MNRAS 504, 356–371 (2021) doi:10.1093/mnras/stab770
Advance Access publication 2021 April 2
Updated parameters of 1743 open clusters based on Gaia DR2
W. S. Dias ,1‹
H. Monteiro,1‹
A. Moitinho ,2
J. R. D. L´epine,3
G. Carraro ,4
E. Paunzen ,5
B. Alessi6
and L. Villela1,7
1Instituto de F´ısica e Qu´ımica, Universidade Federal de Itajub´a, Av. BPS 1303 Pinheirinho, 37500-903 Itajub´a, MG, Brazil
2CENTRA, Faculdade de Ciˆencias, Universidade de Lisboa, Ed. C8, Campo Grande, PL-1749-016 Lisboa, Portugal
3Universidade de S˜ao Paulo, Instituto de Astronomia, Geof´ısica e Ciˆencias Atmosf´ericas, 05508-090 S˜ao Paulo, SP, Brazil
4Department of Physics and Astronomy, University of Padova, Vicolo dell’Osservatorio 3, I-35122 Padova, Italy
5Department of Theoretical Physics and Astrophysics, Marsaryk University, 611 37 Brno, Czech Republic
6Av. Eng. Antˆonio Heitor Eiras Garcia 1236, apto 142. Bairro Jardim Esmeralda CEP 05588-001 S˜ao Paulo, SP, Brazil
7Departamento de Engenharia El´etrica, Universidade Federal do Esp´ırito Santo, Av. Fernando Ferrari, 514, Campus Universit´ario de Goiabeiras,
29075-710 Vit´oria, ES, Brazil
Accepted 2021 March 10. Received 2021 March 9; in original form 2020 November 4
ABSTRACT
In this study, we follow up our recent paper (Monteiro et al. 2020) and present a homogeneous sample of fundamental parameters
of open clusters in our Galaxy, entirely based on Gaia DR2 data. We used published membership probability of the stars derived
from Gaia DR2 data and applied our isochrone fitting code, updated as in Monteiro et al. (2020), to GBP and GRP Gaia DR2
data for member stars. In doing this, we take into account the nominal errors in the data and derive distance, age, and extinction
of each cluster. This work therefore provides parameters for 1743 open clusters and, as a by-product, a list of likely not physical
or dubious open clusters is provided as well for future investigations. Furthermore, it was possible to estimate the mean radial
velocity of 831 clusters (198 of which are new and unpublished so far), using stellar radial velocities from Gaia DR2 catalogue.
By comparing the open cluster distances obtained from isochrone fitting with those obtained from a maximum likelihood estimate
of individual member parallaxes, we found a systematic offset of (−0.05 ± 0.04) mas.
Key words: open clusters and associations: general.
1 INTRODUCTION
Open clusters (OCs) constitute a privileged class of objects for
investigating a range of astronomical topics, from Galactic structure
and dynamics, to the formation, structure, and evolution of stars and
stellar systems, and are steps in the cosmic distance ladder. Their
positions, distances, proper motions and radial velocities, can in
general be determined with better precision than those of individual
stars, especially for distant objects. Most importantly, with isochrone
fitting, their ages can be determined over a broad range with a
precision not at reach for most other astronomical objects.
Since the classic works of Becker & Fenkart (1970) and Janes &
Adler (1982) OCs have played an important role in revealing the
structure and evolution of our Galaxy. Some more recent studies
include the tracing of spiral arms (Moitinho et al. 2006; V´azquez
et al. 2008; Bobylev & Bajkova 2014), the spiral pattern rotation
speed and corotation radius (Dias et al. 2019), the metallicity gradient
(L´epine et al. 2011; Donor et al. 2020), the Galactic warp (V´azquez
et al. 2008; Cantat-Gaudin et al. 2020), and the location of the Sun
with respect to Galactic plane (Cantat-Gaudin et al. 2020). A review
of pre-Gaia Galactic structure results with OCs can be found in
Moitinho (2010). The most widely used catalogues of OCs and their
E-mail: wiltonsdias@yahoo.com.br (WSD); hektor.monteiro@gmail.com
(HM)
fundamental parameters are the New catalogue of optically visible
open clusters and candidates (Dias et al. 2002, hereafter DAML)
and The Milky Way Star clusters (Kharchenko et al. 2013, hereafter
MWSC). Recent, pre-Gaia examples of OCs used in other topics,
such as stellar astrophysics, can be found in Georgy et al. (2013), and
for constraining the distance scale in An, Terndrup & Pinsonneault
(2007).
The Gaia DR2 catalogue (Gaia Collaboration et al. 2018a) presents
more than 1 billion stars with magnitude G ≤21 with high-precision
astrometric and photometric data, improving the stellar membership
determination and characterization of thousands of open clusters
(Cantat-Gaudin et al. 2018; Soubiran et al. 2018; Bossini et al. 2019;
Carrera et al. 2019; Monteiro & Dias 2019; Monteiro et al. 2020).
As a consequence, in addition to the direct contribution to Galactic
structure studies Gaia has allowed the discovery of hundreds of new
OCs (Castro-Ginard et al. 2018, 2019, 2020; Liu & Pang 2019; Sim
et al. 2019; Ferreira et al. 2020), to check the reality of doubtful
objects (Cantat-Gaudin & Anders 2020), Monteiro & Dias (2019).
Despite the exquisite quality of Gaia DR2, the determination of
OC parameters has in many cases remained a challenge. On the one
hand, the parameter fitting algorithms have to deal with a number of
factors, such as degeneracies, that compromise quality of the fits over
the whole range of parameter space. On the other hand, poor clusters
and/or remaining field contamination may lead to ill-defined groups.
As a result, several clusters observed by Gaia did not have yet their
C 2021 The Author(s)
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Open clusters parameters 357
Figure 1. Galactic distribution of the 1743 open clusters analysed in this work. The plot presents the clusters in Galactic coordinates with the main regions of
star formation highlighted. The colour is proportional to the age in the sense blue is young, green is intermediate age and yellow is old.
parameters determined with Gaia DR2 data, and many others have
unreliable determinations.
In Monteiro et al. (2020), we have focused on the determination
of the parameters of 45 difficult clusters, left-overs of previous largescale
Gaia based studies. This study introduced methodological
improvements to isochrone fitting, including an updated extinction
polynomial for the Gaia DR2 photometric band-passes and the
Galactic abundance gradient as a prior for metallicity, which led to
a successful automatic determination of the fundamental parameters
of those clusters.
This paper is a follow-up to Monteiro et al. (2020). Here, we
employ the updated isochrone fitting procedure in a large-scale
homogeneous, Gaia DR2 based, determination of parameters for
1743 OCs with previous membership determinations. Both papers
are part of an ongoing project to bring DAML into the Gaia era.
The remainder of this manuscript is organized as follows. In the
next section, we describe the sample. Section 3 presents the cluster
member stars. In Section 4, we present the determination of the OC
astrometric parameters and mean radial velocity. In Section 5, we
describe our code of isochrone fitting to determine the distances
and ages of the clusters. In Section 8, we compare the results
obtained from Gaia data with those from UBVRI data for a control
sample. Sections 9 and 10 are dedicated to compare our values with
published ones. Section 11 provides general comments on the results.
Section 12 is dedicated to statistics of the parameters determined in
previous sections. In Section 13, we compare the distances from
isochrone fits and from parallaxes. Finally, in the Section 14, we
summarize the results presenting the main conclusions of this work.
2 THE SAMPLE OF OPEN CLUSTERS
INVESTIGATED
In this study, we investigated 2237 open clusters and present a list of
1743 clusters including the parameters here determined, and their
associated uncertainties. The sample is composed of 475 young
clusters (log(age) < 7.5 dex), 1075 intermediate-age open clusters
[log(age) between 7.5 dex and 9.0 dex], and 193 old clusters [log(age)
Figure 2. Distribution of the 1743 clusters in the plane x–y. The Galactic
Centre at (0,0) as reference and the x-axis pointing to the Galactic rotation
direction. The rotation is clockwise or the vector angular velocity is perpendicular
to the x−y plane pointing in the direction of the paper. The y-axis
positive points towards the Galactic anticentre and the Sun is situated at
(0,8.3) kpc position.
