# Revisiting the mass of open clusters with _Gaia_ data

Anderson Almeida,1 Hektor Monteiro${}^{1\href
https://orcid.org/0000-0002-0596-9115{}}$, Wilton S. Dias1
1Instituto de Física e Química, Universidade Federal de Itajubá, Av. BPS 1303
Pinheirinho, 37500-903 Itajubá, MG, Brazil
<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The publication of the _Gaia_ catalogue and improvements in methods to
determine memberships and fundamental parameters of open clusters has led to
major advances in recent years. However, important parameters such as the
masses of these objects, although being studied mostly in some isolated cases,
have not been addressed in large homogeneous samples based on _Gaia_ data,
taking into account details such as binary fractions. Consequently, relevant
aspects such as the existence of mass segregation were not adequately studied.
Within this context, in this work, we introduce a new method to determine
individual stellar masses, including an estimation for the ones in binary
systems. This method allows us to study the mass of open clusters, as well as
the mass functions of the binary star populations. We validate the method and
its efficiency and characterize uncertainties using a grid of synthetic
clusters with predetermined parameters. We highlight the application of the
method to the Pleiades cluster, showing that the results obtained agree with
the current consensus in the literature as well as recent _Gaia_ data. We then
applied the procedure to a sample of 773 open clusters with fundamental
parameters determined using _Gaia Early Data Release 3 (eDR3)_ data, obtaining
their masses. Subsequently, we investigated the relation between the masses
and other fundamental parameters of the clusters. Among the results, we found
no significant evidence that clusters in our sample lose and segregate mass
with age.

###### keywords:

Galaxy: open clusters and associations: general

††pubyear: 2023††pagerange: Revisiting the mass of open clusters with _Gaia_
data–A

##  1 Introduction

Open clusters are an interesting class of objects to investigate the Galaxy
structure and evolution, since their distances and ages can be determined with
good precision. Young open clusters can be used to investigate and understand
the physics of star formation processes (see Krumholz et al. (2019) and Krause
et al. (2020) for a review) and the relationship of mass to other parameters
of those objects, such as distance and age, allows us to understand how they
evolve dynamically over time. These properties also help to constrain the
initial conditions used in N-body simulation models which investigate cluster
evolution (Pijloo et al., 2015; Rossi et al., 2016).

Clusters are affected and disrupted by internal processes (stellar winds,
internal interactions, mass loss due to stellar evolution) and external
processes (supernova, collision with molecular clouds, forces interacting with
the Galactic potential) depending on their lifetime. These processes could
change the mass of the clusters and reduce their size (Spitzer, 1958; Joshi et
al., 2016) although the details are still being debated. Clusters may also
dissolve with dissolution times that can depend on several factors such as
initial cluster mass and internal structure, as well as on the external
effects mentioned previously (see for example Goodwin & Bastian (2006) and
Portegies Zwart et al. (2010) regarding massive young clusters).

The publication of data from the _Gaia_ satellite has led to an increased
number of open clusters for which fundamental parameters have been determined
(see Cantat-Gaudin, 2022, for a review). While the estimation of their mass
remains challenging, various techniques have been employed using kinematic or
photometric data. An important method is based on the density profile of the
cluster, which is described by the King profile (King, 1962). The King profile
method involves fitting a King profile function to the measured density
profile of the cluster, assuming that the cluster is in dynamical equilibrium.
The determined core radius and tidal radius of the cluster are then used to
calculate the mass. Direct use of the Virial theorem has also been used to get
the cluster mass, as discussed in McNamara & Sanders (1983) and Raboud (1996).
Integrated stellar luminosity function is another widely used method involving
the construction of a histogram of the number of stars as a function of their
luminosities and comparing it to theoretical models. Using photometric data,
one of the first works to apply this strategy was van den Bergh & Lafontaine
(1984) based on a sample of 142 clusters. In, Piskunov et al. (2008b) for
example, the authors use the method to study the initial mass function of open
clusters. However, for all strategies mentioned, lack of precise knowledge of
the cluster member stars as well as their binary fractions were important
sources of uncertainties.

In the pre-_Gaia_ years, some results on the structure and dynamics of
clusters are noteworthy due to the quality of the data and/or the method used.
Below, we highlight a non-exhaustive selection of studies relevant to the
present work.

Due to its proximity, Pleiades is one of the most studied open clusters,
however, only in 1998 with the work of Raboud & Mermilliod (1998a) it was
possible to reliably estimate its mass based on a list of 270 members. The
authors found mass segregation in binary and individual stars with masses up
to 1.0 ${M}_{\odot}$. They estimated the mass of the Pleiades through
different methods: tidal radius $(4000\pm 4000)M_{\odot}$, Virial theorem
$(720\pm 220)M_{\odot}$, mass function integration $(950\pm 200)M_{\odot}$ and
by the sum of the stellar masses of the sample $(412)M_{\odot}$.

In Raboud & Mermilliod (1998b) the authors studied the radial structure of
Praesepe and of the very young open cluster NGC 6231. They considered the
structure and dynamics of the clusters using mass estimates of individual
member stars. In both clusters, the masses of the stars were estimated only
for the main sequence by means of a visual isochrone fit. The authors found
mass segregation among the cluster members with a less pronounced degree of
segregation in Praesepe compared to Pleiades: a surprising fact according to
the authors, as ancient clusters, such as Praesepe, were expected to have a
greater degree of segregation. The mass of Praesepe was estimated to be (590)
${M}_{\odot}$ by integrating the mass function.

Only few works present results of mass for dozens of clusters and those were
mainly based on the data from 2MASS catalogue (Skrutskie et al., 2006) and
stellar membership from the ground-based astrometric PPMX catalogue (Röser et
al., 2008) published in MWSC (Kharchenko et al., 2013a). Bonatto & Bica (2005)
determined the mass for 11 nearby open clusters, taking into account the
unobserved main sequence stars by extrapolating the mass functions to the low
mass limit of $0.08$$M_{\odot}$. They also included estimates of the mass of
unobserved evolved stars. They analyzed mass segregation, the dynamic
evolution of clusters, and its implications for the slopes of mass functions,
reporting that cluster size correlates to age, Galactocentric distance, and
mass. Piskunov et al. (2007) and Piskunov et al. (2008a) derived the tidal
radii and masses of 236 clusters, selected from the ASCC-2.5 catalogue,
(Kharchenko et al., 2007) by fitting King profiles (King, 1962). They found
that the tidal radius distribution had peaked at about 1.5 pc and 7-10 pc and
that most clusters have tidal masses in the range $log(M_{c}/M_{\odot})$ = 1.6
and 2.8. Bukowiecki et al. (2012) estimated the mass of a sample of 599
clusters, converting the luminosity function into the mass function using the
fitted isochrone.

Joshi et al. (2016) studied 1241 open clusters, with distances of up to 1.8
kpc from the Sun. Based on data from the MWSC (Kharchenko et al., 2013b)
catalogue and masses from Piskunov et al. (2008a), the work presents
statistical analyses of several fundamental parameters such as spatial
position, age, size, mass, and extinction. They found that massive clusters
with larger radii, within the solar orbit, tend to have better chances of
surviving external interactions and that younger clusters have larger masses
and tend to lose mass at rates of about $(150)M_{\odot}$/Myr.

With the availability of _Gaia_ data, some works have emerged that, among
other aspects, address the cluster mass estimates. For example, Yontan et al.
(2019) studied the clusters ASCC 115, Collinder 421, NGC 6793, NGC 7031, NGC
7039, NGC 7086, Roslund 1, and Stock 21 where combining CCD UBV photometric
and _Gaia_ astrometric data showing that the slopes of the mass functions of
the clusters are in good agreement with the value of Salpeter (1955). In the
work of Rangwal et al. (2019), three clusters were analysed: NGC 6067, NGC
2506, and IC 4651. The photometric data for the clusters were converted into
mass functions using theoretical models. Similar results for IC 4651 were also
observed in Pandey et al. (1992) and Durgapal & Pandey (2001) where the
existence of mass segregation was suggested.

Using fractal statistics, Hetem & Gregorio-Hetem (2019) investigated a sample
of 50 young open clusters in different stages of evolution at different
regions of the Galaxy. The individual stellar masses were obtained by
comparing the observed color-magnitude diagram with theoretical evolutionary
tracks. The authors estimated the mass of the clusters by the sum of the
individual mass of the member stars, which were determined from _Gaia DR2_
astrometric data (Gaia Collaboration et al., 2018). Their results indicate
that 46% of the clusters did not show mass segregation and the majority of the
objects were inconclusive due to large errors, with only 4 objects showing
clear mass segregation.

Combining data from _Gaia DR2_ , 2MASS, WISE, APASS and Pan-STARRS1, Bisht et
al. (2020) studied the open clusters Czernik 14, Haffner 14, Haffner 17, and
King 10 and estimated their mass by integrating their mass function and
concluded that all clusters are dynamically relaxed and show mass segregation.

More recently, two works have studied masses of open clusters. First,
Bhattacharya et al. (2022), using the _Gaia eDR3_ catalogue, studied 46
clusters with relatively elongated morphology to determine their tidal radii
and study their disintegration. In addition, they determined the initial
masses of the clusters and estimated their total observed masses using mass
function integration. The authors concluded that 41 objects had some degree of
mass segregation. Second, Ebrahimi et al. (2022) investigated 15 nearby
clusters using _Gaia DR3_ data. The authors use synthetic clusters, comparing
their stellar populations with the observed ones to determine their current
mass functions. From these mass functions, they estimate the masses and the
binary fractions. They find that the obtained mass functions were consistent
with a single power-law function. Also, a significant correlation between the
mass function slope and the ratio of age to half-mass relaxation time was
found. Their results also indicate that the less evolved objects have a mass
function consistent with that of the solar neighbourhood, indicating a
possible connection between the dissolution of open clusters and the formation
of the Galactic disc.

In this study, we re-examine the potential correlations of open cluster masses
with their ages, radius, and mass segregation, using a substantial sample of
objects. We obtain updated estimates of mass using the _Gaia eDR3_ catalogue
(Gaia Collaboration et al., 2021) in order to investigate these relationships.
In Sec. 2 we present a new procedure to obtain mass estimates of individual
cluster member stars, taking into account binaries and, from those, the total
cluster masses using the present-day mass functions. The section also presents
an extensive validation of the results based on a set of synthetic clusters.
In Sec. 3 the procedure is applied to the open cluster Pleiades, showing that
the results obtained agree with others in the literature, in particular recent
_Gaia DR3_ mass data. In Sec. 4 we apply the method to a sample of 773 real
open clusters and discuss the results, also comparing to previous literature
values when available. In Sec. 5 we give our conclusions.

##  2 Methodology

In this study, we propose a new method to compute the masses of open clusters,
here considered as the mass of member stars, which were determined through
membership methods. The method is based on the determination of individual
cluster member star masses using precise age, distance, metallicity, and
extinction parameters obtained from _Gaia_ data. To estimate the individual
member star masses, synthetic clusters are generated with full control of
fundamental parameters. Finally, a Monte Carlo method is used to obtain the
final individual masses, as well as their uncertainties, by comparing the
observed and generated synthetic clusters. From the individual masses of the
stars and an estimation of the unseen mass in low mass stars as well as
remnants of evolved stars, the masses of the clusters are obtained. We
validate the method by using a set of simulated observations based on
synthetic clusters generated from predefined isochrones of given age,
distance, extinction and metallicitiy as well as binary fraction.

The procedure is summarized in the steps below:

  * •

the fundamental parameters and photometric data are obtained for a sample of
open clusters from Dias et al. (2021), with updated values based on _Gaia
eDR3_ data;

  * •

the fundamental parameters are used in the generation of synthetic clusters
which will be compared to the observed one in a Monte Carlo procedure;

  * •

the Monte Carlo procedure generates a sample of individual mass estimates for
each observed cluster star;

  * •

based on comparison to the synthetic clusters, stars are labeled as binary or
not and a companion mass is estimated if appropriate;

  * •

the final individual star masses (and companions when present) are obtained by
averaging the sample of mass estimates generated by the Monte Carlo procedure;

  * •

the binary fraction and average mass fraction of binary systems are obtained
from the observed stars;

  * •

the final uncertainties are obtained by the standard deviation of the sample
of mass estimates;

  * •

after calculating individual star masses, we obtain the present-day mass
function by fitting a function to the cluster stellar mass distribution
obtained via a histogram of the mass estimates;

  * •

the fitted present-day mass function is subsequently used to extrapolate the
population of unseen low-mass stars, as well as the unseen mass in remnants of
evolved stars;

  * •

the mass obtained for the observed stars (single and binary), the mass of
unseen low mass stars, the mass of remnants of evolved stars and the
contribution of unseen binaries are added to obtain the final mass of the
cluster.

The procedure is described in more detail in the following sections.

###  2.1 Determination of stellar masses

Figure 1: CMD of a simulated open cluster of log(age) = 8.5, distance = 1.0
kpc and $A_{v}$ = 1.0 mag showing 50 single and binary member stars overlaid
on a synthetic cluster generated with the same referenced parameters
consisting of 10000 synthetic stars. The stars in the synthetic cluster are
coloured based on the mass of the companion where the main sequence is set to
$M_{comp}=(0.0)M_{\odot}$. The zoom in the figure shows where the main
sequence region overlaps with the binary star region. Figure 2: Test results
using our mass determination method performed on a synthetic cluster of
log(age)=8.5, distance = 1.0 kpc and $A_{v}$ = 1.0 mag. The relative error
based on the mass estimate ($M_{est}$) and the expected synthetic mass
($M_{synt}$) is presented for single stars (blue) and binary stars (orange).

In our procedure, the estimation of the mass of each member star observed in a
given open cluster is the fundamental necessary step that needs to be carried
out, before the cluster mass can be obtained. As mentioned previously, with
the open cluster member stars defined, the Monte-Carlo method compares
generated synthetic clusters to the observed ones to determine the masses of
the individual member stars. To generate the synthetic cluster we need a given
set of theoretical isochrones and in this work we use the Padova PARSEC
version 1.2S set of isochrones described in detail in Bressan et al.
(2012)111available at http://stev.oapd.inaf.it/cgi-bin/cmd. The synthetic
clusters are generated with a predefined number of stars with masses drawn
from a probability distribution parameterized by the well-known Chabrier
initial mass function (Chabrier, 2003). In this work, we adopted a number of
generated stars of 10000. A fraction of binary stars of 50% is also adopted,
with the binary system companion star masses drawn from a uniform distribution
with values varying from 0 to the primary star mass. Photometric errors, as
per the _Gaia_ data definition (Gaia Collaboration et al., 2016), are also
included in the synthetic cluster.

For each star in the observed cluster, we compared its magnitudes to each of
the 10000 stars generated in the synthetic cluster, finding the one with the
smallest difference in magnitude. This step effectively finds the synthetic
star with the minimum Euclidean distance from the observed one in magnitude
space, according to the following equation:

$d_{i}=\min_{s\in S}~{}\sqrt{\sum_{j=1}^{m}\left(O_{ij}-S_{sj}\right)^{2}}.$
(1)

where $d_{i}$ is the minimum distance of the star of the observed cluster $O$,
to the $s$ stars in the synthetic cluster $S$, measured in the $jth$ magnitude
band of the $m$ distinct bands available (_Gaia eDR3_ : G, GBP and GRP in this
work).

With the closest synthetic star determined, we check if it corresponds to a
binary. If it is, we mark the observed star as a binary and assign to it the
corresponding primary and secondary masses, since for the synthetic cluster
those are known. Else, we assign the mass of the nearest synthetic cluster
star to the observed star. The process is repeated a large number of times,
each time with a distinct synthetic cluster generated by varying individual
stars. The final mass of the observed stars and their companions are adopted
as the median of the respective sample of masses determined. The errors are
obtained by the standard deviation of the estimates in each case. We note here
that, since the method determines masses based on the minimization of
Euclidean distances in magnitude space, the distribution of binary system
companion masses is adopted for the synthetic cluster solely to efficiently
sample the CMD region where binaries are likely to be located. The actual
distribution of mass fractions in binary systems for a given observed cluster
is determined a posteriori from the estimated stellar masses. The procedure is
illustrated in Fig. 1 where we have generated a simulated open cluster with 50
member stars overlaid on a synthetic cluster generated with the same
referenced parameters with 10000 synthetic stars.

To validate the stellar mass estimation method, a grid of synthetic clusters
was generated with log(age) varying from 6.6 to 9.5; reddening from 0.5 to 3.0
magnitudes; distances from 1 to 5 kpc and with 300 observed stars, 50% of
which are binary systems. We then compared the results of our mass estimation
procedure to the input masses of the generated grid. In Fig. 2 we show an
example of the validation for a simulated cluster of log(age) = 8.5, distance
= 1.0 kpc, and $A_{v}$ = 1.0 mag. We can see that results are in good
agreement with the input synthetic masses, with binary systems showing larger
differences as expected.

The individual mass estimates also vary with respect to cluster ages and
distances, as shown in Fig. 3. As expected, the relative errors are worst for
binaries and increase with age and distance, also with increasing spread. The
behaviour is expected as the photometric errors affect proportionally more the
clusters at higher distances. Young clusters also show larger uncertainties
due to their more undefined turn-off region in colour-magnitude space.

Figure 3: Mean relative error committed in the estimate of individual stellar
masses as a function of the cluster age and distance.

We tested the efficiency of the binary detection feature in relation to other
parameters of the simulated clusters and found some relevant systematic
effects as a function of distance and of extinction $A_{V}$. In Fig. 4 we show
the result of comparing the fraction of binaries found by the mass estimation
method to the known binary fraction, adopted as 50% for the whole grid of
simulated clusters. We can see a clear overestimation of the binary fraction
with the increase of both distance and extinction, as well as age. For
clusters with log(age) < 9.0 and distance smaller than about 2.5 Kpc, the
overestimation is about 20%. This effect is a result mainly of the increased
uncertainty in the fainter magnitudes and the smaller sampling of the main
sequence region for clusters at higher ages and distances.

Figure 4: Relative error of the binary fraction ($f_{bin}$) found by the mass
estimation procedure considering the known fraction (adopted as 50% of
binaries) in simulated clusters. In the upper panel where the dependence to
distance is investigated, we set $A_{V}=1.0$ and in the lower panel where the
dependence to $A_{V}$ is investigated we set distance to 1kpc.

Despite the good accuracy and precision shown in our method, we should note
some limitations. In particular, detecting binary stars is a problem in
regions of the CMD where the main sequence and binary star regions overlap. In
Fig. 1 we present a plot of a CMD of a simulated open cluster of log(age) =
8.5, distance = 1.0 kpc and $A_{v}$ = 1.0 mag showing 50 single and binary
member stars overlaid on a synthetic cluster generated with the same
referenced parameters consisting of 10000 synthetic stars. Parallel to the
main sequence, the region of binary stars can be seen as well as the effect of
the varying companion masses, such as the horizontal sequence at about G
$\sim$ 9\. The zoom in the figure shows the main sequence region where an
overlap with the binary star region occurs at about G $\sim$ 10\. It is very
difficult to define a constraint to determine a correct mass value in these
regions of the CMD. Fortunately, this problem occurs in small regions only.
Also, in most cases, the mass estimation error is usually small and does not
show systematic trends, as can be seen in Fig. 2.

###  2.2 Determination of cluster masses

With the individual masses of the member stars of a given observed cluster, we
can obtain its mass by considering the observed mass and an estimation of the
unobserved mass. To estimate the unobserved mass in low mass stars, we obtain
the present-day mass function from the observed star masses and extrapolate it
to the lower mass limit of 0.09$M_{\odot}$, adopted based on the limit of the
isochrones used. We also estimate the unobserved mass of evolved stars by
extrapolating in the high mass interval, if necessary, and obtaining the
number of stars that have evolved to white dwarfs. In our work, we assume that
the mass function can be represented by a two-part segmented linear function,
which is then fit to the mass distribution of observed stars and extrapolated
to the lower mass limit. The two-part segmented linear function is defined as:

$f(x)=\begin{cases}\alpha_{B}x+b_{1},&\text{if }x\leq M_{c}\\\
\alpha_{A}x+b_{2},&\text{if }x>M_{c}\end{cases}$ (2)

where $\alpha_{A}$ and $\alpha_{B}$ represent the slopes of the function for
the high mass slope and low mass slope, and $b_{1}$ and $b_{2}$ are the
corresponding intercepts, respectively. $M_{c}$ is the mass value at which the
transition between the two linear segments occurs. In our fitting procedure
$\alpha_{A}$, $\alpha_{B}$ and $M_{c}$ are free parameters and $b_{1}$ and
$b_{2}$ are taken such that $f(M_{c}^{-})=f(M_{c}^{+})$.

The segmented linear function is fitted to a histogram for the mass
distribution, where the number of bins is obtained using the rule of Sturges
(1926). The fits were performed using the routine
curve_fit222https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html
with the default Trust Region Reflective algorithm. The fits were done for the
entire original sample333A sample of the sequence including the functions used
is available at https://github.com/ander-son-
almeida/DashboardOCmass/blob/main/examples/MF_example.ipynb of 1743 open
clusters from Dias et al. (2021). We then evaluated each result to select only
those that satisfied the requirement that the histogram for the mass
distribution had at least 2 bins on both sides of the fitted transition mass
point $M_{c}$. The final cluster sample consists of 773 objects that satisfied
this criterion.

