11institutetext: 1Centro de Astrobiología (CAB), CSIC-INTA, Camino Bajo del
Castillo s/n, 28692, Villanueva de la Cañada, Madrid, Spain.
2Spanish Virtual Observatory
3Joint ALMA Observatory, Alonso de Córdova 3107, Vitacura, Santiago 763-0355,
Chile
4National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA
22903, USA
5Institut de Ciències del Cosmos, Universitat de Barcelona (IEEC-UB), Martí i
Franquès 1, E-08028 Barcelona, Spain
6European Southern Observatory (ESO), Alonso de Córdova 3107, Vitacura,
Casilla 19001, Santiago de Chile, Chile

# Gaia EDR3 comparative study of protoplanetary disk fractions in young
stellar clusters

I. Mendigutía 11 E. Solano 1122 M. Vioque 3344 L. Balaguer-Nuñez 55 A. Ribas
66 N. Huélamo 11 C. Rodrigo 1122

(Received January 18, 2022; accepted June 5, 2022)

###### Abstract

Context. The lifetime of protoplanetary disks around young stars limits the
timescale when planets form. A disk dissipation timescale $\leq$ 10 Myr was
inferred from surveys counting the relative number of stars with disks -the
disk fraction- in young stellar clusters with different ages. However, most
previous surveys focused on the compact region within $\sim$ 2 pc from the
clusters’ centers, for which the disk fraction information considering the
outer part is practically absent.

Aims. We aim to test if disk fraction estimates change when inferred from an
extended region around the clusters’ centers.

Methods. Gaia EDR3 data and a best-suited, Virtual Observatory (VO)-based tool
-_Clusterix_ -, are used to identify member stars for a representative sample
of 19 young stellar clusters considering two concentric fields of view (FOV)
with radii $\sim$ 20 pc and $\sim$ 2 pc. Inner-disk fractions associated to
each FOV are identically derived from 2MASS color-color diagrams and compared
to each other.

Results. Although the density of members is smaller in the periphery, the
absolute number of member stars is typically $\sim$ 5 times larger outside
$\sim$ 2 pc from the clusters’ centers. In turn, our analysis reveals that the
inner disk fractions inferred from the compact and the extended regions are
equal within $\sim$ $\pm$ 10$\%$. A list of member and disk stars identified
in each cluster is provided and stored in a VO-compliant archive, along with
their membership probabilities, angular distances to the centre, Gaia and
near-infrared data. Averaged values and plots characterizing the whole
clusters are also provided, including HR diagrams based on Gaia colors and
absolute magnitudes for the sources with known extinction.

Conclusions. Our results cover the largest fields ever probed when dealing
with disk fractions for all clusters analysed, and imply that their complete
characterization requires the use of wide FOVs. However, the comparative study
does not support a previous hypothesis proposing that disk fractions should be
significantly larger considering extended regions. The resulting database is a
benchmark for future detailed studies of young clusters, whose disk fractions
must be accurately determined by using multi-wavelength analysis potentially
combined with data from coming Gaia releases.

###### Key Words.:

(Galaxy:) open clusters and associations: general – Protoplanetary disks –
Proper motions – Parallaxes – Virtual observatory tools – Astronomical
databases

##  1 Introduction

Planets form from protoplanetary disks surrounding pre-Main Sequence (PMS)
stars. Thus, the lifetime of such disks constitutes a stringent upper limit to
the timescale when planets assemble. The typical disk dissipation timescale is
inferred by surveying young stellar clusters in order to account for the ratio
between the number of stars with disks and the total number of members -the
disk fraction-. Based on the observed temporal decay of the disk fraction,
less than $\sim$ 10$\%$ of stars retain their disks after 2-6 Myr and almost
all stars are diskless after $\sim$ 10 Myr (e.g. Haisch et al., 2001;
Hernández et al., 2008; Mamajek, 2009; Muzerolle et al., 2010; Fedele et al.,
2010; Ribas et al., 2015).

However, the previous surveys are limited by the narrow field of view (FOV) of
the telescopes used -mainly Spitzer. Being focused on the compact regions
within $\sim$ 15$\arcmin$, they sample the central 2-3 pc at the typical
distances to the clusters, with little information about the outer parts.
Indeed, although the above mentioned numbers characterizing the disk
dissipation timescale are widely accepted, they are not free of some
controversial. For instance, they make our own planetary system somewhat an
exception. Based on metheoritic analysis, Jupiter accreted a significant
amount of gas along more than 4 Myr, similar to the timescale when the gas in
the solar protoplanetary disk dissipated (see e.g. Desch et al., 2018;
Schiller et al., 2018). Moreover, the use of a narrow FOV may constitute a
crucial observational bias playing a fundamental role in our general
understanding of disk dissipation. Pfalzner et al. (2014) suggested that the
use of wide FOVs should lead to disk fractions significantly larger than
inferred in previous surveys that focused on the central regions of the
clusters, indicating that $\geq$ 50$\%$ of stars should have disks at ages of
$\sim$ 10 Myr. The reason for this strong discrepancy with respect to the
normally accepted disk dissipation timescale is mainly based on the assumption
that young clusters significantly expand during the first Myr. In particular,
the use of relatively small FOVs to survey clusters that have already expanded
after $\sim$ 2-3 Myr allows us to probe only the stars initially located in
the central, densest regions of the clusters. A large stellar density would in
turn cause strong interactions leading to disk fractions smaller than if the
stars located in periphery are also considered.

The Gaia mission (Gaia Collaboration et al., 2016) is providing a new view of
stellar clusters thanks to accurate proper motions and parallaxes not limited
to narrow fields or specific star forming regions. In particular, Gaia’s data
have served to confirm previous suggestions indicating that most clusters
expand during the critical period of disk dissipation (Kuhn et al., 2019),
showing that their sizes can be much larger than previously assumed (e.g.
Großschedl et al., 2021; Meingast et al., 2021). Under this new perspective,
it is worth testing whether disk fraction estimates depend on the use of
different FOVs or not, given its potential implications in our view of planet
formation and our own planetary system. This work aims to use Gaia EDR3 data
to compare the relative disk fractions of a representative sample of young
stellar clusters when those are inferred considering two very different
fields, compact and extended, around the center of each cluster. Section 2
details the scope and the methodology. Section 3 describes the results of this
work, which are critically discussed in Sect. 4. Finally, Sect. 5 includes
some concluding remarks.

##  2 Scope and Methodology

Our aim is to test whether sampling fields with different sizes around the
center of stellar clusters lead to significantly different disk fraction
estimates or not. To this end, a sample of 19 young, nearby clusters listed in
Table 1 has been analysed. In particular, the vast majority of the stellar
population within each cluster is in the PMS phase, and 15 out of the 19
clusters are closer than 1.5 kpc. In addition, all them were studied in
previous reference works dealing with the typical disk dissipation timescale
(based on relatively compact FOVs), and show a range of properties in terms of
stellar masses, densities, and cluster expansion.

Because this work is based on stellar members identified through kinematic and
spatial segregation using large regions around the clusters’ centers (Sect.
2.1), those clusters that cannot be unambiguously distinguished from each
other were discarded. Thus, the clusters studied are separated by a wide
enough angular distance, showing clearly different distances and proper
motions otherwise (e.g. NGC 1333 and IC 348). This leaves well known regions
such as the Orion Nebula Cluster and $σ$ Ori excluded from the analysis.
Indeed, the separation between the previous clusters is relatively small,
showing very similar distances and proper motions likely indicating a physical
relation (Kuhn et al., 2019; Großschedl et al., 2021).

It is also out of the scope of this work to derive accurate numbers
representing absolute disk fractions for each cluster (see e.g. the references
in Col. 2 of Table 1). Instead, the comparison between relative disk fractions
estimated from two concentric fields with very different sizes but using
identical methodology is enough for our purposes. Such a methodology is
described next, and its associated caveats and limitations are discussed in
Sect. 4.