> 9.0 dex]. 365 clusters are located within 1 kpc and 1379 farther than
1 kpc. Figs 1 and 2 show the distribution of the sample in the Galaxy.
The statistics of the parameters are discussed in the Section 12.
The sample parameters have the main characteristic of being
homogeneous, since they are determined with the same isochrone
fitting method, using the GBP and GRP magnitudes from Gaia DR2
catalogue.
We also present the mean proper motion and parallax, the number
of astrometric member stars, mean radial velocity and the number
of stars used to estimate them, the apparent radius r50 containing
50 per cent of the identified members, and the maximum radius
rmax, which is the largest angular distance between the member
stars and the central coordinates of each cluster considered as the
mean positions in RA and Dec. of the member stars. The coordinates
are given at epoch J2015.0 (ICRS) as realized by the Gaia DR2
catalogue.
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358 W. S. Dias et al.
Table 1. A portion of the table of the results of mean astrometric parameters obtained using the Gaia DR2 stellar proper motion and parallaxes.
The meaning of the symbols are as follows: RA and DE are the central coordinates of the clusters; r50 is the radius in which half of the identified
members are located; N is the number of cluster stars; μαcosδ and μδ are the proper motion components in mas yr−1; σ is the dispersion of cluster
stars’ proper motions; is the mean parallax of the cluster, and σ is the dispersion of the mean parallax. RV and σRV are the mean and 1σ
dispersion radial velocity obtained for the cluster using Gaia DR2 data.
Name RA DE r50 N μαcosδ σμαcosδ μδ σμδ σ RV σRV N
(deg) (deg) (deg) (mas yr−1) (mas yr−1) (mas yr−1) (mas yr−1) (mas) (mas) (km s−1) (km s−1)
Alessi 1 151.6211 49.5407 0.237 48 6.550 0.152 −6.252 0.293 1.396 0.063 − 3.343 1.024 11
Alessi 10 35.3246 − 10.5442 0.272 73 1.456 0.242 −7.844 0.273 2.227 0.087 − 12.671 1.819 6
Alessi 12 308.3153 23.9029 0.660 313 4.339 0.311 −4.650 0.222 1.825 0.098 − 3.374 2.662 25
Table 2. A portion of the fundamental parameters obtained from the isochrone fits is given.
Name Dist σdist log(age) σlog(age) [Fe/H] σ[Fe/H] AV σAV
(pc) (pc) (dex) (dex) (dex) (dex) (mag) (mag)
Alessi 1 681 15 8.993 0.045 − 0.109 0.132 0.416 0.150
Alessi 10 445 9 8.547 0.131 0.019 0.076 0.496 0.066
Alessi 12 539 10 8.195 0.127 − 0.023 0.079 0.248 0.087
The table with the cluster’s parameters and the tables with Gaia
DR2 data of each star in the field with stellar membership probability
are given electronically at the Centre de Donn´ees Stellaires (CDS).
In this text, a portion of the table with the parameters of the clusters
is presented in Tables 1 and 2.
3 OPEN CLUSTER MEMBERSHIPS
To determine precise fundamental parameters of open clusters, it
is necessary to know the member stars. With data from the Gaia
DR2 catalogue, astrometric membership determination has become
much more precise than using ground-based data (Dias, Monteiro &
Assafin 2018), leading to clearer CMDs and therefore enabling a
more precise and reliable parameters’ determination.
In this work, we selected 2237 clusters with published individual
stellar membership determined from Gaia DR2 astrometric data from
the following studies:
(i) Cantat-Gaudin & Anders (2020), updated Cantat-Gaudin et al.
(2018), and estimated stellar membership probabilities for 1867
open clusters applying the UPMASK procedure (Krone-Martins &
Moitinho 2014).
(ii) Castro-Ginard et al. (2019, 2020) found hundreds new open
clusters looking for overdensities in the astrometric space using
DBSCAN and applying the machine learning to the CMD to check
if the object is real.
(iii) Liu & Pang (2019) used the Friend of Friend method to find
2443 open clusters and to select their members.
(iv) Sim et al. (2019) found 655 cluster candidates (207 new) by
visual inspection of the stellar distributions in proper motion space
and spatial distributions in the Galactic coordinates (l, b) space. The
members were determined using Gaussian mixture model and meanshift
algorithms.
(v) Monteiro et al. (2020) investigated 45 open clusters applying
the maximum likelihood method to estimate stellar membership in
the cluster regions.
(vi) Ferreira et al. (2020) discovered 25 new open clusters and
identified the member stars by applying a decontamination procedure
to the three-dimensional astrometric space.
In the works published by Liu & Pang (2019) and CastroGinard
et al. (2020), the memberships were published as having
Figure 3. Comparison of the members of the open cluster UBC 591 from
Cantat-Gaudin & Anders (2020) (left plot) and from the recalculated memberships
from this work (right plot). The stellar membership is proportional to the
colour, in the sense redder colour represents higher membership probability.
probability equal to one (Pi = 1), for members and zero for nonmembers.
To maintain uniformity with the rest of the sample where
individual membership probabilities were available, we recalculated
the individual membership probability of the stars (Pi) applying a
variation of the classic maximum likelihood approach described
in Dias et al. (2014) and Monteiro et al. (2020). In the classic
approach, a first step is to determine the bivariate probability density
function that represents the distributions of the cluster members and
of the field stars in the space formed by proper motions and parallax
(μαcosδ, μδ, ). The second step is then to use these distributions
for assigning cluster/field membership probabilities to the stars under
analysis. In the variation here employed, we used the stars reported
as members (Pi = 1) in Liu & Pang (2019) and Castro-Ginard et al.
(2020) to directly estimate the shapes of the membership probability
density functions in proper motion and parallax space, and from there
proceed to the membership determinations.
This procedure provided individual stellar membership probabilities
and allowed us to improve the cluster signature in several CMDs,
as shown in Fig. 3 for the case of UBC 591.
Before using the photometric data, we apply filters according to
Gaia Collaboration et al. (2018b), to guarantee that only stars with
good astrometric solutions are used in the isochrone fit. Since we
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Open clusters parameters 359
Figure 4. Comparison of the mean radial velocity for 229 open clusters in
common with Soubiran et al. (2018). The mean difference is 0.4 km s−1 with
standard deviation of 5.9 km s−1 in the sense literature minus our value.
use the G magnitude in the plots, we also applied corrections in this
to correct for systematic effects as mentioned in Gaia Collaboration
et al. (2018b), using the recipe in the Gaia data archive website
(https://www.cosmos.esa.int/web/gaia/dr2-known-issues).
4 PARALLAX, PROPER MOTION, AND RADIAL
VELOCITY OF THE CLUSTERS
We used the stars with membership probability greater than 0.50
to estimate mean proper motion, parallax, and radial velocity of
the clusters. For proper motion and parallax, we adopted the simple
mean, however, to accommodate different numbers of measurements
and also measurements with different errors, the mean radial velocity
of each open cluster was obtained by weighting with the number of
measurements and the error of a single measurement, as used in
Dias et al. (2014) following the recipe of Barford (1967). Before
computing the mean, we applied a 3σ outlier rejection of the radial
velocity values. For mean proper motion and parallax, the standard
deviation (1σ) was adopted to represent the error.
As we use only the clusters with member stars derived from Gaia
DR2 data, this was a limiting criterion, since the Gaia DR2 catalogue
gives radial velocity for stars with G ≤ 12. Even so, mean radial
velocity was estimated for 831 open clusters of which 198 had no
previous published estimates, of which 106 from Liu & Pang (2019),
81 from the work of Castro-Ginard et al. (2020), 1 from Sim et al.