The unobserved mass of evolved stars is obtained by estimating how many of the
cluster stars have evolved to white dwarfs, which are typically not detected
due to their low luminosity. To achieve this, we use the initial to final mass
relation for progenitor stars from 0.85 to 7.50$M_{\odot}$ provided by
Cummings et al. (2018). From the fitted mass function, we calculate the number
of stars in that mass range and then use the relation to obtain the present-
day mass in white dwarfs.

The unobserved mass in the low mass range is obtained by integrating the mass
function from the lowest observed mass to the low mass limit of
0.09$M_{\odot}$. The unobserved low mass range is defined by low luminosity
stars not detected by _Gaia_ , or stars with magnitudes greater than 19, which
were removed from our sample due to Gaia’s incompleteness limit. This
procedure is similar to the one adopted by Bonatto & Bica (2005).

It is important to note that in this step, we do not include the masses of the
binary companion to construct the present-day mass function. Since we do not
know the distribution of binaries in the unobserved portion, we estimate their
contribution to the mass by first obtaining a mean mass fraction for binary
systems, given by $q=\overline{M_{secondary}/M_{primary}}$, from the observed
stars. We then obtain the binary system mass from the estimate of primary
masses in the unobserved mass interval. For these systems, we assume that the
primaries are distributed according to the mass function determined by the
observed stars. The total unseen mass of primaries is estimated by integrating
the extrapolated observed mass function down to the lower mass limit. The
contribution of secondaries is found by multiplying this value by the
estimated mean mass fraction to obtain the masses of the companions, thus
giving the final mass in binaries. The unobserved mass will be a sum of the
mass of single stars and binary systems down to the lower mass limit. The
binary fraction used is also determined from the observed stars. The final
mass of the cluster is then estimated by:

$M_{T}=M_{o}+M_{un}(1+F_{bin}\times q)+M_{WD}$ (3)

where $M_{T}$ is the mass of the cluster, $M_{o}$ is the mass estimated from
observed stars, $M_{un}$ is the mass obtained from the integrated mass
function for unobserved stars, $F_{bin}$ and $q$ are the estimated fraction of
binaries and mean mass ratio in binary systems respectively, estimated from
the observed stars and $M_{WD}$ is the estimated mass of white dwarfs.

Figure 5: Synthetic open cluster of log(age) = 8.5, distance= 0.5 kpc, $A_{v}$
= 1.0 mag, [Fe/H] = 0.0, the mass of 1043$M_{\odot}$ and the respective
segmented line fit to the simulated observation (orange dots). The estimated
unseen mass is the region defined by the blue dots, where the fitted function
is used to obtain the integrated mass.

Figure 6: Distribution of the relative error on the cluster’s mass obtained
for each method used (upper left), average relative error and the respective
1$\sigma$ uncertainty as a function of log(age) (upper right), distance (lower
left) and $A_{V}$ (lower right).

To exemplify the extrapolation of the unobserved region of low-mass stars, in
Fig. 5 we show a mass function obtained for a simulated open cluster with 600
stars with log(age)=8.5, at a distance of 500pc, $A_{V}$=1.0, [Fe/H]=0.0, the
mass of 1043$M_{\odot}$. The segmented line fit (green line) to the simulated
observation (orange dots) is also shown. We see from the figure that the
segmented line function fits well to the higher mass end of the mass function
while less to the lower mass section, especially the unobserved low mass
region (blue dots) which is generated from a Chabrier (Chabrier, 2003) initial
mass function. The mass obtained with the fit to the integrated mass function
in this example was 1071$M_{\odot}$, in agreement with the mass of
1043$M_{\odot}$ of the simulated cluster.

The _Gaia eDR3_ data quality has improved significantly the definition of open
cluster members and features in the CMDs, enabling the determination of mass
functions for individual, primary, and secondary stars in some cases.
Consequently, we were able to investigate two methods to calculate the masses
for a subsample of the open clusters:

  * •

mass function: the determination of the mass of a cluster as described
previously, where we obtain a mass function with all the observed stars,
excluding binary companions, and from that, estimate the unseen mass including
the contribution of binaries;

  * •

detailed mass function: the determination of the mass of the cluster by
summing the observed star masses to the contribution of unobserved stars as
determined from mass functions determined for single, primary and secondary
stars separately.

To validate both procedures and to investigate their limitations, we again
make use of the grid of synthetic clusters with different parameters. In Fig.
6 we present the distribution of the relative error of the mass for each
method used and the error as a function of the age, distance and extinction
$A_{V}$. The results indicate that the mass error tends to increase with
cluster age, distance and extinction being usually under 20%. This behavior is
expected since more distant and old open clusters present a low sampling of
the main-sequence stars and suffer from larger photometric uncertainties.
There is also a small systematic overestimation of the mass by the integrated
mass function method and a small underestimation in the detailed mass function
method. Since it is computationally difficult to obtain individual mass error
estimates for each cluster studied, we will adopt the conservative 20% value
overall as our uncertainty in this work.

##  3 Pleiades: a benchmark cluster

With the method tested and validated in a large grid of synthetic clusters, we
proceeded to apply it to the Pleiades cluster, which can be considered a
benchmark case since there are several studies on its stellar population and
precise astrometric and photometric data. These data, especially from the
_Gaia_ catalogue, have allowed a precise determination of member stars and
features in the cluster CMD. We took the sample of 1236 astrometric members,
determined individual masses and applied the two methods described in the
previous section to determine the cluster mass.

Figure 7: Comparison of individual stellar mass results from our work with
Anders et al. (2022) (upper panel) and Gaia Collaboration et al. (2022) (lower
panel). For the stars in binary systems the mass shown is that of the primary.

We compared our individual mass estimates with the determination of Anders et
al. (2022), which used _Gaia eDR3_ , Pan-STARRS1, SkyMapper, 2MASS, and
AllWISE photometric data. Although estimating the mass was not their main
goal, they provide the values which we compare to our estimates in Fig. 7,
where it is possible to see a general good agreement but also a systematic
deviation in the binary stars. It is important to point out that their method
assumes stars are single, so the values estimated are relative to the star
that dominates the photometry, usually the primary. This fact may explain the
systematic underestimation of the primary mass value seen in their method.

Masses from Gaia Collaboration et al. (2022) in data release DR3 were also
available, and a comparison of the stars in common to our Pleiades member
sample is shown in Fig. 7. As in the previous case, we can see that our
results are in good agreement, especially single stars with masses lower than
$\sim$ $2M_{\odot}$. There are again some disagreements regarding the masses
of the primary stars in binary systems, as _Gaia_ does not estimate the mass
of the secondary stars in possible binary systems. However, here we see better
agreement with our results with no clear systematic deviations.

As an example of individual mass estimate quality, in the observed stars, we
found a mass of 4.94$M_{\odot}$ for the $20Tauri$ star. The mass of this star
determined by our method agrees with other values found in the literature,
such as 4.22$M_{\odot}$ from Zorec et al. (2009), 4.29$M_{\odot}$ from
Bodensteiner et al. (2018) and 4.90$M_{\odot}$ from Kyritsis et al. (2022).

It is also possible to check the consistency of the binary fraction estimated
by our method. From the sample of the Pleiades member stars we identified,
1006 single stars and 230 binary systems, giving a binary fraction of 19%. The
binary fraction estimates found published in the literature ranges from 17% to
50% with many works focusing on the lower mass population (Stauffer, 1982;
Steele & Jameson, 1995; Martín et al., 2003; Lodieu et al., 2007; Pinfield et
al., 2003; Maxted & Jeffries, 2005; Bate et al., 2002). One of the first works
to analyse the frequency of binaries in the Pleiades was Bettis (1975), which
found a 22% binary fraction for main sequence stars. Recently, Torres (2020)
found a fraction of multiple and binary systems of 37% (12/32), considering a
list of 32 stars of spectral type B and A with data from _Gaia DR2_. A study
of spectroscopic monitoring Torres et al. (2021) found a fraction of 17%
(48/289) which, after corrections for incompleteness, took on a value of
($25\pm 3$)%. Our binary fraction estimate is within the reported range and
should be considered as a lower limit since the contamination of false
positive detection of members in the low magnitude interval (G>16) may be
significant.

From the masses of the primary and secondary stars of a binary system, we were
able to calculate the average mass ratio in binary systems. For the binary
stars of Pleiades, we found an average mass ratio of
$q=\overline{M_{secondary}/M_{primary}}=(0.58\pm 0.23)$. This value is close
to that found by Malofeva et al. (2022), who determined ($0.73\pm 0.03$).

Applying the two methods described in the previous section, we proceed to
obtain the mass of the cluster. From the observed stars we obtain the observed
mass and for the unseen stars, we use the mass functions to estimate the
unseen mass. In Fig. 8 we show the present-day mass function obtained from the
observed member stars, excluding companion masses as detailed previously for
the first method to obtain the mass. From this method, we obtained a mass of
($816\pm 165$)$M_{\odot}$. For the second method, we used the mass functions
shown in Fig. 9 where we show the present-day mass functions for single,
primary and secondary stars as identified by our method. We performed
segmented linear fits for each present-day mass function, where we obtained
the slopes and transition mass points for the single, primary and secondary
star populations. The results are presented in Table 1. From the fits, we
obtain the slopes and transition mass points for the single star population
which were: $\alpha_{A}$ = ($-1.99\pm 0.50$), $\alpha_{B}$ = ($0.03\pm 0.24$)
and $M_{c}$ = ($-0.20\pm 0.07$); for primary stars which were $\alpha_{A}$ =
($-1.91\pm 2.20$), $\alpha_{B}$ = ($0.01\pm 0.48$) and $M_{c}$ = ($0.20\pm
0.23$); and for the secondary stars which were $\alpha_{A}$ = ($-2.73\pm
0.55$), $\alpha_{B}$ = ($0.28\pm 0.23$) and $M_{c}$ = ($-0.12\pm 0.05$). We
can see from the results that in general, the slopes for the distinct sections
of the mass function agree within the uncertainties obtained. The only
exception is the high mass slope of the secondary star population, which is
steeper than the others. From these values, we obtain the mass of the cluster
using the detailed mass function as described in Sec. 2.2, with a value of
($847\pm 169$)$M_{\odot}$.

Figure 8: Pleiades integrated mass function results for the sample that
includes all star populations. The slopes and transition mass point are
$\alpha_{A}=(-1.75\pm 0.33$), $\alpha_{B}=(0.23\pm 0.22)$ and $M_{c}=(-0.20\pm
0.07)$. Figure 9: Pleiades present-day mass functions for single, primary and
secondary stars. The slopes and transition mass points for the single star
population are $\alpha_{A}$ = ($-1.99\pm 0.50$), $\alpha_{B}$ = ($0.03\pm
0.24$) and $M_{c}$ = ($-0.20\pm 0.07$), for primary stars $\alpha_{A}$ =
($-1.91\pm 2.20$), $\alpha_{B}$ = ($0.01\pm 0.48$) and $M_{c}$ = ($0.20\pm
0.23$) and the secondary stars $\alpha_{A}$ = ($-2.73\pm 0.55$), $\alpha_{B}$
= ($0.28\pm 0.23$) and $M_{c}$ = ($-0.12\pm 0.05$).

A summary of our results, with a comparison to other values in the literature,
is shown in Table 2 where the distinct methods used to estimate the masses are
specified. We note that our results show general agreement with other authors,
except for the value obtained by Raboud & Mermilliod (1997) which used the
tidal radius to estimate the mass.

Table 1: Parameters of the segmented linear fits obtained for the distinct populations of the Pleiades member stars, present-day mass functions. | Parameters |
---|---|---
| Low mass | Transition mass | High mass |
Single | $0.03\pm 0.24$ | $-0.20\pm 0.07$ | $-1.99\pm 0.50$ |
Primary | $0.01\pm 0.48$ | $0.20\pm 0.23$ | $-1.91\pm 2.19$ |
Secondary | $0.28\pm 0.23$ | $-0.12\pm 0.05$ | $-2.73\pm 0.55$ |
Table 2: Comparison of the mass of Pleiades with the results found in the literature. In the first line, we include the two values determined by us, $(816\pm 36)M_{\odot}$ resulting from the integrated mass function and $(838\pm 21)M_{\odot}$ from the detailed mass function (MF). Reference | $M_{T}(m_{\odot})$ | Method
---|---|---
This work | $816\pm 165$ | integrated MF
| $847\pm 169$ | detailed MF
Raboud & Mermilliod (1997) | 1400 | Tidal radius
| 720 | Virial
| 950 | integrated MF
Pinfield et al. (1998) | 735 | King profile
Adams et al. (2001) | 800 | King profile
Converse & Stahler (2008) | $870\pm 34$ | integrated MF
Gao (2019) | $721\pm 93$ | King profile
Danilov & Seleznev (2020) | $855\pm 104$ | integrated MF
Ebrahimi et al. (2022) | $807\pm 1$ | integrated MF

##  4 Mass of real clusters

In this section, we present the results obtained in our analysis of masses of
real open clusters. We have investigated a sample of 1743 open clusters from
Dias et al. (2021) for which results of individual stellar membership
probabilities as well as fundamental parameters such as age, distance, and
extinction were available. For this sample, we updated the memberships and
fundamental parameters using data from the _Gaia eDR3_ catalogue and obtained
the present-day mass functions using the two methods presented in Section 2.2.

As mentioned before, the final sample was defined with clusters for which the
present-day mass function had at least 2 bins on both sides of the transition
mass point, a criterion that is sufficient to perform a fit with a straight
line. Also, clusters that had visually high star contamination were removed.
With this, we were able to obtain the mass for 773 clusters using the
integrated mass function and 46 using the detailed mass function. Using this
final sample, we investigated relationships with other parameters such as age
and size, and location in the Galaxy, among others.

Figure 10: Relative error histogram comparing the masses of clusters in common
with Piskunov et al. (2008a), Bhattacharya et al. (2022) and Ebrahimi et al.
(2022).

In Table 3, we present an example of the final sample and the masses
determined for each cluster, as well as the fundamental parameters adopted for
each. The full table is available online.

Table 3: Sample table of fundamental parameters and masses determined for the open cluster sample using the two methods described in the text. The full table is available online. Name | log(age) | Dist. (kpc) | Av. (mag.) | Fe/H | $M_{Tint}(m_{\odot})$ | $M_{Tdet}(m_{\odot})$
---|---|---|---|---|---|---
ASCC 10 | 8.29 $\pm$ 0.09 | 0.642 $\pm$ 0.003 | 0.8 $\pm$ 0.1 | 0.004 $\pm$ 0.028 | 229 $\pm$ 45 |
ASCC 105 | 8.12 $\pm$ 0.05 | 0.552 $\pm$ 0.002 | 0.8 $\pm$ 0.0 | 0.252 $\pm$ 0.066 | 304 $\pm$ 60 |
ASCC 107 | 7.65 $\pm$ 0.36 | 0.847 $\pm$ 0.008 | 1.5 $\pm$ 0.2 | 0.253 $\pm$ 0.187 | 409 $\pm$ 81 |
ASCC 108 | 8.24 $\pm$ 0.07 | 1.157 $\pm$ 0.003 | 0.7 $\pm$ 0.0 | 0.097 $\pm$ 0.033 | 935 $\pm$ 187 |
ASCC 11 | 8.44 $\pm$ 0.19 | 0.826 $\pm$ 0.005 | 1.0 $\pm$ 0.1 | 0.121 $\pm$ 0.044 | 529 $\pm$ 105 | 541 $\pm$ 108

###  4.1 Comparison with literature

We compared our results of mass of the clusters with those of the large scale
published in the literature, briefly summarized as follows and presented in
Fig. 10.

We found 102 common objects with Piskunov et al. (2008a), which determined the
mass using the King profile. Many objects show significant discrepancies in
relation to our results. We find only 30 clusters for which the masses are
relatively close to ours, with many objects showing significant discrepancies
in relation to our results. The mean of the relative difference between our
results was 193% and the standard deviation was 380%. The differences can be
explained by the different samples of member stars, as well as the different
parameters (mainly distance and age) adopted for each cluster.

From the work Bhattacharya et al. (2022) we found 32 clusters in common which
are presented in the histogram of relative errors, as shown in Fig. 10. Most
clusters are within 60% of our masses, with a mean relative error of about 35%
and a standard deviation of 20%. The differences observed are likely due to
membership probabilities and fundamental parameters adopted by the authors,
which are distinct from the ones used in this work.

For Bukowiecki et al. (2012), which had determination of masses for 599 open
clusters, we were not able to find a complete table with the masses for
comparison to our results.

The work of Ebrahimi et al. (2022) determined the mass of the Pleiades, which
is close to the one found by us (see Table 2). For the other clusters of the
work, we found 9 in common and 6 of these are close to our values with a
relative error of approximately 15% - 30%. Again, differences are likely due
to membership probabilities and fundamental parameters adopted by the authors,
which are distinct from the ones adopted in this work.

Also, worthy of note, Bonatto & Bica (2005) estimated masses from mass
functions obtained using 2MASS photometry. We found 4 clusters in common to
their sample and, in general, our results give larger masses with some values
agreeing within the uncertainties. For NGC 6694 the authors estimated
($1900\pm 700$)$M_{\odot}$ and we obtained ($1208\pm 242$)$M_{\odot}$ using
integrated mass function method; for NGC 2287 the authors found ($720\pm
90$)$M_{\odot}$ and we find ($1185\pm 237$)$M_{\odot}$ from the methods
detailed mass function and ($1126\pm 225$)$M_{\odot}$ integrated MF,
respectively; for NGC 2548 and authors estimated a mass of ($630\pm
150$)$M_{\odot}$ and our results are ($912\pm 182$)$M_{\odot}$ using detailed
mass function and ($920\pm 184$)$M_{\odot}$ using integrated MF. Finally, for
the case of NGC 2682, a mass of ($990\pm 120$)$M_{\odot}$ was found by the
authors and ($1843\pm 369$)$M_{\odot}$ according to our results from
integrated mass function method.

Finally, some works have mass estimates for isolated clusters. In the work of
Yalyalieva et al. (2022) two estimates of masses using isochrones fits for NGC
225 were obtained: 1) ($155.2\pm 2.0$)$M_{\odot}$ up to magnitude G of 18 of
_Gaia EDR3_ and assuming a binary fraction of zero; 2) ($170.5\pm
2.2$)$M_{\odot}$ with a binary fraction of 0.52. Our results for the
integrated mass function returned a mass of ($124\pm 5$)$M_{\odot}$ and a
fraction of 0.62 binary stars. In Bai et al. (2022) the authors found
$439$$M_{\odot}$ for COIN-Gaia 13 using the integration of the mass function
of the observed stars disregarding the influence of binary stars. Regarding
this cluster our result was ($367\pm 9$)$M_{\odot}$ for detailed mass function
and ($378\pm 16$)$M_{\odot}$ for integrated MF, we also found a fraction of
0.60 of binaries which can explain part of the difference in masses found.

###  4.2 Mass properties of the sample

The large number of masses of the open clusters determined in this study
allowed us to investigate the relation of this parameter with others such as
age, radius, and mass segregation, for example. We start by looking at the
distribution of open clusters in the Galactic plane, as shown in Fig. 11. In
the figure, the size of the dots is proportional to the mass and no clear
pattern of the distribution of massive clusters is seen.

Figure 11: Distribution of the 773 open clusters in the galactic plane, with
their masses determined using the mass function integrated. The Sun is
referenced with a red cross at coordinates (0, 8,3) kpc and the galactic
centre is at (0,0). The vector angular velocity is perpendicular to the x-y
plane, pointing in the direction of the paper. The size of the dots is
proportional to the mass.

In Fig. 12 we show the distribution of cluster masses for our sample. The
weighted mean of this distribution is 544$M_{\odot}$ with a standard deviation
of 447$M_{\odot}$.

Figure 12: Histogram of the mass distribution of clusters in the integrated
mass function sample. The vertical line in red indicates the mean of the
distribution. Figure 13: Mass-radius distribution for the clusters in the
sample of 773 open clusters, with their masses determined by the integrated
mass function. The blue dots represent the clusters within the solar orbit,
while the orange dots the clusters outside the solar orbit. The lines
represent the linear fits for the inner and outer orbit samples, respectively.

In the work by Joshi et al. (2016), the authors investigated the relation of
the radius and age of the cluster to the mass. The idea is that the mass-
radius relationship gives information on the dynamic evolution of the open
cluster since, during their early evolution, clusters are expected to
experience interactions with massive molecular clouds which can lead to mass
loss and a reduction in size. In Fig. 13 we show the results we find for the
mass and cluster radius relationship. The radii of the clusters adopted are
defined as the value that includes 50% of the stars in the system. For
clusters inside the solar orbit we find the correlation $R_{OC}=(2.13\pm
1.07)log(M_{T})-(2.51\pm 2.83)$ and for clusters outside the solar orbit
$R_{OC}=(0.80\pm 0.96)log(M_{T})+(0.53\pm 0.96)$. Our results are in agreement
with those obtained by Joshi et al. (2016), where we find few massive clusters
with smaller radii as well as a lack of low-mass clusters with large radii. We
also see that clusters inside the solar orbit show a steeper correlation,
which can be an indication that massive clusters with larger radii have a
lower chance of surviving interactions in the direction of the Galactic
centre. However, given the uncertainties in the linear fits, the difference is
not significant, which is likely due to the large data dispersion.

Figure 14: Relation of cluster mass to age with red dots representing the
average of the masses in a bin in an interval of log(age) = 0.3. Error bars
are obtained from the standard deviation of the bin sample.