Table 1: General properties of the young stellar clusters

Name | References | Age | Massive? | Expanding? | distance |  $\Sigma$2pc |  $\Sigma$20pc
---|---|---|---|---|---|---|---
… | … | [Myr] | (y/n) | (y/n) | [pc] | [$\times$10-2arcmin-2] | [$\times$10-2arcmin-2]
NGC 1333 |  1 2 3 4 5 6 | 0-2 | n | n | 291$\pm$7 | 1.6 | 0.052
IC 348 |  1 2 3 4 5 6 7 8 | 0-5 | n | n | 314$\pm$8 | 5.4 | 0.12
NGC 1893 | 6 | 1-2 | n | y | 2814$\pm$302 | 80 | 5.9
$\lambda$ Ori |  1 2 4 5 6 | 1-11 | n |  | 393$\pm$8 | 6.2 | 0.37
NGC 1960 | 7 | 15-39†1 | n |  | 1131$\pm$37 | 100 | 2.4
NGC 2169 | 8 | 6-12 | n |  | 943$\pm$43 | 17 | 0.67
NGC 2244 |  1 3 4 6 | 0-4 | y | y | 1414$\pm$85 | 57 | 6.8
NGC 2264 |  1 2 4 6 7 | 0-6 | n | n | 711$\pm$32 | 31 | 1.0
NGC 2353 | 8 | 8-16 | n |  | 1187$\pm$122 | 80 | 4.8
NGC 2362 |  1 2 3 4 6 7 8 | 0-6 | y | n | 1271$\pm$88 | 110 | 5.8
$\gamma$ Vel |  1 2 4 6 | 0-16 | n |  | 359$\pm$19 | 9.7 | 0.80
ASCC 58 | 8 | 7-13∗ | n |  | 470$\pm$15 | 3.5 | 0.35
Tr 15 | 4 | 4-12 | y?†2 | y? | 2358$\pm$261 | 440 | 40
NGC 6231 |  6 8 | 1-9 | y | n | 1588$\pm$115 | 230 | 15
NGC 6531 | 8 | 5-10 | n |  | 1214$\pm$68 | 96 | 7.4
NGC 6611 |  4 6 | 1-4 | y | y | 1602$\pm$126 | 150 | 16
Tr 37 |  1 2 3 4 6 | 0-6 | y†3 |  | 914$\pm$32 | 31 | 2.3
NGC 7129 |  1 2 3 4 6 | 0-6 | n |  | 915$\pm$56 | 12 | 0.38
NGC 7160 |  1 2 3 4 8 | 8-15 | n | n | 920$\pm$48 | 17 | 1.2

Notes: Column 2 lists disk dissipation studies where the clusters in Col. 1
were included. The numbers in Cols 3 and 4 are based on such studies and
references therein. The age range is indicated in Col. 3. Following Mamajek
(2009), an uncertainty of 30$\%$ has been assigned to ages without errorbars.
Column 4 indicates whether the cluster has a total stellar mass above or below
500-1000M⊙ (yes or not), which is in turn indicative of the presence of a
significant number of massive OB stars within the clusters (but note that most
are part of OB associations when larger scales are considered; see e.g.
Wright, 2020). The presence or absence of evidence indicating cluster
expansion (yes or not) is indicated in Col. 5, whenever available in Kuhn et
al. (2019). The last three columns are based on our work. The average Gaia
EDR3 distance (and standard deviation) to each cluster is shown in Col. 6 (see
Appendix C). Columns 7 and 8 show the surface density of member stars for the
inner FOV2pc and the whole FOV20pc, as inferred from Table 3. References:
1Hernández et al. (2008), 2Mamajek (2009), 3Muzerolle et al. (2010) 4Pfalzner
et al. (2014), 5Ribas et al. (2015), 6Guarcello et al. (2021), 7Haisch et al.
(2001), 8Fedele et al. (2010). †1Panja et al. (2021), †2Wang et al. (2011)
†3Saurin et al. (2012).

###  2.1 Searching for member candidates

The Virtual Observatory (VO) compliant tool _Clusterix 2.0_
111http://clusterix.cab.inta-csic.es/clusterix/ was used to find member
candidates for each cluster. This is an interactive tool that determines
membership probabilities using a fully non-parametric method based on proper
motions. Clusterix carries out an empirical determination of the frequency
functions from the vector point diagram without previous assumptions about
their profiles. The complete description and performance of Clusterix are
included in Balaguer-Núñez et al. (2020).

Clusterix was applied to the stars within a circular field centered on each
cluster and radius equivalent to $\sim$ 20 pc at the corresponding distances.
This radius covers the large area potentially having sources unaffected by
stellar interactions after cluster expansion, eventually showing larger disk
fractions than in the compact area with radius $\sim$ 2 pc covered by most
previous surveys (see Pfalzner et al., 2014, and references in Table 1). Both
previous areas are different by a factor 100, will be called FOV20pc and
FOV2pc hereafter, and are analysed independently.

Gaia EDR3 (Gaia Collaboration et al., 2021) stellar magnitudes (Riello et al.,
2021), parallaxes and proper motions (Lindegren et al., 2021) were used for
all stars. Only the ones with magnitude G $\leq$ 17 were considered, given
that the accuracy of their proper motions is the best currently possible (up
to $\sim$ 0.01 mas yr${}^{-}1$). Such a magnitude limit constraints the
minimum stellar mass that can be probed, which increases as the clusters are
further away. For instance, the smallest MS stellar mass that could be probed
at the distance of the furthest cluster ($\sim$ 2814 pc; NGC 1893) is $\sim$
1.0 M⊙, whereas for the closest one ($\sim$ 291 pc; NGC 1333) goes down to
$\sim$ 0.4 M⊙. The previous limits are larger as extinction increases and
smaller for younger sources, thus strictly depending on the specific cluster.
Nevertheless, the lack of stellar mass completeness should not significantly
affect the intra-cluster comparison carried out here (but see Sect. 4.1.2). In
addition, only the sources with parallax $>$ 0, relative parallax error $<$
0.1, and renormalised unit weight error (RUWE) $<$ 1.4 were taken into
account. This way the sources with potentially spurious parallaxes are
excluded and the presence of unresolved binaries minimized (Lindegren et al.,
2021; El-Badry et al., 2021).

The stars whose proper motion-based membership probability is null according
to Clusterix were discarded. Then, the stars whose parallax is not consistent
with that associated to the cluster $\pm$3$\sigma$ (being $\sigma$ the Gaia-
based standard deviations in Cantat-Gaudin & Anders, 2020) were filtered out.
Finally, potential sources showing proper motions different from the median by
more than 3 times the standard deviation were considered outliers and removed
from the analysis too. In short, members were identified based on kinematic
segregation from proper motions, which have associated a non-null membership
probability given by Clusterix, and spatial segregation from parallaxes. These
criteria were equally applied to all clusters, allowing a direct comparison
between the results obtained from the extended region (FOV20pc) with those
from the compact region within it (FOV2pc). Additional filtering was applied
to remove potential contamination by non-members (Sect 4.1).

###  2.2 Estimating inner disk fractions

A near-infrared (IR) H-K vs J-H diagram based on 2MASS photometry (Skrutskie
et al., 2006) was built for the members in each cluster to estimate the disk
fractions associated to FOV20pc and FOV2pc. JHK photometry within 2” from the
Gaia coordinates of each member were filtered by discarding magnitudes without
errorbars and colors with errorbars $>$ 0.5 magnitudes. Members were
classified as disk sources when they show J-H $<$ -0.007 + 1.698 $\times$ H-K,
J-H $>$ 0.20, and H-K $>$ 0.35 (e.g. Lada & Adams, 1992). For a given cluster
and FOV, the disk fraction is f${}_{disk}^{JHK}$ = 100 $\times$
(N${}_{disk}^{JHK}$/N${}_{memb}^{JHK}$), where N${}_{memb}^{JHK}$ and
N${}_{disk}^{JHK}$ are the total number of member stars within the FOV with
JHK photometry and the corresponding number of stars classified as disks
sources, respectively. Errorbars for the disk fractions were derived from the
different N${}_{disk}^{JHK}$ values associated to the colors’ uncertainties.

