to the present study, the limitation applies to the central regions of GCs, where the local star density can be very high.

At the single transit level, completeness is also influenced by the on-board detection algorithm. Every source that enters the SM is assigned a window, prioritizing brighter objects down to the limiting magnitude. The windows follow the stars along the focal plane as Gaia scans the sky, and when the stars exit the field, the window-slots are “freed” and can be assigned to new sources again. For this reason, the central dense areas of the clusters will – statistically speaking – contain more (bright) stars, and thus obtain more windows with respect to the periphery of the cluster, in the AC direction. Different scans, oriented in the sky with different angles, will loose different stars and thus at the end-of-mission, each star that is not entirely lost will have lost part of its transits. This is illustrated in the simulated cluster in Figure 4, and is also visible in the $\omega$ Centauri actual Gaia data shown in a press release888http://www.cosmos.esa.int/web/gaia/iow_20141113.

We do not attempt to simulate these completeness effects in the present paper, as they would require a full end-of-mission simulation of different lines of sight in the sky, including the detailed behaviour of the on-board detection algorithms.

3 Modeling of crowding errors

As mentioned above, our goal is to illustrate what Gaia can do for GC studies, rather than attempting a rigorous simulation of deblending errors. Therefore, we will model available simulations of crowded Gaia data, to derive simple formulaes with as few free parameters as possible.

The crowding error models derivation for different Gaia instruments and different types of blends are described in the following sections. The models describe the expected percentage errors on flux caused by crowding as a function of relevant parameters like the contaminating flux, contaminating colour, and distance of the contaminating object(s).

Later, in Section 4 we will transform our flux errors into errors on other parameters like positions, parallaxes, proper motions, and radial velocities. We will then use these errors to worsen the nominal Gaia post-launch science performances, depending on the crowding level suffered from each of our simulated GC stars.

3.1 ‘Classic’ blends

We term in this paper classic blends those stars that are closer than the AF Gaia PSF (0.177”, see Table 1), and that will remain so along the five years of Gaia observations. Stars that will move apart thanks to their parallax or proper motion differences, or that have radial velocity differences that allow to deblend them, will not be considered as classic blends, but treated as normal Gaia blends (see below).

The precession of Gaia has an important implication for crowding treatment: each time Gaia scans a particular region of the sky, it is oriented differently, and thus the projected distance of two stars in the SM columns, on which the on-board object detection and window assignment are based, are different (see Figure 3). Therefore, as described in Section 2.1.1, even the closest classic blends have a chance to be deblended, although it is difficult to simulate realistically the errors caused by deblending when so many observables enter iteratively the deblending procedure along the whole mission.

In this paper, we will assume that all blends of stars closer than the Gaia PSF will be recognized as such, thanks to the mission long lifetime, its tiny astrometric and photometric errors, and sophisticated data analysis methods. Because of the limited number of classic blends999From 5 to 8% of the total number of stars in our simulations, including field stars, are classic blends, depending on the particular cluster. The classic blends are mostly in the inner parts of GCs, within 1’ approximately. For more details see Section 4.4., this assumption is not going to have a significant impact on the following analysis. If the relatively small number of classic blends comes as a surprise, it has to be noted that Gaia observations only reach V$\simeq$21 mag in GCs, and thus the actual crowding levels are much lower than those of the typically deeper photometry from the ground or with HST.

We will also assume that the actual deblending errors follow the relation adopted for the BP and RP blends (see below), extrapolating the present simulations towards smaller source distances. While highly uncertain, this is our only available estimate of the Gaia deblending capabilities at the present stage. For RVS there currently are no plans to attempt deblending of sources closer than 0.17”, and therefore we will not attempt to simulate the effect of crowding in these RVS sources.

3.2 ‘Gaia’ blends

As discussed in Section 2.1.2, Gaia blends are all those cases in which two stars are closer than half the AC window size of the relevant instrument (Table 1, these all fall into case (a) of Figure 3). Because the AF image deblending will be simpler (the AL profile is sharper) than that of BP, RP, and RVS spectra, we will conservatively base our estimate of crowding errors for deblending on a set of BP and RVS simulations.

For the BP and RP blending simulations, we used a per-transit, partially informed deblending pipeline101010For a detailed description of the various BP/RP deblending pipelines, see Section 2.1.2. What we mean here by ‘partially informed’ is that we used information on the blended stars positions in AF, but we did not use any other information, such as astrophysical parameters (Teff, log$g$, AV, [Fe/H]) and therefore we assumed we did not know the spectral energy distribution of the involved sources. This is still a pessimistic assumption, because towards the end of the mission this kind of information will become available and iteratively improved with every data processing cycle. on the GIBIS (Gaia Instrument and Basic Image Simulator, Babusiaux, 2005) simulated BP spectra of a typical GC red giant, with Teff=4000 K and G=15 mag. The star was blended with other similar stars, having either Teff=4000 or 6000 K, G=15.75 or 17.00 mag, and at different distances equal to 0.25, 0.5, and 1.0*′′* (see Figure 5).

