# Search for Brown Dwarfs in IC 1396 with Subaru HSC: Interpreting the Impact
of Environmental Factors on Sub-stellar Population

Saumya Gupta 1, Jessy Jose1, Swagat R. Das2, Zhen Guo3,4,5,6, Belinda Damian7,
Prem Prakash8, Manash R Samal9,
1 Indian Institute of Science Education and Research (IISER) Tirupati, Rami
Reddy Nagar, Karakambadi Road, Mangalam (P.O.), Tirupati 517 507, India
2 Departamento de Astronomía, Universidad de Chile, Las Condes, 7591245
Santiago, Chile
3Instituto de Física y Astronomía, Universidad de Valparaíso, ave. Gran
Bretaña, 1111, Casilla 5030, Valparaíso, Chile
4Núcleo Milenio de Formación Planetaria (NPF), ave. Gran Bretaña, 1111,
Casilla 5030, Valparaíso, Chile
5Centre for Astrophysics Research, University of Hertfordshire, Hatfield AL10
9AB, UK
6Departamento de Física, Universidad Tecnicá Federico Santa María, Avenida
España 1680, Valparaíso, Chile
7 Christ (Deemed to be University), Bangalore, India
8 Indian Institute of Technology Hyderabad, Kandi, Sangareddy, Telangana,
India
9 Physical Research Laboratory (PRL), Navrangpura, Ahmedabad 380 009, Gujarat,
India
kcsaumya.gupta<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Young stellar clusters are predominantly the hub of star formation and hence,
ideal to perform comprehensive studies over the least explored sub-stellar
regime. Various unanswered questions like the mass distribution in brown dwarf
regime and the effect of diverse cluster environment on brown dwarf formation
efficiency still plague the scientific community. The nearby young cluster, IC
1396 with its feedback-driven environment, is ideal to conduct such study. In
this paper we adopt a multi-wavelength approach, using deep Subaru HSC, Gaia
DR3, Pan-STARRS, UKIDSS/2MASS photometry and machine learning techniques to
identify the cluster members complete down to $\sim$ 0.03 M⊙ in the central
22′ area of IC 1396. We identify 458 cluster members including 62 brown dwarfs
which are used to determine mass distribution in the region. We obtain a star-
to-brown dwarf ratio of $\sim$ 6 for a stellar mass range 0.03 – 1 M⊙ in the
studied cluster. The brown dwarf fraction is observed to increase across the
cluster as radial distance from the central OB-stars increases. This study
also compiles 15 young stellar clusters to check the variation of star-to-
brown dwarf ratio relative to stellar density and UV flux ranging within
4-2500 stars pc-2 and 0.7-7.3 G0 respectively. The brown dwarf fraction is
observed to increase with stellar density but the results about the influence
of incident UV flux are inconclusive within this range. This is the deepest
study of IC 1396 as of yet and it will pave the way to understand various
aspects of brown dwarfs using spectroscopic observations in future.

###### keywords:

stars: brown dwarfs – stars: Hertzsprung–Russell and colour–magnitude diagrams
– methods: data analysis – virtual observatory tools – techniques: photometric
– catalogues

††pubyear: 2024††pagerange: Search for Brown Dwarfs in IC 1396 with Subaru
HSC: Interpreting the Impact of Environmental Factors on Sub-stellar
Population–B

##  1 Introduction

Brown dwarfs, defined as self-gravitating sub-stellar objects with mass
ranging between 0.013 – 0.08 M⊙, have cool temperatures insufficient to
initiate Hydrogen burning in their cores. Several mechanisms proposed for
brown dwarf formation include turbulent fragmentation, disk fragmentation,
dynamical ejection and photo-erosion (Whitworth & Zinnecker 2004; Bonnell et
al. 2008; Stamatellos & Whitworth 2009; Whitworth 2018). These sub-stellar
sources have been the focus of several past and recent studies in different
young star-forming regions such as ONC, NGC 2244, Lupus, $\rho$ Oph, W3,
Taurus, Perseus, Sigma Ori, Serpens, Upper Sco and IC 348 (Scholz et al. 2012;
Zapatero Osorio et al. 2017; Mužić et al. 2017; Luhman et al. 2018; Esplin &
Luhman 2019; Mužić et al. 2019; Jose et al. 2020; Huston & Luhman 2021;
Almendros-Abad et al. 2023; Damian et al. 2023a). In spite of such plethora of
studies, the exact dominant brown dwarf formation mechanism and the factors
which determine the brown dwarf population in a region still remain vague.
Many brown dwarf formation mechanisms suggest that the pre-mature ejection of
a self-gravitating object results in the formation of very low-mass objects as
they are cut-off from the accretion material supply (Whitworth & Zinnecker
2004; Stamatellos & Whitworth 2009; Chabrier et al. 2014; Whitworth 2018). It
is hence, expected that the external factors like turbulence, high energy UV
radiation and stellar density may introduce more dynamical perturbations
leading to an early ejection of the collapsing cores and enhance the census of
brown dwarfs formed in a region. Another interesting yet ambiguous subject to
investigate here is the mass distribution in sub-stellar regime. Deep studies
of Galactic stellar clusters reaching down to the low mass and brown dwarf
realm are helpful to constrain the stellar evolutionary models. It is thus,
pivotal to obtain robust statistical samples of brown dwarfs in various young
stellar clusters ($<$ 10 Myrs) with diverse environments to shed more light on
the ambiguous issues related to the sub-stellar realm.

The young stellar clusters ($<$ 10 Myrs) are not much dynamically evolved
(Portegies Zwart et al. 2010; Longmore et al. 2014; Fujii & Portegies Zwart
2016), hence their current mass distribution is closest to the initial mass
function (IMF) of the cluster (Kroupa & Boily 2002; Lim et al. 2015). Such
young clusters provide a robust sample of stars spanning a wide range of mass
and hence, are the ideal test-beds to perform deep comprehensive studies of
the stellar and sub-stellar population in the region. However, due to obvious
observational constraints and high intrinsic reddening from the cluster, it is
difficult to observe the faint low-mass and sub-stellar population ($<$ 0.5
M⊙) in distant ($>$ 1 kpc) young Galactic star forming regions. On the
contrary, the nearby young clusters affected by minimal extinction like ONC,
$\rho$ Ophuichi, IC 348 and NGC 1333 (AV $\sim$ 2 mag) provide excellent
statistical sample to carry out deeper and wider studies in diverse
environments. In addition, although spectroscopy is the widely adopted
solution of obtaining the stellar parameters in nearby clusters, it is highly
time intensive and restricted to a limited number of sources (Alves de
Oliveira et al. 2012; Burgasser et al. 2019; Pearson et al. 2021; Damian et
al. 2023b). Hence, multi-wavelength photometric studies of such star forming
regions with facilities like Pan-STARRS, Gaia, Subaru Hyper Suprime-Cam (HSC),
GTC, HST, CFHT/WIRCam, and UKIRT/WFCAM are useful to detect the very low-mass
end of stellar population (Mužić et al. 2012; Allers & Liu 2020; Robberto et
al. 2020; Das et al. 2023; Damian et al. 2023b).

It is also crucial to understand the effect of diverse environmental
conditions on the population of brown dwarfs in a cluster. Brown dwarf
fraction is a useful tool to estimate the statistics of brown dwarfs formed in
a given star forming event. Any increase or decrease in the brown dwarf
formation efficiency across diverse cluster environments due to external
factors like UV flux and stellar density, would imply an inverse effect on the
star-to-brown dwarf ratio (Whitworth & Zinnecker 2004; Bonnell et al. 2008;
Stamatellos & Whitworth 2009; Vorobyov et al. 2017). The feedback driven
cluster environment may promote the formation of brown dwarfs in a region by
depleting the supply of accreting material from the fragmented low-mass cores.
Recent studies have also explored the impact from the presence of OB stars on
the formation of brown dwarfs (Mužić et al. 2019; Almendros-Abad et al. 2023)
for the regions covered under the Sub-stellar Objects in Nearby Young Clusters
(SONYC) survey. In the present study, we identify and characterize the brown
dwarfs in a young star forming region, IC 1396 (see details below), and then
compare the star-to-brown dwarf ratio with various star-forming regions. We
also compile fifteen young stellar clusters to investigate the behaviour of
star-to-brown dwarf ratio with varying stellar density and incident FUV flux.

###  1.1 IC 1396

Figure 1: WISE 22 $\mu$m image of IC 1396 with the blue circle marking the 22′
radius region studied in this paper. The yellow cross marks the massive star
HD 206267.

The young star forming H ii region IC 1396 (see Figure 1), almost 3∘ in
diameter, is associated with the Cepheus OB2 association (Patel et al. 1998;
Getman et al. 2007). At a distance of 900 – 910 parsecs (Contreras et al.
2002; Sicilia-Aguilar et al. 2006, 2019; Das et al. 2023), this region is
ionised by the central binary system HD 206267 (Pelayo-Baldárrago et al. 2023
and references therein) and is estimated to have an age ranging between 2–5
Myrs (Patel et al. 1998; Sicilia-Aguilar et al. 2005; Getman et al. 2012;
Sicilia-Aguilar et al. 2013). The cluster hosts a prominent cavity at the
center cleared off the dust and gas as a result of ionization from the central
massive star. The region is also associated with several Bright-rimmed clouds
(BRCs), globules and elephant-trunk structures. The relatively close
proximity, minimal uniform extinction (AV $\sim$ 1 – 1.5 mag (Contreras et al.
2002; Sicilia-Aguilar et al. 2005; Nakano et al. 2012; Sicilia-Aguilar et al.
2013; Sicilia-Aguilar et al. 2019)) and ongoing star formation affected by the
feedback from massive stars in the region (Sicilia-Aguilar et al. 2004, 2006;
Saurin et al. 2012), make it an ideal target to conduct deep studies regarding
low-mass star formation and the factors affecting it.

Several studies have performed the membership classification of the region
using techniques like X-ray observations (Mercer et al. 2009; Getman et al.
2012), spectroscopic surveys (Contreras et al. 2002; Sicilia-Aguilar et al.
2006; Nakano et al. 2012; Sicilia-Aguilar et al. 2013; Sicilia-Aguilar et al.
2019), H$\alpha$ photometry (Barentsen et al. 2011) and infrared disk searches
(Sicilia-Aguilar et al. 2006; Morales-Calderón et al. 2009; Silverberg et al.
2021). The most recent studies of IC 1396 by Pelayo-Baldárrago et al. (2023)
and Das et al. (2023) add extra $\sim$ 500 and 244 new members respectively,
to this list using Gaia astrometry. In total, all these studies identify 2455
sources as members in the entire 3∘ diameter region. However, none of these
studies are complete for stellar masses $<$ 0.5 M⊙ and hence, are inadequate
to explore the sub-stellar population in the region. This calls for deeper
observations using a wide field-of-view camera on a large telescope which can
simultaneously reach down to faint low mass limits while covering a wider
area.