We have also investigated the mass-age relation for our cluster sample, as
shown in Fig. 14. Here the general expectation is that interactions with the
Galactic tidal field or with the molecular clouds affect their structure and a
trend where mass decreases with age should be seen. In our sample, a very
tenuous relation is seen, with a correlation coefficient of -0.1, which is
considerably lower than the value of -0.95 found by Joshi et al. (2016). If we
take the average of the mass in intervals of log(age) in the same manner as
done by Joshi et al. (2016), excluding clusters with ages greater than
log(age) = 9.0 to avoid introducing a selection effect bias, we obtain the
following correlation: $log(M_{T})=(-0.06\pm 0.03)log(age)+(3.06\pm 0.24)$. As
in Joshi et al. (2016), we see in our results that younger clusters tend to
have higher mass and lose mass as they get older, but the effect is
significantly smaller. In, Joshi et al. (2016) the authors found a slope of
-0.36 and a mass loss rate $dM_{\odot}/d(age)=150M_{\odot}$ for the age range
1-10 Myr. In our results we find a mass loss, with a slope of -0.06, that is
less intense and a rate of $dM_{\odot}/d(age)=13M_{\odot}$ for clusters in the
age interval of 1-10 Myr. Here we also performed a LOWESS regression and
inspected the uncertainties, finding that a small effect is present, but it is
not significant.

Figure 15: Mass segregation for Pleiades, using the distribution of star
counts as a function of radius. The member stars were divided into two groups,
one with masses $>1M_{\odot}$ and one with $<1M_{\odot}$. The vertical line in
orange represents the mean radius of mass concentration for stars
$>1M_{\odot}$ and in blue the mean radius for stars $>1M_{\odot}$.

We have also measured the degree of mass segregation within the clusters. To
do this, we separate the member stars of a given cluster into two groups: one
having members with masses $>1M_{\odot}$ and the other with $<1M_{\odot}$.
With these groups, we use two distinct procedures to measure the degree of
mass segregation. One, using the ratio of the mean radius of each group’s
distribution, and the other, using a comparison of the cumulative distribution
of mass with respect to the radius, similar to the one used by Mužić et al.
(2022), where they were concerned in determining whether there was or not mass
segregation. Unlike that work, here we quantify the effect using the
Kolmogorov-Smirnov measure to quantify the difference between the
distributions. As an example, in Fig. 15 we show the distributions of the two
groups as obtained for the Pleiades cluster. In the figure, the difference in
the mean radius of each group is indicated and the distinction is clear. Our
results corroborate the existence of mass segregation, which was also
established by van Leeuwen et al. (1986), Hambly et al. (1995), and Raboud &
Mermilliod (1998a) for this cluster.

For the second method, we could determine the significance level of the
Kolmogorov-Smirnov measure, indicating how reliable the measured differences
between the high and low mass distributions were. With the significance test
(p-value) and the adopted threshold of significance of 0.05, we defined a
subsample of clusters for which p-value<0.05. We found that in our sample, 368
(48%) open clusters had a significant level of mass segregation.

With the mass segregation measure obtained using the two methods, we looked at
how it related to the ages of the clusters in our sample. In Fig. 16 we show
the results for this relation where there is no clear trend in the relation of
mass segregation with age. The trend line is obtained with a LOWESS regression
procedure where the uncertainties were also estimated, and the sample mean of
each segregation statistic is also presented for comparison. In the first
panel, we show the result using the first method, based on the ratio of the
mean radius of the low mass sample ($\overline{R_{lm}}$) to the mean radius of
the high mass sample ($\overline{R_{hm}}$). We see the same behavior for the
second method to estimate mass segregation, shown in the second panel of the
figure, where the Kolmogorov-Smirnov measure was used. No significant
difference between the two methods, as far as the existence of the
correlation, is seen. Some authors have mentioned the possibility that low-
mass members would tend to escape as the cluster evolves and moves towards a
relaxation state. However, we do not detect evidence for that here.

Figure 16: Relation of mass segregation to log(age), as measured by the ratio
of mean radius for high and low mass groups (upper panel) and Kolmogorov-
Smirnov measure (lower panel). The tendency line (red) obtained by LOWESS
regression and its uncertainty, as well as the sample mean, is also shown.

We also investigated other possible correlations with cluster properties,
looking at parameters such as the metallicity, cluster radius, cluster stellar
density and cluster mass. We also investigated the sub-sample based on the
significance level of the Kolmogorov-Smirnov measure, taking only those
clusters for which the distributions showed differences with a p-value lower
than 0.05. The only parameter for which a significant correlation was observed
was cluster mass. The correlation for this parameter using the high
significance sub-sample is shown in Fig. 17 where a trend line based on a
LOWESS regression is shown with its respective uncertainty.

Figure 17: Relation of mass segregation, obtained by Kolmogorov-Smirnov
measure, to cluster mass for the subsample with the significance level of
p<0.05. The tendency line (red) obtained by LOWESS regression and its
uncertainty, as well as the sample mean is also shown.

It is important to note that there is no consensus as to which method to
measure mass segregation is ideal. As mentioned in Mužić et al. (2022),
methods which were considered ideal by Parker & Goodwin (2015), who compared
four different methods which are used to measure mass segregation, were not
effective for the clusters they studied. However, both methods adopted in our
work give results that agree with each other and, at least statistically in
the context of our sample, indicate that mass segregation does not increase
with age as has been suggested by other authors.

##  5 Conclusions

In this work, we present a new method for determining individual stellar
masses and use it to calculate the masses for a sample of 773 open clusters
from the Dias et al. (2021) catalog, with updated memberships and fundamental
parameters based on astrometric and photometric data from _Gaia eDR3_.

The method for determining individual masses uses high-quality data of the
member stars and fundamental parameters of open clusters, to compare to
synthetic clusters generated with full control of relevant parameters, and a
Monte-Carlo method to obtain the individual masses and asses its uncertainties
and limitations. The masses are estimated by comparing the observed stars with
synthetic stars generated in a Monte-Carlo method, finding the nearest star in
magnitude space, assigning it a mass, and marking it as binary if applicable.
The method was validated with a synthetic cluster grid, and the results were
found to be in good agreement with the input masses. Some limitations include
difficulty in detecting binary stars in specific regions of the CMD where the
main sequence and binary regions overlap, leading to incorrect mass estimation
in some cases.

With the individual stellar masses estimated, we determined the mass of the
star clusters using two integration methods. In the first method, we
integrated the mass function, which contains all the stars in the cluster, a
method often used in the literature, and in the second method we performed a
detailed integration, which considers a mass function for each population of
stars within the cluster (individual, primary and secondary). The unobserved
mass was estimated by extrapolating the mass function of the observed stars
and accounting for evolved stars and low-mass stars. The method involves
obtaining the mass function of the observed star masses and fitting a two-part
segmented linear function to it. The contribution of binary systems is
estimated by obtaining the mean mass fraction for binary systems and
multiplying that value by the estimated mass of single stars when using the
integration of the mass function and in detail when using specific population
mass functions of the detailed integration method. The method is validated by
applying it to a grid of synthetic clusters and comparing the results with the
true masses. The results show that we can recover masses with uncertainties
under 20% in most cases, and thus this is the value we adopted as a
conservative error estimate.

We applied our methodology to the observed clusters first examining in detail
the results for the well-known Pleiades open cluster. The individual masses we
estimate for the member stars of this cluster are in agreement with the masses
of Gaia Collaboration et al. (2022) and the StarHorse catalogue (Anders et
al., 2022). The mass obtained for Pleiades using the two methods, the binary
fraction and the average mass ratio of binary systems, showed good agreement
with other results found in the literature.

The comparison of our mass estimates of the open clusters to other works in
the literature shows good agreement with recent works based on _Gaia_ data but
large discrepancies with the works of pre-_Gaia_ catalogues. Large
discrepancies were seen when comparing to the work of Piskunov et al. (2008a)
who determined masses using the tidal radius, determined from the cluster
structural parameters.

After the thorough validation of the procedures, we focused on the
relationship between the mass, cluster radius, and age. The results indicate
that the effect seen by Joshi et al. (2016), that younger clusters tend to
have higher mass and lose mass as they get older, is not significant in our
sample. We find a mass loss rate of 13$M_{\odot}$/Myr which is significantly
lower than the value found by those authors. We find that the correlation
between cluster mass and age is weak, with a correlation coefficient of -0.1.
The discrepancies in the results are likely due to differences in the samples,
memberships and fundamental parameters used.

Looking at the relationship between clusters’ masses and radii, we find few
massive clusters with smaller radius as well as a lack of low-mass clusters
with large radius. The positive correlation between mass and cluster radius
could be an indication that clusters inside the solar orbit have a lower
chance of surviving interactions in the region of the Galactic centre,
however, the difference is not significant. We also looked at the degree of
mass segregation within the clusters by measuring it using two distinct
methods and found that 368 (48%) open clusters show a significant level of
mass segregation. However, we found no clear significant trend in the relation
of mass segregation with age, cluster density, or radius. We did however find
a relation between the cluster mass and segregation, showing that more massive
clusters tend to be less segregated. Regarding mass segregation, our results
are in agreement with Dib et al. (2018), where no significant relation of mass
segregation to age was found.

## Acknowledgements

Wilton Dias would like to thank CNPq grant 310765/2020-0. Hektor Monteiro
would like to thank CNPq grant 436117/2018-5 and FAPEMIG grant APQ 01305-17.
This work has made use of the computing facilities available at the Laboratory
of Computational Astrophysics of the Universidade Federal de Itajubá (LAC-
UNIFEI). The LAC-UNIFEI is maintained with grants from CAPES, CNPq and
FAPEMIG.

## Data Availability

The data underlying this article, that support the plots and other findings,
are available in the article and in its online supplementary material
(https://ocmass.streamlit.app). The updated memberships and individual stellar
masses and any other data relevant to the results presented here will be made
available upon reasonable requests.

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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##  Appendix A Online material

If you want to present additional material which would interrupt the flow of
the main paper, it can be placed in an Appendix which appears after the list
of references.