Alternative diagrams based on IRAS, AKARI, or Spitzer colors and magnitudes
are commonly used to identify disk sources. Nevertheless, they are not ideal
for our comparison purposes because their coverage is partial or limited to
compact regions around the center of most clusters analyzed here. The
situation is similar using the more complete all-sky WISE survey, once
potentially spurious magnitudes are filtered out (Koenig & Leisawitz, 2014).
In contrast, the 2MASS survey typically covers more than 90$\%$ of the
identified members within both FOV20pc and FOV2pc simultaneously. This allows
us to carry out a statistically significant comparison between the disk
fractions inferred from the corresponding color-color diagram for all clusters
and FOVs, guarantying that the inevitable exclusion of the few members without
JHK counterparts has no major effect. It is remarked that the near-IR
photometry used in this work allows us to identify sources with hot inner
disks at distances $\lesssim$ 1 au from the central star, but not colder disks
at longer distances. The caveats and limitations associated to the JHK color-
color diagram are discussed in more detail in Sect. 4.2.

##  3 Results

Appendix A includes the figures and tables summarizing the results. The
distributions of stars in the proper motion plane and the projected directions
of motion of all members identified in each cluster are shown in Figs. 5 and
6. Their on-sky positions and the sizes of the compact and the extended FOVs
are overplotted to an image of the region in the IR in Fig. 7. The JHK color-
color diagrams used to infer the inner disk fractions are in Figure 8.
Additionally, Fig. 9 shows the Gaia color-magnitude diagram of each cluster,
although its representativeness depends on how well the extinction is
characterized (see the legends in that figure and Sect. 4.1). Table 3 lists
the central coordinates of each cluster, along with the angular radius,
fraction of members identified with respect to the field stars, mean
parallaxes and proper motions derived using FOV20pc and FOV2pc. Table 4 lists
the Gaia EDR3 coordinates, proper motions, parallax, and magnitudes, as well
as the angular distance to the center, membership probability and 2MASS colors
-when available- of all member stars. Disk stars identified through the
procedure described in Sect. 2.2 are indicated. Finally, a VO-compliant
archive where all previous data are available is described in Appendix B, and
a comparison with previous Gaia-based results is in Appendix C. Next we focus
on the main results that will be analysed in this work.

Firstly, although the surface density of members closer than 2 pc is larger
than that further out by a factor ranging from $\sim$ 10 to 86 (typically
$\sim$ 28 on average), the absolute number of members in the periphery can be
up to $\sim$ 11 (typically $\sim$ 5) times larger. Thus, the number of members
associated to clusters significantly differs from previous surveys focused on
narrow FOVs within the first $\sim$ 2 pc, which need to be updated to better
account for the whole stellar populations. On the other hand, Cols 3 and 7 of
Table 2 list the inferred disk fractions associated to each cluster and FOV,
whose representativeness is quantified in Cols. 2 and 6 showing the fraction
of member stars with JHK photometry. Figure 1 compares the disk fractions
derived using FOV2pc versus those derived using FOV20pc, illustrating their
similarity. The difference between both is below errorbars in most clusters,
typically smaller than $\sim$ ${}^{+10}_{-5}$ $\%$, and with a mean value =
0.05$\%$. Considering errorbars, the difference between disk fractions can
reach ${}^{+14}_{-13}$ $\%$ (except for NGC 1333). Thus, based on this
analysis the use of a large FOV does not lead to disk fractions significantly
larger than those inferred from compact regions around the clusters’ centers,
in contrast with the proposal in Pfalzner et al. (2014). The previous results
are critically discussed next.

Table 2: Class II inner disk fractions from 2MASS color-color diagrams

| FOV20pc |  | FOV2pc |
---|---|---|---|---
Name | NJHK/Nmemb | f${}_{disk}^{JHK}$ | NJHK/Nmemb (p0) | f${}_{disk}^{JHK}$ (p0) | NJHK/Nmemb | f${}_{disk}^{JHK}$ | NJHK/Nmemb (p0) | f${}_{disk}^{JHK}$ (p0)
NGC 1333 | 91/95 | 8.8${}^{+4.4}_{-1.1}$ | 85/88 (0.2) | 9.4${}^{+3.5}_{-1.2}$ (0.2) | 26/28 | 19.2${}^{+15.4}_{-0.0}$ | 26/28 (0.2) | 19.2${}^{+15.4}_{-0.0}$ (0.2)
IC 348 | 205/209 | 2.4${}^{+0.5}_{-0.0}$ | 148/151 (0.6) | 0.7${}^{+0.7}_{-0.0}$ (0.6) | 95/97 | 2.1${}^{+0.0}_{-0.0}$ | 81/83 (0.6) | 2.5${}^{+0.0}_{-0.0}$ (0.6)
NGC 1893 | 52/59 | 5.8${}^{0.0}_{-0.0}$ | 52/59 (0.5)† | 5.8${}^{+0.0}_{-0.0}$ (0.5)† | 7/8 | 0.0${}^{+0.0}_{-0.0}$ | 7/8 (0.5)† | 0.0${}^{+0.0}_{-0.0}$ (0.5)†
$λ$ Ori | 366/377 | 4.4${}^{+1.9}_{-0.8}$ | 31/31 (0.9) | 12.9${}^{+0.0}_{-0.0}$ (0.9) | 61/63 | 3.3${}^{+3.3}_{-0.0}$ | 16/16 (0.9) | 12.5${}^{+0.0}_{-0.0}$ (0.9)
NGC 1960 | 265/273 | 0.0${}^{+0.0}_{-0.0}$ | 243/250 (0.8) | 0.0${}^{+0.0}_{-0.0}$ (0.8) | 109/114 | 0.0${}^{+0.0}_{-0.0}$ | 106/110 (0.8) | 0.0${}^{+0.0}_{-0.0}$ (0.8)
NGC 2169 | 98/102 | 3.1${}^{+0.0}_{-3.1}$ | 59/62 (0.9) | 3.4${}^{+0.0}_{-3.4}$ (0.9) | 23/26 | 0.0${}^{+0.0}_{-0.0}$ | 21/23 (0.9) | 0.0${}^{+0.0}_{-0.0}$ (0.9)
NGC 2244 | 407/418 | 6.6${}^{+2.5}_{-1.5}$ | 140/147 (0.9) | 7.9${}^{+3.6}_{-1.4}$ (0.9) | 34/35 | 8.8${}^{+0.0}_{-0.0}$ | 28/28 (0.9) | 7.1${}^{+0.0}_{-0.0}$ (0.9)
NGC 2264 | 441/452 | 8.4${}^{+2.0}_{-1.8}$ | 165/166 (0.8) | 13.9${}^{+1.2}_{-2.4}$ (0.8) | 140/142 | 11.4${}^{+2.1}_{-2.9}$ | 91/91 (0.8) | 14.3${}^{+2.2}_{-4.4}$ (0.8)
NGC 2353 | 530/545 | 0.2${}^{+1.5}_{-0.2}$ | 236/243 (0.8) | 0.4${}^{+0.8}_{-0.4}$ (0.8) | 87/92 | 0.0${}^{+0.0}_{-0.0}$ | 75/80 (0.8) | 0.0${}^{+0.0}_{-0.0}$ (0.8)
NGC 2362 | 461/485 | 2.4${}^{+0.6}_{-1.1}$ | 162/170 (0.9) | 2.5${}^{+0.6}_{-1.2}$ (0.9) | 80/90 | 2.5${}^{+1.2}_{-2.5}$ | 56/63 (0.9) | 1.8${}^{+1.8}_{-1.8}$ (0.9)
$γ$ Vel | 780/810 | 0.6${}^{+2.3}_{-0.4}$ | 399/415 (0.5) | 0.8${}^{+2.5}_{-0.5}$ (0.5) | 94/99 | 1.1${}^{+2.1}_{-0.0}$ | 74/78 (0.5) | 0.0${}^{+2.7}_{-0.0}$ (0.5)
ASCC 58 | 150/160 | 0.0${}^{+1.3}_{-0.0}$ | 112/118 (0.5)† | 0.0${}^{+1.8}_{-0.0}$ (0.5)† | 14/16 | 0.0${}^{+0.0}_{-0.0}$ | 13/15 (0.5)† | 0.0${}^{+0.0}_{-0.0}$ (0.5)†
Trumpler 15 | 738/870 | 4.9${}^{+3.9}_{-0.8}$ | 167/207 (0.8) | 3.6${}^{+4.2}_{-1.2}$ (0.8) | 70/94 | 2.9${}^{+1.4}_{-0.0}$ | 34/49 (0.8) | 0.0${}^{+0.0}_{-0.0}$ (0.8)
NGC 6231 | 1477/1726 | 4.1${}^{+4.6}_{-1.3}$ | 616/714 (0.7) | 4.9${}^{+4.1}_{-1.3}$ (0.7) | 225/265 | 3.6${}^{+3.6}_{-1.8}$ | 183/214 (0.7) | 2.7${}^{+3.8}_{-1.1}$ (0.7)
NGC 6531 | 469/696 | 7.5${}^{+6.8}_{-2.8}$ | 282/404 (0.6) | 8.2${}^{+6.0}_{-2.5}$ (0.6) | 65/91 | 6.2${}^{+4.6}_{-4.6}$ | 61/83 (0.6) | 6.6${}^{+4.9}_{-4.9}$ (0.6)
NGC 6611 | 652/809 | 6.1${}^{+6.9}_{-2.4}$ | 35/45 (0.99) | 5.7${}^{+2.9}_{-0.0}$ (0.99) | 61/72 | 6.6${}^{+11.5}_{-4.9}$ | 19/23 (0.99) | 0.0${}^{+5.3}_{-0.0}$ (0.99)
Trumpler 37 | 360/381 | 4.7${}^{+3.1}_{-1.7}$ | 199/216 (0.4) | 7.0${}^{+3.5}_{-1.5}$ (0.4) | 47/52 | 8.5${}^{+6.4}_{-2.1}$ | 38/43 (0.4) | 10.5${}^{+7.9}_{-2.6}$ (0.4)
NGC 7129 | 42/43 | 11.9${}^{+2.4}_{-4.8}$ | 42/43 (0.5)† | 11.9${}^{+2.4}_{-4.8}$ (0.5)† | 13/14 | 7.7${}^{+0.0}_{-0.0}$ | 13/14 (0.5)† | 7.7${}^{+0.0}_{-0.0}$ (0.5)†
NGC 7160 | 185/190 | 1.1${}^{+1.6}_{-0.5}$ | 171/176 (0.2) | 1.2${}^{+1.8}_{-0.6}$ (0.2) | 27/27 | 0.0${}^{+0.0}_{-0.0}$ | 27/27 (0.2) | 0.0${}^{+0.0}_{-0.0}$ (0.2)