(2019), 7 from Monteiro et al. (2020), 2 from Cantat-Gaudin et al.
(2018), and 1 from Ferreira et al. (2020). In Figs 4–6, we check
our mean radial velocities against the values derived by Soubiran
et al. (2018), Carrera et al. (2019), and Tarricq et al. (2021), all
determined using membership from Cantat-Gaudin et al. (2018) and
data from Gaia DR2 and from APOGEE (Majewski et al. 2017) and
GALAH (De Silva et al. 2015) in the case of Carrera et al. (2019).
The differences of 229 clusters with Soubiran et al. (2018) gives a
mean of 0.4 km s−1
with standard deviation of 5.9 km s−1
and the
differences of 79 clusters with Carrera et al. (2019) gives a mean of
−2.0 km s−1
with standard deviation of 10.4 km s−1
, and considering
631 open clusters in common with Tarricq et al. (2021) we obtain a
mean of 0.4 km s−1
with standard deviation of 7.0 km s−1
. All the
values we calculated in the sense literature minus our result.
Figure 5. Comparison of the mean radial velocity for 79 open clusters in
common with Carrera et al. (2019). The mean difference is −2.0 km s−1 with
standard deviation of 10.4 km s−1 in the sense literature minus our value.
Figure 6. Comparison of the mean radial velocity for 631 open clusters in
common with Tarricq et al. (2021). The mean difference is 0.4 km s−1 with
standard deviation of 7.0 km s−1 in the sense literature minus our value.
As for the comparison between our results and those published,
there are five open clusters with differences that exceed 3σ. For
clusters Alessi 19, Harvard 16, IC 1311, NGC 1027 our values differ
with the Soubiran et al. (2018). The authors used four member stars
for Alessi 19 and one member star for the other clusters. For Trumpler
3, our value differs from the Carrera et al. (2019), which used radial
velocity from APOGEE DR14 of four members. The differences
can be explained by the fact that different studies use different ways
of calculating mean radial velocity (weighted or not, with rejection
or not). Thus, despite the works being based on memberships from
Cantat-Gaudin & Anders (2020), either not exactly the same stars
were used or different was the way they were analysed.
In Table 1, we present a portion of the results giving the mean
proper motion, mean parallax and mean radial velocity with the
respective errors represented by the one standard deviation. In the
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360 W. S. Dias et al.
table are also given the number of cluster members, the equatorial
coordinates (α, δ) and the radius (r50) of each cluster.
5 PARAMETERS FROM THE ISOCHRONE FITS
The parameters distance, age, and AV of the clusters were obtained
by fitting theoretical isochrones to Gaia DR2 GBP and GRP photometric
data, applying the cross-entropy continuous multiextremal
optimization method (CE), which takes into account the astrometric
membership of the star as well the nominal errors of the data. It is
exactly the same code used in Monteiro et al. (2020) and to avoid
being repetitive, we opted to present a general description in this text.
Basically, the CE method involves an iterative statistical procedure
where the following loop is done in each iteration:
(i) Random generation of the initial sample of fit parameters,
respecting predefined criteria;
(ii) Selection of the 10 per cent best candidates based on calculated
weighted likelihood values;
(iii) Generation of random fit parameter sample derived from a
new distribution based on the 10 per cent best candidates calculated
in the previous step;
(iv) Repeat until convergence or stopping criteria reached.
Our method uses a synthetic cluster obtained from an isochrone,
sampling from a predefined initial mass function (IMF), randomly
generating a number of stars in the mass range of the original
isochrone.
The code interpolates the Padova (PARSEC version 1.2S) data base
of stellar evolutionary tracks and isochrones (Bressan et al. 2012),
which uses the Gaia filter passbands of Ma´ız Apell´aniz & Weiler
(2018), scaled to solar metal content with Z = 0.0152. The grid
used is constructed from isochrones with steps of 0.05 in log(age)
and 0.002 in metallicity. A search for the best solutions is performed
in the following parameter space:
(i) Age: from log(age) =6.60 to log(age) = 10.15 dex;
(ii) Distance: from 1 to 25 000 parsec;
(iii) AV: from 0.0 to 5.0 mag;
(iv) [Fe/H]: from −0.90 to + 0.70 dex.
To account for the extinction coefficients dependence on colour
and extinction due to the large passbands of Gaia filters, we used the
most updated extinction polynomial for the Gaia DR2 photometric
band-passes, as presented in detail by Monteiro et al. (2020).
While the isochrones used are provided as a function of [M/H], in
this work we assume [M/H] = [Fe/H]. The assumption is justified
by considering the relation from Salaris & Cassisi (2006) that gives
[m/H] ∼ [Fe/H] + log(0.694fα + 0.306), where fα = 10[α/Fe]
. From
Tolstoy, Hill & Tosi (2009, their fig. 11), we can see that for the
range of [Fe/H] in our grid, [α/Fe] is mostly under 0.1. This implies
that for most clusters in our sample the assumption is adequate and
any difference should be within the uncertainties. As an example of
extreme values, we consider the cluster Messier 11 (also catalogued
as NGC 6705) which is known to be α-enhanced with [α/Fe] ∼
0.13−0.17 (Casamiquela et al. 2018), which would give [M/H] ∼
[Fe/H] + 0.07, so there may be some effect for the older clusters. As
it will be shown later, apart from a few cases, most of the clusters in
this work have [Fe/H] < 0.5.
In this work, as in Monteiro et al. (2020), we used priors in
distance, [Fe/H] and AV, adopting the prior probability for each
parameter given by P(X) = n
n=0 P(Xn). For distance, we use
N(μ, σ2
) obtained with Bayesian inference from the parallax ( )
and its uncertainty (σ ) and the variance (σ2
) is obtained from the
Figure 7. Distribution of the uncertainty of the parallax, proper motion,
and radial velocity determined in this study (red colour). The uncertainty of
proper motion and radial velocity distributions are compared with those from
DAML that are presented in green.
distance interval calculated from the inference using the uncertainty
as 1σ . The prior in AV is also adopted as a normal distribution with
μ and variance (σ2
) for each cluster taken from the 3D extinction
map produced by Capitanio et al. (2017).1
The prior for [Fe/H] was
estimated from the Galactic metallicity gradient published by Donor
et al. (2020). For age, there is no prior so we adopt P(Xn) = 1.
In our code, we adopt a likelihood function given in the usual
manner for the maximum likelihood problem as
L(DN |X) =
N
i=1
(I(X), DN ) × Pi, (1)
where X is the vector of parameters (Av, distance d, age log(age),
and [Fe/H]) that define the maximum L and N is the number of
randomly generated, independent sets of model parameters. Pi is the
membership probability of the star.
The likelihood function above is used to define the objective
function [S(X) = −log(P(X) × L(DN |X))] of the optimization algorithm
that define a given isochrone IN. The optimization is done
with respect to N.
Finally, our method does not take into account the differential
extinction in clusters. The grid of PARSEC isochrones does not
include ages younger than ∼ 4 Myr (log(age) = 6.60 dex) and
therefore is not suited for pre-main sequence evolutionary phases
where this effect is expected to be large.
In any case, when we look at the results obtained for clusters
with known differential extinction, we get good agreement with the
literature values. We have 18 clusters from DAML catalogue for
which we know there is differential extinction. When comparing the
results for these objects we find the following mean and standard
deviation differences: distance = (−0.056 ± 0.428) kpc, log(age)
= (0.21 ± 0.42) dex, Av = (0.03 ± 0.29) mag, and [Fe/H]
= (0.14 ± 0.17) dex.
Considering the comparison between our results and those from
DAML, there is no indication of any systematic trend in Av assuring
that both sets agree within the uncertainties. The biggest discrepancies
are in age which is expected since all of the most discrepant
objects are young clusters with the typical problems of poorly
defined turn-off, poor membership estimation, and small number
of members.
In Table 2, we present a portion of the results obtained by the CE.