We then modeled the deblending (relative) errors on the recovered flux as an exponential $\alpha~{}e^{~{}\beta\,\rm{D}}$, where D is the distance between the two blended stars. The coefficients $\alpha$ and $\beta$ vary with the temperature difference and the relative contaminating flux, respectively, as illustrated in Figure 5. For RP, the deblending errors were arbitrarily multiplied by 1.5, owing to the generally wider AL shape of the spectra, that produces worse deblending results than in BP. These simplified recipes are intentionally pessimistic, to accommodate for unexpected sources of error. The approximate range of validity of the model (highlighted in Figure 5) goes from the Gaia PSF size to half the AL size of the BP and RP windows. As discussed in the previous section, we applied an extrapolation of this relation to D$<$0.17” to classic blends, for lack of a more detailed study at this stage.

For RVS, the only available deblending simulations were computed before launch (Allende Prieto, 2008, see also Figure 6), when the windowing scheme and backgound treatment were different (see Section 2.1.3). Thus, the error modeling presented here will be much more uncertain for RVS than for BP and RP, or for AF. The temperature or colour difference between two sources has little impact on the deblending ability of the RVS pipelines, because the spectral shape is approximately flat along the RVS windows. What mostly counts is the relative contaminating flux. As a result, the best-fitting exponential laws had a constant $\beta$, and $\alpha$ varying with the relative contaminating flux. As mentioned above, we did not extend the model below the PSF size for RVS (shaded region in Figure 6).

3.3 Contaminants

For contaminated stars (cases (b) and (c) in Figure 3), the reconstruction of star fluxes at distances larger than the window size is subject to a variety of uncertainty sources, and the relevant pipelines will be effective only when a sufficient history is accumulated to build a scene. Not only the stars positions are needed, but also their spectral energy distributions. Additionally, a complete characterization of the PSF profiles AC and AL, at different wavelengths and positions on the focal plane will be fundamental. Therefore no detailed simulations are available at the moment (Section 2.1.2).

However, we do know that a step-like behaviour is expected in the errors at 1.76*′′*, where the processing switches from decontamination to deblending, in the sense that decontamination pipelines perform slightly worse than the deblending ones. There will be, on purpose, a ‘grey area’ in projected distance between sources, where both pipelines will be applied, for cross-validation purposes. Some tests were performed to develop the current decontamination algorithms (Piersimoni et al., 2011, , and De Luise, private communication). According to those tests, we decided to roughly approximate the decontamination errors with a factor of 2 worsening with respect to deblending errors. This is a pessimistic assumption.

Our modeling of decontamination residual errors is applied to contaminant stars with distances ranging from half the AC window size to the full AL window size or to the contaminating star’s ‘size’, whichever is larger. We modeled the contaminating stars sizes as a linear function of G magnitude (L. Pulone and P. M. Marrese, 2008, private communication, see also Figure 2). Stars fainter than G$\simeq$15 mag are generally smaller than the BP and RP AL window size111111With our linear relation, a G=2 mag star would be able to significantly contaminate stars up to 34.4*′′*. These bright stars are rare: in our eighteen simulated GCs there is only one field star brighter than that, appearing in the six disk GCs..

For RVS, the discrete background pipelines are being presently integrated and tested, so no simulations are available at the moment and we just extended our simplified treatment of the RVS blends (previous section) to RVS contaminants, as done for BP and RP, using the appropriate window sizes.

4 Cluster simulations

We simulated 18 different globular clusters, as summarized in Table 2, with different concentration, background contamination, and distance. The final simulated clusters, after the Gaia science performances and the crowding error simulations are included, are presented in Table 3.

4.1 3D simulated clusters

The simulated clusters were computed with the McLuster code121212http://www.astro.uni-bonn.de/$\sim$akuepper/mcluster/mcluster.html (Küpper et al., 2011), that is designed to produce initial conditions for N-body simulations. We used the code version (mcluster_sse) which implements the stellar evolution recipes by Hurley, Pols, & Tout (2000).

We produced two clusters containing 800 000 stars, with positions and velocities drawn from equilibrium King (1966) models. The two clusters differed only in their concentration parameter, c=log(rt/rc), one having c=1.0 and the other c=2.5. Among the key input parameters for the simulation, the half-mass radius was chosen to produce a (projected) half-light final radius similar to what typically observed for Galactic globular clusters: 4 pc for the c=1.0 cluster and 3 pc for c=2.5 one (see also Harris, 1996, and following updates). Among the key input stellar population parameters, we adopted an age of 12 Gyr, a metallicity of Z=0.0003, corresponding to [Fe/H]=–1.79 dex, and a Kroupa (2001) IMF (Initial Mass Function). The simulations were performed without including binaries, for simplicity, and the resulting clusters are spherical and non-rotating.