Notes. Columns. 2, 3, 6 and 7: ratio between the number of members with JHK
counterparts and the total number of members, and the inner disk fractions (in
$\%$) for each cluster and FOV. Rest of the columns: same values for the stars
whose membership probability is above a certain threshold p0 (indicated
between parentheses). †p0 values were arbitrarily set to 0.5, given that the
KS test already provided a p-value $>$ 0.05 (see Sect. 4.1.1). Listed disk
fractions are valid for comparison purposes but should not be taken as
absolute values, given the limitations of our study (see text).

Figure 1: Inner disk fractions from the compact and extended regions are
plotted against each other in the top panel, and their differences in the
bottom panel. The red and green circles are results based on all members
identified per cluster or on the high-probability members, respectively. The
black dashed lines indicate equal values in both panels, and the mean
differences are shown in the bottom panel with red and green dashed lines.

##  4 Analysis and discussion

###  4.1 Consistency

####  4.1.1 Potential contamination

A proper comparison between disk fractions requires that potential
contamination by non-members equally affects the samples within FOV2pc and
outside that region. One way to assess this requirement is by having
equivalent distributions of membership probabilities for the members
identified within FOV2pc and for the rest. Two-sample Kolmogorov-Smirnov (KS)
tests were applied to both previous sub-samples in each cluster. The p-value
inferred from the KS tests is $<$ 0.05 for most clusters, rejecting the
hypothesis that the membership probabilities are drawn from the same parent
distribution. The reason explaining those cases is that whereas most FOV2pc
members have membership probabilities above a certain value, the rest of the
members located further away have membership probabilities both above and
below that value. Filtered samples with membership probabilities above a
threshold were built, increasing such a threshold until the KS test provided a
p-value $>$ 0.05. The p0 values defining the membership probability thresholds
from which the KS tests support that the member sub-samples are drawn from the
same parent distribution are indicated in Table 2. Considering a more
stringent membership probability $>$ p0 (instead of $>$ 0) results in a
significantly reduced number of members outside 2 pc, whereas the sample
within FOV2pc remains comparatively unaltered in most clusters (see Cols. 2, 4
and 6, 8 in that table).

An example illustrating the previous procedure is shown in Fig. 2. Membership
probabilities are plotted against the angular distance to the center of NGC
6231, which is the cluster with the largest number of members identified in
this work. Although the membership probabilities assigned by Clusterix only
rely on proper motions, the members within 2 pc tend to show comparatively
large probabilities, which is not the case for many sources that are further
away. The observed difference in the probability distributions is confirmed by
the KS test, revealing that such a difference is present until a membership
probability threshold p0 = 0.7 is reached. Thus, in order to make a comparison
addressing potentially uneven contamination in NGC 6231, disk fractions must
be modified by only considering the stars with a membership probability $>$
0.7. The high-probability members within 2 pc represents 81$\%$ of all members
initially identified in that region. In contrast, only 34$\%$ of the members
initially identified outside 2 pc are now considered.

Figure 2: Membership probability against angular distance to the center of NGC
6231 for all members identified in this cluster (log-scale). The vertical
dashed line defines two sub-samples closer and further than 2 pc from the
cluster’s center. The horizontal dashed line indicates the probability
threshold p0 below which the KS test rules out that the probability
distributions of both previous sub-samples are drawn from the same parent
distribution. The resulting high- and low-probability members are indicated
with dark green and orange, respectively.

Modified disk fractions in Cols. 5 and 9 of Table 2 are compared in Fig. 1
(green circles). The result obtained in Sect. 3 based on complete member
samples is supported when only the high-probability members are considered.
The difference between disk fractions inferred from the compact and extended
FOVs is again $\sim$ ${}^{+10}_{-5}$ $\%$, mostly within $\sim$ 13$\%$ even
considering errorbars, and the typical (mean) difference is similar too
(-0.8$\%$). The comparison between disk fractions in clusters with low p0
values (e.g. NGC 1333, NGC 7160) does not change significantly if more
stringent probability cuts are used, although the statistical significance is
reduced because of the smaller sample sizes.

The previous test supports that if some differential contamination is present
this does not significantly affect the result concerning the comparison
between disk fractions. Indeed, the mean proper motions inferred from all
members within FOV2pc and FOV20pc are equal considering errorbars for all
clusters (Table 3), and consistent with previous Gaia-based determinations
using narrower FOVs (Appendix C). The direction of motion of the members
identified inside and outside 2 pc roughly coincides in all clusters too (Fig.
6).

The fact that the comparison between disk fractions remains essentially
unaltered after removing the potential contaminants identified above suggests
that these share a similar evolutionary stage, thus supporting that they
mostly belong to the clusters too. Indeed, if a large enough number of the
low-probability members -mainly located in the periphery- were e.g. MS stars,
disk fractions using FOV20pc should be larger once such wrongly introduced
members are removed. Therefore, we should not see strong differences between
the high-and low- probability members concerning their location on the HR
diagram of each cluster. In order to place the members in the Gaia color-
magnitude diagram (CMD hereafter), the observed BP-RP colors and G magnitudes
should first be corrected from extinction. The Gaia EDR3-based optical
extinction values (Av) in Anders et al. (2022) are the most recent and
complete estimates homogeneously derived, and are best suited for our
purposes. Gaia intrinsic colors (BP-RP)0 were calculated using such Av values,
the wavelength corrections from Casagrande et al. (2021), and a typical total-
to-selective extinction ratio Rv = 3.1. Extinction-corrected absolute MG
magnitudes were derived by also using the Gaia EDR3 geometrical distances to
each member based on Bailer-Jones et al. (2021). Errorbars were inferred
propagating the individual uncertainties in the Gaia magnitudes and
parallaxes, and assigning an additional 10$\%$ error associated to extinction.