6 INTERNAL UNCERTAINTIES
Fig. 7 shows the distribution of the uncertainties in mean parallax,
mean proper motion, and mean radial velocity, determined in this
1The 3D extinction map is available online at https://stilism.obspm.fr/.
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Open clusters parameters 361
Figure 8. Distribution of the uncertainty of the distance, log(age), and AV
determined in this study.
study. The average uncertainties for the sample are about 0.28
mas yr−1
in proper motion, 0.07 mas in parallax and 1.60 km s−1
in radial velocity. The figure also displays the distributions of the
corresponding uncertainties listed in DAML, showing that this work
brings a clear improvement.
The uncertainties of the parameters determined from the isochrone
fitting were estimated applying a Monte Carlo re-sampling of
the member stars with replacement (bootstrapping). The synthetic
clusters were also re-generated in each run. The final parameters
and their uncertainties were estimated as the mean and one standard
deviation of ten runs.
The distribution of the uncertainties of the derived parameters are
given in Fig. 8. Fig. 9 presents the internal uncertainties as a function
of the parameters. The derived parameters and their uncertainties are
given in Table 2, available electronically.
7 THE EFFECT OF THE PRIORS
To assess how much the priors constrain the results we took the
sample of 67 clusters with metallicity determinations for high
resolution spectroscopy compiled by Monteiro et al. (2020, table
A.1). The sample covers practically the full range in distance, age
and AV as well in metallicity.
We start by comparing the values of the parameters obtained from
the isochrone fit with the values of the priors. Fig. 10 shows how the
prior in the distance is very restrictive, which reflects our trust on
the quality of Gaia parallaxes. The prior in [Fe/H] is moderately
restrictive. Because the fits are less sensitive to metallicity, this
avoids solutions with extreme values of metallicity while allowing
for reasonable uncertainty in the metallicity gradient. Finally, the
prior in the AV is shown to be clearly non-restrictive, which reflects
our lower trust in the extinction model as well as our high trust
that the data are sensitive enough to this parameter as verified in
Monteiro et al. (2020). These considerations are also expressed in
the correlation coefficients between the parameters obtained from
the isochrone fits and the values of the priors, which are 0.95, 0.68,
and 0.30 for distance, [Fe/H], and AV, respectively.
We now present in Fig. 11 the comparison of the parameters from
the isochrone fits with and without the adopted priors. The correlation
of the parameters obtained with and without priors are 0.99, 0.98,
0.97, and 0.33 for distance, age, AV, and [Fe/H], respectively.
The differences between the parameters determined with priors
and with no priors are in agreement, considering the errors as pointed
by the mean differences 0.010 kpc in distance, 0.014 dex in log(age),
-0.069 mag in AV and 0.032 dex in [Fe/H] with standard deviation of
0.187 kpc, 0.142 dex, 0.234 mag, 0.237 dex.
Another indication of how much the priors constrain the results
is given by the ratio of the width of the prior distribution, σprior, to
the error of the respective parameter (σdist, σAv, σ[Fe/H]) estimated
from the isochrone fit with no priors. These ratios are presented in
Fig. 12. Note that the errors in the parameters estimated without
prior are essentially a measure of the dispersion of the likelihood
distribution. In this sense, we can say that priors restrict results if the
ratio is much less than the likelihood dispersion. In other words, a
ratio σprior − parameters/σparameter greater than 1 means that a prior is not
very restrictive and smaller than 1 that it is more restrictive.
8 THE CONTROL SAMPLE
In the analysis of UBVRI data, the U band clearly improves
the reliability of the parameters estimated for the open clusters,
since it removes the spectral-type/reddening degeneracy in the
colour−colour diagrams. In this way, the agreement of the results
derived from Gaia DR2, in this study using GBP and GRP magnitudes,
with those from the literature obtained with U filter is a
quality indicator of the efficiency in the determination of cluster’s
parameters.
To perform this check, we use high-quality homogeneous UBVRI
photometry of 20 open clusters published by Moitinho (2001).
Each star observed by Moitinho (2001) was cross-matched with
those from Cantat-Gaudin & Anders (2020) for assigning Gaia-based
memberships to the UBVRI data. In the procedure, we used the SKY
algorithm from TOPCAT (Taylor 2005) to cross-match the data with
coordinates in the J2 000 equinox and same epoch. Note that the
different number of stars in each sample is due to the smaller field
of view of the ground-based observations.
To fit the isochrones to the UBVRI data, we used our code and
the same procedure adopted for the Gaia isochrone fitting described
in Section 5, including the prior in distance and [Fe/H] and adopting
the reddening law from Cardelli, Clayton & Mathis (1989) as used
in Dias et al. (2018). So, the method applied to both data samples is
as similar as possible.
In Fig. 13, we present the CMDs and colour−colour diagram for
NGC 2571 as examples of the results obtained both using Gaia GBP
and GRP and UBVRI data. In Fig. 14 and Table 3, we show the
Figure 9. Distribution of the internal uncertainties for the parameters from isochrone fit determined by the cross-entropy method.
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362 W. S. Dias et al.
Figure 10. Comparison of the values of the parameters obtained from the isochrone fit with the values of the priors used.
Figure 11. Comparison of the values of the parameters obtained from the isochrone fit with and without priors.
Figure 12. Ratio of the width of the prior distribution, σprior, to the error of the respective parameter: σdist (left), σAv (middle), σ[Fe/H] (right).
comparison of the values of the parameters obtained with our code
applied to the Gaia and UBVRI data.
The differences between the parameters determined from UBVRI
data and from Gaia data are in agreement at a 3σ level and
considering the errors indicated by the mean differences (0.005 dex
in log(age), −59 pc in distance, −0.007 mag in AV, and 0.11 dex
in [Fe/H]) with root mean square difference (0.302 dex in log(age),
218 pc in distance, 0.099 mag in AV and 0.16 dex in [Fe/H]), in the
sense of results from Gaia data minus UBVRI data.
However, we can notice some differences at the 1σ level. The
most discrepant cases are clusters with poorer fits in Gaia DR2
data. The difference in distance and/or age of OCs Haffner 19,
NGC 2311, NGC 2367, NGC 2401 occurs due to the poorly defined
main sequence (MS) and/or turn-off (TO) in Gaia DR2 data. The
differences in distance for NGC 2425 and NGC 2635 can be
explained by the differences in AV and metallicity. For the distant
clusters NGC 2401 and Haffner 19, the poorer parameters are in line
with what is expected from the internal uncertainties shown in Fig. 9.
NGC 2367 is a very young cluster with sparse and poorly defined
sequence.
The [Fe/H] values are presented for comparison purposes and
should be considered with caution. As noted in Monteiro et al. (2020)
and in Section 7, the isochrone fits employ a moderately restrictive
metallicity gradient prior. Thus, while individual metallicities are
reasonable estimates, as a group they may be biased towards the
Galactic metallicity gradient used as prior. For AV, the results are
hardly affected by the prior which is mostly non-restrictive.
The results for the clusters in this control sample from Moitinho
(2001), together with the extensive validation performed in Monteiro
et al. (2020) indicate that the parameters here obtained with Gaia
GBP and GRP data are reliable. Still, it should be kept in mind that the
analysis has been performed with a small number of clusters, with
different numbers of stars used in each data set due to the different
sizes of the fields. We note that the results of the isochrone fit depend
on the number of stars used and clearly in the Gaia data there are
many more stars than in the UBVRI data considered in this comparMNRAS
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Open clusters parameters 363
Figure 13. Comparison of the parameters obtained from Gaia data (red isochrones) and from UBVRI data (green isochrones) for NGC 2571. The memberships
from Cantat-Gaudin & Anders (2020) are proportional to the colour in the sense of redder indicating higher membership probability.
Figure 14. Comparison of the parameters obtained from Gaia GBP, and GRP and UBVRI data for a sample of 20 open clusters from Moitinho (2001).
Table 3. Parameters obtained for 20 clusters with UBVRI data from Moitinho (2001). Columns two to six list the parameters determined using Gaia GBP and
GRP data. Columns seven, eight, and nine list the values obtained from UBVRI data.