The main implications of our choices of input parameters are: (i) a blue HB (Horizontal Branch) morphology, which may be useful to test the performance of Gaia on relatively hot stars, and (ii) a stellar M/LV ratio larger ($\geq$3 instead of $\leq$2) than what typically observed in Galactic globular clusters having a present day mass function compatible with a low-exponent power law (Paust et al., 2010). The high M/LV ratio is also due to a relatively large fraction of dark remnants: $\simeq$25% of the cluster mass is contributed by objects with M$>$M*⊙*131313Dark remnants are white dwarf stars, neutron stars, and black holes. Recently, comparable fractions of dark remnants were obtained with state-of-the-art cluster modeling by Sollima et al. (2015) and Sollima et al. (2016).. Independently of the recipes giving raise to such a large fraction of dark remnants and their actual nature, this is not a concern for our purpose: the only effect is that the potential well may be slightly deeper than for most real clusters and, consequently, the velocity dispersion is slightly larger, at fixed total luminosity and scale radius. What is relevant for us is that the central velocity dispersion is still in the right range and that the model is self-consistent.

The resulting simulated clusters have absolute integrated magnitudes of MV=–7.6 mag, i.e., just above the peak of the clusters luminosity function (MV=–7.4 mag, according to Brodie & Strader, 2006). The clusters projected surface density distributions are well fitted by a King (1966) profile, when obtaining rc (the core radius) from the fit. Finally, the derived central velocity dispersions agree well with the predictions by King (1966), where the total mass is obtained by summing the masses of all individual stars.

4.2 Simulated field contamination

We simulated the field Galactic population in three directions using the Besanco̧n models141414http://model.obs-besancon.fr/js (Robin et al., 2003, and references therein), including kinematics and without observational errors. The models produced catalogues of magnitudes (in the Johnson-Cousins system), 3D positions, and 3D motions. We adopted the “standard” extinction law offered by the Besanco̧n simulator, a mean and diffused absorption of 0.7 mag/kpc, neglecting small scale variations, and decreasing away from the Galactic plane with a smooth Einasto profile (for more details, see Robin et al., 2003). We selected all available spectral types in a magnitude range of 0$<$V$<$25 mag. The simulations were computed in a 0.7$\times$0.7 deg square centred on each of the following three directions (see also Table 2):

• •

a rather empty “halo” field at l=150 and b=80 deg, containing $\simeq$2300 stars in total; this is meant to represent the best cases of low background contamination in Gaia observations;

• •

an extremely dense “bulge” field at l=5 and b=5 deg, containing almost 6 millions of stars, which should cover even the most crowded Gaia observations, when two relatively crowded lines of sight overlap on the focal plane (see also Section 2);

• •

a crowded “disk” field in the anticenter direction, at l=180 and b=0, containing roughly 140 000 stars, with a relatively high extinction of up to $\simeq$2 mags in V band (even if these values are only reached in $\simeq$25% of the known GCs in Harris, 1996); while not as extreme as the bulge line of sight, this direction provides still severe crowding levels – on the Galactic plane – coupled with significant reddening.

4.3 Simulated Gaia measurements

Each of the two clusters (see Section 4.1) was projected at three different distances of 5, 10, and 15 kpc and combined with each of the three backgrounds, to produce the 18 clusters in Table 2. A typical systemic radial velocity of 100 km s*-1* was assigned to each cluster (broadly compatible with the values listed in the Harris, 1996, catalogue, in its most recent version), while a proper motion of –5 mas yr*-1* in both the RA and Dec was assigned to all clusters (broadly compatible with the values measured by, e.g., Dinescu et al., 1999). Distances were also converted into parallaxes.

Integrated Gaia magnitudes G, GBP, and GRP (see also Section 2 and Figure 1) were obtained for each star using the formulae provided by Jordi et al. (2010, using their coefficients from Table 3), starting from the B–V colour. For extinction, we adopted the pessimistic hypothesis that the cluster reddening was equal to the corresponding background field’s highest value (i.e., as if the cluster was entirely behind the field population). While this assumption is not completely realistic, it gave us the possibility of exploring higher reddening conditions, at least for the disk projections. This yielded an AV of 0.062 mag for the halo projections, 0.080 mag for the bulge projections, and of 2.149 mag for the disk projections.

4.4 Crowding evaluation

For each simulated star in each GC, we counted all neighbors (with flux above 0.1% of the star) within a specified distance, depending on the considered instrument and on the types of blends (Section 3). We adopted an exhaustive algorithm for neighbors search151515In other words, we looped over the list of (relevant) stars and computed distances with all other (relevant) stars, one object at a time. This was necessary because smarter neighbour searches pre-compute a distance matrix to increase computation speed, and therefore tend to saturate computer memory for datasets containing more than 105 objects (Hendra Gunadi, 2011). Our bulge simulated GCs contain a few million stars, and several tens of millions of relevant pairs..