Table 4: Fundamental parameters and masses integrated and detailed determined for the open cluster sample. Name | log(age) | Dist. (kpc) | Av. (mag.) | Fe/H | $M_{Tint}(m_{\odot})$ | $M_{Tdet}(m_{\odot})$
---|---|---|---|---|---|---
ASCC 10 | 8.292 $\pm$ 0.088 | 0.642 $\pm$ 0.003 | 0.793 $\pm$ 0.068 | 0.004 $\pm$ 0.028 | 229 $\pm$ 45 |
ASCC 105 | 8.117 $\pm$ 0.053 | 0.552 $\pm$ 0.002 | 0.765 $\pm$ 0.006 | 0.252 $\pm$ 0.066 | 304 $\pm$ 60 |
ASCC 107 | 7.652 $\pm$ 0.359 | 0.847 $\pm$ 0.008 | 1.463 $\pm$ 0.204 | 0.253 $\pm$ 0.187 | 409 $\pm$ 81 |
ASCC 108 | 8.241 $\pm$ 0.071 | 1.157 $\pm$ 0.003 | 0.655 $\pm$ 0.050 | 0.097 $\pm$ 0.033 | 935 $\pm$ 187 |
ASCC 11 | 8.443 $\pm$ 0.194 | 0.826 $\pm$ 0.005 | 0.975 $\pm$ 0.101 | 0.121 $\pm$ 0.044 | 529 $\pm$ 105 | 541 $\pm$ 108
ASCC 113 | 8.493 $\pm$ 0.088 | 0.558 $\pm$ 0.001 | 0.245 $\pm$ 0.049 | 0.001 $\pm$ 0.025 | 413 $\pm$ 82 | 426 $\pm$ 85
ASCC 114 | 8.103 $\pm$ 0.089 | 0.900 $\pm$ 0.006 | 1.208 $\pm$ 0.091 | 0.059 $\pm$ 0.055 | 432 $\pm$ 86 |
ASCC 115 | 8.308 $\pm$ 0.187 | 0.747 $\pm$ 0.003 | 0.907 $\pm$ 0.090 | 0.049 $\pm$ 0.063 | 140 $\pm$ 28 |
ASCC 12 | 8.496 $\pm$ 0.318 | 1.014 $\pm$ 0.012 | 1.009 $\pm$ 0.084 | 0.112 $\pm$ 0.033 | 359 $\pm$ 71 | 309 $\pm$ 61
ASCC 127 | 7.549 $\pm$ 0.107 | 0.332 $\pm$ 0.013 | 0.575 $\pm$ 0.055 | 0.005 $\pm$ 0.044 | 207 $\pm$ 41 |
ASCC 128 | 8.388 $\pm$ 0.100 | 0.644 $\pm$ 0.001 | 0.681 $\pm$ 0.069 | 0.052 $\pm$ 0.055 | 241 $\pm$ 48 |
ASCC 13 | 8.134 $\pm$ 0.053 | 1.080 $\pm$ 0.004 | 0.882 $\pm$ 0.049 | 0.120 $\pm$ 0.050 | 576 $\pm$ 115 |
ASCC 16 | 7.301 $\pm$ 0.072 | 0.342 $\pm$ 0.001 | 0.038 $\pm$ 0.053 | 0.180 $\pm$ 0.019 | 441 $\pm$ 88 |
ASCC 21 | 7.011 $\pm$ 0.035 | 0.339 $\pm$ 0.001 | 0.283 $\pm$ 0.065 | 0.118 $\pm$ 0.040 | 367 $\pm$ 73 |
ASCC 23 | 8.489 $\pm$ 0.084 | 0.604 $\pm$ 0.001 | 0.376 $\pm$ 0.044 | 0.069 $\pm$ 0.046 | 248 $\pm$ 49 | 242 $\pm$ 48
ASCC 29 | 8.129 $\pm$ 0.085 | 0.988 $\pm$ 0.011 | 0.245 $\pm$ 0.023 | 0.077 $\pm$ 0.025 | 183 $\pm$ 36 |
ASCC 30 | 8.284 $\pm$ 0.061 | 1.054 $\pm$ 0.014 | 0.662 $\pm$ 0.087 | 0.115 $\pm$ 0.066 | 325 $\pm$ 65 |
ASCC 41 | 8.000 $\pm$ 0.001 | 0.292 $\pm$ 0.001 | 0.010 $\pm$ 0.001 | 0.036 $\pm$ 0.001 | 126 $\pm$ 25 |
ASCC 67 | 7.933 $\pm$ 0.054 | 1.878 $\pm$ 0.051 | 0.826 $\pm$ 0.032 | 0.122 $\pm$ 0.062 | 869 $\pm$ 173 |
ASCC 71 | 8.071 $\pm$ 0.045 | 1.236 $\pm$ 0.023 | 1.001 $\pm$ 0.065 | 0.069 $\pm$ 0.079 | 432 $\pm$ 86 |
ASCC 77 | 8.162 $\pm$ 0.074 | 1.079 $\pm$ 0.012 | 0.824 $\pm$ 0.040 | 0.124 $\pm$ 0.036 | 480 $\pm$ 96 |
ASCC 85 | 8.267 $\pm$ 0.090 | 0.847 $\pm$ 0.006 | 0.747 $\pm$ 0.026 | 0.056 $\pm$ 0.036 | 383 $\pm$ 76 |
ASCC 9 | 7.265 $\pm$ 0.062 | 2.119 $\pm$ 0.050 | 2.579 $\pm$ 0.031 | 0.106 $\pm$ 0.079 | 2154 $\pm$ 430 |
ASCC 97 | 8.070 $\pm$ 0.167 | 0.561 $\pm$ 0.003 | 1.508 $\pm$ 0.065 | 0.075 $\pm$ 0.080 | 280 $\pm$ 56 |
Alessi 10 | 8.558 $\pm$ 0.093 | 0.434 $\pm$ 0.001 | 0.445 $\pm$ 0.033 | 0.049 $\pm$ 0.021 | 122 $\pm$ 24 |
Alessi 12 | 8.369 $\pm$ 0.114 | 0.534 $\pm$ 0.001 | 0.272 $\pm$ 0.035 | 0.003 $\pm$ 0.019 | 485 $\pm$ 97 |
Alessi 2 | 8.502 $\pm$ 0.034 | 0.602 $\pm$ 0.002 | 0.923 $\pm$ 0.058 | 0.086 $\pm$ 0.022 | 317 $\pm$ 63 |
Alessi 21 | 8.000 $\pm$ 0.001 | 0.557 $\pm$ 0.001 | 0.372 $\pm$ 0.001 | 0.048 $\pm$ 0.001 | 386 $\pm$ 77 |
Alessi 37 | 8.417 $\pm$ 0.127 | 0.698 $\pm$ 0.002 | 0.647 $\pm$ 0.061 | 0.009 $\pm$ 0.044 | 309 $\pm$ 61 |
Alessi 6 | 8.624 $\pm$ 0.093 | 0.859 $\pm$ 0.007 | 1.225 $\pm$ 0.085 | 0.191 $\pm$ 0.044 | 598 $\pm$ 119 |
Alessi 62 | 8.936 $\pm$ 0.014 | 0.607 $\pm$ 0.002 | 0.864 $\pm$ 0.094 | 0.035 $\pm$ 0.059 | 285 $\pm$ 57 |
Alessi 8 | 8.320 $\pm$ 0.067 | 0.650 $\pm$ 0.003 | 0.335 $\pm$ 0.046 | 0.051 $\pm$ 0.054 | 163 $\pm$ 32 |
Alessi Teutsch 11 | 8.253 $\pm$ 0.130 | 0.638 $\pm$ 0.002 | 0.257 $\pm$ 0.047 | 0.024 $\pm$ 0.039 | 217 $\pm$ 43 | 217 $\pm$ 43
Alessi Teutsch 3 | 8.173 $\pm$ 0.170 | 0.684 $\pm$ 0.002 | 0.744 $\pm$ 0.043 | 0.039 $\pm$ 0.020 | 235 $\pm$ 47 | 192 $\pm$ 38
Antalova 2 | 6.760 $\pm$ 0.073 | 1.184 $\pm$ 0.030 | 1.336 $\pm$ 0.118 | 0.019 $\pm$ 0.045 | 161 $\pm$ 32 |
BDSB96 | 6.685 $\pm$ 0.055 | 1.083 $\pm$ 0.017 | 1.130 $\pm$ 0.240 | 0.003 $\pm$ 0.088 | 181 $\pm$ 36 |
BH 164 | 7.769 $\pm$ 0.052 | 0.399 $\pm$ 0.007 | 0.422 $\pm$ 0.050 | 0.003 $\pm$ 0.021 | 432 $\pm$ 86 |
BH 200 | 7.416 $\pm$ 0.065 | 2.038 $\pm$ 0.043 | 2.596 $\pm$ 0.025 | 0.130 $\pm$ 0.028 | 976 $\pm$ 195 |
BH 205 | 6.780 $\pm$ 0.064 | 1.616 $\pm$ 0.031 | 1.445 $\pm$ 0.038 | 0.148 $\pm$ 0.045 | 1643 $\pm$ 328 |
BH 23 | 7.449 $\pm$ 0.423 | 0.432 $\pm$ 0.001 | 0.141 $\pm$ 0.425 | 0.013 $\pm$ 0.034 | 181 $\pm$ 36 |
BH 87 | 7.389 $\pm$ 0.193 | 2.041 $\pm$ 0.084 | 1.942 $\pm$ 0.046 | 0.027 $\pm$ 0.054 | 909 $\pm$ 181 |
BH 90 | 7.696 $\pm$ 0.292 | 2.384 $\pm$ 0.082 | 1.979 $\pm$ 0.097 | 0.010 $\pm$ 0.056 | 594 $\pm$ 118 |
BH 92 | 7.449 $\pm$ 0.195 | 2.301 $\pm$ 0.050 | 1.897 $\pm$ 0.060 | 0.009 $\pm$ 0.036 | 215 $\pm$ 43 |
Basel 11a | 8.036 $\pm$ 0.112 | 1.317 $\pm$ 0.027 | 0.582 $\pm$ 0.047 | 0.126 $\pm$ 0.043 | 242 $\pm$ 48 |
Basel 11b | 8.456 $\pm$ 0.045 | 1.660 $\pm$ 0.028 | 1.918 $\pm$ 0.054 | 0.093 $\pm$ 0.049 | 412 $\pm$ 82 |
Basel 17 | 7.913 $\pm$ 0.051 | 2.118 $\pm$ 0.087 | 0.781 $\pm$ 0.033 | 0.016 $\pm$ 0.064 | 798 $\pm$ 159 |
Basel 18 | 7.381 $\pm$ 0.046 | 1.722 $\pm$ 0.045 | 1.154 $\pm$ 0.047 | 0.094 $\pm$ 0.052 | 362 $\pm$ 72 |
Berkeley 1 | 8.179 $\pm$ 0.475 | 3.541 $\pm$ 0.152 | 2.050 $\pm$ 0.083 | 0.141 $\pm$ 0.045 | 617 $\pm$ 123 |
Berkeley 10 | 8.895 $\pm$ 0.020 | 2.093 $\pm$ 0.053 | 2.649 $\pm$ 0.070 | 0.116 $\pm$ 0.055 | 882 $\pm$ 176 |
Berkeley 11 | 7.794 $\pm$ 0.311 | 2.436 $\pm$ 0.147 | 2.750 $\pm$ 0.040 | 0.150 $\pm$ 0.025 | 514 $\pm$ 102 |
Berkeley 15 | 7.468 $\pm$ 0.288 | 2.140 $\pm$ 0.118 | 2.856 $\pm$ 0.071 | 0.138 $\pm$ 0.029 | 544 $\pm$ 108 |
Berkeley 28 | 8.525 $\pm$ 0.084 | 3.585 $\pm$ 0.239 | 2.122 $\pm$ 0.075 | 0.257 $\pm$ 0.053 | 356 $\pm$ 71 |
Berkeley 30 | 8.642 $\pm$ 0.029 | 4.091 $\pm$ 0.139 | 1.596 $\pm$ 0.027 | 0.199 $\pm$ 0.040 | 909 $\pm$ 181 |
Berkeley 37 | 8.996 $\pm$ 0.018 | 4.396 $\pm$ 0.119 | 0.288 $\pm$ 0.024 | 0.222 $\pm$ 0.034 | 598 $\pm$ 119 |
Berkeley 4 | 7.109 $\pm$ 0.049 | 2.698 $\pm$ 0.162 | 2.331 $\pm$ 0.051 | 0.134 $\pm$ 0.044 | 645 $\pm$ 129 |
Berkeley 47 | 7.131 $\pm$ 0.212 | 2.182 $\pm$ 0.126 | 3.931 $\pm$ 0.047 | 0.175 $\pm$ 0.155 | 624 $\pm$ 124 |
Berkeley 6 | 7.562 $\pm$ 0.318 | 2.448 $\pm$ 0.111 | 2.447 $\pm$ 0.063 | 0.114 $\pm$ 0.029 | 845 $\pm$ 169 |
Berkeley 60 | 8.583 $\pm$ 0.084 | 3.060 $\pm$ 0.106 | 2.647 $\pm$ 0.039 | 0.179 $\pm$ 0.020 | 493 $\pm$ 98 |
Berkeley 61 | 7.926 $\pm$ 0.307 | 2.718 $\pm$ 0.085 | 2.540 $\pm$ 0.031 | 0.115 $\pm$ 0.017 | 364 $\pm$ 72 |
Berkeley 62 | 7.274 $\pm$ 0.038 | 2.629 $\pm$ 0.078 | 2.502 $\pm$ 0.025 | 0.127 $\pm$ 0.042 | 1895 $\pm$ 379 |
Berkeley 69 | 8.987 $\pm$ 0.087 | 2.857 $\pm$ 0.375 | 2.102 $\pm$ 0.116 | 0.212 $\pm$ 0.110 | 508 $\pm$ 101 |
Berkeley 7 | 7.576 $\pm$ 0.040 | 2.433 $\pm$ 0.057 | 2.204 $\pm$ 0.033 | 0.058 $\pm$ 0.039 | 472 $\pm$ 94 |
Berkeley 77 | 8.884 $\pm$ 0.039 | 3.753 $\pm$ 0.113 | 0.565 $\pm$ 0.050 | 0.175 $\pm$ 0.050 | 306 $\pm$ 61 |
Berkeley 8 | 9.527 $\pm$ 0.074 | 3.013 $\pm$ 0.101 | 2.209 $\pm$ 0.100 | 0.175 $\pm$ 0.083 | 1073 $\pm$ 214 |
Berkeley 81 | 8.898 $\pm$ 0.058 | 3.096 $\pm$ 0.188 | 3.150 $\pm$ 0.067 | 0.139 $\pm$ 0.035 | 1972 $\pm$ 394 |
Berkeley 86 | 6.869 $\pm$ 0.082 | 1.637 $\pm$ 0.065 | 2.689 $\pm$ 0.033 | 0.051 $\pm$ 0.063 | 585 $\pm$ 117 |
Berkeley 87 | 6.915 $\pm$ 0.050 | 1.665 $\pm$ 0.051 | 3.971 $\pm$ 0.068 | 0.051 $\pm$ 0.070 | 1779 $\pm$ 355 |
Berkeley 94 | 7.110 $\pm$ 0.103 | 3.742 $\pm$ 0.284 | 1.982 $\pm$ 0.049 | 0.117 $\pm$ 0.077 | 572 $\pm$ 114 |
Berkeley 96 | 7.183 $\pm$ 0.250 | 3.327 $\pm$ 0.376 | 1.878 $\pm$ 0.065 | 0.087 $\pm$ 0.066 | 424 $\pm$ 84 |
Berkeley 97 | 7.176 $\pm$ 0.168 | 2.601 $\pm$ 0.124 | 2.614 $\pm$ 0.042 | 0.095 $\pm$ 0.026 | 514 $\pm$ 102 |
Bica 2 | 6.673 $\pm$ 0.045 | 1.588 $\pm$ 0.039 | 4.486 $\pm$ 0.190 | 0.059 $\pm$ 0.094 | 2150 $\pm$ 430 |
Biurakan 2 | 6.907 $\pm$ 0.029 | 1.727 $\pm$ 0.047 | 1.420 $\pm$ 0.033 | 0.027 $\pm$ 0.061 | 627 $\pm$ 125 |
Blanco 1 | 8.000 $\pm$ 0.001 | 0.234 $\pm$ 0.001 | 0.010 $\pm$ 0.001 | 0.024 $\pm$ 0.001 | 338 $\pm$ 67 |
Bochum 3 | 8.402 $\pm$ 0.266 | 2.165 $\pm$ 0.038 | 0.735 $\pm$ 0.078 | 0.099 $\pm$ 0.033 | 300 $\pm$ 60 |
Bochum 4 | 8.244 $\pm$ 0.224 | 1.263 $\pm$ 0.021 | 0.751 $\pm$ 0.064 | 0.080 $\pm$ 0.049 | 93 $\pm$ 18 |
COINGaia 1 | 8.296 $\pm$ 0.131 | 0.631 $\pm$ 0.004 | 1.671 $\pm$ 0.122 | 0.004 $\pm$ 0.097 | 266 $\pm$ 53 |
COINGaia 10 | 8.168 $\pm$ 0.231 | 0.994 $\pm$ 0.017 | 1.514 $\pm$ 0.172 | 0.082 $\pm$ 0.073 | 200 $\pm$ 40 |
COINGaia 11 | 8.753 $\pm$ 0.078 | 0.638 $\pm$ 0.005 | 1.876 $\pm$ 0.053 | 0.001 $\pm$ 0.053 | 332 $\pm$ 66 | 336 $\pm$ 67
COINGaia 12 | 8.767 $\pm$ 0.041 | 0.923 $\pm$ 0.007 | 0.516 $\pm$ 0.069 | 0.081 $\pm$ 0.039 | 229 $\pm$ 45 |
COINGaia 13 | 8.215 $\pm$ 0.134 | 0.500 $\pm$ 0.001 | 0.393 $\pm$ 0.065 | 0.092 $\pm$ 0.041 | 378 $\pm$ 75 | 367 $\pm$ 73
COINGaia 15 | 7.986 $\pm$ 0.090 | 1.139 $\pm$ 0.017 | 1.628 $\pm$ 0.055 | 0.012 $\pm$ 0.040 | 402 $\pm$ 80 |
COINGaia 17 | 8.125 $\pm$ 0.194 | 1.057 $\pm$ 0.012 | 1.438 $\pm$ 0.060 | 0.142 $\pm$ 0.040 | 264 $\pm$ 52 |
COINGaia 18 | 8.275 $\pm$ 0.101 | 0.987 $\pm$ 0.011 | 1.147 $\pm$ 0.080 | 0.093 $\pm$ 0.045 | 251 $\pm$ 50 |
COINGaia 19 | 8.506 $\pm$ 0.229 | 1.195 $\pm$ 0.016 | 0.956 $\pm$ 0.073 | 0.037 $\pm$ 0.050 | 261 $\pm$ 52 |
COINGaia 20 | 8.254 $\pm$ 0.091 | 1.024 $\pm$ 0.007 | 1.081 $\pm$ 0.081 | 0.128 $\pm$ 0.051 | 220 $\pm$ 44 |
COINGaia 21 | 7.238 $\pm$ 0.048 | 1.340 $\pm$ 0.035 | 1.502 $\pm$ 0.038 | 0.029 $\pm$ 0.053 | 199 $\pm$ 39 |
COINGaia 22 | 8.322 $\pm$ 0.104 | 1.767 $\pm$ 0.042 | 1.284 $\pm$ 0.052 | 0.067 $\pm$ 0.065 | 297 $\pm$ 59 |
COINGaia 23 | 8.329 $\pm$ 0.239 | 0.910 $\pm$ 0.003 | 0.737 $\pm$ 0.057 | 0.068 $\pm$ 0.031 | 245 $\pm$ 49 |
COINGaia 24 | 8.252 $\pm$ 0.154 | 0.953 $\pm$ 0.012 | 1.107 $\pm$ 0.044 | 0.082 $\pm$ 0.029 | 185 $\pm$ 37 |
COINGaia 25 | 8.791 $\pm$ 0.049 | 0.787 $\pm$ 0.005 | 0.660 $\pm$ 0.083 | 0.046 $\pm$ 0.047 | 311 $\pm$ 62 |
COINGaia 26 | 8.148 $\pm$ 0.089 | 1.309 $\pm$ 0.014 | 1.746 $\pm$ 0.026 | 0.025 $\pm$ 0.041 | 352 $\pm$ 70 |
COINGaia 27 | 8.618 $\pm$ 0.219 | 1.057 $\pm$ 0.019 | 1.758 $\pm$ 0.128 | 0.154 $\pm$ 0.072 | 265 $\pm$ 53 |
COINGaia 28 | 7.953 $\pm$ 0.126 | 1.490 $\pm$ 0.030 | 1.071 $\pm$ 0.053 | 0.105 $\pm$ 0.019 | 388 $\pm$ 77 |
COINGaia 3 | 8.022 $\pm$ 0.205 | 1.151 $\pm$ 0.030 | 1.970 $\pm$ 0.126 | 0.251 $\pm$ 0.124 | 350 $\pm$ 70 |
COINGaia 30 | 8.254 $\pm$ 0.095 | 0.712 $\pm$ 0.004 | 1.683 $\pm$ 0.168 | 0.072 $\pm$ 0.076 | 211 $\pm$ 42 |
COINGaia 32 | 8.211 $\pm$ 0.181 | 1.209 $\pm$ 0.018 | 1.674 $\pm$ 0.080 | 0.121 $\pm$ 0.104 | 114 $\pm$ 22 |
COINGaia 34 | 7.877 $\pm$ 0.618 | 0.969 $\pm$ 0.059 | 1.938 $\pm$ 0.207 | 0.029 $\pm$ 0.118 | 79 $\pm$ 15 |
COINGaia 35 | 7.745 $\pm$ 0.513 | 2.423 $\pm$ 0.080 | 2.826 $\pm$ 0.073 | 0.099 $\pm$ 0.046 | 454 $\pm$ 90 |
COINGaia 37 | 8.037 $\pm$ 0.062 | 0.966 $\pm$ 0.012 | 1.962 $\pm$ 0.053 | 0.046 $\pm$ 0.064 | 150 $\pm$ 30 |
COINGaia 7 | 8.031 $\pm$ 0.069 | 1.349 $\pm$ 0.033 | 1.718 $\pm$ 0.126 | 0.002 $\pm$ 0.067 | 254 $\pm$ 50 |
COINGaia 9 | 8.274 $\pm$ 0.195 | 0.848 $\pm$ 0.007 | 1.222 $\pm$ 0.053 | 0.001 $\pm$ 0.042 | 162 $\pm$ 32 |
Collinder 115 | 8.149 $\pm$ 0.109 | 1.852 $\pm$ 0.060 | 1.153 $\pm$ 0.056 | 0.088 $\pm$ 0.055 | 824 $\pm$ 164 |
Collinder 140 | 7.620 $\pm$ 0.042 | 0.378 $\pm$ 0.010 | 0.194 $\pm$ 0.055 | 0.005 $\pm$ 0.028 | 308 $\pm$ 61 |
Collinder 185 | 8.036 $\pm$ 0.061 | 1.442 $\pm$ 0.026 | 0.757 $\pm$ 0.056 | 0.031 $\pm$ 0.052 | 245 $\pm$ 49 |
Collinder 205 | 6.788 $\pm$ 0.050 | 1.650 $\pm$ 0.057 | 2.561 $\pm$ 0.094 | 0.024 $\pm$ 0.070 | 355 $\pm$ 71 |