Results from Gaia data Results from UBVRI data
Cluster Distance log(Age) Av [Fe/H] Distance log(Age) Av [Fe/H]
(pc) (dex) (mag) (dex) (pc) (dex) (mag) (dex)
Haffner 16 2862 ± 186 7.513 ± 0.210 0.750 ± 0.037 − 0.160 ± 0.127 2759 ± 154 7.794 ± 0.271 0.656 ± 0.055 − 0.258 ± 0.113
Haffner 19 3745 ± 413 7.938 ± 0.510 1.221 ± 0.131 − 0.210 ± 0.159 4428 ± 1254 6.959 ± 0.076 1.462 ± 0.090 − 0.473 ± 0.492
NGC 2302 1162 ± 27 8.038 ± 0.186 0.733 ± 0.119 − 0.025 ± 0.043 1084 ± 096 8.245 ± 0.183 0.806 ± 0.059 − 0.338 ± 0.127
NGC 2309 2076 ± 71 8.343 ± 0.136 1.326 ± 0.041 − 0.111 ± 0.073 2235 ± 095 8.542 ± 0.053 1.254 ± 0.053 − 0.143 ± 0.069
NGC 2311 1839 ± 62 7.777 ± 0.175 1.092 ± 0.091 − 0.079 ± 0.057 1801 ± 120 8.465 ± 0.252 1.053 ± 0.031 − 0.295 ± 0.106
NGC 2335 1462 ± 82 7.812 ± 0.220 1.480 ± 0.076 − 0.071 ± 0.101 1603 ± 163 7.917 ± 0.061 1.486 ± 0.080 0.118 ± 0.239
NGC 2343 1068 ± 36 8.174 ± 0.088 0.743 ± 0.078 0.063 ± 0.110 1018 ± 080 8.236 ± 0.155 0.776 ± 0.045 − 0.181 ± 0.082
NGC 2353 1140 ± 16 8.127 ± 0.185 0.522 ± 0.046 − 0.055 ± 0.049 1158 ± 058 8.357 ± 0.134 0.437 ± 0.046 − 0.104 ± 0.068
NGC 2367 1722 ± 244 7.490 ± 0.394 1.025 ± 0.156 − 0.065 ± 0.125 1918 ± 452 6.731 ± 0.282 1.106 ± 0.075 − 0.383 ± 0.327
NGC 2383 2815 ± 79 8.382 ± 0.091 1.175 ± 0.031 − 0.174 ± 0.043 2925 ± 154 8.454 ± 0.074 1.095 ± 0.033 − 0.171 ± 0.100
NGC 2401 3940 ± 165 8.322 ± 0.046 1.044 ± 0.040 − 0.168 ± 0.081 4281 ± 417 7.820 ± 0.373 1.220 ± 0.029 − 0.346 ± 0.227
NGC 2425 2714 ± 123 9.604 ± 0.071 0.836 ± 0.060 0.047 ± 0.089 3288 ± 726 9.403 ± 0.344 1.038 ± 0.507 − 0.314 ± 0.219
NGC 2432 1651 ± 51 8.971 ± 0.031 0.735 ± 0.095 0.014 ± 0.105 1722 ± 080 8.970 ± 0.047 0.891 ± 0.022 − 0.183 ± 0.074
NGC 2439 3386 ± 136 7.334 ± 0.081 1.350 ± 0.024 − 0.117 ± 0.074 3385 ± 155 7.523 ± 0.147 1.180 ± 0.026 − 0.205 ± 0.094
NGC 2453 3842 ± 283 7.498 ± 0.265 1.624 ± 0.079 − 0.171 ± 0.063 3865 ± 571 7.617 ± 0.051 1.565 ± 0.034 − 0.217 ± 0.318
NGC 2533 2613 ± 180 8.871 ± 0.066 1.307 ± 0.121 − 0.103 ± 0.080 2529 ± 151 8.937 ± 0.059 1.277 ± 0.047 − 0.261 ± 0.102
NGC 2571 1293 ± 46 7.517 ± 0.138 0.419 ± 0.041 0.058 ± 0.106 1154 ± 076 7.644 ± 0.225 0.280 ± 0.037 − 0.118 ± 0.117
NGC 2635 4049 ± 167 8.720 ± 0.066 1.250 ± 0.061 − 0.218 ± 0.117 4523 ± 160 8.649 ± 0.030 1.157 ± 0.048 − 0.177 ± 0.060
Ruprecht 18 2259 ± 130 8.114 ± 0.427 1.953 ± 0.152 0.123 ± 0.155 1830 ± 130 8.256 ± 0.083 2.110 ± 0.045 − 0.500 ± 0.168
Trumpler 7 1546 ± 60 8.185 ± 0.278 1.027 ± 0.141 − 0.100 ± 0.083 1439 ± 162 8.052 ± 0.285 0.968 ± 0.198 − 0.286 ± 0.198
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364 W. S. Dias et al.
ison. On the other hand, UBVRI photometry can better constrain the
results, since it is not so affected by degeneracies in the parameter
determinations. We also tested the isochrone fitting with UBVRI data
using no prior in distance and [Fe/H]. The results of the parameters
agree within the estimated errors showing no statistical distinction.
In the next sections, we present more evidence supporting that the
results obtained in this work are reliable and improve upon published
ones that used Gaia DR2 data.
9 COMPARISON WITH THE LITERATURE
AFTER GAIA
The large-scale results of cluster parameters, mainly distance and
age, published after the Gaia DR2 catalogue can briefly summarized
as follows:
(i) Cantat-Gaudin et al. (2020) estimate the distance, age, and interstellar
reddening for 1867 clusters, using artificial neural networks
applied to G, GBP, and GRP magnitudes of member stars brighter than
G = 18.
(ii) Bossini et al. (2019) estimated age, distance modulus, and
extinction for a sample of 269 open clusters applying BASE-9 (von
Hippel et al. 2006), to fit stellar isochrones on the observed G,
GBP, and GRP magnitudes of the high probability member stars from
Cantat-Gaudin et al. (2018).
(iii) Liu & Pang (2019) used its own algorithm to automatic
isochrone fitting applied to CMD of 2443 cluster candidates, considering
stars with G ≤ 17.
(iv) Sim et al. (2019) used least-squares fitting of isochrones to
CMDs, considering the mode of distribution of the parallaxes of the
member stars as cluster distance. The authors used for interstellar
reddening E(GBP − GRP) and the extinction in the G band, AG, using
the extinction values from Gaia DR2.
Fig. 15 gives the comparison of the parameters for 1259, 257, 149,
and 128 open clusters in common with Cantat-Gaudin et al. (2020),
Bossini et al. (2019), Liu & Pang (2019), and Sim et al. (2019),
respectively.
The comparisons should be made carefully since the mentioned
studies determine open cluster parameters through isochrone fitting
using different methods and strategies. Although the works cited
used PADOVA isochrones (Bressan et al. 2012), scaled to solar metal
content with Z = 0.0152, Cantat-Gaudin et al. (2020), Bossini et al.
(2019), and Sim et al. (2019) opted to use a fixed metallicity while
Liu & Pang (2019) considered metallicity as a free parameter in the
isochrone fit.
The study of Liu & Pang (2019) uses stars with G ≤ 17 and the
other works used stars limited to G = 18. Since we used the stellar
membership previously published, we follow the same magnitude
cut-offs that impose limitations to obtain adequate results for more
distant open clusters due to the low sampling of the main sequence.
For that reason, the oldest known open clusters as Berkeley 15 and
ESO 393 12 and many others are not present in our sample.
The comparison of our values with those derived by Cantat-Gaudin
et al. (2020) shows systematic trends in AV and distance, in the sense
of our AV being larger and distance being smaller than those of CantatGaudin
et al. (2020). Despite the large dispersion (σ = 0.33), no trend
in age is detected. The same systematic trends in AV and distance
can be seen in the comparison with the values by Bossini et al.