Fully representative CMDs can be built for NGC 1960, NGC 2353, ASCC 58, and
NGC 6231, given that Av values in Anders et al. (2022) are available for
$\geq$ 90$\%$ of their members. An example is shown in Fig. 3, once again
focused on NGC 6231 (see Fig. 2). PARSEC isochrones and evolutionary tracks
from Bressan et al. (2012) are overplotted for reference. High- and low-
probability members are similarly distributed, their location in the CMD being
above the Zero Age Main Sequence (ZAMS) and consistent with the PMS phase in
almost all cases. The majority of the members have ages in between 1 and 10
Myr, in agreement with previous estimates (Table 1). The $\sim$ 4-12 M⊙ and
$\sim$ 2 M⊙ stars showing ages $<$ 1 Myr, as well as more evolved sources, are
both low- and high- probability members. Particularly, the fraction of members
with extinction values that are already in the MS is the same for the low- and
high-probability sub-samples, $<$ 0.5$\%$. All previous similarities support
that the vast majority of the members identified actually belong to the same
cluster, explaining why the comparison between disk fractions leads to
virtually the same result regardless of the use of the whole sample or the
high-probability sub-sample.

The same exercise was applied to the rest of the clusters. It is noted,
however, that for most of them extinction values are available only for a
fraction of members $<$ 90$\%$, being $<$ 50$\%$ for NGC 1333, IC 348,
$\lambda$ Ori, NGC 2264, and NGC 7129. With the previous caveat in mind, we
find no evidence indicating that the location of the high- and low-
probability members in the Gaia CMDs generally differs. For this reason, and
because the overall comparison between disk fractions remains essentially the
same (Fig. 1), all members identified are equally considered in this
work222Membership probabilities are provided for all stars in each cluster in
Table 4, for which different probability cuts could be applied by the
interested readers.. Gaia CMDs for all clusters are included in Fig. 9. The
distinction in this figure between the FOV2pc and the FOV20pc members will be
used in the remaining discussion.

Figure 3: Extinction corrected Gaia CMD of NGC 6231, where the high- and low-
probability members are indicated with dark green and orange as identified in
Fig. 2. In this case 90$\%$ and 91$\%$ of the high- and low-probability
members are shown, given that extinction values are not available for the
rest. The ZAMS loci is indicated with the black solid curve. PMS isochrones
and evolutionary tracks are overplotted in black and gray for the stellar ages
and masses indicated.

####  4.1.2 Potential mass and age biases

Disk fraction studies specifically devoted to intermediate-mass young stars
are not abundant, but they suggest that disk dissipation is slightly faster
than that for lower-mass objects (Hernández et al., 2007; Yasui et al., 2014;
Ribas et al., 2015). In addition, evolutionary studies based on disk fractions
assume that all stars in a given cluster are roughly coeval (see e.g. the
references in Sect. 1 and Table 1). Therefore, The interpretation of the
result indicating similar disk fractions within each cluster when using FOV2pc
and FOV20pc may depend on whether such fractions refer to stars with similar
stellar masses and ages or not.

Figure 4 compares the typical (mean) extinctions of the inner and outer
regions of the clusters analysed in this work, as inferred from the individual
AV values of the members from Anders et al. (2022). Errorbars reflect the
corresponding standard deviations. For the majority of the clusters there is
no difference between the typical extinctions within $\pm$1$\sigma$. Thus, the
lower mass limit that could be probed within each of the previous clusters is
the same regardless of the FOV. A closer look to the Gaia CMDs (Fig. 9) of the
four clusters with the best extinction characterization (ASCC 58, NGC 1960,
NGC 2353, and NGC 6231) confirms that the mass ranges probed by FOV2pc and
FOV20pc are indeed the same within each cluster. Therefore, the comparison
between the corresponding disk fractions is consistent at least concerning the
stellar mass range that they represent. On the other hand, the CMDs reveal
that the strongest differences between the smallest stellar mass probed
through FOV2pc and FOV20pc are shown by NGC 1333 and IC 348, which results
from the strong differential extinction between the inner and outer regions.
In such cases (see also e.g. NGC 7129 and Tr 37) the innermost region probes
masses $\gtrsim$ 1M⊙ whereas the outer region goes down to $\sim$ 0.5M⊙.
Although small differences in the disk dissipation timescales -and thus on
disk fractions- are expected mainly when the mass ranges compared differ by a
larger amount (see the references above, but also Hernández et al., 2010)
these cases should be viewed with caution given the current lack of
information concerning extinction.

Figure 4: Mean optical extinction from the stars located closer and further
than 2 pc from the center of each cluster are plotted against each other in
the top panel (log-scale), and their differences in the bottom panel. The
dashed lines indicate equal values in both panels. Standard deviations within
each cluster are adopted as errorbars in the top panel. Uncertainties in the
bottom panel are derived from the propagation of the individual 1$\sigma$
deviations. The fraction of member stars for which extinction values from
Anders et al. (2022) are available for each cluster is indicated above the
arrows in the bottom panel.

Regarding the evolutionary stage, although the vast majority of the members
identified in each cluster consistently fall within the PMS location in the
CMDs, age spread is apparent in several of them. This is not surprising, based
on the scatter found in the literature for the clusters in this work analysed
from a variety of data and inferred from different sub-populations, as
referred in Table 1. Clusters in that table with narrow age ranges like NGC
1333 are indeed mainly based on single works focused on compact regions and
specific sub-samples (Wilking et al., 2004), although our data shows that an
older population is also present in that cluster (see the corresponding panel
in Fig. 9). More recent Gaia-based works already find considerable age scatter
in regions comparable to FOV2pc for many young clusters (e.g. Getman et al.,
2018; Prisinzano et al., 2019), confirming previous findings from the pre-Gaia
era (e.g. Getman et al., 2014b, a; Jeffries, 2017, and references therein).

Nevertheless, the comparison between disk fractions is not compromised as long
as the fractions of members with different ages are similar for both FOVs.
This is the case for the majority of the clusters, based on their CMDs in Fig.
9. Following with the same representative example of NGC 6231, $\sim$85$\%$ of
the members have ages $>$ 1 Myr (with 0.4$\%$ already in the MS) and the
remaining $\sim$ 15$\%$ are younger, such fractions being very similar both
for the FOV20pc and a FOV2pc sub-samples. Then the fact that the disk
fractions inferred using both FOVs are equal within errorbars can be
interpreted in terms of a similar disk dissipation timescale regardless of the
distance to the center of the cluster. A relevant exception is NGC 1893. The
majority of the members within FOV2pc have ages in between 1 and 10 Myr, but a
significant fraction of the members identified in the outer region are younger
than 1Myr. This difference would explain why NGC 1893 shows a FOV20pc-based
disk fraction larger above errorbars than that based on FOV2pc (Fig. 1).
Similarly, the fact that NGC 1333 is the other cluster showing the largest
differences between the FOV2pc\- and FOV20pc-based disk fractions is probably
related to a significant age spread depending on the radial distance to the
center. However, in this case the inner region is probably younger than the
outer one. Although such an age difference is motivated by the presence of
very young, embedded Class 0/I sources in the inner region of NGC 1333 (e.g.
Young et al., 2015; Fiorellino et al., 2021) and the observed differential
extinction (Fig. 4), that age gradient cannot be assessed solely based on its
Gaia CMD. As it was mentioned before, this is barely representative given the
lack of enough extinction information.

In other clusters, sub-populations with specific ages present only in FOV20pc
are that small that their presence/absence is virtually irrelevant for the
disk fraction estimate (e.g. NGC 2353). In particular, the presence of a few
MS stars in the Gaia CMDs of some clusters does not affect the disk fraction
comparison. Disk fractions were indeed recalculated in all cases showing such
evolved sources assuming the percentages of MS stars inferred from the CMDs in
Fig. 9, and that they are contaminants not belonging to the cluster. No
significant difference with respect to the values already provided in Table 2
was found.

###  4.2 Limitations

On top of the already mentioned caveats concerning the methodology described
in Sect. 2, additional limitations should be considered when the disk
fractions associated to the compact and extended regions are compared to each
other.