Collinder 258 | 8.168 $\pm$ 0.028 | 1.210 $\pm$ 0.009 | 0.793 $\pm$ 0.068 | 0.039 $\pm$ 0.030 | 405 $\pm$ 81 |
Collinder 269 | 8.585 $\pm$ 0.057 | 1.617 $\pm$ 0.024 | 0.998 $\pm$ 0.046 | 0.013 $\pm$ 0.070 | 477 $\pm$ 95 |
Collinder 272 | 7.470 $\pm$ 0.044 | 2.038 $\pm$ 0.028 | 1.540 $\pm$ 0.044 | 0.130 $\pm$ 0.038 | 1316 $\pm$ 263 |
Collinder 277 | 8.942 $\pm$ 0.031 | 1.568 $\pm$ 0.027 | 0.952 $\pm$ 0.063 | 0.026 $\pm$ 0.042 | 874 $\pm$ 174 |
Collinder 292 | 7.941 $\pm$ 0.158 | 1.747 $\pm$ 0.023 | 1.574 $\pm$ 0.046 | 0.185 $\pm$ 0.051 | 828 $\pm$ 165 |
Collinder 307 | 8.151 $\pm$ 0.248 | 1.704 $\pm$ 0.033 | 2.588 $\pm$ 0.015 | 0.171 $\pm$ 0.025 | 713 $\pm$ 142 |
Collinder 338 | 8.300 $\pm$ 0.112 | 0.642 $\pm$ 0.001 | 0.713 $\pm$ 0.063 | 0.066 $\pm$ 0.055 | 144 $\pm$ 28 |
Collinder 394 | 8.081 $\pm$ 0.091 | 0.705 $\pm$ 0.002 | 0.888 $\pm$ 0.049 | 0.055 $\pm$ 0.049 | 545 $\pm$ 109 | 560 $\pm$ 112
Collinder 419 | 6.693 $\pm$ 0.049 | 0.989 $\pm$ 0.012 | 1.236 $\pm$ 0.079 | 0.044 $\pm$ 0.080 | 155 $\pm$ 31 |
Collinder 421 | 7.853 $\pm$ 0.341 | 1.148 $\pm$ 0.018 | 2.445 $\pm$ 0.060 | 0.051 $\pm$ 0.075 | 626 $\pm$ 125 |
Collinder 74 | 9.222 $\pm$ 0.185 | 2.261 $\pm$ 0.164 | 1.470 $\pm$ 0.229 | 0.100 $\pm$ 0.052 | 662 $\pm$ 132 |
Collinder 95 | 6.856 $\pm$ 0.106 | 0.649 $\pm$ 0.002 | 0.911 $\pm$ 0.581 | 0.111 $\pm$ 0.058 | 379 $\pm$ 75 |
Czernik 1 | 7.227 $\pm$ 0.173 | 2.693 $\pm$ 0.062 | 2.394 $\pm$ 0.016 | 0.079 $\pm$ 0.044 | 201 $\pm$ 40 |
Czernik 13 | 7.978 $\pm$ 0.168 | 2.820 $\pm$ 0.041 | 2.201 $\pm$ 0.033 | 0.163 $\pm$ 0.027 | 850 $\pm$ 170 |
Czernik 16 | 8.403 $\pm$ 0.072 | 2.291 $\pm$ 0.061 | 2.941 $\pm$ 0.034 | 0.111 $\pm$ 0.050 | 452 $\pm$ 90 |
Czernik 19 | 8.176 $\pm$ 0.101 | 2.117 $\pm$ 0.062 | 2.153 $\pm$ 0.026 | 0.133 $\pm$ 0.035 | 623 $\pm$ 124 |
Czernik 2 | 8.545 $\pm$ 0.184 | 1.759 $\pm$ 0.057 | 1.791 $\pm$ 0.090 | 0.037 $\pm$ 0.067 | 398 $\pm$ 79 |
Czernik 23 | 8.481 $\pm$ 0.031 | 3.226 $\pm$ 0.085 | 1.794 $\pm$ 0.024 | 0.192 $\pm$ 0.029 | 565 $\pm$ 113 |
Czernik 27 | 9.103 $\pm$ 0.026 | 4.062 $\pm$ 0.127 | 0.387 $\pm$ 0.042 | 0.162 $\pm$ 0.036 | 595 $\pm$ 119 |
Czernik 31 | 7.471 $\pm$ 0.353 | 2.783 $\pm$ 0.065 | 1.718 $\pm$ 0.036 | 0.150 $\pm$ 0.035 | 576 $\pm$ 115 |
Czernik 43 | 7.939 $\pm$ 0.344 | 2.276 $\pm$ 0.062 | 2.054 $\pm$ 0.071 | 0.094 $\pm$ 0.072 | 502 $\pm$ 100 |
Czernik 5 | 8.350 $\pm$ 0.169 | 3.207 $\pm$ 0.111 | 3.177 $\pm$ 0.050 | 0.174 $\pm$ 0.037 | 919 $\pm$ 183 |
Czernik 6 | 7.363 $\pm$ 0.514 | 2.430 $\pm$ 0.242 | 1.576 $\pm$ 0.105 | 0.099 $\pm$ 0.129 | 238 $\pm$ 47 |
Czernik 8 | 7.732 $\pm$ 0.185 | 2.534 $\pm$ 0.143 | 2.993 $\pm$ 0.073 | 0.112 $\pm$ 0.067 | 438 $\pm$ 87 |
Czernik 9 | 8.540 $\pm$ 0.313 | 2.512 $\pm$ 0.124 | 3.278 $\pm$ 0.087 | 0.146 $\pm$ 0.056 | 489 $\pm$ 97 |
DBSB 7 | 7.387 $\pm$ 0.032 | 2.153 $\pm$ 0.100 | 2.063 $\pm$ 0.103 | 0.098 $\pm$ 0.055 | 1235 $\pm$ 247 |
Dias 5 | 6.715 $\pm$ 0.153 | 1.264 $\pm$ 0.018 | 1.537 $\pm$ 0.528 | 0.064 $\pm$ 0.056 | 517 $\pm$ 103 |
Dolidze 3 | 6.999 $\pm$ 0.072 | 1.894 $\pm$ 0.037 | 2.266 $\pm$ 0.032 | 0.009 $\pm$ 0.091 | 436 $\pm$ 87 |
Dolidze 5 | 7.348 $\pm$ 0.255 | 1.984 $\pm$ 0.079 | 2.669 $\pm$ 0.047 | 0.074 $\pm$ 0.074 | 964 $\pm$ 192 |
ESO 130 06 | 8.237 $\pm$ 0.181 | 0.795 $\pm$ 0.002 | 0.514 $\pm$ 0.087 | 0.014 $\pm$ 0.074 | 164 $\pm$ 32 |
ESO 130 08 | 8.179 $\pm$ 0.141 | 1.295 $\pm$ 0.008 | 1.240 $\pm$ 0.044 | 0.018 $\pm$ 0.031 | 460 $\pm$ 92 |
ESO 130 13 | 7.722 $\pm$ 0.139 | 2.202 $\pm$ 0.058 | 1.619 $\pm$ 0.018 | 0.068 $\pm$ 0.067 | 607 $\pm$ 121 |
ESO 166 04 | 8.275 $\pm$ 0.115 | 1.074 $\pm$ 0.016 | 0.690 $\pm$ 0.074 | 0.120 $\pm$ 0.076 | 107 $\pm$ 21 |
ESO 332 13 | 6.796 $\pm$ 0.059 | 1.562 $\pm$ 0.046 | 1.420 $\pm$ 0.042 | 0.152 $\pm$ 0.071 | 549 $\pm$ 109 |
ESO 368 11 | 8.683 $\pm$ 0.276 | 1.991 $\pm$ 0.056 | 1.769 $\pm$ 0.111 | 0.006 $\pm$ 0.029 | 511 $\pm$ 102 |
FSR 0198 | 6.860 $\pm$ 0.085 | 1.843 $\pm$ 0.080 | 2.901 $\pm$ 0.172 | 0.103 $\pm$ 0.135 | 545 $\pm$ 109 |
FSR 0224 | 6.722 $\pm$ 0.049 | 1.653 $\pm$ 0.037 | 3.284 $\pm$ 0.069 | 0.040 $\pm$ 0.091 | 177 $\pm$ 35 |
FSR 0236 | 6.904 $\pm$ 0.081 | 1.551 $\pm$ 0.052 | 3.813 $\pm$ 0.154 | 0.134 $\pm$ 0.072 | 659 $\pm$ 131 |
FSR 0241 | 9.080 $\pm$ 0.022 | 2.060 $\pm$ 0.071 | 1.320 $\pm$ 0.050 | 0.031 $\pm$ 0.035 | 551 $\pm$ 110 |
FSR 0278 | 9.403 $\pm$ 0.034 | 1.665 $\pm$ 0.024 | 0.857 $\pm$ 0.073 | 0.017 $\pm$ 0.029 | 542 $\pm$ 108 |
FSR 0342 | 8.981 $\pm$ 0.062 | 2.468 $\pm$ 0.142 | 1.666 $\pm$ 0.083 | 0.074 $\pm$ 0.060 | 1503 $\pm$ 300 |
FSR 0357 | 7.430 $\pm$ 0.265 | 4.150 $\pm$ 0.174 | 1.752 $\pm$ 0.051 | 0.140 $\pm$ 0.039 | 375 $\pm$ 75 |
FSR 0384 | 8.520 $\pm$ 0.116 | 1.847 $\pm$ 0.024 | 1.272 $\pm$ 0.054 | 0.002 $\pm$ 0.023 | 136 $\pm$ 27 |
FSR 0385 | 8.789 $\pm$ 0.059 | 2.004 $\pm$ 0.091 | 2.603 $\pm$ 0.035 | 0.028 $\pm$ 0.083 | 304 $\pm$ 60 |
FSR 0398 | 7.244 $\pm$ 0.082 | 0.913 $\pm$ 0.014 | 2.071 $\pm$ 0.035 | 0.048 $\pm$ 0.127 | 155 $\pm$ 31 |
FSR 0430 | 8.243 $\pm$ 0.215 | 2.460 $\pm$ 0.144 | 3.027 $\pm$ 0.056 | 0.077 $\pm$ 0.047 | 467 $\pm$ 93 |
FSR 0441 | 7.779 $\pm$ 0.367 | 3.093 $\pm$ 0.150 | 2.397 $\pm$ 0.059 | 0.094 $\pm$ 0.069 | 379 $\pm$ 75 |
FSR 0448 | 8.869 $\pm$ 0.269 | 2.687 $\pm$ 0.122 | 3.102 $\pm$ 0.101 | 0.071 $\pm$ 0.041 | 519 $\pm$ 103 |
FSR 0496 | 8.868 $\pm$ 0.082 | 1.377 $\pm$ 0.043 | 3.066 $\pm$ 0.087 | 0.020 $\pm$ 0.101 | 661 $\pm$ 132 |
FSR 0498 | 7.562 $\pm$ 0.138 | 2.459 $\pm$ 0.080 | 1.448 $\pm$ 0.047 | 0.034 $\pm$ 0.038 | 329 $\pm$ 65 |
FSR 0537 | 7.661 $\pm$ 0.057 | 2.838 $\pm$ 0.067 | 1.754 $\pm$ 0.039 | 0.118 $\pm$ 0.022 | 335 $\pm$ 67 |
FSR 0551 | 7.035 $\pm$ 0.019 | 0.892 $\pm$ 0.014 | 1.688 $\pm$ 0.056 | 0.061 $\pm$ 0.017 | 95 $\pm$ 19 |
FSR 0553 | 8.885 $\pm$ 0.299 | 2.350 $\pm$ 0.185 | 2.014 $\pm$ 0.072 | 0.063 $\pm$ 0.104 | 122 $\pm$ 24 |
FSR 0591 | 7.239 $\pm$ 0.093 | 2.354 $\pm$ 0.125 | 2.201 $\pm$ 0.079 | 0.115 $\pm$ 0.059 | 403 $\pm$ 80 |
FSR 0667 | 8.615 $\pm$ 0.087 | 1.097 $\pm$ 0.015 | 1.685 $\pm$ 0.086 | 0.111 $\pm$ 0.065 | 115 $\pm$ 23 |
FSR 0716 | 9.087 $\pm$ 0.036 | 3.361 $\pm$ 0.159 | 1.154 $\pm$ 0.071 | 0.262 $\pm$ 0.023 | 513 $\pm$ 102 |
FSR 0728 | 8.059 $\pm$ 0.189 | 1.535 $\pm$ 0.033 | 2.137 $\pm$ 0.099 | 0.040 $\pm$ 0.033 | 321 $\pm$ 64 |
FSR 0735 | 8.670 $\pm$ 0.450 | 2.568 $\pm$ 0.109 | 1.638 $\pm$ 0.133 | 0.175 $\pm$ 0.034 | 392 $\pm$ 78 |
FSR 0761 | 8.746 $\pm$ 0.155 | 2.442 $\pm$ 0.122 | 1.420 $\pm$ 0.247 | 0.119 $\pm$ 0.119 | 188 $\pm$ 37 |
FSR 0771 | 8.498 $\pm$ 0.023 | 1.462 $\pm$ 0.044 | 2.179 $\pm$ 0.072 | 0.016 $\pm$ 0.067 | 222 $\pm$ 44 |
FSR 0811 | 8.890 $\pm$ 0.068 | 2.470 $\pm$ 0.069 | 0.904 $\pm$ 0.119 | 0.131 $\pm$ 0.031 | 239 $\pm$ 47 |
FSR 0850 | 8.576 $\pm$ 0.217 | 1.889 $\pm$ 0.101 | 1.714 $\pm$ 0.105 | 0.099 $\pm$ 0.041 | 513 $\pm$ 102 |
FSR 0883 | 8.283 $\pm$ 0.320 | 2.446 $\pm$ 0.084 | 2.123 $\pm$ 0.141 | 0.111 $\pm$ 0.059 | 301 $\pm$ 60 |
FSR 0893 | 8.588 $\pm$ 0.070 | 1.957 $\pm$ 0.105 | 2.918 $\pm$ 0.106 | 0.125 $\pm$ 0.047 | 973 $\pm$ 194 |
FSR 0904 | 7.176 $\pm$ 0.030 | 2.045 $\pm$ 0.042 | 2.197 $\pm$ 0.035 | 0.096 $\pm$ 0.034 | 900 $\pm$ 180 |
FSR 0905 | 8.778 $\pm$ 0.060 | 1.410 $\pm$ 0.041 | 0.526 $\pm$ 0.071 | 0.086 $\pm$ 0.056 | 145 $\pm$ 29 |
FSR 0935 | 8.796 $\pm$ 0.082 | 2.262 $\pm$ 0.107 | 1.335 $\pm$ 0.098 | 0.117 $\pm$ 0.045 | 317 $\pm$ 63 |
FSR 0948 | 8.651 $\pm$ 0.102 | 3.630 $\pm$ 0.146 | 1.735 $\pm$ 0.157 | 0.205 $\pm$ 0.072 | 351 $\pm$ 70 |
FSR 0951 | 8.792 $\pm$ 0.262 | 1.585 $\pm$ 0.040 | 1.210 $\pm$ 0.091 | 0.110 $\pm$ 0.025 | 916 $\pm$ 183 |
FSR 0968 | 7.653 $\pm$ 0.122 | 2.245 $\pm$ 0.049 | 1.543 $\pm$ 0.038 | 0.157 $\pm$ 0.042 | 214 $\pm$ 42 |
FSR 0974 | 7.334 $\pm$ 0.559 | 2.612 $\pm$ 0.245 | 1.828 $\pm$ 0.172 | 0.175 $\pm$ 0.033 | 630 $\pm$ 126 |
FSR 0977 | 8.930 $\pm$ 0.198 | 1.781 $\pm$ 0.117 | 1.595 $\pm$ 0.198 | 0.147 $\pm$ 0.060 | 200 $\pm$ 40 |
FSR 0985 | 8.592 $\pm$ 0.254 | 1.950 $\pm$ 0.028 | 1.461 $\pm$ 0.080 | 0.122 $\pm$ 0.019 | 245 $\pm$ 49 |
FSR 1085 | 8.183 $\pm$ 0.138 | 1.526 $\pm$ 0.025 | 0.867 $\pm$ 0.058 | 0.147 $\pm$ 0.031 | 208 $\pm$ 41 |
FSR 1144 | 8.255 $\pm$ 0.182 | 1.786 $\pm$ 0.033 | 0.880 $\pm$ 0.047 | 0.095 $\pm$ 0.027 | 308 $\pm$ 61 |
FSR 1150 | 8.798 $\pm$ 0.107 | 3.091 $\pm$ 0.159 | 1.627 $\pm$ 0.063 | 0.114 $\pm$ 0.080 | 368 $\pm$ 73 |
FSR 1163 | 8.991 $\pm$ 0.049 | 2.263 $\pm$ 0.088 | 1.617 $\pm$ 0.091 | 0.115 $\pm$ 0.029 | 613 $\pm$ 122 |
FSR 1180 | 8.713 $\pm$ 0.236 | 2.552 $\pm$ 0.069 | 1.595 $\pm$ 0.096 | 0.115 $\pm$ 0.016 | 758 $\pm$ 151 |
FSR 1211 | 9.105 $\pm$ 0.723 | 3.074 $\pm$ 0.486 | 0.033 $\pm$ 0.003 | 0.027 $\pm$ 0.188 | 381 $\pm$ 76 |
FSR 1252 | 8.998 $\pm$ 0.034 | 2.884 $\pm$ 0.131 | 1.159 $\pm$ 0.054 | 0.165 $\pm$ 0.056 | 554 $\pm$ 110 |
FSR 1253 | 8.492 $\pm$ 0.102 | 3.644 $\pm$ 0.179 | 2.192 $\pm$ 0.067 | 0.183 $\pm$ 0.060 | 968 $\pm$ 193 |
FSR 1284 | 8.882 $\pm$ 0.051 | 2.316 $\pm$ 0.068 | 1.053 $\pm$ 0.082 | 0.045 $\pm$ 0.069 | 195 $\pm$ 39 |
FSR 1342 | 7.142 $\pm$ 0.066 | 3.363 $\pm$ 0.230 | 2.697 $\pm$ 0.099 | 0.148 $\pm$ 0.040 | 1021 $\pm$ 204 |
FSR 1360 | 8.032 $\pm$ 0.109 | 2.244 $\pm$ 0.058 | 1.552 $\pm$ 0.036 | 0.044 $\pm$ 0.031 | 409 $\pm$ 81 |
FSR 1361 | 8.740 $\pm$ 0.054 | 2.190 $\pm$ 0.110 | 2.051 $\pm$ 0.115 | 0.093 $\pm$ 0.054 | 1067 $\pm$ 213 |
FSR 1363 | 7.946 $\pm$ 0.190 | 3.237 $\pm$ 0.084 | 1.318 $\pm$ 0.061 | 0.105 $\pm$ 0.053 | 278 $\pm$ 55 |
FSR 1399 | 8.771 $\pm$ 0.207 | 2.556 $\pm$ 0.315 | 3.125 $\pm$ 0.100 | 0.017 $\pm$ 0.074 | 351 $\pm$ 70 |
FSR 1443 | 8.623 $\pm$ 0.423 | 3.003 $\pm$ 0.286 | 1.805 $\pm$ 0.262 | 0.120 $\pm$ 0.059 | 192 $\pm$ 38 |
FSR 1484 | 8.418 $\pm$ 0.206 | 2.074 $\pm$ 0.075 | 2.827 $\pm$ 0.096 | 0.052 $\pm$ 0.040 | 263 $\pm$ 52 |
FSR 1723 | 8.119 $\pm$ 0.068 | 1.484 $\pm$ 0.029 | 1.583 $\pm$ 0.032 | 0.075 $\pm$ 0.021 | 412 $\pm$ 82 |
Gulliver 1 | 9.122 $\pm$ 0.038 | 2.585 $\pm$ 0.077 | 0.911 $\pm$ 0.077 | 0.033 $\pm$ 0.049 | 885 $\pm$ 177 |
Gulliver 11 | 8.341 $\pm$ 0.296 | 0.898 $\pm$ 0.005 | 1.349 $\pm$ 0.066 | 0.001 $\pm$ 0.065 | 106 $\pm$ 21 |
Gulliver 12 | 8.221 $\pm$ 0.168 | 1.701 $\pm$ 0.045 | 1.006 $\pm$ 0.081 | 0.012 $\pm$ 0.036 | 142 $\pm$ 28 |
Gulliver 13 | 8.815 $\pm$ 0.310 | 1.472 $\pm$ 0.024 | 1.579 $\pm$ 0.101 | 0.115 $\pm$ 0.068 | 351 $\pm$ 70 |
Gulliver 14 | 8.672 $\pm$ 0.079 | 1.187 $\pm$ 0.068 | 1.874 $\pm$ 0.124 | 0.201 $\pm$ 0.061 | 170 $\pm$ 34 |
Gulliver 17 | 8.019 $\pm$ 0.083 | 1.664 $\pm$ 0.027 | 1.255 $\pm$ 0.033 | 0.137 $\pm$ 0.047 | 511 $\pm$ 102 |
Gulliver 18 | 8.063 $\pm$ 0.015 | 1.515 $\pm$ 0.022 | 2.074 $\pm$ 0.061 | 0.106 $\pm$ 0.054 | 888 $\pm$ 177 |
Gulliver 20 | 8.853 $\pm$ 0.085 | 0.415 $\pm$ 0.008 | 0.297 $\pm$ 0.041 | 0.025 $\pm$ 0.036 | 136 $\pm$ 27 |
Gulliver 21 | 8.177 $\pm$ 0.177 | 0.638 $\pm$ 0.001 | 0.046 $\pm$ 0.016 | 0.111 $\pm$ 0.156 | 281 $\pm$ 56 |
Gulliver 24 | 8.266 $\pm$ 0.191 | 1.415 $\pm$ 0.016 | 1.515 $\pm$ 0.078 | 0.005 $\pm$ 0.056 | 218 $\pm$ 43 |
Gulliver 25 | 8.472 $\pm$ 0.204 | 1.292 $\pm$ 0.017 | 1.072 $\pm$ 0.083 | 0.110 $\pm$ 0.055 | 258 $\pm$ 51 |
Gulliver 26 | 8.670 $\pm$ 0.187 | 2.444 $\pm$ 0.155 | 2.116 $\pm$ 0.070 | 0.123 $\pm$ 0.101 | 357 $\pm$ 71 |
Gulliver 27 | 8.200 $\pm$ 0.196 | 2.537 $\pm$ 0.094 | 1.794 $\pm$ 0.090 | 0.008 $\pm$ 0.038 | 555 $\pm$ 111 |
Gulliver 28 | 9.001 $\pm$ 0.469 | 0.502 $\pm$ 0.127 | 1.297 $\pm$ 0.463 | 0.229 $\pm$ 0.051 | 180 $\pm$ 36 |
Gulliver 31 | 8.249 $\pm$ 0.115 | 2.129 $\pm$ 0.059 | 1.556 $\pm$ 0.035 | 0.112 $\pm$ 0.060 | 371 $\pm$ 74 |
Gulliver 32 | 8.737 $\pm$ 0.536 | 1.627 $\pm$ 0.068 | 1.553 $\pm$ 0.280 | 0.164 $\pm$ 0.084 | 181 $\pm$ 36 |
Gulliver 35 | 8.091 $\pm$ 0.223 | 2.025 $\pm$ 0.051 | 1.342 $\pm$ 0.064 | 0.058 $\pm$ 0.061 | 281 $\pm$ 56 |
Gulliver 36 | 8.849 $\pm$ 0.141 | 1.278 $\pm$ 0.018 | 0.969 $\pm$ 0.129 | 0.080 $\pm$ 0.063 | 260 $\pm$ 52 |