(2019). While all studies used the same member stars, deviations are
expected due to differences in the methods, which include different
extinction laws and priors in Bossini et al. (2019) and Cantat-Gaudin
et al. (2020).
Regarding the discrepancies in ages, we found 22 clusters with
differences larger than 3σ. The objects are presented in Table A1.
An inspection of the CMDs reveals considerable scatter and/or poor
membership determination that leads to poor isochrone fit, mainly
due to lack of clear turn-off, which justifies the differences obtained
between our parameters and those from Cantat-Gaudin et al. (2020).
We expect that these cases can have better results with the catalogue
Gaia EDR3.
The comparison with Sim et al. (2019) shows no expected systematic
trend in distances. This is because their method estimates the
distances from the mode of the parallaxes of the members corrected
of zero-point offset of −0.029 mas from Lindegren et al. (2018).
The authors used the colour excess E(GBP − GRP) and absorption AG
from the Gaia DR2 catalogue to estimate the interstellar extinction
in their isochrone fitting. However, Arenou et al. (2018) have shown
that the extinction values published in Gaia DR2 are not very reliable
and even exhibit large spreads within the same OC. These artefacts
in interstellar extinction, the adoption of solar metallicity as well as
some possible bias in distance may have affected the ages determined
by Sim et al. (2019). A more detailed analysis would be needed to
understand the contribution of each factor to the difference in the
estimated ages, but that is beyond the scope of this study.
Regarding the comparison with Liu & Pang (2019), we note that
there is no good agreement. The plot of the comparison of [Fe/H]
shows steps of 0.25 dex used by the authors in the isochrone fit.
Possibly as happened with the results of Sim et al. (2019), the values
of the metallicity may have affected the ages determined by the
authors. Note that since class 3 objects in Liu & Pang (2019) contains
very young clusters with log(age) ≤ 6.8 dex, the highest density in
the young clusters shown in the plot of age comparison is expected
as pointed by Liu & Pang (2019, their fig. 7).
Finally, we quantitatively evaluate the reliability of the parameters
obtained from the isochrone fit by comparing them with the data.
For this, we use as a figure of merit the likelihood provided in
equation (1). According to this definition, the best fit is the one
that maximizes the likelihood, or as in our algorithm, minimizes the
objective function constructed from it. Thus, the likelihood-ratio test,
or the ratio of the values of the objective function, from two distinct
solutions can indicate which was the best.
Since our method uses synthetic clusters obtained from model
isochrones, we performed Monte Carlo runs calculating the value of
the likelihood for random samples of generated clusters with a given
set of input parameters. The process was performed 100 times and we
adopted the mean of the likelihood sample as the final value and 1σ
as uncertainty. To calculate the likelihood value from the literature
parameters, we use the same data and extinction law provided by
Monteiro et al. (2020). In Fig. 16, the logarithm of the likelihood
values are presented for our sample and those of Cantat-Gaudin et al.
(2020), Bossini et al. (2019), and Sim et al. (2019). The results
show that, within our specified constraints and minimization criteria
(isochrones, priors, extinction law, etc.), we are obtaining the best
solution.
10 COMPARISON WITH THE CATALOGS
BEFORE GAIA DR2
In this section, we compare our results with the New Catalog of
Optically Visible Open Clusters and Candidates (Dias et al. 2002)
(DAML) and Milky Way Star Cluster catalog (Kharchenko et al.
2013) (hereafter MWSC) both published before Gaia DR2 and used
in hundreds of works. A detailed discussion of the differences,
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Open clusters parameters 365
Figure 15. Comparison of the parameters age, distance, AV, and [Fe/H] for 1216, 257, 149, and 128 open cluster in common with Cantat-Gaudin et al. (2020),
Bossini et al. (2019), Liu & Pang (2019), and Sim et al. (2019), respectively.
advantages and disadvantages of both catalogues are presented in
Monteiro et al. (2020).
Briefly, the MWSC catalogue is based in the PPMXL catalogue
(Roeser, Demleitner & Schilbach 2010) and 2MASS catalogue
(Skrutskie et al. 2006) to determine kinematic and photometric
membership probabilities for stars in a cluster region. The authors
defined a combined stellar membership probability and determined
parameters of 3006 clusters using near infra-red J, H, and Ks data.
Version 3.5 of DAML presents 2174 clusters with parameters
compiled from the literature, giving priority to observational data
including the U filter, due to its importance in the determination of
the E(B − V) through the colour−colour diagram that allows more
reliable determinations of distances and ages. In the comparison with
DAML catalogue, all results from MWSC catalogue were removed.
In Fig. 17, we present the comparison of the parameters for 744
and 933 open clusters with DAML and MWSC, respectively. The
differences obtained for each parameter are shown in Table 4.
The results of the comparison show the same characteristic scatter
and trends seen in the similar comparisons by Monteiro et al. (2020),
Cantat-Gaudin et al. (2020), and Bossini et al. (2019). While the
Gaia-based results represent overall a clear improvement over the
pre-Gaia catalogues, it must be noted that distant, more reddened
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366 W. S. Dias et al.
Figure 16. Comparison of the likelihood (log(L)) for open clusters in common with Cantat-Gaudin et al. (2020), Bossini et al. (2019), and Sim et al. (2019),
respectively.
Figure 17. Comparison of the parameters determined in this work with the values published by DAML and MWSC catalogues.
Table 4. Comparison of our results with those published in the literature. In the first column are given the
reference. The values in the subsequent columns are in the sense our results minus literature. N is the number
of common clusters.
Ref Distance σdist log(age) σlog(age) AV σAV [Fe/H] σ[Fe/H] N
(pc) (pc) (dex) (dex) (mag) (mag) (dex) (dex)
DAML 111 1046 −0.048 0.582 0.048 0.920 0.095 0.243 744
MWSC 120 906 −0.088 0.571 − 0.033 0.751 0.112 0.256 933
Cantat−Gaudin −167 414 −0.057 0.384 0.289 0.268 1216
Bossini −138 262 −0.067 0.250 0.170 0.174 257
Sim −4 18 −0.089 0.477 128
LP −0.557 0.896 0.090 0.777 149
Notes. DAML = Dias et al. (2002); MWSC = Kharchenko et al. (2013); Cantat−Gaudin = Cantat-Gaudin
et al. (2020); Bossini = Bossini et al. (2019); Sim = Sim et al. (2019); LP = Liu & Pang (2019).
and older clusters are fainter and do not have Gaia-based photometry
and membership determinations. For those clusters, the pre-Gaia
catalogues remain useful and the comparisons here presented give
an idea of their expected precision.
11 GENERAL COMMENTS
The 1743 open clusters included in this work pass the empirical
criteria for bona fide clusters with Gaia proposed by Cantat-Gaudin &
Anders (2020) and a visual inspection of the CMD with the fitted
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Open clusters parameters 367
Figure 18. Examples of CMDs of cases classified as dubious.
isochrone overplotted. Typical cluster detected in Gaia DR2 show
small total proper motion dispersion, clear features in the CMD (e.g.
main sequence, turn-off, red clump), 50 per cent of their members
are within a radius of 15 pc, parallax dispersion of the member
stars adequate to the group’s distance, and a minimum number of 10
member stars.
Visual inspection of the CMDs indicates that many clusters
detected with Gaia DR2 by Liu & Pang (2019) and some by CastroGinard
et al. (2020) are dubious or not physical objects although we
recalculated the individual membership probability of the stars.
This is in agreement with the original classification by the authors.
Liu & Pang (2019) considered 1747 (72 per cent) candidates as class
3 and 127 (5 per cent) as class 2, using as criterion the width of
the MS, age and quality of the isochrone fitting. Castro-Ginard
et al. (2020) considered 101 (15 per cent) candidates as class B
and 235 (36 per cent) as class C, considering the concentration of
member stars in the astrometric parameters and the contamination in
the CMD. We estimate that objects in class A from Castro-Ginard
et al. (2020) and class 1 from Liu & Pang (2019) are likely star
clusters candidates, while the candidates in the other classes need
confirmation.