This study aims to perform a brown dwarf population analysis within the 22′
region, centered at R.A: 324.74∘ ; Dec: 57.49∘ around the massive star HD
206267. The area is specifically chosen for study as more than 60$\%$ of the
previously identified cluster members as well as disk sources are located
within this area. The complex is assumed to have multiple generations of
stellar population in BRCs (Sicilia-Aguilar et al. 2006; Sicilia-Aguilar et
al. 2014; Pelayo-Baldárrago et al. 2023; Das et al. 2023) and we focus on the
central portion of the cluster.

This work is a premier study to investigate the brown dwarf population in IC
1396. It presents a compiled comparative analysis of fifteen star forming
regions, which will aid the current colloquy about the role played by external
factors on brown dwarf formation efficiency. This paper is organized as
follows: Section 2 presents the multi-wavelength data sets used for this
study. Section 3 discusses the various machine learning techniques, spectral
energy distribution (SED) fitting and pre-main sequence locus based
identification to obtain a reliable set of members. Consequently, we identify
the sub-stellar sources and determine the mass distribution in Section 4. We
perform a comparative study of the brown dwarf fraction across fifteen star
forming regions and discuss its variation relative to stellar density and
incident FUV flux in Section 5. A summary of our work along with the future
plans are presented in Section 6. Finally, we present the identified brown
dwarfs in Section 7.

##  2 Data Sets Used

The multi-wavelength broadband photometry is a useful approach to detect a
substantial sample of sub-stellar objects in nearby young star forming regions
(Alves de Oliveira et al. 2013; Esplin & Luhman 2017; Luhman et al. 2018).
However, the multi-wavelength photometry approach also requires a reliable
member sample which can be used as a template for other sources. The Gaia
astrometry including proper motion and parallax values for individual sources
is ideal to generate such a model member sample. This can be further applied
to obtain a deeper set of members using machine learning (ML) techniques. We
use optical (Subaru HSC, Pan-STARRS DR1 and Gaia DR3) in conjunction with
near-IR (NIR) (UKIDSS DR11, 2MASS) data to perform a deep study of the brown
dwarf realm of the target region.

###  2.1 Subaru HSC Data

We obtained Subaru HSC observations for two pointings (central RA: 324.27∘;
Dec: 57.91∘ and RA: 326.37∘; Dec: 57.72∘, respectively), each covering an area
of 1.5∘ diameter. The HSC observations were taken on 18th August’2017 (PI: J.
Jose; Program ID: S17B0108N), using EAO111East Asian Observatory time in three
broad-band optical filters, namely, r2, i2 and Y (Kawanomoto et al. 2018). The
data reduction is conducted following the steps designed in Gupta et al.
(2021). The raw data is reduced by HSC pipeline version 6.7 which performs (1)
Single-visit Processing which involves detrending of the raw data (2) Joint
Calibration which conducts an internal calibration across different
visits222observing shots (3) Coaddition of various visits to form a single
deep image and finally, (4) Coadd Processing/ Multiband Analysis which detects
individual sources using source extraction and performs photometry on coadded
images in the individual filters. For more details on the HSC data reduction
please refer Aihara et al. (2018); Bosch et al. (2018); Gupta et al. (2021).
We obtain a total of 2,401,026 sources detected in either of the three filters
(r2, i2 or Y), after data reduction for the entire observed region. However,
we will only use the data restricted within the radius of 22′ around the
ionizing source HD 206267 for our analysis due to the aforementioned reasons
(see Section 1.1). The photometric results and analysis of a wider area of the
complex will be presented in a forthcoming paper (Das et al., in preparation).
Approximately 254,022 HSC sources are located within the area of interest with
photometry in either of the three bands. In order to select sources with good
photometry as well as avoid losing genuine sources, we consider only those
which have photometric error $\leq$ 0.1 mag in individual HSC filters (Gupta
et al. 2021). The data is observed to saturate at r2 $\sim$ 15.0 mag
corresponding to a source of $\sim$ 1 M⊙, and is 90$\%$ complete down to 24.5
mag which corresponds to a 0.03 - 0.035 M⊙ source, at a distance of 900
parsecs, age $\sim$ 2 Myrs and AV $\sim$ 1 mag (Baraffe et al. 2015). We
obtain the 90$\%$ completeness limit here using the turnover point of source
count approach (for details see Jose et al. (2017); Damian et al. (2021);
Gupta et al. (2021)). With the help of such deep optical data, we are able to
explore well into the sub-stellar realm as discussed in Section 4.

###  2.2 Pan-STARRS DR1 Data

In addition to HSC, we use Pan-STARRS DR1 data333downloaded from
https://vizier.u-strasbg.fr/viz-bin/VizieR (Chambers et al. 2016) in r, i and
Y filters to generate the optical catalog used for our analysis. We consider
only those sources for which number of stack detections is $>$ 2, magnitude in
individual bands $\geq$ 12 mag to avoid source saturation and photometric
error in individual filters is $\leq$ 0.1 mag (Chambers et al. 2016). We use
transformation equations given in Gupta et al. (2021) to convert the
photometry from Pan-STARRS filter system to HSC system. Pan-STARRS photometry
is mainly used here to add sources, especially at the bright end, which are
missed in HSC photometry. In total, we have a combined optical catalog of
258,602 sources which will be further used to identify members in the area of
study. We will refer this combined data set as the deep optical catalog
henceforth.

###  2.3 Gaia DR3 Data

We obtained the Gaia DR3 data consisting of 48,185 sources from Gaia Science
archive (Gaia Collaboration et al. 2022) in the 22′ radius of IC 1396 and use
it to obtain a reliable training set for the identification of members using
machine learning techniques as elaborated in further sections. In order to
select genuine Gaia sources, we give certain constraints such as parallax $>$
0, re-normalised unit weight error (RUWE) $<$ 1.4, detection in all Gaia
filters (Lindegren et al. 2021; Pelayo-Baldárrago et al. 2022; Prisinzano et
al. 2022) while retrieving the data using Astronomical Data Query Language
(ADQL) interface. Since, Gaia data is complete between 19 $\leq$ G $\leq$ 20
mag (Gaia Collaboration et al. 2021; Marton et al. 2022), we restrict the
sources down to G $\leq$ 19.5 mag (average of range 19–20). We thus, obtain
19,432 Gaia sources within the 22′ radius of IC 1396.

###  2.4 UKIDSS GPS DR11 / 2MASS Data

The NIR photometry when used along with deep optical data, gives a broad
wavelength range particularly useful for performing SED fitting of the cluster
members and obtaining the relevant stellar parameters (Mužić et al. 2019;
Damian et al. 2021; Kubiak et al. 2021). We use the deep archived UKIDSS GPS
DR11444http://wsa.roe.ac.uk/dr11plus_release.html (Lucas et al. 2008) in J, H
and K bands (Hewett et al. 2006; Lawrence et al. 2007) for this purpose. The
UKIDSS GPS DR11 data is retrieved from WFCAM Science archive after applying
constraints like J $\geq$ 13 mag and photometric errors less than 0.1 mag to
only obtain sources with good photometry. In order to include brighter
sources, we make use of the 2MASS NIR data (Cutri et al. 2003) downloaded from
Vizier in JHK bands with J $<$ 13\. Also, we select good 2MASS sources based
on the quality flags such as ph$\\_$qual $\neq$ F,E,U, rd$\\_$flg $\neq$ 6 and
cc$\\_$flg $\neq$ p,d,s,b (Cutri et al. 2003; Guarcello et al. 2021). The
concatenated list of sources from 2MASS (J $<$ 13 mag) and UKIDSS (J $\geq$ 13
mag) forms the deep NIR catalog of the central 22′ radius region of IC 1396,
comprising of 87,614 sources to be used further for our analysis.

##  3 Membership analysis

The identification of cluster members based on the stellar proper motion and
parallax information is one of the most reliable and widely used methods
(Olivares et al. 2019; Miret-Roig et al. 2019; Kubiak et al. 2021; Prisinzano
et al. 2022; Pelayo-Baldárrago et al. 2023; Das et al. 2023). Thanks to the
consecutive Gaia data releases, we now have complete astrometric solutions
(proper motion and parallax) available for 1.46 billion stars (Gaia
Collaboration et al. 2022). However, the primary drawback here is that it is
only complete down to G $\sim$ 19 - 20 mag (Gaia Collaboration et al. 2021;
Prisinzano et al. 2022; Marton et al. 2022) and hence, quite shallow to
identify the faint low-mass cluster members. Machine learning is an
extensively used tool which comes to our rescue at this juncture with its
unsupervised and supervised techniques like Gaussian Mixture Model (GMM) and
Random Forest classifier (RF). Such techniques can accurately classify cluster
members and young stellar objects from non-members in young star forming
regions based on the input features (Sarro et al. 2014; Gao 2018b, 2019;
Olivares et al. 2019; Melton 2020; Pelayo-Baldárrago et al. 2023; Das et al.
2023).

In this study, we use Gaia archived data to form a set of training data by
clustering them into members and non-members using the GMM technique. Reliable
members and non-members are then utilized in training the RF classifier to
identify the probable members among the input deep optical data set. This is
followed by SED analysis of the probable members to select confirmed members
and deduce their stellar parameters. We briefly describe the procedure adopted
to identify members in the area of interest, down to very faint low-mass and
sub-stellar sources ($\sim$ 0.03 M⊙). Please refer Das et al. (2023) for more
details about the procedure followed.

###  3.1 GMM

GMM is an unsupervised machine learning technique which categorizes a data set
into different clusters based on the probability of each data point associated
with a particular group. The technique makes a reasonable assumption that the
data set is a collection of normally distributed groups (Sarro et al. 2014;
Gao 2018a, b; Cantat-Gaudin et al. 2019; Galli et al. 2020). We initiate our
cluster member selection process by generating an efficient training set using
Gaia DR3 data for the 22′ radius region. However, one of the major limitations
of this method is failure to identify clusters due to overcrowding of field
stars (Gao 2018a, b; Das et al. 2023). In order to avoid this, we impose few
more constraints on astrometric parameters such as proper motion values in the
range –20 $\leq$ $\mu_{\alpha}$cos$\delta$ $\leq$ 20 mas/yr , –20 $\leq$
$\mu_{\delta}$ $\leq$ 20 mas/yr (Errmann et al. 2013) and distance range
within 500 parsecs – 1500 parsecs (de Zeeuw et al. 1999; Pelayo-Baldárrago et
al. 2023) while using the Gaia data here. We use the distance estimates from
Bailer-Jones et al. (2021). The mentioned constraints on the distance and
proper motions are relaxed enough so as not to lose any probable members as
well as ensure reduction in the foreground and background contamination in
accordance with the values estimated by the previous studies. This aids in
generating a robust training data set.