Firstly, because the departure point to identify members are the Gaia
magnitudes in the optical, we are probing essentially Class II stars but not
most of the embedded Class 0/I sources. Indeed, the ratio between the number
of Class II and Class 0/I sources can change depending on the cluster, e.g. a
factor $\sim$ 2 in NGC 1333 or $\sim$ 10 in IC 348 (Young et al., 2015). Thus,
the inferred disk fractions are lower limits for the less evolved clusters
hosting Class 0/I sources. However, embedded stars are mainly located in the
densest and more extincted parts of the clusters (e.g. Gutermuth et al.,
2008), which tend to be closer to the center (Fig. 4). Therefore, although the
inclusion of these sources would make the absolute disk fractions larger than
provided here, such an increase would be mainly related to those obtained
using using FOV2pc. In this respect, accurate disk fractions based on compact
regions should be upper limits to those inferred from extended FOVs, and not
the other way around (Pfalzner et al., 2014).

Secondly, the use of JHK color-color diagrams allows us to identify ”full”
disks with IR excess starting at $\sim$ 1.2 – 2.2 $\mu$m, but not
”transitional” disks with excesses only observable at longer wavelengths. The
number of transitional disks is larger in older clusters, representing around
10$\%$ to 50$\%$ of disk stars (Currie & Sicilia-Aguilar, 2011; Balog et al.,
2016). This again indicates that the disk fractions provided here are lower
limits, in this case specially affecting the evolved clusters. However, to our
knowledge there is no evidence suggesting that the location of transitional
disks with respect to the center of the clusters is different than that of
full disks. Assuming that transitional and full disks are similarly
distributed within the clusters, our result based on the comparison between
relative disk fractions inferred from the compact and the extended regions
remains unaltered.

On the other hand, disk dispersal shows roughly similar timescales regardless
of the wavelength or the observational tracer used (e.g. the review in
Ercolano & Pascucci, 2017, and references therein), but it is not clear if
this applies to environmental effects that promote disk destruction. Indeed,
the presence of massive stars or stellar interactions in the densest and more
massive clusters may lead to a fast disappearance of the outer disk probed at
sub-mm and mm wavelengths (e.g. Anderson et al., 2013; Ansdell et al., 2017;
Vincke & Pfalzner, 2018; van Terwisga et al., 2019). The eventual influence of
such environmental effects is the subject of ongoing debate (see e.g. the
discussion in Parker et al., 2021, and references therein), but it does not
seem to affect the bulk of the disks probed at shorter IR wavelengths (e.g.
Richert et al., 2015). Such a possible difference with the outer disk
dispersal depending on the environment cannot be analysed based on the JHK
photometry used in this work, which we remark again that only refers to inner
dust disks.

A major limitation concerning the JHK color-color diagram is that although it
is very efficient identifying inner disks around intermediate-mass Herbig
Ae/Be stars, up to $\sim$ 30$\%$ of classical T Tauri stars (TTs) may fall in
the region associated to extincted MS stars, therefore remaining undetected
(Lada & Adams, 1992; Haisch et al., 2001; Mamajek, 2009). This is not
problematic for our comparative study of disk fractions, unless the relative
number of undetected TTs changes with the FOV. In particular, for certain
clusters one may expect that the central regions are more extincted than
further away (Fig. 4). Then the relative number of members located between the
bands defining extincted MS stars in the JHK diagram should be larger within
FOV2pc than within FOV20pc. Indeed, Fig. 8 shows that this is the case for
extincted clusters like NGC 1333, and IC 348. Consequently, the disk fractions
inferred using FOV2pc may significantly increase in these clusters once TTs
potentially falling within the extinction region for MS stars in the JHK
diagram are identified as disk stars. This is once again indicating that disk
fractions inferred from FOV20pc cannot generally be significantly larger than
those from FOV2pc, but the case is probably the opposite. Assuming the worst
case scenario in which our disk fractions only account for 70$\%$ of classical
TTs (i.e. f${}_{disk}^{real}$ = fdisk/0.7), the maximum differences between
disk fractions estimated from both FOVs would increase from $\sim$ 10$\%$ to
$\sim$ 14$\%$.

##  5 Concluding remarks

A representative sample of young clusters has been analysed aiming to compare
the inner disk fractions associated to a compact and an extended region with
radii $\sim$ 2 and 20 pc from the center of each cluster. This size is larger
than that probed in all previous reference surveys studying disk fractions and
in more recent Gaia-based studies for the majority of the clusters. Although
the density of members in the periphery is smaller than in the compact region,
the absolute number is on average factor $\sim$ 5 larger at distances further
than 2 pc from the clusters’ centers. This motivates future, detailed studies
of young clusters including more complete samples by probing extended regions,
which may affect e.g. the typical ages or the age dispersion within the
clusters. Our analysis also reveals that inner disk fractions based on the
extended region are not generally larger than those from the compact region by
$\sim$ 50$\%$ or more, contrasting with previous predictions (Pfalzner et al.,
2014). On the contrary, the found differences are typically $\lesssim$ 10$\%$,
and none of the relatively old clusters with negligible disk fractions in the
literature (NGC 1960, NGC 2169, NGC 2353, ASCC 58, Trumpler 15, and NGC 7160)
shows such a significant increase when the extended region is considered.

The limitations and caveats affecting our study have been discussed in detail
along the text, and must be taken into account when interpreting the previous
result. Particularly relevant is that although the presence of massive stars
or stellar interactions in the densest and more massive clusters may lead to a
fastest disappearance of the outer disks, these cannot be probed based solely
on the near-IR photometry used in this work. It is also noted that for this
study we limited ourselves to a maximum radius of 20 pc from the clusters’
centers, but their true extension could be significantly larger. For instance,
a preliminary analysis of NGC 1333 indeed shows new members up to a radial
distance of $\sim$ 40 pc, when no additional ones are found based on proper
motion analysis with Clusterix.

Multi-wavelength analysis, potentially combined with data coming from future
Gaia releases -e.g. radial velocities-, are necessary to provide accurate disk
fractions and better constraint the number and properties of the cluster’s
members. The database resulting from this work is available online and
constitutes a benchmark for such detailed studies.

###### Acknowledgements.

The authors acknowledge the anonymous referee, whose constructive suggestions
have served to improve the manuscript. IM, ES, LBN, NH, and CR acknowledge
support by the Spanish MICIN/AEI/10.13039/501100011033. IM, ES, NH, and CR are
partially funded by MDM-2017-0737 Unidad de Excelencia María de Maeztu \-
Centro de Astrobiología (CSIC-INTA). IM is funded by a RyC2019-026992-I grant.
ES has been funded through grant PID2020-112949GB-I00. LBN acknowledges
support by ”ERDF A way of making Europe” by the “European Union” through grant
RTI2018-095076-B-C21, and the Institute of Cosmos Sciences University of
Barcelona (ICCUB, Unidad de Excelencia ’María de Maeztu’) through grant
CEX2019-000918-M. NH has been partially funded by the AEI Project
ESP2017-87676-C5-1-R. This research is based on Clusterix 2.0 service at CAB
(INTA-CSIC), and has made extensive use of TOPCAT (Taylor, 2005). This work
has made use of data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. This publication makes use
of data products from the Two Micron All Sky Survey and the Wide-field
Infrared Survey Explorer, which are joint projects of the University of
Massachusetts and the Infrared Processing and Analysis Center/California
Institute of Technology; and the University of California, Los Angeles, and
the Jet Propulsion Laboratory/California Institute of Technology, funded by
the National Aeronautics and Space Administration and the National Science
Foundation.

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##  Appendix A Results. Figures and tables

Figure 5: Proper motion distributions for the different clusters where the
field stars within FOV20pc having absolute proper motions $\leq$ 75 mas yr-1
and the member stars are indicated in black and yellow, respectively. The top
left sub-panels focus on the proper motions of the members, where the blue and
red circles correspond to those identified within FOV20pc and FOV2pc,
respectively. Typical (mean) uncertainties in proper motions are $\sim$ 0.04
mas yr-1, roughly comparable to the size of such circles for most cases.

Figure 6:  Sky projections (North to the top and East to the left) for the
different clusters where the blue and red arrows indicate the directions of
motion of all members identified within FOV20pc and FOV2pc, respectively.

Figure 7: Sky projections for the different clusters where the yellow squares
indicate the positions of all members identified within FOV20pc and FOV2pc,
whose corresponding sizes are indicated with the blue and red circles,
respectively. Background images are colored according to the ALLWISE W1, W2,
and W4 bands (except for Trumpler 15, NGC 6231, NGC 6531, and NGC 6611, where
2MASS images are used for a better visualization).