The relative number of each type of neighbours (classic blends, Gaia blends, contaminants) for the 18 simulated clusters is shown in Figure 8 as a function of distance from the GC center. As can be seen, the parameter that dominates the fraction of classic blends is the GC concentration: core collapsed clusters have more than twice the number of classically blended stars in their central parts compared to normal GCs. The vast majority of classic blends are in the GC central regions, and are blends of GC members with other GC members. Distance and reddening have a curious effect: because GCs become fainter with increasing distance and reddening, their luminosity function crosses the detection limit of Gaia where it is less populous. As a consequence, not only the number of stars detected by Gaia decreases, but also the probability of blending, and so the blends and contaminant fractions. On the other hand, the effect of field contaminants is to increase the fraction of Gaia blends and contaminants at all distances from the center. Extreme cases are the bulge background GCs, where the vast majority of stars are blended and/or contaminated to some degree at all radii, mostly by field stars.

We listed in Table 2 some key quantities resulting from the crowding evaluation. As can be seen, the number of stars that are clean (i.e., contaminated by less than 1 mmag) can be substantial when the background is not extreme. The vast majority of Gaia blends and contaminants will be known, as a large fraction of the classic blends (see Section 2.1.1). Therefore, it will always be possible to select a reliable sample of clean stars from Gaia data.

Additionally, we report here that already in the first Gaia release, which does not contain stars in truncated windows or stars with low-quality measurements (Gaia Collaboration et al., 2016b), more than 200 000 stars were actually detected in the $\omega$ Cen field. This compares well with our #1 cluster, which is reasonable considering the higher mass of $\omega$ Cen, and gives support to the figures discussed above and reported in Table 2.

4.5 Simulated Gaia errors

To compute the Gaia errors, we combined the post-launch Gaia science performances (Gaia Collaboration, 2016a) with our crowding error estimates. For the magnitudes we combined the two errors in quadrature, because they are fully independent. For the astrometric and spectroscopic measurements, the crowding errors are not fully independent from the Gaia science performances, because they both depend on the star magnitude. Therefore we conservatively summed the errors in modulus.

4.5.1 Crowding errors

We used the modeling described in Section 3, which provided a relative error on the flux of each star, caused by the various type of blends and contaminants affecting it. These modeled errors represent well the crowding errors for G, GBP, and GRP, i.e., on the photometry.

To evaluate the crowding errors on astrometry, we considered two components: the error on centroiding and a chromatic shift. For the centroiding errors, only classic blends were considered, because only stars closer than the PSF are expected to have a significant impact on the final centroid measurement of a star. We expect that the PSF of a star will be perturbed by the residual flux left by the close companions after the deblending procedure, and these residuals will depend on the contaminating flux and distance of the blending stars, as modeled in Section 3. We therefore computed the percentual flux in the residuals as an average of the bended star and the blending ones, weighted on distance and flux of the blending stars. We then assumed that the percentual centroiding error caused by blending was equal to this residual contaminating flux, a pessimistic assumption. The resulting centroiding errors caused by crowding are typically of the order of $\sim$10 $\mu$as yr*-1* (with maximum values of $\sim$100), but they affect a relatively low number of stars in each GC (see Table 2).

For the chromaticity correction, we know that chromatic effects for Gaia are relevant, because of its high accuracy, and they are corrected using the BP/RP information. If an error is made on that colour determination because of blends, the error is transported into the astrometric measurements as well. It was estimated that the shift on the single Gaia measurement could amout to 500–800 $\mu$as, depending on the spectral type and on the position along the focal plane. By averaging out transits and by correcting the effect of spectral type with GBP-GRP, the residual end-of-mission errors would amount to 0.4–1.4 $\mu$as (Jordi et al., 2006)161616These estimates were computed using the Gaia filter system, now abondoned, but there are no other estimates available of the Gaia residual chromatic displacement in the literature at the moment. in most of the well-behaved stars. However, for objects with non-stellar or peculiar colours, such as a Quasar or a (multiple) stellar blend, the residual error could be still be roughly 30 $\mu$as, as computed from the typical residual centroid shift difference between a B and an M star, after chromaticity correction (Jordi et al., 2006). We thus approximated linearly171717The entity of the chromatic correction errors caused by crowding is small for the simulated GCs (a few $\mu$as or $\mu$as yr*-1*) compared to the Gaia science performances (see also Figure 10), and therefore a linear approximation was considered adequate. the additional chromatic error as 0.002 $\mu$as for each K of temperature difference between each blended stars pair (both classic and Gaia blends), multiplied by the relative contaminating flux. The typical residuals from chromatic errors caused by crowding are of a few $\mu$as, but can be substantially higher for companions that are very bright or have a very different colour (up to $\simeq$30–50 $\mu$as in our simulations).