Figs 18 and 19 show typical cases we found with dubious and
non-real objects for which our code was unable to obtain reliable
solutions. In short, some clusters as UBC 625 and fof sc 2002 have
few members and despite the low dispersion in proper motion, the
CMDs do not show the typical clear features of a real cluster. Other
cases as UBC 649 and fof sc 2213 have CMDs with a gap of more
than 1 mag in the possible main sequence of the cluster that cannot
be explained by the theory of stellar evolution. A number of clusters,
as fof sc 1605, have very spread MS on the CMD without a feature
of a cluster. The list of likely not real open clusters (85 not real and
82 dubious) is given in Tables B1 and B2 for further investigations.
The large number of doubtful cases mainly from Liu & Pang
(2019) can be explained as due to objects that are not real open
clusters. Fig. 20 presents a comparison of the total proper motion
dispersion of real open clusters from Cantat-Gaudin & Anders (2020)
Figure 19. Examples of CMDs of cases classified as not real clusters.
Figure 20. Upper panels: Comparison of the total observed proper motion
dispersion ( (μα cos δ)2 + (μδ)2) in mas yr−1 of the open clusters from
Cantat-Gaudin et al. (2020) (red), Liu & Pang (2019) class 1 (green), class
2 (blue) and class 3 (orange). The plot on the right gives the total observed
proper motion dispersion as a function of the cluster mean parallax with
the x-axis on a log scale. Bottom panels: The same for open clusters from
Castro-Ginard et al. (2020) with colour codes for their class A (green), class
B (blue), and class C (orange).
and the sample of the open clusters from Liu & Pang (2019). The
figure shows a clear separation of their class 2 (lower isochrone fit
quality) and class 3 (lower isochrone fit quality and scattered CMD)
samples both with many clusters with total proper motion dispersion
greater than their class 1 (higher quality results) and mainly greater
than the real clusters from Cantat-Gaudin et al. (2020). On the
other hand, Fig. 20 shows the same analysis to UBC open clusters,
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368 W. S. Dias et al.
Figure 21. Saurer 2 is a typical old and distant cluster for which the data
do not define a main sequence and our code fails in the estimation of the
parameters.
considering the classification from Castro-Ginard et al. (2020). Here,
we note that the majority of cases fall within the proper motion
dispersion of real-open clusters from Cantat-Gaudin et al. (2020).
Although the dispersion of the proper motion is not a definitive
proof, it does provide indication that a large proportion of class 2 and
3 objects from Liu & Pang (2019) are not real clusters. We understand
that these cases need further confirmation. For this reason, we opted
to give a list of dubious cases and revisit it in a more detailed study
in another work.
Finally, we point out that older and more distant open clusters,
such as Saurer 2 presented in Fig. 21, do not define clear main
sequences with published members and our code results in poor
parameter estimates. Nevertheless, the reality of Saurer 2, which
was not discovered based on Gaia data, is not in question. This is a
case of real cluster that is too faint to have enough Gaia DR2 based
membership determinations to define a clear CMD sequence. These
cases were eliminated from the final list in the visual inspection
phase.
12 STATISTICS
Although determinations of distance, extinction, number of members,
and proper motion dispersion may change using deeper photometric
surveys or improved astrometric precision, the statistical
description of the results from this work can provide a useful
reference, in addition to the bona fide criteria from Cantat-Gaudin &
Anders (2020), for assessing if an object is or not a real OC.
Fig. 22 shows the distribution of the parameters of the 1743 open
clusters investigated in this study. It is noted that 70 per cent of
the clusters have up to 50 members, 90 per cent have total proper
motion dispersion less than 0.5 mas yr−1
(regardless of the distance)
and 99 per cent have a radius smaller than 15 pc (considering r50).
The clusters have distances from the Sun that vary from 47 pc
(Melotte 25 = Hyades) to 8978 pc (Tombaugh 2) with 21 per cent
of the sample located within 1 kpc from the Sun. The maximum AV
determined in this study was about 6 mag for cluster UPK 402. The
range in log(age) is 6.7 dex (FSR 1352) to 10.0 dex (Berkeley 17).
Finally, we also investigated the relations between cluster parameters
and distance to the Galactic Centre, but no significant correlation
was found.
13 COMPARISON OF DISTANCES FROM
PARALLAXES AND ISOCHRONE FITING
Studies comparing the distances obtained using Gaia DR2 parallaxes
with those from other methods show the existence of a systematic
offset. The value of the offset ranges from −0.082 to −0.029 mas,
depending on the objects and the method used, as shown by Arenou
et al. (2017).
Stassun & Torres (2018) estimated a systematic offset of
(−0.082 ± 0.033) mas using a sample of 158 eclipsing binary. Riess
et al. (2018) determined a global offset of (−0.046 ± 0.013) mas
using 50 Cepheids. Zinn et al. (2019) finds (−0.0528 ± 0.0024)
mas using more than 3000 stars with asteroseismically determined.
Kounkel et al. (2018) used 55 young stars with Very Large Baseline
Array parallaxes and finds an offset of (−0.074 ± 0.034) mas.
A global zero-point of −0.029 mas was found by Lindegren
et al. (2018), using the high-precision sample of about 493
thousands quasars. Arenou et al. (2017) presented a residual
zero-point in parallaxes of (−0.067 ± 0.120) mas for MWSC and
(−0.064 ± 0.170) mas for DAML, comparing the stars in about 200
clusters. Finally, Perren et al. (2020) performed a combined analysis
of UBVI photometry and Gaia DR2 data with the ASteCA code for
inference of cluster parameters and report an offset of −0.026 mas,
using a sample of 10 clusters.
Fig. 23 presents a comparison of the distances determined from
isochrone fits and from parallaxes for the 1743 open clusters in this
study. The distances obtained from parallaxes were determined with
a maximum likelihood estimation, assuming a normal distribution
for individual member stars and taking into account individual
parallax uncertainties. The errors were estimated by considering a
symmetric distribution so that σ = r95 − r5/(2 × 1.645), which is
equivalent to a 1σ Gaussian uncertainty, where r5 and r95 are the 5th
and 95th percentile confidence intervals. To estimate the individual
cluster offsets, we maximize the following maximum likelihood
formulation:
L ∝
i=1
P(x|diso, i, σ i ) =
i=1
1
2πσ2
i
exp −
[( i + x) − 1
diso
]2
2σ2
i
, (2)
where P(x|diso, i, σ i ) is the probability of obtaining an offset x
given the cluster diso, the distance from the isochrone fit (in kpc),
the value of i (in mas) for the parallax of cluster member star i
and its uncertainty σ i . An important assumption here is that the
size of the cluster is smaller than its distance and so the procedure
will not be ideal for large nearby objects. We have also neglected the
correlations between parallax measurements.
With the procedure outlined above, we found a global offset of
(−0.05 ± 0.04) mas and (−0.05 ± 0.03) mas, using the mean
and median of the sample of differences, respectively. Our analysis
follows the suggestion of Zinn et al. (2019) that the offset may
increase with the distances, as can be seen in Fig. 23.
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Open clusters parameters 369
Figure 22. Distribution of the parameters of the 1743 open clusters presented in this work. r50 is the apparent radius containing 50 per cent of the cluster’s
members and the maximum radius rmax is the greatest angular distance between the member stars and the central coordinates of each cluster. The total proper
motion dispersion is given by ( (μα cos δ)2 + (μδ)2).
Figure 23. Comparison of the distances determined from isochrone fits and
from parallaxes. The bottom plot shows the difference in distance in the sense
distance from isochrones minus from parallaxes as a function of the distance
from parallaxes.
14 CONCLUSIONS
We presented an update of parameters for 1743 Galactic open clusters
from isochrone fits to Gaia DR2 data, using the improved extinction
polynomial and metallicity gradient prior as presented in Monteiro
et al. (2020), and in addition a weak prior in interstellar extinction.