In total, we obtain 2771 Gaia sources after applying the above constraints.
Among these stars, GMM identifies two groups, namely members and non-members
and assigns each star the probability of being associated to each group. This
assignment is based on astrometric parameters, i.e, positions, proper motions
and parallax information of the star. The sources identified as members and
with probability $\geq$ 0.8 (Gao 2019) are selected for further analysis. The
sources identified as non-members by GMM based on their astrometric
information, are used as non-member training set further in RF classifier.
Since IC 1396 is a young cluster with age $<$ 10 Myrs (Sicilia-Aguilar et al.
2005; Das et al. 2023), we further refine the Gaia member selection by
considering only those sources which are located to the right of the 10 Myr
isochrone, corrected for a distance $\sim$ 900 parsecs and AV $\sim$ 1 mag
(Baraffe et al. 2015) in all the colour-magnitude combinations ((G–RP) vs G,
(BP–RP) vs BP, (BP–G) vs BP). We present the pmra vs pmdec plots, BP - RP vs
BP and r2 \- Y vs r2 CMD in Fig 2 and Fig 3 for the identified Gaia-based
members. We eventually secure 411 Gaia members which form an ideal training
set for RF classifier.

Figure 2: (Left) Proper motion RA vs proper motion Dec plot obtained after
performing GMM. (Right) Zoomed version of proper motion RA vs proper motion
Dec plot focused on GMM identified members.

Figure 3:  (Left) BP - RP vs BP (Right) r2 \- Y vs r2 CMD for members and non-
members obtained after performing GMM.

###  3.2 Random Forest Classifier

RF classifier is a widely used supervised learning technique (Galli et al.
2020; Mužić et al. 2022; Das et al. 2023) which performs classification of a
new data set based on the training data by using the majority voting approach.
The algorithm builds individual decision trees which generate output for each
of the different sample subsets of the data. The eventual output of the
classification is considered based on the results of the majority of the
subsets (Pedregosa et al. 2011). Due to this approach, RF classifier is immune
to dimensionality of the feature555input attributes useful in learning
distinction between different classes space. We identify probable members
among the deep optical data by executing RF classifier in three phases. We use
the above identified Gaia members and non-members with HSC counterparts (see
Section 3.1) as the training data set. In the first phase, RF classifier is
applied to the 34,859 HSC sources with Gaia DR3 counterparts devoid of any
constraints applied to it. In this phase, we are able to use Gaia parallax and
proper motions along with the optical colours ((r2–i2) vs r2 ; (r2–Y) vs r2)
and magnitude ratios (Y/r2 ; i2/r2) of stars as input training features. The
RF model, thus trained on the basis of training features mentioned above
identifies 792 probable members.

In the second phase, we use this obtained member and non-member set as the
training sample for the remaining HSC sources without Gaia counterparts and
hence, devoid of any parallax and proper motion information of the sources.
The RF classifier in this phase uses the same optical colours and magnitude
ratios as mentioned above for the training purpose. Using magnitude ratios
along with optical HSC colours as input features aids in improving the quality
of segregation between the members and non-members, as evident from the
receiver operating characteristic (ROC) curves (shown in Appendix 12). The
hyper-parameters used for RF classifier are also listed in Appendix 12. For
each run of RF classifier, we evaluate the model using train-test-split with
test size equal to 40$\%$ of the data set and random state equal to 50. We
train our algorithm using 5-fold cross-validation with an average cross
validation (CV) score of 0.985 and using ROC as the measure of performance.
Although, the member sample retrieved so far still does not serve our purpose
of investigating the sub-stellar end of the cluster, it provides a robust
training sample required to augment the identification of probable cluster
members down to the very low mass end.

Training feature | Feature importance
---|---
Phase 1 | Phase 2 | Phase 3
pmdec | 0.25 | - | -
Y/r2 | 0.21 | 0.34 | 0.36
pmra | 0.14 | - | -
r2 \- Y | 0.13 | 0.21 | 0.20
i2/r2 | 0.12 | 0.26 | 0.25
r2 \- i2 | 0.07 | 0.20 | 0.20
Distance | 0.07 | - | -
Table 1: Training features used in phase 1, phase 2 and phase 3 of RF
classifier and their respective importance

We understand that the primary reason for the inability of RF classifier to
identify cluster members down to the sub-stellar regime in one run is that the
training sample gets biased by the colours of the brighter member stars (r2
$\leq$ 19.5) which forms $\sim$ 50$\%$ of the training set. Due to the low
signal to noise ratio, the scatter in optical colours increases as one
approaches the fainter magnitudes. This increase in the deviation in optical
colours is considered in fair estimate if we curtail the training and test set
to sources with r2 $>$ 19.5 mag for the next phase of RF classifier. The
particular threshold of r2 $>$ 19.5 mag is taken because approximately 50$\%$
of the probable members procured as of yet, are fainter than this chosen value
which, provides a substantial training sample. We hence, use the training set
comprising of member and non-member sample (r${}_{2}>$ 19.5 mag) obtained
above, and re-apply the RF classifier to the HSC sources with r${}_{2}>$ 19.5
mag. With this approach, the classifier technique predicts probable members
down to r${}_{2}\sim$ 28 mag ($\sim$ 0.012 - 0.015 M⊙ for an age $\sim$ 2 Myrs
and AV $\sim$ 1 mag), which is well into the sub-stellar regime. We have
provided the input features used in all the RF classifier phases along with
their relative feature importance in Table 1. The quality parameters attained
for each phase are also provided in Table 4 and Figure 12. In order to be
explicit, no probability threshold has been used while selecting probable
members during the entire RF classifier method. Another point to note here is
that the sources identified as members in all the RF classifier phases are
just the probable members. Hence, to remove all the possible contaminants and
obtain a clean and accurate list of members along with their stellar
parameters like age, mass etc., we further perform SED fitting of the probable
members as described in the following section.

###  3.3 VO SED Analyzer (VOSA) fitting

SED fitting is very useful to estimate the stellar parameters such as age,
mass and effective temperature (Teff) in a star forming region (Povich et al.
2019; Winston et al. 2020; Olsen et al. 2021). The determination of these
parameters helps to understand the evolution of the stellar cluster with
respect to age, mass and environmental factors. In order to obtain a precise
estimation of these stellar parameters, a broad wavelength range for the
spectral fitting is favourable. Hence, we use UKIDSS DR11/ 2MASS NIR data
along with the deep optical data for this purpose. Among the RF classifier
identified probable members, we consider only those 1156 HSC sources, which
have counterparts in the deep NIR catalog.
We use the VOSA666http://svo2.cab.inta-csic.es/theory/vosa/ tool to build the
SEDs using optical to NIR wavelengths (Bayo et al. 2008; Damian et al. 2021;
Guzmán-Díaz et al. 2021; Mejías et al. 2022). However as per the requirements
of VOSA, we consider only those sources for SED fitting which have photometry
in atleast five filters. In addition to the provided photometry, VOSA also
uses Pan-STARRS photometry from the online catalogues whenever present using
VO services. We also input a distance (900 $\pm$ 10 parsecs) as well as the
extinction range (AV $\sim$ 1 - 1.5 mag) estimates in accordance with the past
studies (see references mentioned in Section 1.1), to deredden the SEDs.
Subsequently, theoretical models (BT-Settl, Allard et al. (2012)) for solar
metallicity are used to obtain the best fitting model using chi-square
minimization. This gives us the physical properties like Teff and luminosity
of the stars. The age and mass is derived by fitting the sources in the
Hertzsprung-Russell (HR) diagram with BHAC15 isochrones (Baraffe et al. 2015)
for a mass range 0.01 - 1.4 M⊙ and age ranging between 0.5 - 10 Myrs. Those
sources which do not fulfill these constraints are rejected as contaminants.
At this stage, we also remove those sources with Gaia DR3 counterparts which
do not fulfil the constraints mentioned in Section 3.1 and Section 2.3 (for
example, 500 parsecs $\leq$ distance $\leq$ 1500 parsecs, ruwe $<$ 1.4, –20
$\leq$ $\mu_{\alpha}$cos$\delta$ $\leq$ 20 mas/yr , –20 $\leq$ $\mu_{\delta}$
$\leq$ 20 mas/yr). This finally gives us 393 sources as confirmed member
sources within the target region of study using machine-learning methods.

We summarise the machine-learning based approach used to identify the cluster
members within the central 22′ radius region here. We first obtain a Gaia-
based member sample with probability $\geq$ 0.8 using GMM. This sample is then
used as the training set in RF classifier to identify cluster members among
the sources with both HSC and Gaia photometry. The members identified at this
step are further used as training sample for the next phases of RF classifier
to segregate members among the HSC sources without Gaia counterparts. The
members obtained at each step are compiled together and cross-matched with the
deep NIR catalog. SED fitting of these probable members with both optical and
NIR photometry is performed using VOSA. We remove sources with Gaia
counterparts which do not comply with membership constraints. We finally
select 393 sources with age $<$ 10 Myrs, as cluster members. The identified
members however suffer from the restricted sensitivity of UKIDSS (complete
down to $\sim$ 0.09 M⊙) due to the pre-requisite of having NIR counterparts
which is essential for SED fitting. Hence, we adopt an additional approach to
identify fainter cluster members by defining a pre-main sequence locus as
explained below in Section 3.4.

###  3.4 Additional members from pre-main sequence locus

Figure 4: (Left) r2 \- i2 vs r2 colour-magnitude (Right) r2 \- Y vs r2 colour-
magnitude diagram to obtain members using pre-main sequence locus (green
curve). Blue curve shows the 10 Myrs BHAC15 isochrone. The newly added members
are presented as black triangles.

It is crucial to extend the member identification to deeper sensitivity
independent of NIR counterparts, to perform a comprehensive study of the low-
mass population in IC 1396. In order to detect lower mass cluster members ($<$
0.09 M⊙), we define the respective empirical pre-main sequence (PMS) locus for
all optical colour-magnitude combinations ((r2 \- i2) vs r2, (r2 \- Y) vs r2
and (i2 \- Y) vs i2) by dividing the magnitude range into 1 mag bins. For each
bin, we take mean of the magnitude and median of the colour of sources inside
the bin (Damian et al. 2021; Gupta et al. 2021). We then select only those
sources which are fainter than r2 $=$ 22 mag and within 1 $\sigma$ (where
$\sigma$ is the standard deviation) limits of the empirical locus defined for
the respective colour-magnitude combination. Also, the sources are required to
be common in all the colour-magnitude combinations, which adds to the
validation of these sources as cluster members. The particular threshold of r2
$>$ 22 mag is chosen to select the members here as this corresponds to a
stellar mass less than $\sim$ 0.09 M⊙ (for cluster age and distance). This
corresponds to the data completeness of UKIDSS data which restricts the
sensitivity of ML-based members obtained in Section 3.3. We obtain 65 members
with this approach, thus increasing the total number of cluster members to 458
and detection limit down to 0.03 M⊙.