For RV error computations, the first consideration is that everytime a star is contaminated by another star with a net RV difference above $\simeq$30 km s*-1* (roughly the Gaia resolution element FWHM), there is a chance of separating the two RVs, depending on the relative flux contamination. The percentage of flux contamination (obtained as in Section 3) was used to degrade the signal of the contaminated (or blended) star. We thus recomputed the magnitude of each blended or contaminated star, taking into account the residual errors after deblending or decontamination. We similarly recomputed the colours taking into account the residual colour errors. The recomputed colours and magnitudes were fed into the RV error equation (Gaia Collaboration, 2016a), to derive the error on RV implied by the magnitude and colour deblending errors. The second consideration is that an artificial RV shift of roughly 30 km s*-1* can also be obtained if two blended stars are offset, in the AL direction, by at least 4 AL pixels (or 0.235”), therefore we treated these stars as in the above case. We finally did not attempt to simulate any RV measurement for stars closer than the Gaia PSF (i.e., one AC pixel or 0.177”) as explained previously. Moreover, we did not compute RVs or RV errors for stars fainter than G=16 mag.

5 Results

We illustrate in the following sections the type of data quality we expect from Gaia at the end of the mission, based on our simulations. As mentioned already, given all the conservative assumptions and the use of preliminary deblending pipelines, the presented results have to be considered pessimistic, in the sense that the pipelines will be more sophisticated in a few years from now.

We will show in all figures three simulated GCs: an easy case with D=5 kpc, c=1.0, and a halo background (cluster #1, plotted in green in all figures); an intermediate case with 10 kpc, c=1.0, and a disk background, with a relatively high reddening for GCs (cluster #5, plotted in yellow); and a difficult case with D=15 kpc, c=2.5, and a bulge background, which is an extreme condition for Gaia (cluster #18, plotted in red).

5.1 Proper motions

Because proper motions are determined with AF, the impact of crowding is less severe than on BP/RP spectro-photometry, or on RVS spectra. Figure 9 shows the histogram of the differences between the final proper motion – including all error sources – and the initial error-free simulated one, for the known cluster members. The median systemic proper motion can be recovered with a bias of 5–10 $\mu$as yr*-1*, i.e., with a systematic error of roughly 0.1–0.2%. The intrinsic spread of the simulated GCs is of the order of 100 $\mu$as yr*-1*, depending on the GC. The observed spread is around 400–500 $\mu$as yr*-1*, if one includes all the simulated stars down to the magnitude limit. It is almost entirely explained with the nominal post-launch performances applied on top of the intrinsic spread, especially when including faint stars. In fact (see Section 4.5.1) the crowding errors on the affected stars are in the worst cases a few 100 $\mu$as yr*-1* for the centroiding determination, and $\simeq$30 $\mu$as yr*-1* for chromaticity errors caused by GBP/RP crowding errors.

Concerning individual stars, Figure 10 shows the behaviour of the final simulated errors as a function of G magnitude. It can be useful to compare these simulations with the first results from the HST PROMO project for M15 (Hubble Space Telescope PROper MOtion project, Bellini et al., 2014). Their typical error around the G=15 mag is 5–10 times higher than the error expected from Gaia, about 0.1 mas yr*-1*, but at G=21 mag they are about half the Gaia error, at 0.5 mas yr*-1*. Moreover, HST proper motions can reach several magnitudes below the Gaia limit. On the other hand, the advantage of Gaia’s proper motions is that they cover a larger area around each GC – actually, the whole sky – and that they are absolute proper motions.

We show in Figure 11 the typical vector diagrams of all simulated stars, including faint stars and background contaminants. The clusters are always easily separated from the field population, except in the case of the extreme bulge background. In the following sections, we will select the probable members with a loose criterium, i.e., stars within 1 mas yr*-1* from the systemic GC motion, and with a strict criterium, i.e., within 0.3 mas yr*-1* from the systemic GC motion.

5.1.1 Measurement of derived quantities

To assess the derived quantities that will be measurable from Gaia data, we performed a basic test on the easy case GC. We excluded all stars that were clearly unrelated to the GC with a very loose proper motion selection ($\pm$3 mas yr*-1*) and all the classic blends. We then converted proper motions in the RA and Dec directions into velocities, using the GC distance and propagating its error (see Section 5.2). We then estimated the RV spreads $\sigma_{\rm{RA}}$ and $\sigma_{\rm{Dec}}$ as a function of distance from the GC center with their errors. We used the maximum likelihood estimation method (MLE) with the likelihood formulation described by Pryor & Meylan (1993), Walker et al. (2006) and Martin et al. (2007), which takes into account the errors on measurements as well. The actual errors on the RV dispersions in each radial bin are of about 0.4–1.4 km s*-1*. The result is displayed in Figure 12, showing that Gaia will be able to determine the radial profile of the RV dispersion of nearby GCs with errors of about 1 km s*-1* in the nearest GCs.

More in general, we can say that:

Proper motions obtained by Gaia in GCs will allow the study of dynamical relaxation in the 5–10 closest GCs (see also Section 5.3 and Figure 14). This is because at least a few magnitudes below the GC turn-off point are required to adequately sample a range of stellar masses. Figure 14 clearly shows that this is possible only for clusters at $\simeq$5 kpc or less, because of the Gaia detection limit. Therefore, these studies will have to rely on deeper proper motion data sets for more distant GCs181818Deeper measurements could be obtained if the mission lifetime is extended beyond its nominal 5-year duration. The SEA pipelines also have the potential of recovering faint stars. Finally, the use of the 2D images obtained for some crowded fields will help by directly recovering some faint stars and by improving the deblending pipelines, thus recovering more faint stars also in other regions.. 2. 2.