Figure 8: JHK color-color diagrams for the different clusters. In each panel,
the solid line represents the expected position of non-extincted MS stars in
the diagram, and the dashed lines the direction of the extinction vector and
thus the rough boundaries for extincted MS stars (crosses within the dashed
lines indicate an optical extinction increase of 5 magnitudes). Sources
located to the right of the right hand dashed line and within the dotted lines
are considered disk stars. Inner disk fractions are indicated in the legends,
as inferred from all identified members within FOV20pc and within FOV2pc (blue
and red symbols, respectively)

Figure 9: Extinction corrected Gaia CMDs for the different clusters. The ZAMS
loci is indicated with the black solid curve. PMS isochrones and evolutionary
tracks from Bressan et al. (2012) are overplotted in black and gray for the
stellar ages and masses indicated. The representativeness of the diagrams is
limited to the fraction of all members identified within FOV20pc and FOV2pc
having optical extinction estimates in Anders et al. (2022), which is
indicated in the legends.  Table 3: Young Stellar Clusters. Regions and
membership

|  |  |  | FOV20pc |  |  | FOV2pc |  |  |
---|---|---|---|---|---|---|---|---|---|---
Name | RAcent | DECcent | R | Nmemb/Ntot | $\pi$ | pmRA | pmDEC | R | Nmemb/Ntot | $\pi$ | pmRA | pmDEC
… | (∘) | (∘) | ($\arcmin$) | … | (mas) | (mas yr-1) | (mas yr-1) | ($\arcmin$) | … | (mas) | (mas yr-1) | (mas yr-1)
NGC 1333 | 52.2968 | 31.3097 | 240 | 95/43277 | 3.40$\pm$0.08 | 6.94$\pm$0.73 | -9.37$\pm$0.67 | 24 | 28/244 | 3.39$\pm$0.08 | 7.00$\pm$0.80 | -9.79$\pm$0.46
IC 348 | 56.0608 | 32.1560 | 240 | 209/53819 | 3.15$\pm$0.08 | 4.36$\pm$0.59 | -6.30$\pm$0.64 | 24 | 97/312 | 3.14$\pm$0.06 | 4.48$\pm$0.53 | -6.33$\pm$0.52
NGC 1893 | 80.7237 | 33.4438 | 18 | 59/922 | 0.32$\pm$0.04 | -0.30$\pm$0.14 | -1.41$\pm$0.17 | 1.8 | 8/22 | 0.31$\pm$0.03 | -0.32$\pm$0.04 | -1.38$\pm$0.12
$\lambda$ Ori | 83.7802 | 9.9091 | 180 | 377/55430 | 2.50$\pm$0.05 | 1.14$\pm$0.47 | -2.06$\pm$0.30 | 18 | 63/577 | 2.50$\pm$0.05 | 1.00$\pm$0.41 | -2.02$\pm$0.19
NGC 1960 | 84.0840 | 34.1350 | 60 | 273/9263 | 0.85$\pm$0.02 | -0.21$\pm$0.15 | -3.39$\pm$0.17 | 6 | 114/227 | 0.85$\pm$0.02 | -0.21$\pm$0.14 | -3.43$\pm$0.13
NGC 2169 | 92.1250 | 13.9510 | 70 | 102/10500 | 1.03$\pm$0.04 | -1.25$\pm$0.25 | -1.58$\pm$0.17 | 7 | 26/153 | 1.03$\pm$0.04 | -1.10$\pm$0.13 | -1.59$\pm$0.12
NGC 2244 | 97.9817 | 4.9390 | 44 | 418/4255 | 0.68$\pm$0.04 | -1.65$\pm$0.38 | 0.39$\pm$0.41 | 4.4 | 35/75 | 0.67$\pm$0.04 | -1.75$\pm$0.21 | 0.35$\pm$0.21
NGC 2264 | 100.2471 | 9.8755 | 120 | 452/32665 | 1.37$\pm$0.06 | -1.78$\pm$0.38 | -3.68$\pm$0.29 | 12 | 142/242 | 1.38$\pm$0.05 | -1.68$\pm$0.30 | -3.68$\pm$0.22
NGC 2353 | 108.6242 | -10.2711 | 60 | 545/11452 | 0.82$\pm$0.08 | -1.05$\pm$0.43 | 0.77$\pm$0.38 | 6 | 92/206 | 0.84$\pm$0.05 | -1.09$\pm$0.16 | 0.76$\pm$0.20
NGC 2362 | 109.6658 | -24.9557 | 52 | 485/12410 | 0.76$\pm$0.05 | -2.61$\pm$0.46 | 2.93$\pm$0.39 | 5.2 | 90/212 | 0.77$\pm$0.03 | -2.75$\pm$0.21 | 2.98$\pm$0.20
$\gamma$ Vel | 122.3831 | -47.3366 | 180 | 810/134095 | 2.76$\pm$0.14 | -6.20$\pm$0.44 | 9.08$\pm$0.64 | 18 | 99/1364 | 2.87$\pm$0.12 | -6.48$\pm$0.40 | 9.53$\pm$0.56
ASCC 58 | 153.8180 | -55.0003 | 120 | 160/99215 | 2.11$\pm$0.07 | -13.42$\pm$0.48 | 2.70$\pm$0.38 | 12 | 16/1068 | 2.08$\pm$0.03 | -13.32$\pm$0.31 | 2.71$\pm$0.28
Trumpler 15 | 161.1743 | -59.3664 | 26 | 870/6216 | 0.40$\pm$0.04 | -6.31$\pm$0.35 | 2.14$\pm$0.31 | 2.6 | 94/139 | 0.39$\pm$0.03 | -6.13$\pm$0.21 | 2.08$\pm$0.18
NGC 6231 | 253.5356 | -41.8284 | 60 | 1726/26977 | 0.60$\pm$0.04 | -0.64$\pm$0.32 | -2.12$\pm$0.38 | 6 | 265/546 | 0.60$\pm$0.04 | -0.58$\pm$0.21 | -2.19$\pm$0.22
NGC 6531 | 271.0576 | -22.4935 | 55 | 696/15689 | 0.79$\pm$0.04 | 0.50$\pm$0.34 | -1.46$\pm$0.34 | 5.5 | 91/257 | 0.80$\pm$0.04 | 0.54$\pm$0.21 | -1.42$\pm$0.22
NGC 6611 | 274.6993 | -13.8090 | 40 | 809/7796 | 0.59$\pm$0.05 | 0.16$\pm$0.53 | -1.63$\pm$0.58 | 4 | 72/133 | 0.56$\pm$0.04 | 0.20$\pm$0.31 | -1.66$\pm$0.27
Trumpler 37 | 324.7486 | 57.4782 | 73 | 381/18293 | 1.07$\pm$0.04 | -2.43$\pm$0.52 | -4.28$\pm$0.75 | 7.3 | 52/290 | 1.07$\pm$0.04 | -2.43$\pm$0.33 | -4.47$\pm$0.62
NGC 7129 | 325.7401 | 66.1140 | 60 | 43/8627 | 1.07$\pm$0.06 | -1.77$\pm$0.33 | -3.41$\pm$0.39 | 6 | 14/63 | 1.10$\pm$0.04 | -1.77$\pm$0.18 | -3.45$\pm$0.32
NGC 7160 | 328.4142 | 62.6020 | 72 | 190/20532 | 1.06$\pm$0.05 | -3.42$\pm$0.23 | -1.44$\pm$0.34 | 7.2 | 27/213 | 1.09$\pm$0.04 | -3.51$\pm$0.19 | -1.38$\pm$0.18

Notes. Columns 1 to 3 list the name of the cluster and the coordinates of its
central position. Columns 4 to 8 refer to FOV20pc, listing the associated
angular radius, number of members identified divided by the total number of
sources within the FOV having Gaia EDR3 proper motions and reliable parallaxes
(as defined in Sect. 2.1), and inferred mean parallax and proper motions
(uncertainties refer to the standard deviations). The rest of the columns are
equivalent to the previous, but related to FOV2pc.