Figure 4 shows r2 \- i2 vs r2 and r2 \- Y vs r2 colour-magnitude diagrams
overplotted with ML-based, pre-main sequence locus based cluster members, the
defined pre-main sequence locus and 10 Myrs BHAC15 isochrone (Baraffe et al.
2015). The BHAC15 isochrone is corrected for an extinction AV $\sim$ 1 mag and
distance $\sim$ 900 parsecs. We use the Wang & Chen (2019) empirical laws to
correct for the extinction. Since BHAC15 isochrones are not available for
Subaru HSC photometric system, we first convert the available Pan-STARRS 10
Myrs isochrone to HSC system using the transformation equations given in Gupta
et al. (2021). Subsequently, we correct the 10 Myr isochrone for the distance
and reddening of the cluster. In order to determine the mass, these 65 members
are first de-reddened for the uniform cluster reddening and age. The mass for
each source is then determined using the mass - magnitude relation obtained
using BHAC15 models. This member sample is useful to identify brown dwarfs and
obtain the mass distribution in the region. We would like to mention here that
although, reddening across the central 22′ radius region of IC 1396 is uniform
with AV $\sim$ 1 - 1.5 mag, we check if the variation in reddening values may
change the output member sample significantly. Hence, we verify the error
introduced by varying the AV upto 1.5 mag and find that a minimal error of
$\sim$ 2$\%$ is introduced in the statistics of cluster members. Since, the
output is approximately uniform, we continue using AV $=$ 1 for our analysis.

In order to verify the validity of member sample obtained by this approach, we
perform field subtraction of the central 10′ radius region of IC 1396. For
this purpose, we choose a control field of the same area towards the periphery
of the region (HSC data for this peripheral region is available by the wide
field observations of IC 1396 as mentioned in Section 2). The 10′ radius
region is used due to the lack of a larger control field. The statistical
field subtraction is then performed, the details of which are provided in
Appendix B. The same approach as described above in this section is then used
to select members among these statistically field decontaminated sources. We
find that the statistics of members and corresponding mass distribution
obtained in Section 4.3 remain approximately same whether or not prior field
subtraction is performed. This uniformity hence, validates the approach
adopted by us above. We therefore, continue with the members obtained above
without using field decontamination for further analysis in the paper
(detailed supporting reasons are explained in Appendix B).

###  3.5 Comparison with previous studies

The identified cluster members are high-quality sources with photometric error
$\leq$ 0.1 in optical filters. The proper motions and parallax range of the
obtained sources with Gaia counterparts ($\sim$ 85$\%$) are in excellent
accordance with that for literature based sources (Contreras et al. 2002;
Sicilia-Aguilar et al. 2006; Getman et al. 2007, 2012; Sicilia-Aguilar et al.
2013; Cantat-Gaudin et al. 2018; Pelayo-Baldárrago et al. 2023; Das et al.
2023), as shown in Figure 11 Top and Bottom. The central 22′ radius area of IC
1396 comprises of 857 members ascertained by previous studies such as those
mentioned above. An additional $\sim$ 330 members have been identified by the
recent Gaia based studies like Cantat-Gaudin et al. (2018); Pelayo-Baldárrago
et al. (2022) and Das et al. (2023) within the area of study. Out of the total
458 member sources confirmed in our study, we retrieve 328 members with
counterparts in the literature studies (including both previous studies and
recent Gaia-based studies mentioned above). The remaining 130 members without
counterparts in literature are low mass stars with r2 $\geq$ 18 mag, that is,
mass $<$ 0.5 M⊙. This low and sub-stellar mass range is still unexplored for
IC 1396 which explains the absence of literature counterparts of these faint
sources.

Our study adds 130 new members to the existing cluster member catalog with
detection limit down to $\sim$ 26.5 mag in r2-band, which corresponds to a
$\sim$ 0.025 M⊙ source for the distance and age of the cluster. This
significantly enhances the sensitivity down to where IC 1396 can be studied in
future. The Hess plot of the HR diagram of members identified in the present
study is presented in Figure 5. We use this member list for further analysis
in this paper.

Figure 5:  Hess plot of HR diagram of the members obtained from VOSA. BHAC15
isochrones of 0.5, 2 and 10 Myr are over-plotted along with mass evolutionary
tracks as white dashed curves.

##  4 Results and Analysis

###  4.1 Sub-stellar members and their characteristics

We use the obtained members to perform statistical analysis of the region. We
determine the sub-stellar population and consequently determine the mass
distribution within the studied area. We use the obtained stellar masses of
individual member sources in Section 3.3 and Section 3.4 to determine if they
can be classified as a sub-stellar object. We identify 80 sources with mass
$\leq$ 0.1 M⊙ as sub-stellar objects. Out of these, 62 sources have mass
$\leq$ 0.08 M⊙, which we classify as brown dwarfs. We also derive the age of
the member sample using isochrone fitting method. In this method, for each
star a weighted average of the age of two nearest isochrones is assigned as
the age of the star. We converge this distribution within 2$\sigma$ limits
from the mean age after 3 iterations (Gupta et al. 2021). We find the median
age of the 2$\sigma$ converged sample to be log (Age) $\sim$ 6.3
${}^{+0.2}_{-0.5}$, which complies with the age of the IC 1396 cluster as
estimated in literature (Sicilia-Aguilar et al. 2005; Getman et al. 2012;
Nakano et al. 2012; Das et al. 2023).

###  4.2 Colour-magnitude and Colour-colour diagrams

Figure 6:  (Top Left) Hess plot of (r2–Y) vs r2 CMD (Top Center) (r2–Y) vs r2
CMD scatter plot (Top Right) (r2–i2) vs r2 CMD scatter plot (Bottom Left) Hess
plot of (r2–J) vs J–K colour-colour plots (Bottom Right) (r2–J) vs J–K scatter
colour-colour plots overplotted with 10 Myrs BHAC15 isochrone(Baraffe et al.
2015) and identified members (dark green dots).

We present here the various colour-magnitude and two-colour diagrams for the
22′ radius area of study in IC 1396. Both the Hess plots of (r2–Y) vs r2 CMD
and (r2–J) vs (J–K) two colour plot (Figure 6 (Top Left) and (Bottom Left))
exhibit a distinct pre-main sequence branch. The corresponding scatter plots
(Figure 6 (Top Center, Top Right and Bottom Right)) are overplotted with the
identified members and 10 Myr BHAC15 isochrone corrected for the cluster
extinction AV $\sim$ 1 mag and distance $\sim$ 900 parsecs. In these plots, we
observe that the identified stellar and sub-stellar members in the region pre-
dominantly occupy the distinct pre-main sequence branch, which is a typical
feature of young star forming regions (Jose et al. 2017; Damiani et al. 2019;
Damian et al. 2021; Gupta et al. 2021; Ksoll et al. 2021).

###  4.3 Mass distribution

The distribution of stellar mass in a cluster is crucial to understand as well
as constrain the star formation process (Kirkpatrick et al. 2012; Offner et
al. 2014; Kirkpatrick et al. 2021, 2023). The obtained member population
provides a fair sample of low-mass sources to investigate the nature of mass
distribution towards the sub-stellar end. It is also helpful to check the role
played by the feedback regulated cluster environment of IC 1396 on the mass
apportionment in the region. Due to data completeness issues, we consider the
members within the mass range 0.03 – 1 M⊙ for our analysis. The distribution
of stellar mass among the cluster members is estimated by dividing the entire
logarithmic mass range into bins of size, log M $=$ 0.15 and the corresponding
number of sources in each bin is calculated. The corresponding histogram is
shown in Figure 7. The Poisson error in the count of sources is represented by
the error-bars in each mass bin of the histogram. We observe a bimodal nature
of mass distribution with a secondary peak at $\sim$ 0.06 M⊙ (log (M/M⊙)
$\sim$ -1.2) as the distribution advances in sub-stellar regime. We also
observe a sharp dip in the distribution at $\sim$ 0.10 - 0.15 M⊙. The bimodal
nature of the mass distribution with a secondary peak at $\sim$ 0.06 M⊙ and
the pronounced dip at the stellar-sub-stellar boundary agrees well with that
observed for ONC by Drass et al. (2016). The authors observed a similar
bimodal nature of IMF in the feedback-driven ONC region. This suggests a
similar brown dwarf formation scenario in both IC 1396 and ONC with similar
feedback affected cluster environments. A similar secondary peak has been
observed in NGC 2024 by Levine et al. (2006) and Trapezium cluster by Slesnick
et al. (2004) at $\sim$ 0.03 - 0.05 M⊙. However, uncertainties in the derived
age of sources affects the mass-luminosity relation, which may influence shape
of mass distribution. The current study pioneers to explore mass distribution
down to the so far unexplored sub-stellar realm in the central 22′ radius
region of IC 1396.

Figure 7:  Mass distribution plot for the identified cluster members. The
primary peak is $\sim$ 0.4 M⊙. A secondary peak is observed at $\sim$ 0.06 M⊙
and a dip is observed at $\sim$ 0.1 - 0.15 M⊙. The error-bars represent the
Poisson error in the count of sources in each mass bin.

###  4.4 Star-to-Brown Dwarf Ratio

Figure 8:  Variation of the star-to-brown dwarf ratio with respect to distance
from the central OB-stars (HD 206267), across the 22′ radius area of study in
IC 1396. Each point refers to the star-to-brown dwarf ratio in individual
annular bin and the corresponding Poisson error represented as error bar.

Another useful quantity which gives a fair estimate of the abundance of brown
dwarfs in a region is the star-to-brown dwarf ratio R. A high R value
indicates lower brown dwarf fraction in a stellar cluster. The ratio thus
implies the brown dwarf formation efficiency in a cluster. An objective
comparison of the ratio across varying star forming environments is important
to understand if the brown dwarf formation is impacted by the external factors
(Mužić et al. 2015; Mužić et al. 2017; Mužić et al. 2019; Huston & Luhman
2021; Damian et al. 2023b; Almendros-Abad et al. 2023). We consider brown
dwarfs only within 0.03 - 0.08 M⊙ mass range for the R value calculation,
since the completeness of the data is down to 0.03 M⊙. With the count of stars
ranging within 0.08 - 1 M⊙ estimated as 391, the star-to-brown dwarf ratio in
IC 1396 turns out to be $\sim$ 6.0 $\pm$ 0.8, i.e $\sim$ 6 stars for each
brown dwarf in the region. The error in R is calculated as the Poisson error
for the ratio. We emphasize that due to the completeness issues mentioned
above, the obtained R value is evaluated for the stellar mass range 0.03 - 1
M⊙. The upper limit of stellar mass to determine R is taken as 1 M⊙ so as to
make a fair comparison between IC 1396 and other star forming regions. We
observe that although towards the higher end, the obtained ratio R is
compatible with other young star forming regions within the statistical
uncertainties for the mass range 0.03 - 1 M⊙. For example, the ratio R ranges
within 2 - 6 in literature for several star forming regions with diverse
cluster environments like $\rho$ Oph, IC348, Lupus3, NGC 2264, NGC 2244 (Mužić
et al. 2012; Scholz et al. 2013; Mužić et al. 2015; Damian et al. 2023b;
Almendros-Abad et al. 2023; Kirkpatrick et al. 2023) as given in Table 2. This
implies a similar brown dwarf formation process across various star forming
regions in the Galaxy.