Gulliver 37 | 8.261 $\pm$ 0.161 | 1.479 $\pm$ 0.032 | 1.893 $\pm$ 0.062 | 0.036 $\pm$ 0.106 | 306 $\pm$ 61 |
Gulliver 39 | 8.852 $\pm$ 0.177 | 2.465 $\pm$ 0.119 | 1.769 $\pm$ 0.123 | 0.048 $\pm$ 0.060 | 373 $\pm$ 74 |
Gulliver 40 | 7.901 $\pm$ 0.204 | 1.524 $\pm$ 0.021 | 0.671 $\pm$ 0.102 | 0.151 $\pm$ 0.071 | 131 $\pm$ 26 |
Gulliver 44 | 8.788 $\pm$ 0.096 | 1.178 $\pm$ 0.017 | 1.471 $\pm$ 0.096 | 0.031 $\pm$ 0.070 | 379 $\pm$ 75 |
Gulliver 47 | 8.621 $\pm$ 0.039 | 1.847 $\pm$ 0.045 | 0.448 $\pm$ 0.051 | 0.116 $\pm$ 0.032 | 466 $\pm$ 93 |
Gulliver 5 | 7.083 $\pm$ 0.051 | 2.054 $\pm$ 0.094 | 2.117 $\pm$ 0.068 | 0.075 $\pm$ 0.062 | 394 $\pm$ 78 |
Gulliver 50 | 8.023 $\pm$ 0.151 | 1.657 $\pm$ 0.029 | 1.081 $\pm$ 0.033 | 0.054 $\pm$ 0.051 | 421 $\pm$ 84 |
Gulliver 56 | 8.520 $\pm$ 0.140 | 1.956 $\pm$ 0.055 | 0.899 $\pm$ 0.086 | 0.084 $\pm$ 0.033 | 269 $\pm$ 53 |
Gulliver 59 | 8.019 $\pm$ 0.349 | 1.944 $\pm$ 0.094 | 1.550 $\pm$ 0.145 | 0.079 $\pm$ 0.041 | 411 $\pm$ 82 |
Gulliver 6 | 7.124 $\pm$ 0.014 | 0.408 $\pm$ 0.001 | 0.485 $\pm$ 0.088 | 0.034 $\pm$ 0.024 | 365 $\pm$ 73 |
Gulliver 60 | 7.992 $\pm$ 0.179 | 1.047 $\pm$ 0.012 | 1.360 $\pm$ 0.066 | 0.184 $\pm$ 0.059 | 347 $\pm$ 69 |
Gulliver 8 | 7.437 $\pm$ 0.076 | 1.037 $\pm$ 0.020 | 1.049 $\pm$ 0.077 | 0.022 $\pm$ 0.085 | 156 $\pm$ 31 |
Haffner 13 | 7.541 $\pm$ 0.026 | 0.551 $\pm$ 0.001 | 0.247 $\pm$ 0.029 | 0.057 $\pm$ 0.032 | 393 $\pm$ 78 |
Haffner 16 | 8.324 $\pm$ 0.331 | 2.786 $\pm$ 0.072 | 0.388 $\pm$ 0.033 | 0.058 $\pm$ 0.054 | 511 $\pm$ 102 |
Haffner 20 | 8.271 $\pm$ 0.275 | 3.542 $\pm$ 0.107 | 2.224 $\pm$ 0.057 | 0.174 $\pm$ 0.043 | 377 $\pm$ 75 |
Haffner 21 | 8.804 $\pm$ 0.055 | 2.683 $\pm$ 0.072 | 0.366 $\pm$ 0.028 | 0.020 $\pm$ 0.047 | 270 $\pm$ 54 |
Haffner 23 | 8.695 $\pm$ 0.097 | 1.965 $\pm$ 0.051 | 0.839 $\pm$ 0.081 | 0.021 $\pm$ 0.038 | 561 $\pm$ 112 |
Haffner 26 | 8.820 $\pm$ 0.036 | 2.635 $\pm$ 0.058 | 0.620 $\pm$ 0.057 | 0.055 $\pm$ 0.055 | 602 $\pm$ 120 |
Haffner 3 | 8.722 $\pm$ 0.098 | 2.332 $\pm$ 0.041 | 1.329 $\pm$ 0.075 | 0.142 $\pm$ 0.028 | 275 $\pm$ 55 |
Haffner 4 | 8.865 $\pm$ 0.428 | 4.203 $\pm$ 0.258 | 1.489 $\pm$ 0.184 | 0.237 $\pm$ 0.038 | 1119 $\pm$ 223 |
Haffner 6 | 8.633 $\pm$ 0.120 | 4.106 $\pm$ 0.188 | 2.079 $\pm$ 0.079 | 0.219 $\pm$ 0.026 | 1745 $\pm$ 349 |
Haffner 7 | 8.838 $\pm$ 0.035 | 4.016 $\pm$ 0.119 | 0.811 $\pm$ 0.052 | 0.106 $\pm$ 0.063 | 422 $\pm$ 84 |
Haffner 8 | 8.532 $\pm$ 0.164 | 2.496 $\pm$ 0.049 | 1.290 $\pm$ 0.061 | 0.116 $\pm$ 0.060 | 633 $\pm$ 126 |
Haffner 9 | 7.970 $\pm$ 0.267 | 2.647 $\pm$ 0.105 | 2.215 $\pm$ 0.056 | 0.145 $\pm$ 0.029 | 582 $\pm$ 116 |
Harvard 10 | 8.267 $\pm$ 0.099 | 0.671 $\pm$ 0.004 | 0.586 $\pm$ 0.049 | 0.024 $\pm$ 0.029 | 425 $\pm$ 85 | 422 $\pm$ 84
Harvard 20 | 8.027 $\pm$ 0.099 | 2.234 $\pm$ 0.071 | 0.936 $\pm$ 0.059 | 0.002 $\pm$ 0.063 | 483 $\pm$ 96 |
Hogg 16 | 7.415 $\pm$ 0.056 | 1.996 $\pm$ 0.041 | 1.486 $\pm$ 0.041 | 0.119 $\pm$ 0.051 | 232 $\pm$ 46 |
Hogg 22 | 6.945 $\pm$ 0.071 | 2.416 $\pm$ 0.102 | 2.169 $\pm$ 0.018 | 0.064 $\pm$ 0.073 | 444 $\pm$ 88 |
Hogg 4 | 8.999 $\pm$ 0.038 | 3.484 $\pm$ 0.164 | 1.917 $\pm$ 0.065 | 0.046 $\pm$ 0.065 | 2165 $\pm$ 433 |
IC 1369 | 8.490 $\pm$ 0.229 | 2.870 $\pm$ 0.099 | 2.563 $\pm$ 0.058 | 0.009 $\pm$ 0.030 | 1262 $\pm$ 252 |
IC 1434 | 8.118 $\pm$ 0.266 | 3.016 $\pm$ 0.128 | 1.454 $\pm$ 0.045 | 0.047 $\pm$ 0.066 | 1432 $\pm$ 286 |
IC 1442 | 7.465 $\pm$ 0.087 | 2.808 $\pm$ 0.112 | 1.547 $\pm$ 0.050 | 0.082 $\pm$ 0.052 | 1473 $\pm$ 294 |
IC 1590 | 6.871 $\pm$ 0.139 | 2.532 $\pm$ 0.188 | 1.315 $\pm$ 0.088 | 0.128 $\pm$ 0.073 | 651 $\pm$ 130 |
IC 2157 | 7.738 $\pm$ 0.282 | 1.877 $\pm$ 0.049 | 1.587 $\pm$ 0.048 | 0.037 $\pm$ 0.055 | 189 $\pm$ 37 |
IC 2391 | 7.761 $\pm$ 0.021 | 0.149 $\pm$ 0.001 | 0.088 $\pm$ 0.032 | 0.124 $\pm$ 0.040 | 215 $\pm$ 43 |
IC 2395 | 7.122 $\pm$ 0.023 | 0.693 $\pm$ 0.004 | 0.474 $\pm$ 0.044 | 0.034 $\pm$ 0.039 | 484 $\pm$ 96 | 482 $\pm$ 96
IC 2488 | 8.184 $\pm$ 0.036 | 1.287 $\pm$ 0.012 | 0.979 $\pm$ 0.024 | 0.019 $\pm$ 0.025 | 1190 $\pm$ 238 | 1234 $\pm$ 246
IC 2581 | 7.135 $\pm$ 0.079 | 2.421 $\pm$ 0.114 | 1.435 $\pm$ 0.022 | 0.041 $\pm$ 0.071 | 834 $\pm$ 166 |
IC 2602 | 7.700 $\pm$ 0.043 | 0.149 $\pm$ 0.001 | 0.104 $\pm$ 0.064 | 0.121 $\pm$ 0.060 | 264 $\pm$ 52 |
IC 2948 | 6.814 $\pm$ 0.063 | 2.242 $\pm$ 0.081 | 1.351 $\pm$ 0.023 | 0.007 $\pm$ 0.084 | 1025 $\pm$ 205 |
IC 361 | 9.014 $\pm$ 0.034 | 3.385 $\pm$ 0.113 | 2.374 $\pm$ 0.044 | 0.229 $\pm$ 0.041 | 2459 $\pm$ 491 |
IC 4665 | 8.309 $\pm$ 0.270 | 0.310 $\pm$ 0.013 | 0.510 $\pm$ 0.148 | 0.112 $\pm$ 0.066 | 308 $\pm$ 61 |
IC 4996 | 7.027 $\pm$ 0.023 | 1.912 $\pm$ 0.080 | 1.863 $\pm$ 0.049 | 0.076 $\pm$ 0.065 | 500 $\pm$ 100 |
Juchert 20 | 8.005 $\pm$ 0.619 | 2.603 $\pm$ 0.078 | 2.410 $\pm$ 0.163 | 0.188 $\pm$ 0.047 | 707 $\pm$ 141 |
Kharchenko 1 | 8.671 $\pm$ 0.077 | 2.407 $\pm$ 0.093 | 1.549 $\pm$ 0.114 | 0.186 $\pm$ 0.041 | 348 $\pm$ 69 |
King 12 | 7.259 $\pm$ 0.097 | 2.491 $\pm$ 0.099 | 1.837 $\pm$ 0.053 | 0.099 $\pm$ 0.059 | 300 $\pm$ 60 |
King 13 | 8.760 $\pm$ 0.045 | 3.230 $\pm$ 0.107 | 2.194 $\pm$ 0.051 | 0.155 $\pm$ 0.030 | 1577 $\pm$ 315 |
King 14 | 7.470 $\pm$ 0.110 | 2.232 $\pm$ 0.086 | 1.681 $\pm$ 0.040 | 0.019 $\pm$ 0.042 | 870 $\pm$ 174 |
King 15 | 8.006 $\pm$ 0.537 | 2.730 $\pm$ 0.079 | 2.063 $\pm$ 0.082 | 0.109 $\pm$ 0.039 | 452 $\pm$ 90 |
King 16 | 7.378 $\pm$ 0.322 | 2.506 $\pm$ 0.046 | 2.528 $\pm$ 0.049 | 0.063 $\pm$ 0.055 | 633 $\pm$ 126 |
King 17 | 7.559 $\pm$ 0.450 | 3.318 $\pm$ 0.075 | 1.876 $\pm$ 0.096 | 0.263 $\pm$ 0.034 | 281 $\pm$ 56 |
King 18 | 8.404 $\pm$ 0.049 | 2.501 $\pm$ 0.079 | 2.096 $\pm$ 0.063 | 0.090 $\pm$ 0.027 | 718 $\pm$ 143 |
King 19 | 8.775 $\pm$ 0.042 | 2.487 $\pm$ 0.081 | 2.438 $\pm$ 0.062 | 0.005 $\pm$ 0.046 | 676 $\pm$ 135 |
King 20 | 7.623 $\pm$ 0.128 | 1.709 $\pm$ 0.030 | 2.589 $\pm$ 0.037 | 0.113 $\pm$ 0.078 | 471 $\pm$ 94 |
King 21 | 7.196 $\pm$ 0.107 | 2.811 $\pm$ 0.147 | 2.597 $\pm$ 0.034 | 0.114 $\pm$ 0.050 | 1078 $\pm$ 215 |
King 4 | 7.923 $\pm$ 0.347 | 2.203 $\pm$ 0.062 | 2.535 $\pm$ 0.051 | 0.112 $\pm$ 0.044 | 888 $\pm$ 177 |
King 5 | 8.961 $\pm$ 0.038 | 2.186 $\pm$ 0.114 | 2.586 $\pm$ 0.046 | 0.129 $\pm$ 0.030 | 1275 $\pm$ 255 |
King 6 | 8.072 $\pm$ 0.193 | 0.702 $\pm$ 0.001 | 1.909 $\pm$ 0.062 | 0.041 $\pm$ 0.060 | 497 $\pm$ 99 |
Koposov 10 | 8.279 $\pm$ 0.348 | 2.377 $\pm$ 0.120 | 2.505 $\pm$ 0.099 | 0.192 $\pm$ 0.036 | 457 $\pm$ 91 |
Koposov 12 | 8.651 $\pm$ 0.122 | 2.105 $\pm$ 0.066 | 1.852 $\pm$ 0.062 | 0.101 $\pm$ 0.030 | 851 $\pm$ 170 |
Koposov 36 | 7.623 $\pm$ 0.417 | 1.640 $\pm$ 0.060 | 2.577 $\pm$ 0.236 | 0.112 $\pm$ 0.062 | 537 $\pm$ 107 |
Koposov 43 | 9.040 $\pm$ 0.042 | 4.658 $\pm$ 0.284 | 2.047 $\pm$ 0.097 | 0.307 $\pm$ 0.079 | 948 $\pm$ 189 |
Kronberger 4 | 8.908 $\pm$ 0.072 | 6.866 $\pm$ 0.742 | 2.575 $\pm$ 0.103 | 0.072 $\pm$ 0.086 | 750 $\pm$ 150 |
LP 0201 | 7.313 $\pm$ 0.114 | 3.408 $\pm$ 0.196 | 2.320 $\pm$ 0.039 | 0.142 $\pm$ 0.051 | 656 $\pm$ 131 |
LP 0665 | 9.056 $\pm$ 0.054 | 3.331 $\pm$ 0.163 | 1.333 $\pm$ 0.100 | 0.068 $\pm$ 0.058 | 573 $\pm$ 114 |
LP 0733 | 7.523 $\pm$ 0.031 | 2.613 $\pm$ 0.082 | 1.108 $\pm$ 0.021 | 0.149 $\pm$ 0.039 | 936 $\pm$ 187 |
LP 0782 | 8.256 $\pm$ 0.177 | 3.152 $\pm$ 0.111 | 1.882 $\pm$ 0.111 | 0.001 $\pm$ 0.037 | 346 $\pm$ 69 |
LP 1406 | 8.646 $\pm$ 0.314 | 2.597 $\pm$ 0.155 | 1.535 $\pm$ 0.130 | 0.172 $\pm$ 0.047 | 270 $\pm$ 54 |
LP 1540 | 9.161 $\pm$ 0.026 | 2.454 $\pm$ 0.076 | 0.814 $\pm$ 0.064 | 0.008 $\pm$ 0.039 | 934 $\pm$ 186 |
LP 1614 | 7.804 $\pm$ 0.337 | 2.121 $\pm$ 0.073 | 3.276 $\pm$ 0.066 | 0.152 $\pm$ 0.036 | 818 $\pm$ 163 |
LP 1800 | 8.277 $\pm$ 0.112 | 1.329 $\pm$ 0.030 | 1.761 $\pm$ 0.065 | 0.038 $\pm$ 0.039 | 1017 $\pm$ 203 |
LP 1809 | 8.338 $\pm$ 0.292 | 2.596 $\pm$ 0.148 | 2.857 $\pm$ 0.078 | 0.016 $\pm$ 0.055 | 487 $\pm$ 97 |
LP 198 | 8.441 $\pm$ 0.275 | 2.840 $\pm$ 0.065 | 1.177 $\pm$ 0.060 | 0.127 $\pm$ 0.038 | 916 $\pm$ 183 |
LP 1994 | 8.824 $\pm$ 0.039 | 1.812 $\pm$ 0.040 | 1.461 $\pm$ 0.047 | 0.040 $\pm$ 0.045 | 638 $\pm$ 127 |
LP 2000 | 8.157 $\pm$ 0.083 | 1.313 $\pm$ 0.016 | 1.783 $\pm$ 0.036 | 0.154 $\pm$ 0.045 | 654 $\pm$ 130 |
LP 2059 | 7.996 $\pm$ 0.076 | 2.149 $\pm$ 0.050 | 0.762 $\pm$ 0.045 | 0.107 $\pm$ 0.038 | 607 $\pm$ 121 |
LP 2068 | 8.270 $\pm$ 0.061 | 1.831 $\pm$ 0.033 | 2.170 $\pm$ 0.047 | 0.130 $\pm$ 0.033 | 850 $\pm$ 170 |
LP 2094 | 8.334 $\pm$ 0.114 | 1.614 $\pm$ 0.028 | 0.876 $\pm$ 0.038 | 0.042 $\pm$ 0.030 | 569 $\pm$ 113 |
LP 2123 | 8.128 $\pm$ 0.057 | 1.547 $\pm$ 0.076 | 2.127 $\pm$ 0.051 | 0.046 $\pm$ 0.088 | 305 $\pm$ 61 |
LP 2219 | 8.031 $\pm$ 0.071 | 1.416 $\pm$ 0.018 | 1.303 $\pm$ 0.046 | 0.043 $\pm$ 0.003 | 1444 $\pm$ 288 |
LP 2220 | 8.705 $\pm$ 0.063 | 1.288 $\pm$ 0.012 | 1.057 $\pm$ 0.106 | 0.100 $\pm$ 0.057 | 365 $\pm$ 73 |
LP 2238 | 8.712 $\pm$ 0.150 | 1.146 $\pm$ 0.012 | 0.440 $\pm$ 0.081 | 0.105 $\pm$ 0.050 | 288 $\pm$ 57 |
LP 2253 | 8.045 $\pm$ 0.144 | 1.384 $\pm$ 0.023 | 1.611 $\pm$ 0.106 | 0.027 $\pm$ 0.073 | 384 $\pm$ 76 |
LP 2312 | 8.162 $\pm$ 0.216 | 1.025 $\pm$ 0.010 | 1.753 $\pm$ 0.105 | 0.042 $\pm$ 0.097 | 198 $\pm$ 39 |
LP 2339 | 7.948 $\pm$ 0.232 | 1.034 $\pm$ 0.008 | 2.652 $\pm$ 0.039 | 0.156 $\pm$ 0.047 | 244 $\pm$ 48 |
LP 589 | 8.702 $\pm$ 0.043 | 2.826 $\pm$ 0.060 | 0.268 $\pm$ 0.036 | 0.117 $\pm$ 0.033 | 524 $\pm$ 104 |
LP 597 | 8.795 $\pm$ 0.306 | 2.004 $\pm$ 0.085 | 2.942 $\pm$ 0.115 | 0.119 $\pm$ 0.053 | 1099 $\pm$ 219 |
LP 658 | 9.013 $\pm$ 0.020 | 1.400 $\pm$ 0.020 | 0.811 $\pm$ 0.070 | 0.103 $\pm$ 0.039 | 420 $\pm$ 84 |
LP 866 | 9.521 $\pm$ 0.154 | 2.104 $\pm$ 0.171 | 2.261 $\pm$ 0.159 | 0.099 $\pm$ 0.047 | 1219 $\pm$ 243 |
LP 930 | 9.200 $\pm$ 0.031 | 2.276 $\pm$ 0.064 | 1.046 $\pm$ 0.080 | 0.032 $\pm$ 0.062 | 508 $\pm$ 101 |
Loden 1194 | 8.373 $\pm$ 0.069 | 0.717 $\pm$ 0.004 | 0.764 $\pm$ 0.046 | 0.027 $\pm$ 0.027 | 140 $\pm$ 28 |
Loden 372 | 8.149 $\pm$ 0.105 | 1.665 $\pm$ 0.041 | 1.087 $\pm$ 0.060 | 0.092 $\pm$ 0.058 | 380 $\pm$ 76 |
Loden 46 | 8.915 $\pm$ 0.062 | 1.093 $\pm$ 0.006 | 0.483 $\pm$ 0.135 | 0.119 $\pm$ 0.063 | 288 $\pm$ 57 |
Lynga 2 | 8.050 $\pm$ 0.121 | 0.918 $\pm$ 0.007 | 1.026 $\pm$ 0.031 | 0.050 $\pm$ 0.035 | 367 $\pm$ 73 |
Majaess 65 | 8.054 $\pm$ 0.093 | 0.926 $\pm$ 0.007 | 0.808 $\pm$ 0.044 | 0.048 $\pm$ 0.040 | 98 $\pm$ 19 |
Mamajek 4 | 8.772 $\pm$ 0.041 | 0.442 $\pm$ 0.010 | 0.335 $\pm$ 0.073 | 0.006 $\pm$ 0.056 | 506 $\pm$ 101 | 497 $\pm$ 99
Markarian 38 | 7.164 $\pm$ 0.161 | 1.662 $\pm$ 0.048 | 1.061 $\pm$ 0.048 | 0.031 $\pm$ 0.071 | 156 $\pm$ 31 |
Melotte 22 | 8.005 $\pm$ 0.016 | 0.135 $\pm$ 0.001 | 0.349 $\pm$ 0.036 | 0.017 $\pm$ 0.010 | 816 $\pm$ 163 | 838 $\pm$ 167
Melotte 72 | 9.097 $\pm$ 0.026 | 2.578 $\pm$ 0.089 | 0.230 $\pm$ 0.016 | 0.066 $\pm$ 0.063 | 709 $\pm$ 141 |
NGC 1027 | 8.104 $\pm$ 0.129 | 1.069 $\pm$ 0.004 | 1.486 $\pm$ 0.062 | 0.038 $\pm$ 0.047 | 879 $\pm$ 175 |
NGC 103 | 7.996 $\pm$ 0.142 | 2.984 $\pm$ 0.064 | 1.723 $\pm$ 0.041 | 0.123 $\pm$ 0.035 | 841 $\pm$ 168 |
NGC 1220 | 7.553 $\pm$ 0.224 | 2.493 $\pm$ 0.049 | 2.477 $\pm$ 0.028 | 0.113 $\pm$ 0.027 | 255 $\pm$ 51 |
NGC 129 | 7.963 $\pm$ 0.038 | 1.723 $\pm$ 0.026 | 1.854 $\pm$ 0.026 | 0.002 $\pm$ 0.052 | 1577 $\pm$ 315 |
NGC 1342 | 8.605 $\pm$ 0.095 | 0.636 $\pm$ 0.003 | 1.263 $\pm$ 0.045 | 0.005 $\pm$ 0.028 | 925 $\pm$ 185 | 835 $\pm$ 167
NGC 146 | 7.400 $\pm$ 0.079 | 2.598 $\pm$ 0.103 | 1.849 $\pm$ 0.030 | 0.093 $\pm$ 0.048 | 759 $\pm$ 151 |
NGC 1496 | 8.544 $\pm$ 0.116 | 1.529 $\pm$ 0.033 | 1.808 $\pm$ 0.078 | 0.091 $\pm$ 0.071 | 199 $\pm$ 39 |
NGC 1502 | 6.881 $\pm$ 0.065 | 1.019 $\pm$ 0.010 | 2.236 $\pm$ 0.045 | 0.170 $\pm$ 0.093 | 728 $\pm$ 145 |
NGC 1513 | 8.230 $\pm$ 0.186 | 1.352 $\pm$ 0.019 | 2.228 $\pm$ 0.045 | 0.004 $\pm$ 0.040 | 850 $\pm$ 170 |