Two past studies dealt with the determination of masses in GCs with Gaia data (An, Evans, & Deason, 2012; Sollima et al., 2015) yielding somewhat conflicting results. The main problem is to break the mass-anisotropy degeneracy, with the anisotropy signal being stronger outside the central regions where relaxation has the highest effect. Therefore, blends by cluster members are irrelevant there, as discussed in Section 4.4 and shown in Figure 8. And even in the case of heavy background contamination, proper motions will be only mildly affected (Figure 10). The assumption by Sollima et al. (2015) that one can only use stars contaminated by less than 10% of the flux by objects more distant than 3.54”, is far too pessimistic. The simulations by An, Evans, & Deason (2012), prove that 10% mass estimates can be provided for GCs if one can count on at least 100 tracers (we can use red giants) with proper motion errors $<$100 $\mu$as. As shown in Table 2 and Figure 10, the number of stars per GC with these errors will be more like a few 103–104, except maybe for the most extreme cases of bulge clusters. Moreover, our test with the easy GC above shows that RV spreads can be measured as a function of distance from the center with 1 km s*-1* errors at 5 kpc. Therefore, as concluded by An, Evans, & Deason (2012), it will be possible to determine GC masses with an error of 10% or less at least up to 15 kpc. This requires ground-based RVs to complement Gaia proper motions191919For the closest GCs, Gaia will provide some good RVs as well, see also Section 5.4, for more details.. 3. 3.

Gaia will be able to provide the necessary quantities for computing accurate GC orbits within the Galaxy, because, as we saw, it will provide high-quality systemic proper motions for each GC, with a bias of a few $\mu$as yr*-1* and errors of the order of 1%. Distances will be obtained with similar errors, as discussed below (Section 5.2). 4. 4.

Once the orbits are obtained they could in turn be used to look for extra tidal stars and tidal tails. Even if the G$<$20.7 mag limit reduces the density of targets that will be actually measured by Gaia around GCs, the proper motion signal of escaped GC stars should be very sharp, and in most cases significantly different – within the uncertainties – from that of the surrounding field population (see also Figure 11). 5. 5.

Gaia could be able to help in the open and hotly debated problem of multiple populations (Kraft, 1994; Gratton, Sneden, & Carretta, 2004), in particular by revealing kinematical differences among different GC sub-populations, if they are present. For example, Bellazzini et al. (2012) reported the possible detection of a different rotation pattern between the Na-rich and Na-poor stars in some of the GCs in their sample, with rotation amplitude differences not larger than $\simeq$5 km s*-1*. Depending on the distance and the inclination of the rotation axis, this would correspond, in terms of proper motions, to a difference in rotatation of the order of 1 mas yr*-1*, which would be detectable for those GCs having at least 100 stars with measurement errors of a few 10 $\mu$as.

5.2 Parallaxes

The major problem in deriving distances from parallaxes, especially when the error is comparable to the measurement, is that the errors on distances are not symmetric: by simply inverting the parallax one could obtain a very wrong distance estimate (Bailer-Jones, 2015). Statistically speaking, it is also possible to obtain negative parallaxes, as illustrated in Figure 13, which would result in meaningless distance estimates if not treated properly.

When one is interested in the systemic distance of a GC, however, negative parallaxes are useful to assess the uncertainty on the measurements and their distribution. Figure 13 shows the distribution of parallaxes for probable members, as defined in Section 5.1. As can be seen, not only the average parallax of the clusters is very well recovered, but also its uncertainty, provided that one makes use also of the negative parallaxes. The exception is the case of the difficult cluster, which has a background contamination that overwhelms the signal from the cluster members. As can be seen, the recovered parallax is strongly biased by the background contaminants. A more strict members selection apparently produces better results (but see below). However, the resulting distribution of strict members is still asymmetric, because of the blends between cluster and field stars.

This type of problem is not specific of Gaia data, of course, but it is extremely important to employ a reliable membership selection and robust statistical modeling of the parallax distribution, which can be skewed and is heteroscedastic. We employed an MLE analysis of the 18 simulated GCs using the strict and loose membership criteria described above. We used the likelihood estimator described by Pryor & Meylan (1993), Walker et al. (2006), and Martin et al. (2007), which takes into account the highly variable errors, and we computed the most probable parallax $\varpi$ and its error $\delta\varpi$. The result is displayed in Table 4. We first note that the depth of a GC, as measured with parallaxes, can correspond at most to a few $\mu$as for the nearest GCs that have large radii, even if one considers the tidal radius, and in the majority of cases is well below 1 $\mu$as. Thus the observed spread is caused almost entirely by measurement errors. The bias itself, i.e., the difference between the true input parallax and the recovered one, is always 1% or smaller, even for the difficult case GC. The formal error on the recovered $\varpi$ is of the same order. We also note that choosing a more restrictive membership selection can often increase the formal errors without resulting in a better $\varpi$ determination. On the contrary, the bias is slightly increased when applying a more restrictive membership selection (see also Bailer-Jones, 2015).