In addition, we check the variation of ratio R with increasing radial distance
from the central O-star HD 206267, as shown in Figure 8. This is obtained by
dividing the 22′ radius region into annular bins of equal area, here taken to
be 50$\pi^{\prime}$2. The star-to-brown dwarf ratio is then calculated for
each annular bin based on the number of stars and brown dwarfs present in it.
The error bars at each point represent the Poisson error obtained for the
ratio R in each bin. The limited census of brown dwarfs account for the high
error observed in the ratio R in the inner annular bins towards the center of
the cluster. The ratio R is observed to decrease as one moves radially
outwards away from the center. This implies that more brown dwarfs are located
towards the outskirts of the studied area of interest compared to its central
part where the ionizing system HD 206267 is located. The obtained R ($\sim$ 6)
averaged over our area of study is clearly biased by the very low brown dwarf
fraction (and hence, considerably higher R values) towards the inner radii
($<$ 3 parsecs, $\sim$ 12′) of IC 1396. This is likely contributed by the
O-stars at the center of the cluster. As evident from Figure 8, the ratio R
falls to lower values at distances $>$ 3 parsecs from the center. The presence
of O-stars thus, seems to inhibit the formation of brown dwarfs towards the
center of IC 1396. The brown dwarf fraction increases as the incident FUV flux
from the central massive stars decreases across the region. It is hence
evident that the feedback driven cluster environment of IC 1396 affects the
spatial distribution of brown dwarfs within the region.

##  5 Discussion

The cluster environment in which stars are born plays a crucial role in
constraining the star formation and regulating the timescale for related
processes like brown dwarf formation, disk evolution and planet formation. The
quantitative effect of environmental factors on these processes is an
interesting problem yet to be fully understood. Although many studies (Bastian
et al. 2010; Offner et al. 2014; Damian et al. 2021) suggest a uniformity in
IMF behaviour in the high-mass end and hence, a similar star formation process
across various star forming regions, but a non-uniform IMF has been claimed in
extreme environments like the Galactic centre and least luminous Milky Way
satellites (Lu et al. 2013; Gennaro et al. 2018). Similarly, various
theoretical studies also suggest an enhancement in the census of sub-stellar
objects in the presence of high gas and stellar density or in the vicinity of
massive stars (Whitworth & Zinnecker 2004; Bate 2012; Vorobyov & Basu 2013;
Stamatellos 2014). However, more observational evidences in different star
forming environments are still required to support results from theoretical
simulations. In this section we interpret our results and compare them with
other star forming regions as well.

We observe from our study that the mass distribution has a secondary peak in
the brown dwarf regime (log (M/M⊙) $\leq$ -1.1). Reipurth & Clarke (2001) find
that the bimodal IMF may be attributed to the expulsion of low-mass objects
from small clusters of protostars or from the fragmentation of circumstellar
discs. A secondary peak towards the brown dwarf regime may suggest different
formation mechanisms for stars and brown dwarfs. We discuss further the
dependence of brown dwarf population on stellar density and UV flux across
various star forming regions.

###  5.1 Comparison with other star forming regions

S.no. | Cluster name | Star-to-brown dwarf-ratio | Surface density | log (fluxFUV)
---|---|---|---|---
|  |  | (parsec-2) | (G0)
1 |  $\sigma$ Ori | 5.4 $\pm$ 1.0 | 36 | 4.00
2 | IC 348 | 3.4 $\pm$ 0.6 | 200 | 2.61
3 | NGC 1333 | 2.1 $\pm$ 0.2 | 185 | 3.00
4 | Chameleon I | 4.0 $\pm$ 0.5 | 30 | 0.90
5 | Lupus 3 | 4.3 $\pm$ 0.5 | 20 | 0.70
6 | ONC | 2.4 $\pm$ 0.2 | 350 | 5.50
7 | NGC 2244 | 2.2 $\pm$ 0.3 | 28 | 5.74
8 | RCW 38 | 2.0 $\pm$ 0.6 | 2500 | 6.30
9 |  $\rho$ Oph | 5.1 $\pm$ 0.4 | 79 | 2.00
10 | 25 Ori | 5.9 $\pm$ 0.8 | 4 | 4.00
11 | NGC 6611 | 4.4 $\pm$ 0.7 | 138 | 6.03
12 | Westerlund 1 | 1.5 $\pm$ 0.2 | 295 | 7.32
13 | NGC 2024 | 3.5 $\pm$ 0.4 | 80 | 4.80
14 | Taurus | 4.0 $\pm$ 0.6 | 5 | 1.30
15 | IC 1396 | 6.0 $\pm$ 0.8 | 15 | 5.20
Table 2:  shows various star forming regions with their star-to brown dwarf
ratio for mass range 0.03 - 1 M⊙, stellar surface density and dominant FUV
flux. the reference studies for each region according to their serial number
is as follows: (1) Béjar et al. (2011); Peña Ramírez et al. (2012); Winter &
Haworth (2022); Damian et al. (2023b) and references therein; (2) Scholz et
al. (2013); Mužić et al. (2019); Luhman & Hapich (2020); Damian et al. (2021)
and references therein; (3) Scholz et al. (2013); Mužić et al. (2019); Knight
et al. (2022); (4),(5) Mužić et al. (2015, 2019); Winter (2019); (6) Andersen
et al. (2011); Mužić et al. (2019); Kim et al. (2022); (7) Almendros-Abad et
al. (2023); Mužić et al. (2019) and references therein ,Damian et al. (2021);
(8) Winston et al. (2011); Mužić et al. (2017); Mužić et al. (2019); (9) Okada
et al. (2006); Mužić et al. (2012); Miret-Roig et al. (2022);(10) Briceño et
al. (2007); Downes et al. (2014); Suárez et al. (2019); (11) Oliveira et al.
(2009); Damian et al. (2021); (12) Lim et al. (2013); Andersen et al. (2017);
Winter & Haworth (2022); (13) Levine et al. (2006); Oliveira et al. (2009);
Winter & Haworth (2022); (14) Oliveira et al. (2009); Esplin & Luhman (2019)
(15) Sicilia-Aguilar et al. (2005); Das et al. (2023)

We have compiled a list of 15 star forming regions with the related
information about their ratio R for mass range 0.03 - 1 M⊙, stellar surface
density and incident FUV flux in Table 2. As evident, the obtained ratio R for
IC 1396 is compatible with that estimated for other star forming regions by
different studies. The obtained R value is however, at the higher end of the
standard range (2 - 6) for the star-to-brown dwarf ratio. As discussed in
Section 4.4 this is due to the steep values of R ($>$ 8) observed towards the
inner regions ($<$ 3 parsecs) of the cluster. The steep R values are
attributed to the higher stellar densities observed in the vicinity of central
O-stars as compared to the outskirts, which is a result of sequential star
formation episodes (Getman et al. 2007; Nakano et al. 2012; Das et al. 2023).
Also the FUV flux from O-stars inhibits the brown dwarf formation near the
cluster center. Although the ratio R decreases with increasing radial distance
from the center, when averaged over the area of study it tends towards a
higher value. The star-to-brown dwarf ratio is clearly impacted by the
presence of OB-stars ratio across the cluster.

The compiled stellar clusters in Table 2 are well-studied massive Galactic
star forming regions with extreme to low feedback driven cluster environments.
These clusters host a stellar density ranging between $\sim$ 4 - 2500 stars
pc-2 and log (fluxFUV) $\sim$ 0.7 - 7.3 G0. We take the mean value of star-to-
brown dwarf ratios for a cluster if a range of values is calculated in the
corresponding reference studies which are listed in the caption of Table 2. In
case of different values of the ratio given in multiple reference studies for
any region, we adopt the value determined by the most recent available
reference study for that cluster. The error bars represent the error in the
ratio for each region, either taken directly from the respective reference
study or derived by calculating the Poisson error for the ratio. Also, for
some regions like NGC 2024 and Westerlund 1 clusters, we have derived the
ratio R from their respective mass functions given in the corresponding
reference studies since a direct value was not available (see Table 2). For
this purpose, we simply calculate number of sources corresponding to the mass
function fit performed by the respective authors in the desired mass range
(0.03 - 1 M⊙). The stellar densities for individual regions were taken
directly from the respective reference studies for each region mentioned in
the caption of Table 2. The regions for which kernel density estimation plots
are available in Mužić et al. (2019) (e.g. ONC, IC 348, Lupus 3, NGC 1333, RCW
38, NGC 2244 and Cha I), we have considered the stellar density associated
with 50$\%$ contour. This is consistent with the methods applied in Mužić et
al. (2019) to compare the R values among different star forming regions. In
order to find the incident FUV flux in each region we use the respective
reference studies and obtain the O-stars catalog for each region. We then use
the results from Guarcello et al. (2016) and Winter & Haworth (2022) to
determine the FUV luminosity and thereby, Habing flux7771 G0 = 1.6 x 10-3
erg/cm2/s (G0) corresponding to the spectral type for O-type stars in
individual regions. The FUV fluxes given in Table 2 are the approximate values
as we do not add the B-type star fluxes if the region is dominated by O-type
stars.

It is important to note here that the larger value of star-to-BD ratio R in
the cluster centre is not an effect of sample bias. This is because IC 1396 is
a very sparse cluster and the central crowding does not affect any source
detection. However, for crowded star forming regions (some of them included in
Table 2), it may be more difficult to detect brown dwarfs in the presence of a
concentration of much brighter stars, especially towards the central regions
of such clusters. This may have biased the ratio R in such regions towards a
higher value.

###  5.2 Impact of cluster environment

Brown dwarfs form by the gravitational core-collapse of a molecular core which
may get deficient of dust and gas due to its expulsion from the material
reservoir (Vorobyov et al. 2017; Riaz et al. 2018). The factors leading to
this depletion of material range from photo-erosion due to radiative feedback
from nearby massive stars, turbulence to disk instability and subsequent
ejection of the low-mass core, thus leaving the formed object in sub-stellar
regime (Stamatellos & Whitworth 2009; Chabrier et al. 2014; Whitworth 2018).
However, whether the environmental factors play a significant role in deciding
the dominant formation mechanism or the census of brown dwarfs in a region is
yet to be confirmed. Here we investigate the behaviour of star-to-brown dwarf
ratio with respect to the two main factors, that is, stellar density and
incident far-UV (FUV) flux impacting the cluster environment.

Figure 9:  Variation of star-to-brown dwarf ratio versus (Left) stellar
surface density (Right) incident FUV flux. Different coloured points represent
different star forming regions.