Table 4: Young Stellar Clusters. Members identified

RA | DEC | pmRA | pmDEC | $\pi$ | BP | RP | G | dcent | PROB | H-K | J-H | disk?
---|---|---|---|---|---|---|---|---|---|---|---|---
∘ | ∘ | mas yr-1 | mas yr-1 | mas | mag | mag | mag | ∘ | … | mag | mag | …
|  |  |  |  |  | NGC 1333 |  |  |  |  |  |
55.6003 | 32.1583 | 6.96 $\pm$ 0.08 | -9.56 $\pm$ 0.06 | 3.32 $\pm$ 0.09 | 18.651 $\pm$ 0.023 | 15.577 $\pm$ 0.006 | 16.846 $\pm$ 0.003 | 2.9348 | 1.000 | 0.26 $\pm$ 0.04 | 0.71 $\pm$ 0.04 |
52.3399 | 31.3528 | 7.64 $\pm$ 0.06 | -9.59 $\pm$ 0.05 | 3.41 $\pm$ 0.06 | 18.149 $\pm$ 0.015 | 14.594 $\pm$ 0.005 | 15.957 $\pm$ 0.003 | 0.0567 | 0.993 | 0.35 $\pm$ 0.04 | 0.67 $\pm$ 0.04 |
52.1815 | 31.2934 | 7.27 $\pm$ 0.13 | -9.74 $\pm$ 0.10 | 3.35 $\pm$ 0.12 | 19.312 $\pm$ 0.088 | 15.196 $\pm$ 0.034 | 16.805 $\pm$ 0.011 | 0.0998 | 0.980 | 0.82 $\pm$ 0.03 | 1.26 $\pm$ 0.04 |
|  |  |  |  |  | IC 348 |  |  |  |  |  |
56.1558 | 32.1032 | 4.36 $\pm$ 0.05 | -6.38 $\pm$ 0.03 | 3.10 $\pm$ 0.05 | 16.683 $\pm$ 0.013 | 14.011 $\pm$ 0.005 | 15.205 $\pm$ 0.003 | 0.0962 | 1.000 | 0.28 $\pm$ 0.03 | 0.94 $\pm$ 0.03 |
55.3089 | 31.9961 | 4.58 $\pm$ 0.02 | -6.08 $\pm$ 0.02 | 3.28 $\pm$ 0.02 | 12.590 $\pm$ 0.003 | 11.151 $\pm$ 0.004 | 11.945 $\pm$ 0.003 | 0.6569 | 1.000 | 0.18 $\pm$ 0.03 | 0.34 $\pm$ 0.03 |
56.0903 | 32.1069 | 4.70 $\pm$ 0.07 | -6.15 $\pm$ 0.05 | 3.12 $\pm$ 0.08 | 17.776 $\pm$ 0.024 | 14.688 $\pm$ 0.009 | 15.984 $\pm$ 0.003 | 0.0551 | 1.000 | 0.29 $\pm$ 0.03 | 0.93 $\pm$ 0.03 |
|  |  |  |  |  | NGC 1893 |  |  |  |  |  |
80.6932 | 33.4024 | -0.60 $\pm$ 0.03 | -1.54 $\pm$ 0.02 | 0.30 $\pm$ 0.03 | 14.938 $\pm$ 0.003 | 13.667 $\pm$ 0.004 | 14.395 $\pm$ 0.003 | 0.0486 | 1.000 | 0.30 $\pm$ 0.04 | 0.50 $\pm$ 0.04 |
80.6866 | 33.4435 | -0.50 $\pm$ 0.03 | -1.37 $\pm$ 0.02 | 0.34 $\pm$ 0.02 | 11.412 $\pm$ 0.003 | 11.000 $\pm$ 0.004 | 11.274 $\pm$ 0.003 | 0.0310 | 0.998 | 0.03 $\pm$ 0.03 | 0.05 $\pm$ 0.03 |
80.6833 | 33.4407 | -0.50 $\pm$ 0.03 | -1.33 $\pm$ 0.02 | 0.37 $\pm$ 0.03 | 10.332 $\pm$ 0.003 | 9.940 $\pm$ 0.004 | 10.204 $\pm$ 0.003 | 0.0338 | 0.996 | 0.05 $\pm$ 0.03 | 0.02 $\pm$ 0.03 |
|  |  |  |  |  | … |  |  |  |  |  |

Notes. Columns 1 to 10 list the Gaia EDR3 coordinates, proper motions,
parallax, BP, RP and G magnitudes, angular distance to the center of the
cluster, and membership probability (ordered from higher to lower) of each
member identified (PROB $>$ 0) within FOV20pc. The members within FOV2pc can
be retrieved from dcent and the corresponding angular radius (see Col. 9 in
Table 3). Columns 11 and 12 list the 2MASS colors, when available. Objects
identified as disk stars or potential disk stars based on the JHK colors and
errorbars are tagged with ”yes” and ”yes?” in the last column. The absence of
such tags does not necessarily mean that the star is diskless (Sects. 2.2 and
4.2). Only the three first rows for the three first clusters are shown. A
complete version of this table is available online.

##  Appendix B Virtual Observatory compliant, online catalogue

In order to help the astronomical community on using the information obtained
in this paper, we developed an archive system that can be accessed from a
webpage333http://svocats.cab.inta-csic.es/diskfrac or through a Virtual
Observatory ConeSearch444e.g. http://svocats.cab.inta-
csic.es/diskfrac/cs.php?RA=152.799&DEC=-54.423&SR=0.1&VERB=2.

The archive system implements a very simple search interface that allows
queries by coordinates and radius as well as by cluster name and other
parameters of interest. The user can also select the maximum number of sources
(with values from 10 to unlimited). The result of the query is a HTML table
with all the sources found in the archive fulfilling the search criteria. The
result can also be downloaded as a VOTable or a CSV file. Detailed information
on the output fields can be obtained placing the mouse over the question mark
located close to the name of the column. The archive also implements the
SAMP555http://www.ivoa.net/documents/SAMP (Simple Application Messaging)
Virtual Observatory protocol. SAMP allows Virtual Observatory applications to
communicate with each other in a seamless and transparent manner for the user.
This way, the results of a query can be easily transferred to other VO
applications, such as, for instance, Topcat (Taylor 2005).

##  Appendix C Comparison with previous Gaia-based results

Figure 10 compares our results with those in Cantat-Gaudin & Anders (2020),
which provides a complete Gaia DR2-based census of Galactic clusters including
all analysed here. Cantat-Gaudin & Anders (2020) reported the use of FOVs
significantly larger than in the previous reference papers by Dias et al.
(2002) and Kharchenko et al. (2013), although the specific sizes were not
systematically listed. Based on the positions of the members located furthest
from the clusters’ centers, a reasonable estimate of the FOVs used in Cantat-
Gaudin & Anders (2020) can be derived. Such FOVs, as well as the total number
of potential members (i.e. with non-null membership probability) from Cantat-
Gaudin & Anders (2020), are compared to those from this work in the top left
panel of Fig. 10. Our FOV20pc and number of potential members are $\sim$ 4.3
and $\sim$ 1.4 times larger on average. It is noted that this is a rough
comparison that does not take into account the different methodologies for
membership identification or the limiting magnitudes considered. In this
particular, although Cantat-Gaudin & Anders (2020) probed more sources by
including stars 1 Gaia G-magnitude fainter than here, we still identify a
larger number of members for the majority of the clusters because of the use
of a larger FOV. The rest of the panels in Fig. 10 compare the parallaxes and
proper motions. Values and errorbars refer to the means and standard
deviations derived from FOV20pc (see Table 3) and to the ones tabulated in
Cantat-Gaudin & Anders (2020). Despite of the above mentioned differences
concerning methodologies, FOVs, and the number of members identified,
parallaxes and proper motions coincide within $\pm$1$\sigma$ for all clusters.
Mean distances to each cluster were derived from the ones of all members
within FOV20pc, based on the parallax-distance geometrical transformation in
Bailer-Jones et al. (2021). Distances are indicated in the top right panel of
Fig. 10, and were listed in Table 1 along with the corresponding standard
deviations.

Figure 10: Comparison between data from this work and from Cantat-Gaudin &
Anders (2020) (Top left): ratio between the FOVs used versus ratio between the
total number of members identified. The dotted lines indicate the typical
(mean) values in each axis. (Top right, bottom left, and bottom right):
Comparison between parallaxes and proper motions. The dashed lines indicate
equal values. Distances are indicated in the opposite y-axis of the top right
panel for reference.