NGC 1528 | 8.540 $\pm$ 0.106 | 0.986 $\pm$ 0.008 | 1.149 $\pm$ 0.036 | 0.007 $\pm$ 0.040 | 925 $\pm$ 185 |
NGC 1545 | 8.126 $\pm$ 0.238 | 0.692 $\pm$ 0.004 | 1.237 $\pm$ 0.081 | 0.030 $\pm$ 0.044 | 287 $\pm$ 57 |
NGC 1582 | 8.188 $\pm$ 0.150 | 0.941 $\pm$ 0.008 | 1.278 $\pm$ 0.025 | 0.096 $\pm$ 0.030 | 534 $\pm$ 106 |
NGC 1605 | 7.799 $\pm$ 0.423 | 2.463 $\pm$ 0.102 | 2.679 $\pm$ 0.087 | 0.151 $\pm$ 0.038 | 610 $\pm$ 122 |
NGC 1662 | 8.847 $\pm$ 0.083 | 0.388 $\pm$ 0.014 | 1.159 $\pm$ 0.088 | 0.170 $\pm$ 0.055 | 397 $\pm$ 79 | 391 $\pm$ 78
NGC 1664 | 8.744 $\pm$ 0.039 | 1.279 $\pm$ 0.013 | 0.923 $\pm$ 0.054 | 0.005 $\pm$ 0.044 | 778 $\pm$ 155 | 823 $\pm$ 164
NGC 1708 | 8.296 $\pm$ 0.113 | 0.906 $\pm$ 0.010 | 1.767 $\pm$ 0.057 | 0.175 $\pm$ 0.048 | 390 $\pm$ 78 |
NGC 1750 | 8.187 $\pm$ 0.149 | 0.695 $\pm$ 0.003 | 1.236 $\pm$ 0.048 | 0.001 $\pm$ 0.025 | 705 $\pm$ 141 |
NGC 1758 | 8.742 $\pm$ 0.028 | 0.850 $\pm$ 0.011 | 1.268 $\pm$ 0.065 | 0.018 $\pm$ 0.038 | 333 $\pm$ 66 |
NGC 1778 | 7.989 $\pm$ 0.129 | 1.538 $\pm$ 0.021 | 1.382 $\pm$ 0.029 | 0.069 $\pm$ 0.038 | 535 $\pm$ 107 |
NGC 1857 | 8.436 $\pm$ 0.045 | 2.512 $\pm$ 0.059 | 1.670 $\pm$ 0.036 | 0.123 $\pm$ 0.029 | 732 $\pm$ 146 |
NGC 1883 | 8.627 $\pm$ 0.092 | 3.802 $\pm$ 0.158 | 1.823 $\pm$ 0.057 | 0.293 $\pm$ 0.049 | 591 $\pm$ 118 |
NGC 189 | 8.806 $\pm$ 0.098 | 1.208 $\pm$ 0.028 | 1.831 $\pm$ 0.118 | 0.048 $\pm$ 0.116 | 281 $\pm$ 56 |
NGC 1901 | 8.887 $\pm$ 0.116 | 0.416 $\pm$ 0.001 | 0.208 $\pm$ 0.089 | 0.030 $\pm$ 0.018 | 197 $\pm$ 39 |
NGC 1907 | 8.815 $\pm$ 0.058 | 1.450 $\pm$ 0.027 | 1.502 $\pm$ 0.079 | 0.115 $\pm$ 0.049 | 677 $\pm$ 135 | 636 $\pm$ 127
NGC 1912 | 8.505 $\pm$ 0.043 | 1.069 $\pm$ 0.012 | 0.998 $\pm$ 0.032 | 0.022 $\pm$ 0.025 | 1462 $\pm$ 292 | 1447 $\pm$ 289
NGC 1960 | 7.451 $\pm$ 0.032 | 1.119 $\pm$ 0.011 | 0.904 $\pm$ 0.024 | 0.026 $\pm$ 0.028 | 629 $\pm$ 125 |
NGC 2126 | 9.181 $\pm$ 0.021 | 1.254 $\pm$ 0.018 | 0.806 $\pm$ 0.060 | 0.141 $\pm$ 0.050 | 275 $\pm$ 55 |
NGC 2129 | 7.357 $\pm$ 0.137 | 1.815 $\pm$ 0.051 | 2.213 $\pm$ 0.063 | 0.080 $\pm$ 0.091 | 453 $\pm$ 90 |
NGC 2169 | 6.899 $\pm$ 0.058 | 0.936 $\pm$ 0.016 | 0.805 $\pm$ 0.056 | 0.179 $\pm$ 0.057 | 234 $\pm$ 46 |
NGC 2183 | 6.858 $\pm$ 0.108 | 0.825 $\pm$ 0.010 | 1.657 $\pm$ 0.522 | 0.120 $\pm$ 0.043 | 258 $\pm$ 51 |
NGC 2184 | 8.970 $\pm$ 0.047 | 0.562 $\pm$ 0.002 | 0.655 $\pm$ 0.072 | 0.121 $\pm$ 0.052 | 196 $\pm$ 39 |
NGC 2192 | 9.149 $\pm$ 0.037 | 3.382 $\pm$ 0.132 | 0.436 $\pm$ 0.046 | 0.164 $\pm$ 0.057 | 765 $\pm$ 153 |
NGC 2215 | 8.817 $\pm$ 0.051 | 0.922 $\pm$ 0.007 | 0.794 $\pm$ 0.071 | 0.048 $\pm$ 0.052 | 371 $\pm$ 74 |
NGC 2225 | 9.095 $\pm$ 0.044 | 2.889 $\pm$ 0.141 | 1.630 $\pm$ 0.056 | 0.199 $\pm$ 0.036 | 470 $\pm$ 94 |
NGC 2232 | 7.451 $\pm$ 0.036 | 0.314 $\pm$ 0.006 | 0.236 $\pm$ 0.034 | 0.035 $\pm$ 0.040 | 227 $\pm$ 45 |
NGC 2236 | 8.954 $\pm$ 0.024 | 2.421 $\pm$ 0.053 | 1.674 $\pm$ 0.044 | 0.153 $\pm$ 0.043 | 1331 $\pm$ 266 |
NGC 225 | 8.238 $\pm$ 0.142 | 0.668 $\pm$ 0.004 | 0.923 $\pm$ 0.078 | 0.143 $\pm$ 0.091 | 124 $\pm$ 24 |
NGC 2259 | 8.499 $\pm$ 0.082 | 2.619 $\pm$ 0.074 | 1.996 $\pm$ 0.050 | 0.160 $\pm$ 0.026 | 406 $\pm$ 81 |
NGC 2262 | 8.983 $\pm$ 0.061 | 2.824 $\pm$ 0.266 | 2.294 $\pm$ 0.080 | 0.142 $\pm$ 0.039 | 1004 $\pm$ 200 |
NGC 2264 | 6.744 $\pm$ 0.076 | 0.692 $\pm$ 0.006 | 0.328 $\pm$ 0.110 | 0.041 $\pm$ 0.046 | 368 $\pm$ 73 |
NGC 2266 | 9.021 $\pm$ 0.023 | 3.114 $\pm$ 0.094 | 0.436 $\pm$ 0.061 | 0.232 $\pm$ 0.040 | 840 $\pm$ 168 |
NGC 2269 | 8.397 $\pm$ 0.188 | 2.046 $\pm$ 0.070 | 1.358 $\pm$ 0.094 | 0.105 $\pm$ 0.032 | 306 $\pm$ 61 |
NGC 2281 | 8.736 $\pm$ 0.043 | 0.508 $\pm$ 0.001 | 0.341 $\pm$ 0.057 | 0.032 $\pm$ 0.037 | 681 $\pm$ 136 |
NGC 2286 | 8.752 $\pm$ 0.086 | 2.042 $\pm$ 0.055 | 1.133 $\pm$ 0.121 | 0.108 $\pm$ 0.052 | 557 $\pm$ 111 |
NGC 2287 | 8.296 $\pm$ 0.067 | 0.714 $\pm$ 0.004 | 0.225 $\pm$ 0.032 | 0.078 $\pm$ 0.025 | 1126 $\pm$ 225 | 1185 $\pm$ 237
NGC 2301 | 8.306 $\pm$ 0.053 | 0.835 $\pm$ 0.006 | 0.251 $\pm$ 0.012 | 0.031 $\pm$ 0.018 | 725 $\pm$ 145 | 793 $\pm$ 158
NGC 2302 | 8.090 $\pm$ 0.072 | 1.167 $\pm$ 0.004 | 0.734 $\pm$ 0.047 | 0.033 $\pm$ 0.018 | 190 $\pm$ 38 |
NGC 2311 | 7.798 $\pm$ 0.193 | 1.910 $\pm$ 0.040 | 1.186 $\pm$ 0.054 | 0.045 $\pm$ 0.040 | 365 $\pm$ 73 |
NGC 2318 | 8.709 $\pm$ 0.087 | 1.278 $\pm$ 0.023 | 1.075 $\pm$ 0.106 | 0.013 $\pm$ 0.026 | 561 $\pm$ 112 |
NGC 2343 | 8.190 $\pm$ 0.150 | 1.040 $\pm$ 0.014 | 0.674 $\pm$ 0.095 | 0.013 $\pm$ 0.058 | 194 $\pm$ 38 |
NGC 2354 | 9.204 $\pm$ 0.020 | 1.262 $\pm$ 0.022 | 0.488 $\pm$ 0.052 | 0.061 $\pm$ 0.035 | 847 $\pm$ 169 |
NGC 2355 | 9.094 $\pm$ 0.028 | 1.777 $\pm$ 0.020 | 0.301 $\pm$ 0.019 | 0.004 $\pm$ 0.044 | 705 $\pm$ 141 | 660 $\pm$ 132
NGC 2360 | 9.106 $\pm$ 0.029 | 1.036 $\pm$ 0.009 | 0.396 $\pm$ 0.041 | 0.083 $\pm$ 0.027 | 1327 $\pm$ 265 | 1317 $\pm$ 263
NGC 2374 | 8.575 $\pm$ 0.047 | 1.211 $\pm$ 0.012 | 0.515 $\pm$ 0.047 | 0.029 $\pm$ 0.041 | 257 $\pm$ 51 |
NGC 2383 | 8.451 $\pm$ 0.067 | 2.822 $\pm$ 0.082 | 1.087 $\pm$ 0.027 | 0.144 $\pm$ 0.037 | 763 $\pm$ 152 |
NGC 2384 | 7.372 $\pm$ 0.118 | 2.270 $\pm$ 0.130 | 0.910 $\pm$ 0.040 | 0.130 $\pm$ 0.123 | 313 $\pm$ 62 |
NGC 2396 | 8.202 $\pm$ 0.055 | 1.375 $\pm$ 0.027 | 0.569 $\pm$ 0.031 | 0.129 $\pm$ 0.036 | 670 $\pm$ 134 |
NGC 2401 | 7.812 $\pm$ 0.277 | 4.239 $\pm$ 0.223 | 1.285 $\pm$ 0.054 | 0.220 $\pm$ 0.032 | 444 $\pm$ 88 |
NGC 2414 | 7.157 $\pm$ 0.058 | 4.173 $\pm$ 0.170 | 1.828 $\pm$ 0.013 | 0.224 $\pm$ 0.027 | 1384 $\pm$ 276 |
NGC 2421 | 7.833 $\pm$ 0.171 | 2.368 $\pm$ 0.063 | 1.447 $\pm$ 0.038 | 0.109 $\pm$ 0.034 | 1344 $\pm$ 268 |
NGC 2423 | 9.048 $\pm$ 0.021 | 0.901 $\pm$ 0.009 | 0.353 $\pm$ 0.042 | 0.024 $\pm$ 0.044 | 999 $\pm$ 199 |
NGC 2428 | 8.888 $\pm$ 0.023 | 1.299 $\pm$ 0.013 | 0.272 $\pm$ 0.022 | 0.030 $\pm$ 0.025 | 461 $\pm$ 92 |
NGC 2432 | 8.968 $\pm$ 0.043 | 1.731 $\pm$ 0.029 | 0.772 $\pm$ 0.066 | 0.003 $\pm$ 0.062 | 705 $\pm$ 141 |
NGC 2439 | 7.379 $\pm$ 0.066 | 3.330 $\pm$ 0.076 | 1.351 $\pm$ 0.020 | 0.178 $\pm$ 0.023 | 2656 $\pm$ 531 |
NGC 2448 | 8.117 $\pm$ 0.186 | 1.070 $\pm$ 0.018 | 0.062 $\pm$ 0.013 | 0.059 $\pm$ 0.044 | 450 $\pm$ 90 |
NGC 2451A | 7.716 $\pm$ 0.041 | 0.192 $\pm$ 0.001 | 0.073 $\pm$ 0.037 | 0.045 $\pm$ 0.037 | 342 $\pm$ 68 | 371 $\pm$ 74
NGC 2451B | 7.631 $\pm$ 0.026 | 0.354 $\pm$ 0.004 | 0.463 $\pm$ 0.053 | 0.011 $\pm$ 0.015 | 367 $\pm$ 73 |
NGC 2453 | 7.457 $\pm$ 0.218 | 3.838 $\pm$ 0.089 | 1.645 $\pm$ 0.037 | 0.151 $\pm$ 0.034 | 656 $\pm$ 131 |
NGC 2479 | 9.101 $\pm$ 0.025 | 1.561 $\pm$ 0.016 | 0.069 $\pm$ 0.010 | 0.066 $\pm$ 0.041 | 395 $\pm$ 79 | 327 $\pm$ 65
NGC 2482 | 8.827 $\pm$ 0.048 | 1.208 $\pm$ 0.035 | 0.096 $\pm$ 0.022 | 0.102 $\pm$ 0.112 | 313 $\pm$ 62 |
NGC 2489 | 8.565 $\pm$ 0.095 | 1.778 $\pm$ 0.055 | 1.514 $\pm$ 0.050 | 0.051 $\pm$ 0.070 | 1136 $\pm$ 227 |
NGC 2509 | 9.146 $\pm$ 0.001 | 2.831 $\pm$ 0.001 | 0.055 $\pm$ 0.001 | 0.426 $\pm$ 0.001 | 1453 $\pm$ 290 |
NGC 2533 | 9.001 $\pm$ 0.044 | 2.532 $\pm$ 0.100 | 1.040 $\pm$ 0.100 | 0.032 $\pm$ 0.055 | 632 $\pm$ 126 |
NGC 2539 | 8.890 $\pm$ 0.019 | 1.239 $\pm$ 0.009 | 0.135 $\pm$ 0.011 | 0.005 $\pm$ 0.023 | 1152 $\pm$ 230 | 1083 $\pm$ 216
NGC 2546 | 8.244 $\pm$ 0.030 | 0.903 $\pm$ 0.005 | 0.536 $\pm$ 0.039 | 0.023 $\pm$ 0.036 | 558 $\pm$ 111 | 606 $\pm$ 121
NGC 2547 | 7.551 $\pm$ 0.095 | 0.384 $\pm$ 0.004 | 0.352 $\pm$ 0.132 | 0.032 $\pm$ 0.076 | 362 $\pm$ 72 |
NGC 2548 | 8.714 $\pm$ 0.032 | 0.747 $\pm$ 0.004 | 0.127 $\pm$ 0.016 | 0.002 $\pm$ 0.026 | 920 $\pm$ 184 | 912 $\pm$ 182
NGC 2571 | 7.419 $\pm$ 0.166 | 1.248 $\pm$ 0.023 | 0.435 $\pm$ 0.028 | 0.038 $\pm$ 0.043 | 345 $\pm$ 69 |
NGC 2587 | 8.831 $\pm$ 0.037 | 2.751 $\pm$ 0.079 | 0.223 $\pm$ 0.025 | 0.006 $\pm$ 0.050 | 649 $\pm$ 129 |
NGC 2645 | 7.318 $\pm$ 0.086 | 1.707 $\pm$ 0.046 | 1.439 $\pm$ 0.028 | 0.001 $\pm$ 0.088 | 348 $\pm$ 69 |
NGC 2659 | 7.543 $\pm$ 0.180 | 1.909 $\pm$ 0.031 | 1.598 $\pm$ 0.048 | 0.003 $\pm$ 0.055 | 404 $\pm$ 80 |
NGC 2669 | 8.114 $\pm$ 0.073 | 1.110 $\pm$ 0.009 | 0.866 $\pm$ 0.060 | 0.003 $\pm$ 0.034 | 509 $\pm$ 101 |
NGC 2670 | 8.098 $\pm$ 0.054 | 1.394 $\pm$ 0.019 | 1.417 $\pm$ 0.040 | 0.148 $\pm$ 0.073 | 562 $\pm$ 112 |
NGC 2671 | 8.617 $\pm$ 0.314 | 1.335 $\pm$ 0.022 | 2.823 $\pm$ 0.071 | 0.020 $\pm$ 0.036 | 943 $\pm$ 188 |
NGC 2682 | 9.578 $\pm$ 0.021 | 0.842 $\pm$ 0.005 | 0.164 $\pm$ 0.029 | 0.045 $\pm$ 0.041 | 1843 $\pm$ 368 |
NGC 2818 | 9.099 $\pm$ 0.031 | 2.908 $\pm$ 0.093 | 0.535 $\pm$ 0.087 | 0.097 $\pm$ 0.070 | 1100 $\pm$ 220 |
NGC 2866 | 8.045 $\pm$ 0.132 | 2.370 $\pm$ 0.048 | 2.052 $\pm$ 0.033 | 0.015 $\pm$ 0.035 | 364 $\pm$ 72 |
NGC 2910 | 8.017 $\pm$ 0.111 | 1.220 $\pm$ 0.011 | 0.790 $\pm$ 0.059 | 0.051 $\pm$ 0.061 | 419 $\pm$ 83 |
NGC 2925 | 8.320 $\pm$ 0.194 | 0.738 $\pm$ 0.005 | 0.260 $\pm$ 0.074 | 0.008 $\pm$ 0.050 | 219 $\pm$ 43 | 203 $\pm$ 40
NGC 2972 | 8.631 $\pm$ 0.078 | 1.816 $\pm$ 0.056 | 1.575 $\pm$ 0.084 | 0.029 $\pm$ 0.032 | 335 $\pm$ 67 |
NGC 3033 | 8.841 $\pm$ 0.065 | 1.689 $\pm$ 0.034 | 1.028 $\pm$ 0.079 | 0.040 $\pm$ 0.022 | 441 $\pm$ 88 |
NGC 3228 | 7.721 $\pm$ 0.128 | 0.461 $\pm$ 0.014 | 0.205 $\pm$ 0.071 | 0.001 $\pm$ 0.067 | 228 $\pm$ 45 |
NGC 3255 | 8.546 $\pm$ 0.135 | 4.777 $\pm$ 0.145 | 1.305 $\pm$ 0.091 | 0.036 $\pm$ 0.030 | 992 $\pm$ 198 |
NGC 3293 | 7.145 $\pm$ 0.039 | 2.283 $\pm$ 0.068 | 0.947 $\pm$ 0.017 | 0.017 $\pm$ 0.036 | 1975 $\pm$ 395 |
NGC 3496 | 8.734 $\pm$ 0.024 | 2.158 $\pm$ 0.038 | 1.553 $\pm$ 0.045 | 0.153 $\pm$ 0.039 | 2044 $\pm$ 408 |
NGC 3590 | 7.151 $\pm$ 0.035 | 2.259 $\pm$ 0.109 | 1.615 $\pm$ 0.032 | 0.041 $\pm$ 0.071 | 735 $\pm$ 147 |
NGC 3680 | 9.302 $\pm$ 0.041 | 1.013 $\pm$ 0.009 | 0.310 $\pm$ 0.102 | 0.137 $\pm$ 0.060 | 366 $\pm$ 73 |
NGC 381 | 8.548 $\pm$ 0.095 | 1.119 $\pm$ 0.011 | 1.436 $\pm$ 0.047 | 0.011 $\pm$ 0.048 | 369 $\pm$ 73 |
NGC 3960 | 8.975 $\pm$ 0.041 | 2.098 $\pm$ 0.078 | 1.098 $\pm$ 0.142 | 0.021 $\pm$ 0.079 | 1152 $\pm$ 230 |
NGC 433 | 7.856 $\pm$ 0.070 | 1.817 $\pm$ 0.058 | 2.242 $\pm$ 0.050 | 0.104 $\pm$ 0.052 | 459 $\pm$ 91 |
NGC 4337 | 9.172 $\pm$ 0.012 | 2.367 $\pm$ 0.044 | 1.291 $\pm$ 0.037 | 0.047 $\pm$ 0.029 | 1049 $\pm$ 209 |
NGC 436 | 7.924 $\pm$ 0.105 | 2.829 $\pm$ 0.059 | 1.595 $\pm$ 0.026 | 0.088 $\pm$ 0.057 | 829 $\pm$ 165 |
NGC 4439 | 7.723 $\pm$ 0.055 | 1.780 $\pm$ 0.056 | 1.234 $\pm$ 0.032 | 0.055 $\pm$ 0.070 | 282 $\pm$ 56 |
NGC 4463 | 7.492 $\pm$ 0.181 | 1.684 $\pm$ 0.043 | 1.615 $\pm$ 0.062 | 0.134 $\pm$ 0.045 | 555 $\pm$ 111 |
NGC 4609 | 7.878 $\pm$ 0.070 | 1.366 $\pm$ 0.019 | 1.233 $\pm$ 0.048 | 0.097 $\pm$ 0.042 | 943 $\pm$ 188 |
NGC 4852 | 8.056 $\pm$ 0.060 | 1.245 $\pm$ 0.019 | 1.448 $\pm$ 0.021 | 0.007 $\pm$ 0.062 | 983 $\pm$ 196 |
NGC 5138 | 8.023 $\pm$ 0.160 | 1.840 $\pm$ 0.044 | 0.842 $\pm$ 0.056 | 0.125 $\pm$ 0.086 | 448 $\pm$ 89 |
NGC 5168 | 8.848 $\pm$ 0.051 | 2.554 $\pm$ 0.086 | 1.947 $\pm$ 0.096 | 0.099 $\pm$ 0.049 | 795 $\pm$ 159 |
NGC 5269 | 8.226 $\pm$ 0.200 | 1.850 $\pm$ 0.046 | 1.477 $\pm$ 0.060 | 0.168 $\pm$ 0.050 | 386 $\pm$ 77 |
NGC 5281 | 7.802 $\pm$ 0.091 | 1.461 $\pm$ 0.023 | 1.031 $\pm$ 0.026 | 0.028 $\pm$ 0.055 | 423 $\pm$ 84 |
NGC 5288 | 8.588 $\pm$ 0.347 | 2.287 $\pm$ 0.075 | 1.705 $\pm$ 0.138 | 0.094 $\pm$ 0.055 | 475 $\pm$ 95 |
NGC 5316 | 8.138 $\pm$ 0.186 | 1.395 $\pm$ 0.023 | 1.133 $\pm$ 0.062 | 0.052 $\pm$ 0.053 | 453 $\pm$ 90 |
NGC 5460 | 8.249 $\pm$ 0.160 | 0.707 $\pm$ 0.003 | 0.475 $\pm$ 0.073 | 0.052 $\pm$ 0.033 | 379 $\pm$ 75 |
NGC 559 | 8.757 $\pm$ 0.037 | 2.353 $\pm$ 0.041 | 2.214 $\pm$ 0.036 | 0.095 $\pm$ 0.034 | 1949 $\pm$ 389 |
NGC 5593 | 8.297 $\pm$ 0.076 | 1.002 $\pm$ 0.012 | 0.916 $\pm$ 0.065 | 0.011 $\pm$ 0.053 | 245 $\pm$ 49 |
NGC 5662 | 8.074 $\pm$ 0.176 | 0.749 $\pm$ 0.004 | 1.116 $\pm$ 0.047 | 0.021 $\pm$ 0.034 | 658 $\pm$ 131 | 691 $\pm$ 138