####  5.2.1 Impact of stellar density

According to theoretical simulations, dynamical interactions among the self-
gravitating cores in isolated parts of dense molecular clouds or inside
filaments and circumstellar disks may lead to the subsequent ejection of
stellar embryos (Bonnell et al. 2008; Whitworth 2018). Such low-mass
collapsing cores, depleted of the material reservoir required for accretion
eventually form sub-stellar objects (Bonnell et al. 2008; Stamatellos &
Whitworth 2009; Chabrier et al. 2014; Vorobyov et al. 2017; Whitworth 2018;
Riaz et al. 2018). External factors like stellar density may play a crucial
role in the pre-mature ejection of sub-stellar cores. For example, close
dynamical encounters with nearby stars are a common phenomenon in cluster
environments with high stellar density. Such gravitational encounters can
enhance the dynamical interactions among the isolated fragments or introduce
perturbations in the star-disk system (Winter et al. 2018) thus, leading to
the early ejection of stellar embryos (Bonnell et al. 2008; Stamatellos &
Whitworth 2009; Portegies Zwart 2016; Vorobyov et al. 2017). Bonnell et al.
(2008) find that the fraction of brown dwarfs in a region becomes twice as the
stellar density enhances by an order of magnitude. The authors hence
hypothesize that high density favours brown dwarf formation. Similarly
Vorobyov et al. (2017) conclude that prograde close encounter can result into
early ejection of fragments of brown dwarf mass regime. Riaz et al. (2018)
also find a moderate impact of density perturbations on the formation of brown
dwarfs and very low mass stars. In the recent studies by Mužić et al. (2017);
Mužić et al. (2019), the authors perform observational analysis of RCW 38 and
NGC 2244, the two cluster environments with remarkably contrasting stellar
densities, but are inconclusive about any variation in the brown dwarf
formation efficiency with respect to either stellar density or presence of OB
stars. The most recent study by Almendros-Abad et al. (2023) also supports
this result and does not find any dependence of the star-to-brown dwarf ratio
on the stellar density. However, these studies lack a comprehensive analysis
for a miscellany of star forming regions and are restricted to inner regions
of the respective clusters.

We check the variation of star-to-brown dwarf ratio with respect to stellar
density across 15 star forming regions in Figure 9 (Left). The error bars on
each point denote the uncertainty in star-to-brown dwarf ratio for the
respective star forming region. We observe that the star-to-brown dwarf ratio
tends towards lower values at high stellar densities which, agrees with the
theoretical hypothesis that high stellar densities favour the formation of
brown dwarfs (Bonnell et al. 2008). This behaviour is however, more
conspicuous at stellar densities $>$ 50 stars/parsec2, which suggests that
stellar densities ought to be sufficiently high so as to promote dynamical
encounters and effectuate the ejection of sub-stellar cores. We also calculate
the correlation coefficient to support our results. Since from Figure 9
(Left), the star-to-brown dwarf ratio and stellar density appear to be
monotonically related, we evaluate the Spearman’s rank correlation coefficient
($\rho$). We find the coefficient $\rho$, to be $\sim-0.7$ which indicates a
strong correlation between the two variables, with a statistical significance
of 0.5$\%$ which emphasizes the relation to be monotonic as well (Spearman
1987). We hereby conclude that the brown dwarf formation efficiency may get
impacted by high stellar densities ($>$ 50 stars/parsec-2) but do not quantify
these results as it is beyond the scope of this study.

####  5.2.2 Impact of FUV flux

Photo-erosion of self-gravitating cores in the vicinity of massive OB-stars is
another mechanism of formation of brown dwarfs. The incident FUV and EUV
radiation from the surrounding massive stars ionises and erodes the infalling
material before it can accrete onto the central core, thus resulting in the
formation of a sub-stellar object (Whitworth & Zinnecker 2004). However,
whether this is a dominant formation mechanism or not is still ambiguous. For
example, the recent study by Almendros-Abad et al. (2023) does not find any
direct dependence of the brown dwarf formation on OB-stars but, observes brown
dwarfs to be located in close proximity to OB stars in NGC 2244. The study is
thus, inconclusive regarding the role of OB-stars on brown dwarf formation. In
our present study, we try to explore the variation of star-to-brown dwarf
ratio relative to the presence of massive stars. We use the compiled list in
Table 2 to plot the variation of star-to-brown dwarf ratio R with the incident
FUV flux in Figure 9 (Right), along with the respective error bars
representing error in star-to-brown dwarf ratio for various star forming
regions.

Looking at Figure 9 (Right), we are unable to make out a distinct correlation
between the incident flux and star-to-brown dwarf ratio. The ratio however,
appears to decline with increasing flux at log(fluxFUV) $>$ 4 G0. This could
likely be the effect of photo-erosion at high UV-fluxes or high stellar
density observed in these regions since both the factors, that is high stellar
density and high incident UV flux cannot be decoupled in massive star
clusters. We are hence inconclusive regarding the effect of the presence of OB
stars on brown dwarf formation efficiency. This result is also supported by
Mužić et al. (2019) and Almendros-Abad et al. (2023), who do not find any
clear dependence of brown dwarf fraction on the presence of OB stars based on
the comparison among seven star forming regions. This suggests that photo-
erosion may not be the dominant mode of brown dwarf formation. However, more
comprehensive sub-stellar studies of massive clusters with rich OB-stars
population like Cygnus OB2, NGC 3603, W3/W4/W5, Arches and Quintuplet cluster
etc. are required to draw any conclusive results.

We caution the readers that although for the same mass range (0.03 - 1 M⊙),
our comparative analysis however covers different areas of study considered in
the respective reference studies to calculate the ratio R in different star
forming regions. Another obvious caveat in such comparisons with literature
values is the method by which the masses are estimated in each study. We do
not consider the mass segregation effect or variation in spatial distribution
of brown dwarfs as it is beyond the scope of this study.

##  6 Summary and Future Works

Brown dwarfs form the bridge between stars and planets and hence, it is
crucial to study the nature of mass distribution down to sub-stellar regime.
The effect of cluster environment on the brown dwarf formation efficiency is
another crucial aspect which still requires comprehensive studies, both
theoretical and observational. We study the central 22′ radius region of IC
1396, a nearby ($<$ 1 kpc) prominent H ii region with feedback driven cluster
environment ideal for our study.

1) We observed 2 pointings each of 1.5∘ diameter centred at IC 1396 with
Subaru HSC in r2, i2 and Y filters. We however perform a deep analysis of the
central 22′ radius region as it covers $\sim$ 60$\%$ of the previously
identified sources. This is the deepest study of this region as of yet with
detected sources reaching down to r2 $\sim$ 28 mag.

2) We perform a multi-wavelength study of the region using Subaru HSC, Gaia,
Pan-STARRS and UKIDSS / 2MASS data and obtain the candidate members using
machine learning tools such as GMM and RF classifier. We then perform SED
fitting of the probable members using VOSA tool. We also define the pre-main
sequence locus and include sources within 1$\sigma$ as members. Eventually we
obtain 458 good quality sources along with their stellar parameters as cluster
members.

3) Among these members we identify 62 sources as brown dwarfs with mass $\leq$
0.08 M⊙ and obtain the mass distribution down to sub-stellar regime for a mass
range 0.03 - 1 M⊙. The star-to-brown dwarf ratio R turns out to be $\sim$ 6.0
$\pm$ 0.8 which is compatible with the range found for other star forming
regions for the same mass range.

4) We find that within IC 1396, the brown dwarf fraction increases with
increasing radial distance from the central massive star HD 206267. The
O-stars present in IC 1396 influence the star-to-brown dwarf ratio across the
region.

5) We perform a comprehensive analysis of 15 star forming regions to test the
influence of environmental factors like stellar density ($\sim$ 4-2500 stars
pc-2) and incident FUV flux ($\sim$ 0.7-7.3 G0), on the star-to-brown dwarf
ratio. We conclude that brown dwarf formation efficiency may be affected by
high stellar densities but the effect of the incident FUV flux within this
range is unclear.

As the next step, we aim to perform a similar analysis for the entire observed
region of IC 1396 and obtain the sub-stellar mass distribution for the
complex. We also plan to identify the young stellar objects in the region and
perform a circumstellar disk analysis to understand the variation of disk
fraction with external factors like stellar density and incident FUV flux
across the cluster.

##  7 Data Availability

Table 3 presents the optical HSC photometry along with the mass of the brown
dwarfs identified in this study. The complete catalog of the identified
members underlying this article will be shared on reasonable request to the
corresponding author.