The scientific implications of $\simeq$1% distances for most of the GCs in the Galaxy are far reaching. They directly help in the determination and modeling of GC orbits, that can then be used for dynamical studies of the MW, of the GC themselves, and of the interactions between the two. For example they would help simulations that use the GC orbits and tidal tails and streams to constrain the Galactic potential (Peñarrubia, Koposov, & Walker, 2012; Price-Whelan et al., 2014), or they can help discerning the origin of the GC themselves through dinamical modeling. But the area in which significant breakthrough is expected lies in the determinations of stellar ages (Gratton et al., 1997) and masses (Feuillet et al., 2016). Distance has in fact a similar effect as age when using high-quality CMDs (from HST or ground-based observations) to estimate the absolute ages of GCs. By reducing the distance determination errors by more than a factor of 10, we can expect a significant improvement on the age determinations, obtaining absolute ages with errors below 10%. On the other hand, $\simeq$1% distances can help in constraining the stellar masses and more importantly, the surface gravities. When trying to determine relative ages in GCs with multiple stellar populations, one needs to disentangle the effects of chemical composition – mainly Helium and C+N+O abundance – from age effects. A very accurate surface gravity determination would remove one of the major sources of uncertainty in the determination of stellar chemistry from spectroscopy.

5.3 Photometry

The Gaia colour magnitude diagrams (CMD) of the three example clusters are shown in figure 14. The top panels show all the simulated stars, including the background, while the bottom panels show only the probable members, selected with the loose criterium described in the previous section. As can be seen, background contamination is the first obvious cause of crowding errors for Gaia photometry. A large reddening (like in the case of the disk cluster) or a distance larger than 10 kpc also impact the quality of the CMD, because the photometric errors, especially those on the GBP–GRP colour, increase quite rapidly with magnitude.

It will therefore not be possibile to reach the nominal photometric errors promised by Gaia in those clusters that lie on a bulge or disk background. This is mainly caused by the extended shape of the BP and RP dispersed images, while the G magnitudes will not suffer significantly from crowding. However, for clusters that are relatively free from background contamination, the BP/RP photometry of stars brighter than G$\simeq$15 mag will have an extremely good quality, comparable to HST photometry. Fainter stars down to G$\simeq$18–19 mag will still have a BP/RP quality that is comparable with the best ground-based catalogues.

While HST photometry will certainly be preferable for some applications, Gaia photometry will have a few advantages: (1) the field of view of Gaia is not limited by any field size: it covers the whole sky; (2) each star that has Gaia astrometry from AF, also has BP/RP spectra from which rough stellar parameters and a reddening estimate can be obtained (Gaia Collaboration, 2016a); (3) brighter stars, generally red giants in the case of GCs, will also have RVs and more accurate estimates of parameters and reddening from RVS spectra202020Accurate reddening estimates can also be obtained from diffuse interstellar bands, that are included in the Gaia RVS wavelength range (see for example Puspitarini et al., 2015, and references therein). (Kordopatis et al., 2012); and (4) the absolute photometric calibration of Gaia will be based on one the largest, most homogeneous, and and most accurate set of spectro-photometric standard stars to date (Pancino et al., 2012; Altavilla et al., 2015; Marinoni et al., 2016), that will grant an accuracy of $\simeq$1–3% with respect to Vega (Bohlin & Gilliland, 2004).

5.4 Radial velocities

Stars brighter than G$\simeq$17 mag will have RVs measurements. Gaia has already produced billions of RVS spectra and by the end of the mission, each star will be observed on average 40 times. This can be compared with the extremely successful RAVE survey (Radial VElocity Experiment, Kordopatis et al., 2013), which measured RVs for half a million stars with V$<$12 mag. The Gaia end-of-mission errors will vary with the star’s colour and will be of the order of 1 km s*-1* for the bright red stars (G$<$12.5 mag and cooler than F types) and will be about 15–20 km s*-1* or more for fainter and bluer stars. Crowding will affect RVS more than any of the other instruments on board. Even if the magnitude limit is brighter, the AL size of the spectra is more than an arcminute on the sky (see Table 1).

Figure 15 shows the simulated RV measurements, as a function of the G magnitude, for the three example cases. Given the limitations of our simulations, we immediately note that only a handful of reliable members in the intermediate case have meaningful RV determinations, because of the combined effect of high reddening – for a GC – and background contamination. We also note the large scatter in RV for the faintest stars in the difficult case, where background contamination takes its toll. However, for the easy case, we notice that a sample of more than 100 stars with magnitudes above $\simeq$13–14 mag is available, with errors around 1 or few km s*-1*. This will happen for the closest 10–20 GCs. The stars with large errors between 13.5 and 14.5 mag are hotter horizontal branch stars. To conclude, we note that a mission extension would increase the quality of the RVS spectra.