The isochrone fitting code, described in Monteiro et al. (2017,
2020), uses a cross-entropy global optimization procedure to fit
isochrones to GBP and GRP magnitudes from Gaia DR2 to determine
the distance, age, AV, and [Fe/H] of the clusters. The membership
probability of stars and their nominal photometric errors are taken
into account. The parameters are given with associated uncertainties,
with mean values for the sample are about 170 pc in distance, 0.24
dex in log(age), and 0.12 mag in Av.
In this study, we used stellar membership probabilities published in
the literature. However, for the clusters from Liu & Pang (2019) and
Castro-Ginard et al. (2020), the values were recalculated applying
a maximum likelihood approach that allowed the construction of
clearer CMDs and better weights for the isochrone-fitting code.
The mean radial velocities of the clusters were determined from
Gaia DR2 radial velocities of member stars. In total, radial velocity
were calculated for 831 clusters of which 198 had no previous
published estimates.
The parameters of the sample indicate that the clusters detected in
Gaia DR2 50 per cent of their members are within a radius of 15 pc
and total proper motion dispersion smaller than 0.5−0.8 mas yr−1
.
Analysis of the differences in distances determined from isochrone
fitting and parallax indicates an offset in the Gaia DR2 parallax of
(−0.05 ± 0.04) mas and (−0.05 ± 0.03) mas, using the mean and
median of the differences, respectively.
In addition to the cluster parameters, all membership probabilities
and individual stellar data are also made available, which can be
useful for other research, as well as for the selection of targets for
spectroscopy.
This paper is a follow-up to Monteiro et al. (2020). Both papers
are part of an ongoing project to bring DAML into the Gaia era.
ACKNOWLEDGEMENTS
We thank the referee for the valuable suggestions that improved
the quality of the paper. WSD acknowledges CNPq (fellowship
310765/2020-0) and the S˜ao Paulo State Agency FAPESP (fellowMNRAS
504, 356–371 (2021)
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370 W. S. Dias et al.
ship 2013/01115-6). HM would like to thank FAPEMIG grants APQ-
02030-10 and CEX-PPM-00235-12. AM acknowledges the support
from the Portuguese FCT Strategic Programme UID/FIS/00099/2019
for CENTRA. This research was performed using the facilities
of the Laborat´orio de Astrof´ısica Computacional da Universidade
Federal de Itajub´a (LAC-UNIFEI). This work has made use of
data from the European Space Agency (ESA) mission Gaia (http:
//www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC; http://www.cosmos.esa.int/web/g
aia/dpac/consortium). We employed catalogues from CDS/Simbad
(Strasbourg) and Digitized Sky Survey images from the Space
Telescope Science Institute (US Government grant NAG W-2166).
DATA AVAILABILITY STATEMENT
The data underlying this article that support the plots and other
findings are available in the article and in its online supplementary
material.
This work has made use of data from the European Space Agency
(ESA) Gaia (http://www.cosmos.esa.int/gaia) mission, processed by
the Gaia Data Processing and Analysis Consortium (DPAC; http:
//www.cosmos.esa.int/web/gaia/dpac/consortium).
We also employed catalogs from CDS/Simbad (Strasbourg) and
Digitized Sky Survey images from the Space Telescope Science
Institute (US Government grant NAG W-2166).
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SUPPORTING INFORMATION
Supplementary data are available at MNRAS online.
Table 1. A portion of the table of the results of mean astrometric
parameters obtained using the Gaia DR2 stellar proper motion and
parallaxes.
Table 2. A portion of the fundamental parameters obtained from the
isochrone fits is given.
Please note: Oxford University Press is not responsible for the content
or functionality of any supporting materials supplied by the authors.
Any queries (other than missing material) should be directed to the
corresponding author for the article.
APPENDIX A: LIST OF CLUSTERS WITH DISCREPANT AGES
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Open clusters parameters 371
Table A1. List of 22 objects with differences out of 3σ in ages with CantatGaudin
et al. (2020).
Alessi 18 SAI 25 UBC 594
Barkhatova 1 UBC 276 UBC 668
Berkeley 1 UBC 322 –
Berkeley 79 UBC 428 –
COIN-Gaia 41 UBC 432 –
FSR 1363 UBC 473 –
Juchert 20 UBC 474 –
LP 1218 UBC 491 –
NGC 1977 UBC 521 –
NGC 6664 UBC 548 –
APPENDIX B: LIST OF LIKELY NOT REAL CLUSTERS
Table B1. List of objects that were found to likely not to be real open
clusters. Clusters with the fof and UBC prefixes are from Liu & Pang (2019)
and Castro-Ginard et al. (2020), respectively.
fof sc0160 fof sc0880 fof sc1467 fof sc1676 fof sc2175
fof sc0259 fof sc0888 fof sc1477 fof sc1688 fof sc2213
fof sc0317 fof sc0889 fof sc1481 fof sc1701 UBC 10b
fof sc0401 fof sc0895 fof sc1484 fof sc1702 UBC 625
fof sc0456 fof sc0988 fof sc1485 fof sc1703 UBC 649
fof sc0471 fof sc1024 fof sc1488 fof sc1712 –
fof sc0611 fof sc1042 fof sc1514 fof sc1722 –
fof sc0659 fof sc1052 fof sc1515 fof sc1723 –
fof sc0660 fof sc1144 fof sc1537 fof sc1737 –
fof sc0674 fof sc1148 fof sc1591 fof sc1752 –
fof sc0692 fof sc1152 fof sc1605 fof sc1782 –
fof sc0693 fof sc1154 fof sc1615 fof sc1811 –
fof sc0730 fof sc1159 fof sc1627 fof sc2002 –
fof sc0732 fof sc1210 fof sc1638 fof sc2004 –
fof sc0736 fof sc1243 fof sc1649 fof sc2097 –
fof sc0814 fof sc1245 fof sc1664 fof sc2112 –
fof sc0834 fof sc1262 fof sc1665 fof sc2158 –
fof sc0837 fof sc1305 fof sc1667 fof sc2167 –
fof sc0841 fof sc1307 fof sc1670 fof sc2169 –
fof sc0871 fof sc1308 fof sc1671 fof sc2173 –
Table B2. List of objetcs that were found dubious open clusters. Clusters
with the fof and UBC prefixes are from Liu & Pang (2019) and Castro-Ginard
et al. (2020), respectively.
fof sc0253 fof sc0949 fof sc1547 fof sc1951 UBC 644
fof sc0396 fof sc0996 fof sc1548 fof sc1988 –
fof sc0522 fof sc1026 fof sc1566 fof sc1999 –
fof sc0559 fof sc1083 fof sc1574 fof sc2032 –
fof sc0661 fof sc1084 fof sc1602 fof sc2035 –
fof sc0696 fof sc1169 fof sc1637 fof sc2089 –
fof sc0728 fof sc1176 fof sc1642 fof sc2155 –
fof sc0743 fof sc1192 fof sc1668 fof sc2159 –
fof sc0751 fof sc1194 fof sc1689 fof sc2160 –
fof sc0809 fof sc1195 fof sc1711 fof sc2171 –
fof sc0810 fof sc1202 fof sc1714 UBC 325 –
fof sc0838 fof sc1203 fof sc1715 UBC 359 –
fof sc0839 fof sc1208 fof sc1716 UBC 416 –
fof sc0883 fof sc1225 fof sc1727 UBC 505 –
fof sc0903 fof sc1239 fof sc1765 UBC 573 –
fof sc0905 fof sc1385 fof sc1766 UBC 575 –
fof sc0909 fof sc1387 fof sc1774 UBC 577 –
fof sc0929 fof sc1428 fof sc1791 UBC 579 –
fof sc0946 fof sc1452 fof sc1792 UBC 592 –
fof sc0948 fof sc1461 fof sc1808 UBC 593 –
This paper has been typeset from a TEX/LATEX file prepared by the author.
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