Table 3: Brown dwarfs within the central 22′ radius region identified in this study. The columns present the RA, Dec, photometry and the respective errors in r2, i2 and Y filters and the mass of these sources. RA | Dec | r2 | r${}_{2_{err}}$ | i2 | i${}_{2_{err}}$ | Y | Yerr | Mass
---|---|---|---|---|---|---|---|---
(deg) | (deg) | (mag) | (mag) | (mag) | (mag) | (mag) | (mag) | (M⊙)
325.0996 | 57.7831 | 23.74 | 0.01 | 20.61 | 0.00 | 18.34 | 0.00 | 0.07
325.2094 | 57.7277 | 24.22 | 0.01 | 20.30 | 0.00 | 18.57 | 0.00 | 0.06
324.7828 | 57.4264 | 24.07 | 0.01 | 20.56 | 0.00 | 18.91 | 0.00 | 0.06
324.0923 | 57.4959 | 23.85 | 0.01 | 20.54 | 0.00 | 18.78 | 0.00 | 0.06
324.4811 | 57.4484 | 23.69 | 0.01 | 20.11 | 0.00 | 18.40 | 0.00 | 0.06
324.4575 | 57.4969 | 26.06 | 0.06 | 21.49 | 0.00 | 19.65 | 0.00 | 0.04
324.3343 | 57.7497 | 25.55 | 0.03 | 21.08 | 0.00 | 19.01 | 0.00 | 0.03
324.1520 | 57.5092 | 24.45 | 0.02 | 20.98 | 0.00 | 19.29 | 0.00 | 0.06
324.1435 | 57.5154 | 24.92 | 0.03 | 21.04 | 0.00 | 19.30 | 0.00 | 0.06
325.1902 | 57.5676 | 24.23 | 0.01 | 20.86 | 0.00 | 19.17 | 0.00 | 0.06
324.4685 | 57.3126 | 22.74 | 0.00 | 20.11 | 0.00 | 18.40 | 0.00 | 0.07
324.3183 | 57.5488 | 22.72 | 0.00 | 19.96 | 0.00 | 18.33 | 0.00 | 0.07
324.1370 | 57.5015 | 23.51 | 0.01 | 20.74 | 0.00 | 19.22 | 0.00 | 0.06
324.2120 | 57.6214 | 22.73 | 0.00 | 20.01 | 0.00 | 18.50 | 0.00 | 0.07
325.3353 | 57.3186 | 22.79 | 0.00 | 20.24 | 0.00 | 18.70 | 0.00 | 0.07
325.3433 | 57.3237 | 22.85 | 0.00 | 20.31 | 0.00 | 18.76 | 0.00 | 0.07
325.1490 | 57.2933 | 22.50 | 0.00 | 20.03 | 0.00 | 18.64 | 0.00 | 0.07
325.1416 | 57.3540 | 23.36 | 0.00 | 20.63 | 0.00 | 19.06 | 0.00 | 0.06
324.9703 | 57.4901 | 22.66 | 0.00 | 19.86 | 0.00 | 18.29 | 0.00 | 0.07
325.0021 | 57.5585 | 22.83 | 0.00 | 20.22 | 0.00 | 18.69 | 0.00 | 0.07
325.1468 | 57.6155 | 22.80 | 0.00 | 20.27 | 0.00 | 18.65 | 0.00 | 0.07
324.9589 | 57.3731 | 23.33 | 0.01 | 20.57 | 0.00 | 18.78 | 0.00 | 0.07
324.9279 | 57.4383 | 22.71 | 0.00 | 20.09 | 0.00 | 18.38 | 0.00 | 0.07
324.9290 | 57.4600 | 23.03 | 0.00 | 20.42 | 0.00 | 18.69 | 0.00 | 0.07
324.9169 | 57.5325 | 23.47 | 0.01 | 20.75 | 0.00 | 18.98 | 0.00 | 0.06
324.5742 | 57.2674 | 23.91 | 0.01 | 21.04 | 0.00 | 19.34 | 0.00 | 0.06
324.3852 | 57.4135 | 24.95 | 0.02 | 21.79 | 0.00 | 19.66 | 0.00 | 0.06
324.4519 | 57.4703 | 23.22 | 0.01 | 20.14 | 0.00 | 18.74 | 0.00 | 0.07
324.4618 | 57.4889 | 23.83 | 0.01 | 20.57 | 0.00 | 18.60 | 0.00 | 0.06
324.5109 | 57.4804 | 24.43 | 0.02 | 20.87 | 0.00 | 19.16 | 0.00 | 0.06
324.5797 | 57.5147 | 23.87 | 0.01 | 20.88 | 0.00 | 19.30 | 0.00 | 0.06
324.4841 | 57.5443 | 23.76 | 0.01 | 20.54 | 0.00 | 18.70 | 0.00 | 0.06
324.1735 | 57.5382 | 23.53 | 0.01 | 20.54 | 0.00 | 18.32 | 0.00 | 0.06
324.2134 | 57.5346 | 24.34 | 0.01 | 20.91 | 0.00 | 19.15 | 0.00 | 0.06
324.1619 | 57.5102 | 25.72 | 0.06 | 21.93 | 0.00 | 19.89 | 0.00 | 0.06
324.1149 | 57.6079 | 24.68 | 0.02 | 21.06 | 0.00 | 19.43 | 0.00 | 0.06
324.9834 | 57.2734 | 23.68 | 0.01 | 20.78 | 0.00 | 18.97 | 0.00 | 0.06
325.2606 | 57.3339 | 23.23 | 0.01 | 20.25 | 0.00 | 18.51 | 0.00 | 0.07
325.1878 | 57.4292 | 24.15 | 0.01 | 21.15 | 0.00 | 19.25 | 0.00 | 0.06
325.0855 | 57.3392 | 24.07 | 0.01 | 21.01 | 0.00 | 19.30 | 0.00 | 0.06
325.0216 | 57.5352 | 24.29 | 0.01 | 20.83 | 0.00 | 19.29 | 0.00 | 0.06
325.0511 | 57.6162 | 23.92 | 0.01 | 20.96 | 0.00 | 19.13 | 0.00 | 0.06
325.1674 | 57.6198 | 24.99 | 0.02 | 21.74 | 0.00 | 19.95 | 0.00 | 0.06
325.1083 | 57.7926 | 23.97 | 0.01 | 21.03 | 0.00 | 18.95 | 0.00 | 0.06
325.0825 | 57.7862 | 26.36 | 0.06 | 22.62 | 0.00 | 20.49 | 0.00 | 0.05
324.7593 | 57.1508 | 23.92 | 0.01 | 20.67 | 0.01 | 18.82 | 0.00 | 0.06
324.8858 | 57.2525 | 22.92 | 0.00 | 20.08 | 0.00 | 18.42 | 0.00 | 0.07
324.9626 | 57.4817 | 23.20 | 0.01 | 20.32 | 0.00 | 18.49 | 0.00 | 0.07
324.9151 | 57.5068 | 24.70 | 0.02 | 21.11 | 0.00 | 18.81 | 0.00 | 0.06
324.8126 | 57.5849 | 23.38 | 0.01 | 20.50 | 0.00 | 18.70 | 0.00 | 0.06
324.9211 | 57.6997 | 25.34 | 0.03 | 21.72 | 0.00 | 19.79 | 0.00 | 0.06
324.8863 | 57.7422 | 24.23 | 0.01 | 20.83 | 0.00 | 19.24 | 0.00 | 0.06
324.8643 | 57.2352 | 22.46 | 0.00 | 19.77 | 0.00 | 18.38 | 0.00 | 0.07
324.5316 | 57.5287 | 22.50 | 0.00 | 19.37 | 0.00 | 17.60 | 0.00 | 0.07
324.5085 | 57.6752 | 23.20 | 0.01 | 19.79 | 0.00 | 17.90 | 0.00 | 0.07
324.2213 | 57.5187 | 23.68 | 0.01 | 20.08 | 0.00 | 18.42 | 0.00 | 0.06
324.2461 | 57.4858 | 22.46 | 0.00 | 18.80 | 0.00 | 17.05 | 0.00 | 0.07
324.1375 | 57.4803 | 22.25 | 0.00 | 18.85 | 0.00 | 17.32 | 0.00 | 0.08
324.7057 | 57.4316 | 22.33 | 0.00 | 19.41 | 0.00 | 18.10 | 0.00 | 0.08
324.6640 | 57.6054 | 22.58 | 0.00 | 19.61 | 0.00 | 18.23 | 0.00 | 0.07
325.1605 | 57.4679 | 23.16 | 0.00 | 18.91 | 0.00 | 17.42 | 0.00 | 0.07
324.6305 | 57.4982 | 22.31 | 0.00 | 19.68 | 0.00 | 18.08 | 0.00 | 0.08

## Acknowledgements

The authors thank the referee for the useful constructive comments which has
refined the overall structure, quality and comprehensibility of this paper.
This research is based on data collected at Subaru Telescope with Hyper
Suprime-Cam, which is operated by the National Astronomical Observatory of
Japan. We are honored and grateful for the opportunity of observing the
Universe from Mauna Kea, which has the cultural, historical and natural
significance in Hawaii. We are grateful to The East Asian Observatory which is
supported by The National Astronomical Observatory of Japan; Academia Sinica
Institute of Astronomy and Astrophysics; the Korea Astronomy and Space Science
Institute; the Operation, Maintenance and Upgrading Fund for Astronomical
Telescopes and Facility Instruments, budgeted from the Ministry of Finance
(MOF) of China and administrated by the Chinese Academy of Sciences (CAS), as
well as the National Key R&D Program of China (No. 2017YFA0402700). We use
Pan-STARRS and GAIA DR3 data for the membership analysis in this work. The
Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been made
possible through contributions by the Institute for Astronomy, the University
of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its
participating institutes, the Max Planck Institute for Astronomy, Heidelberg
and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns
Hopkins University, Durham University, the University of Edinburgh, the
Queen’s University Belfast, the Harvard-Smithsonian Center for Astrophysics,
the Las Cumbres Observatory Global Telescope Network Incorporated, the
National Central University of Taiwan, the Space Telescope Science Institute,
the National Aeronautics and Space Administration under Grant No. NNX08AR22G
issued through the Planetary Science Division of the NASA Science Mission
Directorate, the National Science Foundation Grant No. AST-1238877, the
University of Maryland, Eotvos Lorand University (ELTE), the Los Alamos
National Laboratory, and the Gordon and Betty Moore Foundation. This work has
made use of data from the European Space Agency (ESA) mission GAIA processed
by Gaia Data processing and Analysis Consortium (DPAC:
https://www.cosmos.esa.int/web/gaia/dpac/consortium). This publication makes
use of VOSA, developed under the Spanish Virtual Observatory
(https://svo.cab.inta-csic.es) project funded by
MCIN/AEI/10.13039/501100011033/ through grant PID2020-112949GB-I00. VOSA has
been partially updated by using funding from the European Union’s Horizon 2020
Research and Innovation Programme, under Grant Agreement nº 776403
(EXOPLANETS-A). We gratefully acknowledge the use of high performance
computing facilities at IUCAA, Pune for the HSC data reduction.

The authors thank Kora Mu$\check{z}$i$\acute{c}$ for the valuable review and
suggestions which have improved the quality of the paper overall, Surhud More
for his help during HSC data reduction. We thank Gregory J. Herczeg for his
valuable help with the observing proposal for Subaru HSC for IC 1396
observations. We thank Isabelle Baraffe for providing us with isochrone models
for an interval of log (Age) = 0.01, through personal communication. JJ
acknowledges the financial support received through the DST-SERB grant
SPG/2021/003850. S.R.D. acknowledges support from FONDECYT Postdoctoral
fellowship (project code: 3220162). ZG is supported by the ANID FONDECYT
Postdoctoral program No. 3220029. ZG acknowledge support by ANID, – Millennium
Science Initiative Program – NCN19_171.