5.5 The central arcminute

As discussed in Section 2.2, it is not feasible to simulate the degree of completeness of Gaia data, because it varies across the sky, based on the number of different passages and on their respective orientation. As discussed in that section, nearby and relatively sparse GCs like $\omega$ Cen should be 100% complete down to V$\simeq$16 mag, even in the very core. This might appear surprising, but it is a beneficial byproduct of the relatively shallow Gaia magnitude limit.

However, still the question remains: how far into the GC core can we obtain reliable measurements, at least for the stars that we will be able to measure? Figure 16 shows the end-of-mission error distributions for all member stars, down to G=20.7 mag, for the central arcminute of the simulated clusters. As can be seen, astrometry is not too badly affected by crowding: the maximum errors are of 1 mas yr*-1* for proper motions and 0.7 mas for parallaxes (to compare with Figure 10). The majority of stars have performances of the order of a few hundred $\mu$as yr*-1* or $\mu$as, and this including also the faintest stars. If this appears surprising, we recall that what mostly governs the end-of-mission astrometric errors caused by crowding in Gaia is the PSF size, which is comparable to that of HST.

The situation is different for BP/RP photometry or RVS, because even if the PSF in the AC direction is still small, and thus allows to detect blends quite efficiently, the AL size of the window is larger, and aligned with the dispersion axis of the spectra. The performances in the central arcminute are in fact significantly worse for these instruments than for the AF and the G band magnitude in the case of crowded fields.

6 Summary and conclusions

We used all the available information on the presently available Gaia deblending pipelines, along with their results on simulated data, to model the behaviour of Gaia in crowded areas. We computed additional crowding errors that were combined with the post-launch science performances of Gaia and applied to a set of simulated GCs with different concentration (c=1.0 and 2.5), distance (5, 10, and 15 kpc), and field population (halo, disk, and bulge).

We showed that:

Gaia will provide estimates of the parallax and systemic motion of GCs with unprecedented accuracies: $\simeq$1% and $<<$1%, respectively, for all GCs as far as 15 kpc at least. Also, systemic RVs with errors of a few km s*-1* will be obtained for the 10–20 closest GCs, although our RVS simulations are not as accurate as for the other Gaia instruments. This will allow for a very accurate modeling of GC orbits. 2. 2.

The astrometry, obtained through the AF together with G magnitudes, will be only marginally affected by crowding, having performances not too dissimilar from the nominal Gaia performances even for the most field-contaminated bulge GCs. This is an effect of the tiny Gaia PSF (0.17”) in AF. The G magnitudes will have mmag performances and space quality to G$\simeq$17–18 mag. 3. 3.

The proper motions of individual stars within GCs have sufficient quality to obtain mass estimates with 10% errors for GCs as far as 15 kpc at least, and to identify small variations of the properties (rotations, spreads) of a few km s*-1* for GCs as far as 10 kpc. 4. 4.

The distances of GCs will be obtained with errors of $\simeq$1%, and for GCs heavily contaminated by field stars to a few percent. The impact on the determinations of stellar masses and ages will be significant. It is expected that GC absolute ages with errors below 10% will be obtained. Also, better estimates of surface gravities for GC stars with known distances will remove one of the major uncertainty sources from abundance determinations with high-resolution spectroscopy. 5. 5.

While it is difficult to simulate the exact completeness level of Gaia in GCs, we have shown that the astrometric performances are still exceptional in the central arcminute of the simulated GCs: most of the stars have errors around a few 100 $\mu$as or $\mu$as yr*-1*. 6. 6.

The BP/RP photometry and the RVS spectra, on the other hand, have larger AL sizes and therefore suffer more from crowding effects. The most important factor for these intruments is crowding by field stars, especially in the most extreme cases like the bulge field, which acts at all distances from the GC center and combines with the crowding effects from GC stars in the central regions.

The imminent decision of whether to extend the Gaia mission lifetime will certainly have a beneficial impact on all the above measurements. However, the simulations presented here are already pessimistc and the pipelines are expected to evolve significantly in the next few years. Therefore, we conclude that Gaia measurements will revolutionize our kowledge of GCs.

Acknowledgements

We warmly thank A. Brown, M. Castellani, A. Di Cecco, F. De Luise, D. Harrison, H. E. Huckle, K. Janssen, C. Jordi, P. M. Marrese, D. Pourbaix, L. Pulone, and G. Seabroke, for providing useful information about Gaia BP, RP, and RVS deblending and decontamination, and for enlightening discussions about Gaia and crowded fields treatment in general. This work used simulated data provided by the Simulation Unit (CU2) of the Gaia Data Processing Analysis Consortium (DPAC), run with GIBIS at CNES (Centre national d’études spatiales). This research made use of the R programming language (https://www.r-project.org/) and more specifically of its ‘data.table’ package, for the treatment of very large datasets. Some of the figures were prepared with TopCat (Taylor, 2005).

Appendix A List of acronyms

Table 5 lists all the acronyms used.