NGC 5715 | 8.676 $\pm$ 0.104 | 1.919 $\pm$ 0.059 | 2.118 $\pm$ 0.071 | 0.155 $\pm$ 0.033 | 927 $\pm$ 185 |
NGC 5749 | 8.122 $\pm$ 0.059 | 1.071 $\pm$ 0.011 | 1.176 $\pm$ 0.044 | 0.027 $\pm$ 0.061 | 276 $\pm$ 55 |
NGC 581 | 7.822 $\pm$ 0.184 | 2.329 $\pm$ 0.045 | 1.407 $\pm$ 0.031 | 0.078 $\pm$ 0.058 | 715 $\pm$ 143 |
NGC 5999 | 8.213 $\pm$ 0.204 | 2.294 $\pm$ 0.081 | 1.944 $\pm$ 0.045 | 0.135 $\pm$ 0.051 | 1203 $\pm$ 240 |
NGC 6025 | 8.173 $\pm$ 0.078 | 0.753 $\pm$ 0.003 | 0.690 $\pm$ 0.031 | 0.001 $\pm$ 0.017 | 575 $\pm$ 115 | 609 $\pm$ 121
NGC 6031 | 7.705 $\pm$ 0.202 | 1.705 $\pm$ 0.030 | 1.632 $\pm$ 0.054 | 0.137 $\pm$ 0.063 | 527 $\pm$ 105 |
NGC 6087 | 8.192 $\pm$ 0.083 | 0.924 $\pm$ 0.014 | 0.704 $\pm$ 0.027 | 0.118 $\pm$ 0.077 | 668 $\pm$ 133 | 678 $\pm$ 135
NGC 6134 | 9.096 $\pm$ 0.024 | 1.078 $\pm$ 0.009 | 1.300 $\pm$ 0.037 | 0.025 $\pm$ 0.029 | 1912 $\pm$ 382 | 1824 $\pm$ 364
NGC 6152 | 8.309 $\pm$ 0.098 | 1.534 $\pm$ 0.026 | 1.283 $\pm$ 0.045 | 0.040 $\pm$ 0.027 | 1228 $\pm$ 245 |
NGC 6178 | 7.123 $\pm$ 0.068 | 0.849 $\pm$ 0.018 | 0.868 $\pm$ 0.096 | 0.026 $\pm$ 0.085 | 122 $\pm$ 24 |
NGC 6192 | 7.677 $\pm$ 0.234 | 1.553 $\pm$ 0.030 | 2.222 $\pm$ 0.059 | 0.140 $\pm$ 0.050 | 1840 $\pm$ 368 |
NGC 6204 | 8.013 $\pm$ 0.073 | 1.129 $\pm$ 0.016 | 1.523 $\pm$ 0.024 | 0.070 $\pm$ 0.029 | 628 $\pm$ 125 |
NGC 6208 | 9.269 $\pm$ 0.023 | 1.142 $\pm$ 0.009 | 1.082 $\pm$ 0.067 | 0.228 $\pm$ 0.040 | 1689 $\pm$ 337 |
NGC 6242 | 7.833 $\pm$ 0.086 | 1.219 $\pm$ 0.016 | 1.374 $\pm$ 0.024 | 0.126 $\pm$ 0.041 | 1529 $\pm$ 305 |
NGC 6249 | 7.346 $\pm$ 0.042 | 1.144 $\pm$ 0.012 | 1.570 $\pm$ 0.060 | 0.076 $\pm$ 0.060 | 297 $\pm$ 59 |
NGC 6253 | 9.525 $\pm$ 0.014 | 1.594 $\pm$ 0.023 | 1.036 $\pm$ 0.055 | 0.036 $\pm$ 0.055 | 2861 $\pm$ 572 |
NGC 6268 | 8.343 $\pm$ 0.052 | 1.409 $\pm$ 0.023 | 1.562 $\pm$ 0.050 | 0.044 $\pm$ 0.045 | 536 $\pm$ 107 |
NGC 637 | 7.265 $\pm$ 0.054 | 2.316 $\pm$ 0.088 | 1.962 $\pm$ 0.027 | 0.003 $\pm$ 0.048 | 430 $\pm$ 86 |
NGC 6425 | 8.712 $\pm$ 0.024 | 0.969 $\pm$ 0.011 | 1.094 $\pm$ 0.070 | 0.050 $\pm$ 0.059 | 415 $\pm$ 83 |
NGC 6444 | 8.451 $\pm$ 0.383 | 1.638 $\pm$ 0.087 | 1.616 $\pm$ 0.148 | 0.188 $\pm$ 0.065 | 630 $\pm$ 126 |
NGC 6475 | 8.667 $\pm$ 0.001 | 0.273 $\pm$ 0.001 | 0.204 $\pm$ 0.001 | 0.114 $\pm$ 0.001 | 791 $\pm$ 158 | 767 $\pm$ 153
NGC 6520 | 7.937 $\pm$ 0.304 | 1.572 $\pm$ 0.064 | 1.337 $\pm$ 0.066 | 0.162 $\pm$ 0.069 | 555 $\pm$ 111 |
NGC 6568 | 8.891 $\pm$ 0.025 | 1.019 $\pm$ 0.008 | 0.828 $\pm$ 0.062 | 0.151 $\pm$ 0.041 | 784 $\pm$ 156 |
NGC 659 | 7.374 $\pm$ 0.089 | 2.634 $\pm$ 0.058 | 2.174 $\pm$ 0.047 | 0.083 $\pm$ 0.055 | 1094 $\pm$ 218 |
NGC 6604 | 6.809 $\pm$ 0.057 | 1.935 $\pm$ 0.037 | 2.881 $\pm$ 0.037 | 0.103 $\pm$ 0.077 | 871 $\pm$ 174 |
NGC 6633 | 8.901 $\pm$ 0.175 | 0.391 $\pm$ 0.002 | 0.549 $\pm$ 0.238 | 0.117 $\pm$ 0.043 | 512 $\pm$ 102 |
NGC 6694 | 8.001 $\pm$ 0.159 | 1.675 $\pm$ 0.037 | 1.892 $\pm$ 0.029 | 0.173 $\pm$ 0.024 | 1208 $\pm$ 241 |
NGC 6709 | 8.197 $\pm$ 0.049 | 1.043 $\pm$ 0.006 | 1.082 $\pm$ 0.023 | 0.047 $\pm$ 0.021 | 679 $\pm$ 135 | 687 $\pm$ 137
NGC 6728 | 8.762 $\pm$ 0.041 | 1.699 $\pm$ 0.021 | 0.876 $\pm$ 0.092 | 0.122 $\pm$ 0.049 | 1170 $\pm$ 234 | 1201 $\pm$ 240
NGC 6793 | 8.517 $\pm$ 0.169 | 0.583 $\pm$ 0.002 | 1.170 $\pm$ 0.057 | 0.126 $\pm$ 0.053 | 409 $\pm$ 81 |
NGC 6811 | 9.003 $\pm$ 0.012 | 1.107 $\pm$ 0.007 | 0.255 $\pm$ 0.042 | 0.021 $\pm$ 0.025 | 646 $\pm$ 129 | 646 $\pm$ 129
NGC 6830 | 7.722 $\pm$ 0.212 | 2.024 $\pm$ 0.046 | 1.857 $\pm$ 0.034 | 0.159 $\pm$ 0.018 | 699 $\pm$ 139 |
NGC 6866 | 8.892 $\pm$ 0.031 | 1.377 $\pm$ 0.021 | 0.514 $\pm$ 0.078 | 0.063 $\pm$ 0.064 | 449 $\pm$ 89 |
NGC 6910 | 6.989 $\pm$ 0.040 | 1.640 $\pm$ 0.031 | 3.311 $\pm$ 0.101 | 0.030 $\pm$ 0.039 | 1528 $\pm$ 305 |
NGC 6913 | 6.921 $\pm$ 0.037 | 1.636 $\pm$ 0.047 | 2.832 $\pm$ 0.163 | 0.003 $\pm$ 0.072 | 903 $\pm$ 180 |
NGC 6939 | 9.183 $\pm$ 0.017 | 1.719 $\pm$ 0.040 | 1.397 $\pm$ 0.034 | 0.007 $\pm$ 0.036 | 2031 $\pm$ 406 |
NGC 6940 | 9.022 $\pm$ 0.017 | 1.000 $\pm$ 0.009 | 0.709 $\pm$ 0.055 | 0.008 $\pm$ 0.045 | 1393 $\pm$ 278 | 1645 $\pm$ 329
NGC 6991 | 9.157 $\pm$ 0.013 | 0.551 $\pm$ 0.010 | 0.320 $\pm$ 0.052 | 0.070 $\pm$ 0.032 | 672 $\pm$ 134 | 610 $\pm$ 122
NGC 6997 | 8.631 $\pm$ 0.081 | 0.857 $\pm$ 0.013 | 2.038 $\pm$ 0.092 | 0.124 $\pm$ 0.088 | 535 $\pm$ 107 |
NGC 7039 | 7.124 $\pm$ 0.037 | 0.739 $\pm$ 0.006 | 0.517 $\pm$ 0.079 | 0.031 $\pm$ 0.051 | 218 $\pm$ 43 |
NGC 7062 | 8.650 $\pm$ 0.166 | 2.124 $\pm$ 0.059 | 1.679 $\pm$ 0.076 | 0.036 $\pm$ 0.041 | 568 $\pm$ 113 |
NGC 7063 | 8.187 $\pm$ 0.169 | 0.656 $\pm$ 0.003 | 0.325 $\pm$ 0.039 | 0.002 $\pm$ 0.025 | 131 $\pm$ 26 |
NGC 7067 | 7.085 $\pm$ 0.044 | 4.654 $\pm$ 0.167 | 2.565 $\pm$ 0.034 | 0.083 $\pm$ 0.047 | 701 $\pm$ 140 |
NGC 7082 | 8.225 $\pm$ 0.099 | 1.295 $\pm$ 0.016 | 0.985 $\pm$ 0.052 | 0.028 $\pm$ 0.065 | 847 $\pm$ 169 |
NGC 7086 | 7.741 $\pm$ 0.230 | 1.555 $\pm$ 0.025 | 2.325 $\pm$ 0.045 | 0.005 $\pm$ 0.047 | 2152 $\pm$ 430 |
NGC 7092 | 8.565 $\pm$ 0.142 | 0.327 $\pm$ 0.023 | 0.047 $\pm$ 0.004 | 0.179 $\pm$ 0.132 | 331 $\pm$ 66 |
NGC 7128 | 7.189 $\pm$ 0.090 | 3.133 $\pm$ 0.184 | 2.941 $\pm$ 0.031 | 0.046 $\pm$ 0.031 | 1366 $\pm$ 273 |
NGC 7142 | 9.502 $\pm$ 0.031 | 2.168 $\pm$ 0.069 | 1.429 $\pm$ 0.065 | 0.099 $\pm$ 0.067 | 3434 $\pm$ 686 |
NGC 7160 | 7.260 $\pm$ 0.136 | 0.894 $\pm$ 0.015 | 1.188 $\pm$ 0.079 | 0.036 $\pm$ 0.055 | 205 $\pm$ 41 |
NGC 7209 | 8.625 $\pm$ 0.095 | 1.178 $\pm$ 0.017 | 0.699 $\pm$ 0.089 | 0.048 $\pm$ 0.064 | 1087 $\pm$ 217 | 982 $\pm$ 196
NGC 7226 | 8.591 $\pm$ 0.311 | 4.098 $\pm$ 0.250 | 1.856 $\pm$ 0.151 | 0.126 $\pm$ 0.032 | 432 $\pm$ 86 |
NGC 7235 | 7.148 $\pm$ 0.055 | 3.112 $\pm$ 0.104 | 2.702 $\pm$ 0.030 | 0.125 $\pm$ 0.038 | 1635 $\pm$ 327 |
NGC 7243 | 8.130 $\pm$ 0.084 | 0.864 $\pm$ 0.005 | 0.803 $\pm$ 0.042 | 0.004 $\pm$ 0.037 | 587 $\pm$ 117 |
NGC 7245 | 8.796 $\pm$ 0.043 | 2.798 $\pm$ 0.094 | 1.288 $\pm$ 0.074 | 0.085 $\pm$ 0.033 | 1186 $\pm$ 237 |
NGC 7296 | 8.400 $\pm$ 0.176 | 2.410 $\pm$ 0.058 | 0.793 $\pm$ 0.076 | 0.089 $\pm$ 0.057 | 642 $\pm$ 128 |
NGC 7423 | 9.124 $\pm$ 0.042 | 3.688 $\pm$ 0.125 | 2.111 $\pm$ 0.098 | 0.186 $\pm$ 0.059 | 776 $\pm$ 155 |
NGC 743 | 7.823 $\pm$ 0.304 | 1.045 $\pm$ 0.025 | 1.768 $\pm$ 0.089 | 0.001 $\pm$ 0.055 | 178 $\pm$ 35 |
NGC 744 | 8.343 $\pm$ 0.135 | 1.265 $\pm$ 0.026 | 1.268 $\pm$ 0.112 | 0.046 $\pm$ 0.041 | 315 $\pm$ 63 |
NGC 7510 | 7.020 $\pm$ 0.031 | 2.950 $\pm$ 0.115 | 3.065 $\pm$ 0.038 | 0.187 $\pm$ 0.056 | 2997 $\pm$ 599 |
NGC 7762 | 9.206 $\pm$ 0.024 | 0.931 $\pm$ 0.014 | 2.543 $\pm$ 0.040 | 0.052 $\pm$ 0.051 | 1394 $\pm$ 278 |
NGC 7790 | 7.457 $\pm$ 0.295 | 2.853 $\pm$ 0.074 | 1.931 $\pm$ 0.033 | 0.109 $\pm$ 0.048 | 1273 $\pm$ 254 |
NGC 886 | 8.510 $\pm$ 0.110 | 0.988 $\pm$ 0.013 | 1.825 $\pm$ 0.082 | 0.017 $\pm$ 0.077 | 613 $\pm$ 122 |
NGC 957 | 7.375 $\pm$ 0.079 | 2.050 $\pm$ 0.070 | 2.291 $\pm$ 0.014 | 0.029 $\pm$ 0.052 | 2071 $\pm$ 414 |
Patchick 3 | 9.141 $\pm$ 0.037 | 1.587 $\pm$ 0.049 | 1.365 $\pm$ 0.081 | 0.123 $\pm$ 0.074 | 213 $\pm$ 42 |
Pismis 11 | 6.833 $\pm$ 0.101 | 2.211 $\pm$ 0.190 | 3.411 $\pm$ 0.085 | 0.006 $\pm$ 0.130 | 467 $\pm$ 93 |
Pismis 12 | 9.072 $\pm$ 0.041 | 2.099 $\pm$ 0.090 | 2.022 $\pm$ 0.119 | 0.128 $\pm$ 0.081 | 911 $\pm$ 182 |
Pismis 15 | 9.091 $\pm$ 0.049 | 2.089 $\pm$ 0.103 | 2.183 $\pm$ 0.048 | 0.042 $\pm$ 0.048 | 554 $\pm$ 110 |
Pismis 27 | 6.948 $\pm$ 0.023 | 1.763 $\pm$ 0.067 | 2.161 $\pm$ 0.196 | 0.098 $\pm$ 0.057 | 205 $\pm$ 41 |
Pismis 4 | 8.306 $\pm$ 0.058 | 0.677 $\pm$ 0.003 | 0.207 $\pm$ 0.028 | 0.051 $\pm$ 0.025 | 235 $\pm$ 47 |
Pismis 5 | 7.002 $\pm$ 0.087 | 0.905 $\pm$ 0.011 | 1.586 $\pm$ 0.122 | 0.051 $\pm$ 0.058 | 332 $\pm$ 66 |
Pismis 8 | 7.146 $\pm$ 0.131 | 1.747 $\pm$ 0.072 | 2.227 $\pm$ 0.059 | 0.037 $\pm$ 0.123 | 250 $\pm$ 50 |
Pismis Moreno 1 | 7.046 $\pm$ 0.127 | 0.894 $\pm$ 0.016 | 1.898 $\pm$ 0.049 | 0.054 $\pm$ 0.091 | 164 $\pm$ 32 |
Platais 8 | 7.709 $\pm$ 0.050 | 0.135 $\pm$ 0.001 | 0.055 $\pm$ 0.063 | 0.153 $\pm$ 0.037 | 129 $\pm$ 25 |
Platais 9 | 7.836 $\pm$ 0.071 | 0.187 $\pm$ 0.002 | 0.253 $\pm$ 0.092 | 0.005 $\pm$ 0.042 | 136 $\pm$ 27 |
Pozzo 1 | 7.105 $\pm$ 0.074 | 0.343 $\pm$ 0.008 | 0.269 $\pm$ 0.059 | 0.042 $\pm$ 0.044 | 610 $\pm$ 122 |
RSG 1 | 8.383 $\pm$ 0.105 | 0.310 $\pm$ 0.014 | 0.736 $\pm$ 0.069 | 0.101 $\pm$ 0.068 | 179 $\pm$ 35 |
RSG 5 | 7.758 $\pm$ 0.030 | 0.329 $\pm$ 0.010 | 0.069 $\pm$ 0.006 | 0.077 $\pm$ 0.054 | 259 $\pm$ 51 |
Roslund 3 | 8.020 $\pm$ 0.075 | 1.617 $\pm$ 0.028 | 1.149 $\pm$ 0.059 | 0.112 $\pm$ 0.080 | 496 $\pm$ 99 |
Roslund 5 | 8.333 $\pm$ 0.138 | 0.533 $\pm$ 0.001 | 0.353 $\pm$ 0.023 | 0.049 $\pm$ 0.015 | 346 $\pm$ 69 |
Roslund 6 | 8.514 $\pm$ 0.102 | 0.347 $\pm$ 0.004 | 0.062 $\pm$ 0.006 | 0.070 $\pm$ 0.016 | 502 $\pm$ 100 |
Roslund 7 | 8.034 $\pm$ 0.163 | 1.219 $\pm$ 0.020 | 1.127 $\pm$ 0.064 | 0.009 $\pm$ 0.070 | 617 $\pm$ 123 |
Ruprecht 1 | 8.685 $\pm$ 0.077 | 1.459 $\pm$ 0.020 | 0.736 $\pm$ 0.078 | 0.065 $\pm$ 0.059 | 403 $\pm$ 80 |
Ruprecht 105 | 8.179 $\pm$ 0.270 | 1.858 $\pm$ 0.075 | 1.959 $\pm$ 0.171 | 0.112 $\pm$ 0.095 | 540 $\pm$ 108 |
Ruprecht 107 | 8.090 $\pm$ 0.223 | 3.260 $\pm$ 0.084 | 1.652 $\pm$ 0.090 | 0.131 $\pm$ 0.030 | 533 $\pm$ 106 |
Ruprecht 108 | 8.242 $\pm$ 0.193 | 0.961 $\pm$ 0.013 | 0.804 $\pm$ 0.067 | 0.111 $\pm$ 0.056 | 83 $\pm$ 16 |
Ruprecht 111 | 9.058 $\pm$ 0.043 | 1.388 $\pm$ 0.025 | 1.706 $\pm$ 0.115 | 0.035 $\pm$ 0.062 | 740 $\pm$ 148 |
Ruprecht 119 | 7.997 $\pm$ 0.160 | 1.882 $\pm$ 0.040 | 1.972 $\pm$ 0.083 | 0.180 $\pm$ 0.050 | 874 $\pm$ 174 |
Ruprecht 120 | 7.391 $\pm$ 0.385 | 1.755 $\pm$ 0.082 | 2.407 $\pm$ 0.081 | 0.177 $\pm$ 0.057 | 221 $\pm$ 44 |
Ruprecht 127 | 7.125 $\pm$ 0.064 | 2.137 $\pm$ 0.084 | 2.989 $\pm$ 0.044 | 0.153 $\pm$ 0.040 | 913 $\pm$ 182 |
Ruprecht 128 | 8.716 $\pm$ 0.422 | 1.702 $\pm$ 0.109 | 2.759 $\pm$ 0.149 | 0.134 $\pm$ 0.097 | 846 $\pm$ 169 |
Ruprecht 145 | 8.985 $\pm$ 0.020 | 0.588 $\pm$ 0.001 | 0.691 $\pm$ 0.073 | 0.062 $\pm$ 0.039 | 496 $\pm$ 99 | 444 $\pm$ 88
Ruprecht 148 | 7.439 $\pm$ 0.266 | 3.009 $\pm$ 0.248 | 2.292 $\pm$ 0.071 | 0.140 $\pm$ 0.063 | 388 $\pm$ 77 |
Ruprecht 16 | 8.370 $\pm$ 0.107 | 2.610 $\pm$ 0.095 | 1.027 $\pm$ 0.050 | 0.046 $\pm$ 0.043 | 369 $\pm$ 73 |
Ruprecht 171 | 9.482 $\pm$ 0.017 | 1.468 $\pm$ 0.028 | 0.934 $\pm$ 0.035 | 0.070 $\pm$ 0.048 | 2687 $\pm$ 537 | 2573 $\pm$ 514
Ruprecht 18 | 8.160 $\pm$ 0.198 | 2.305 $\pm$ 0.070 | 2.127 $\pm$ 0.057 | 0.053 $\pm$ 0.052 | 1263 $\pm$ 252 |
Ruprecht 19 | 7.931 $\pm$ 0.125 | 1.371 $\pm$ 0.023 | 0.344 $\pm$ 0.031 | 0.048 $\pm$ 0.031 | 217 $\pm$ 43 |
Ruprecht 25 | 8.933 $\pm$ 0.066 | 5.623 $\pm$ 0.188 | 1.859 $\pm$ 0.099 | 0.366 $\pm$ 0.041 | 400 $\pm$ 80 |
Ruprecht 28 | 9.413 $\pm$ 0.099 | 3.679 $\pm$ 0.240 | 0.901 $\pm$ 0.147 | 0.045 $\pm$ 0.052 | 707 $\pm$ 141 |
Ruprecht 34 | 8.340 $\pm$ 0.131 | 2.489 $\pm$ 0.058 | 1.104 $\pm$ 0.057 | 0.095 $\pm$ 0.032 | 374 $\pm$ 74 |
Ruprecht 35 | 7.400 $\pm$ 0.219 | 3.249 $\pm$ 0.231 | 1.953 $\pm$ 0.034 | 0.153 $\pm$ 0.051 | 450 $\pm$ 90 |
Ruprecht 4 | 8.850 $\pm$ 0.042 | 3.584 $\pm$ 0.069 | 1.666 $\pm$ 0.063 | 0.175 $\pm$ 0.046 | 738 $\pm$ 147 |
Ruprecht 41 | 8.398 $\pm$ 0.352 | 3.676 $\pm$ 0.158 | 1.298 $\pm$ 0.074 | 0.114 $\pm$ 0.042 | 798 $\pm$ 159 |
Ruprecht 42 | 8.452 $\pm$ 0.182 | 5.205 $\pm$ 0.128 | 1.550 $\pm$ 0.078 | 0.236 $\pm$ 0.038 | 689 $\pm$ 137 |
Ruprecht 44 | 7.217 $\pm$ 0.055 | 4.139 $\pm$ 0.234 | 1.972 $\pm$ 0.026 | 0.232 $\pm$ 0.042 | 1171 $\pm$ 234 |
Ruprecht 48 | 7.970 $\pm$ 0.255 | 3.223 $\pm$ 0.072 | 1.493 $\pm$ 0.040 | 0.115 $\pm$ 0.046 | 515 $\pm$ 103 |
Ruprecht 50 | 8.922 $\pm$ 0.052 | 1.978 $\pm$ 0.072 | 0.330 $\pm$ 0.037 | 0.035 $\pm$ 0.057 | 81 $\pm$ 16 |
Ruprecht 54 | 8.153 $\pm$ 0.360 | 3.839 $\pm$ 0.129 | 1.488 $\pm$ 0.123 | 0.158 $\pm$ 0.038 | 781 $\pm$ 156 |