## References

  * Aihara et al. (2018) Aihara H., et al., 2018, PASJ, 70, S8
  * Allard et al. (2012) Allard F., Homeier D., Freytag B., 2012, Philosophical Transactions of the Royal Society of London Series A, 370, 2765
  * Allers & Liu (2020) Allers K. N., Liu M. C., 2020, PASP, 132, 104401
  * Almendros-Abad et al. (2023) Almendros-Abad V., et al., 2023, A&A, 677, A26
  * Alves de Oliveira et al. (2012) Alves de Oliveira C., Moraux E., Bouvier J., Bouy H., 2012, A&A, 539, A151
  * Alves de Oliveira et al. (2013) Alves de Oliveira C., Moraux E., Bouvier J., Duchêne G., Bouy H., Maschberger T., Hudelot P., 2013, A&A, 549, A123
  * Andersen et al. (2011) Andersen M., Meyer M. R., Robberto M., Bergeron L. E., Reid N., 2011, A&A, 534, A10
  * Andersen et al. (2017) Andersen M., Gennaro M., Brandner W., Stolte A., de Marchi G., Meyer M. R., Zinnecker H., 2017, A&A, 602, A22
  * Bailer-Jones et al. (2021) Bailer-Jones C. A. L., Rybizki J., Fouesneau M., Demleitner M., Andrae R., 2021, AJ, 161, 147
  * Baraffe et al. (2015) Baraffe I., Homeier D., Allard F., Chabrier G., 2015, A&A, 577, A42
  * Barentsen et al. (2011) Barentsen G., et al., 2011, MNRAS, 415, 103
  * Bastian et al. (2010) Bastian N., Covey K. R., Meyer M. R., 2010, ARA&A, 48, 339
  * Bate (2012) Bate M. R., 2012, MNRAS, 419, 3115
  * Bayo et al. (2008) Bayo A., Rodrigo C., Barrado Y Navascués D., Solano E., Gutiérrez R., Morales-Calderón M., Allard F., 2008, A&A, 492, 277
  * Béjar et al. (2011) Béjar V. J. S., Zapatero Osorio M. R., Rebolo R., Caballero J. A., Barrado D., Martín E. L., Mundt R., Bailer-Jones C. A. L., 2011, ApJ, 743, 64
  * Bonnell et al. (2008) Bonnell I. A., Clark P., Bate M. R., 2008, MNRAS, 389, 1556
  * Bosch et al. (2018) Bosch J., et al., 2018, PASJ, 70, S5
  * Briceño et al. (2007) Briceño C., Hartmann L., Hernández J., Calvet N., Vivas A. K., Furesz G., Szentgyorgyi A., 2007, ApJ, 661, 1119
  * Burgasser et al. (2019) Burgasser A., et al., 2019, BAAS, 51, 547
  * Cantat-Gaudin et al. (2018) Cantat-Gaudin T., et al., 2018, A&A, 618, A93
  * Cantat-Gaudin et al. (2019) Cantat-Gaudin T., et al., 2019, A&A, 624, A126
  * Chabrier et al. (2014) Chabrier G., Johansen A., Janson M., Rafikov R., 2014, in Beuther H., Klessen R. S., Dullemond C. P., Henning T., eds, Protostars and Planets VI. pp 619–642 (arXiv:1401.7559), doi:10.2458/azu_uapress_9780816531240-ch027
  * Chambers et al. (2016) Chambers K. C., et al., 2016, arXiv e-prints, p. arXiv:1612.05560
  * Contreras et al. (2002) Contreras M. E., Sicilia-Aguilar A., Muzerolle J., Calvet N., Berlind P., Hartmann L., 2002, AJ, 124, 1585
  * Cutri et al. (2003) Cutri R. M., et al., 2003, 2MASS All Sky Catalog of point sources.
  * Damian et al. (2021) Damian B., Jose J., Samal M. R., Moraux E., Das S. R., Patra S., 2021, MNRAS, 504, 2557
  * Damian et al. (2023a) Damian B., Jose J., Biller B., Paul K. T., 2023a, Journal of Astrophysics and Astronomy, 44, 77
  * Damian et al. (2023b) Damian B., et al., 2023b, ApJ, 951, 139
  * Damiani et al. (2019) Damiani F., Prisinzano L., Pillitteri I., Micela G., Sciortino S., 2019, A&A, 623, A112
  * Das et al. (2023) Das S. R., Gupta S., Prakash P., Samal M., Jose J., 2023, ApJ, 948, 7
  * Downes et al. (2014) Downes J. J., et al., 2014, MNRAS, 444, 1793
  * Drass et al. (2016) Drass H., Haas M., Chini R., Bayo A., Hackstein M., Hoffmeister V., Godoy N., Vogt N., 2016, MNRAS, 461, 1734
  * Errmann et al. (2013) Errmann R., et al., 2013, Astronomische Nachrichten, 334, 673
  * Esplin & Luhman (2017) Esplin T. L., Luhman K. L., 2017, The Astronomical Journal, 154, 134
  * Esplin & Luhman (2019) Esplin T. L., Luhman K. L., 2019, AJ, 158, 54
  * Fujii & Portegies Zwart (2016) Fujii M. S., Portegies Zwart S., 2016, ApJ, 817, 4
  * Gaia Collaboration et al. (2021) Gaia Collaboration et al., 2021, A&A, 649, A1
  * Gaia Collaboration et al. (2022) Gaia Collaboration et al., 2022, arXiv e-prints, p. arXiv:2208.00211
  * Galli et al. (2020) Galli P. A. B., et al., 2020, A&A, 643, A148
  * Gao (2018a) Gao X.-H., 2018a, Ap&SS, 363, 232
  * Gao (2018b) Gao X., 2018b, ApJ, 869, 9
  * Gao (2019) Gao X.-h., 2019, PASP, 131, 044101
  * Gennaro et al. (2018) Gennaro M., et al., 2018, ApJ, 855, 20
  * Getman et al. (2007) Getman K. V., Feigelson E. D., Garmire G., Broos P., Wang J., 2007, ApJ, 654, 316
  * Getman et al. (2012) Getman K. V., Feigelson E. D., Sicilia-Aguilar A., Broos P. S., Kuhn M. A., Garmire G. P., 2012, MNRAS, 426, 2917
  * Guarcello et al. (2016) Guarcello M. G., et al., 2016, arXiv e-prints, p. arXiv:1605.01773
  * Guarcello et al. (2021) Guarcello M. G., et al., 2021, A&A, 650, A157
  * Gupta et al. (2021) Gupta S., et al., 2021, MNRAS, 508, 3388
  * Guzmán-Díaz et al. (2021) Guzmán-Díaz J., et al., 2021, A&A, 650, A182
  * Hewett et al. (2006) Hewett P. C., Warren S. J., Leggett S. K., Hodgkin S. T., 2006, MNRAS, 367, 454
  * Huston & Luhman (2021) Huston M. J., Luhman K. L., 2021, AJ, 161, 138
  * Jose et al. (2017) Jose J., Herczeg G. J., Samal M. R., Fang Q., Panwar N., 2017, ApJ, 836, 98
  * Jose et al. (2020) Jose J., et al., 2020, ApJ, 892, 122
  * Kawanomoto et al. (2018) Kawanomoto S., et al., 2018, PASJ, 70, 66
  * Kim et al. (2022) Kim J. S., Hartman P., Haworth Thomas J., Fang M., Facchini S., Pascucci I., Heo J.-E., 2022, in Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun. Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun. p. 196, doi:10.5281/zenodo.7591727
  * Kirkpatrick et al. (2012) Kirkpatrick J. D., et al., 2012, ApJ, 753, 156
  * Kirkpatrick et al. (2021) Kirkpatrick J. D., et al., 2021, ApJS, 253, 7
  * Kirkpatrick et al. (2023) Kirkpatrick J. D., et al., 2023, arXiv e-prints, p. arXiv:2312.03639
  * Knight et al. (2022) Knight C., Peeters E., Wolfire M., Stock D. J., 2022, MNRAS, 510, 4888
  * Kroupa & Boily (2002) Kroupa P., Boily C. M., 2002, MNRAS, 336, 1188
  * Ksoll et al. (2021) Ksoll V. F., et al., 2021, AJ, 161, 257
  * Kubiak et al. (2021) Kubiak K., Mužić K., Sousa I., Almendros-Abad V., Köhler R., Scholz A., 2021, A&A, 650, A48
  * Lawrence et al. (2007) Lawrence A., et al., 2007, MNRAS, 379, 1599
  * Levine et al. (2006) Levine J. L., Steinhauer A., Elston R. J., Lada E. A., 2006, ApJ, 646, 1215
  * Lim et al. (2013) Lim B., Chun M.-Y., Sung H., Park B.-G., Lee J.-J., Sohn S. T., Hur H., Bessell M. S., 2013, AJ, 145, 46
  * Lim et al. (2015) Lim B., Sung H., Hur H., Park B.-G., 2015, arXiv e-prints, p. arXiv:1511.01118
  * Lindegren et al. (2021) Lindegren L., et al., 2021, A&A, 649, A2
  * Longmore et al. (2014) Longmore S. N., et al., 2014, in Beuther H., Klessen R. S., Dullemond C. P., Henning T., eds, Protostars and Planets VI. p. 291 (arXiv:1401.4175), doi:10.2458/azu_uapress_9780816531240-ch013
  * Lu et al. (2013) Lu J. Y., Liu Z. Q., Kabin K., Jing H., Zhao M. X., Wang Y., 2013, Journal of Geophysical Research (Space Physics), 118, 3113
  * Lucas et al. (2008) Lucas P. W., et al., 2008, MNRAS, 391, 136
  * Luhman & Hapich (2020) Luhman K. L., Hapich C. J., 2020, AJ, 160, 57
  * Luhman et al. (2018) Luhman K. L., Herrmann K. A., Mamajek E. E., Esplin T. L., Pecaut M. J., 2018, The Astronomical Journal, 156, 76
  * Marton et al. (2022) Marton G., et al., 2022, arXiv e-prints, p. arXiv:2206.05796
  * Mejías et al. (2022) Mejías A., Minniti D., Alonso-García J., Beamín J. C., Saito R. K., Solano E., 2022, A&A, 660, A131
  * Melton (2020) Melton E., 2020, AJ, 159, 200
  * Mercer et al. (2009) Mercer E. P., Miller J. M., Calvet N., Hartmann L., Hernandez J., Sicilia-Aguilar A., Gutermuth R., 2009, AJ, 138, 7
  * Miret-Roig et al. (2019) Miret-Roig N., et al., 2019, A&A, 631, A57
  * Miret-Roig et al. (2022) Miret-Roig N., Galli P. A. B., Olivares J., Bouy H., Alves J., Barrado D., 2022, A&A, 667, A163
  * Morales-Calderón et al. (2009) Morales-Calderón M., et al., 2009, ApJ, 702, 1507
  * Mužić et al. (2012) Mužić K., Scholz A., Geers V., Jayawardhana R., Tamura M., 2012, ApJ, 744, 134
  * Mužić et al. (2017) Mužić K., Schödel R., Scholz A., Geers V. C., Jayawardhana R., Ascenso J., Cieza L. A., 2017, MNRAS, 471, 3699
  * Mužić et al. (2019) Mužić K., Scholz A., Peña Ramírez K., Jayawardhana R., Schödel R., Geers V. C., Cieza L. A., Bayo A., 2019, ApJ, 881, 79
  * Mužić et al. (2022) Mužić K., Almendros-Abad V., Bouy H., Kubiak K., Peña Ramírez K., Krone-Martins A., Moitinho A., Conceição M., 2022, A&A, 668, A19
  * Mužić et al. (2015) Mužić K., Scholz A., Geers V. C., Jayawardhana R., 2015, The Astrophysical Journal, 810, 159
  * Nakano et al. (2012) Nakano M., Sugitani K., Watanabe M., Fukuda N., Ishihara D., Ueno M., 2012, AJ, 143, 61
  * Offner et al. (2014) Offner S. S. R., Clark P. C., Hennebelle P., Bastian N., Bate M. R., Hopkins P. F., Moraux E., Whitworth A. P., 2014, in Beuther H., Klessen R. S., Dullemond C. P., Henning T., eds, Protostars and Planets VI. p. 53 (arXiv:1312.5326), doi:10.2458/azu_uapress_9780816531240-ch003
  * Okada et al. (2006) Okada Y., Onaka T., Nakagawa T., Shibai H., Tomono D., Yui Y. Y., 2006, ApJ, 640, 383
  * Olivares et al. (2019) Olivares J., et al., 2019, A&A, 625, A115
  * Oliveira et al. (2009) Oliveira J. M., Jeffries R. D., van Loon J. T., 2009, MNRAS, 392, 1034
  * Olsen et al. (2021) Olsen C., et al., 2021, ApJ, 913, 45
  * Patel et al. (1998) Patel N. A., Goldsmith P. F., Heyer M. H., Snell R. L., Pratap P., 1998, ApJ, 507, 241
  * Peña Ramírez et al. (2012) Peña Ramírez K., Béjar V. J. S., Zapatero Osorio M. R., Petr-Gotzens M. G., Martín E. L., 2012, ApJ, 754, 30
  * Pearson et al. (2021) Pearson S., Scholz A., Teixeira P. S., Mužić K., Almendros-Abad V., 2021, MNRAS, 507, 4074
  * Pedregosa et al. (2011) Pedregosa F., et al., 2011, Journal of Machine Learning Research, 12, 2825
  * Pelayo-Baldárrago et al. (2022) Pelayo-Baldárrago M. E., Sicilia-Aguilar A., Fang M., Roccatagliata V., Kim J. S., García-Álvarez D., 2022, arXiv e-prints, p. arXiv:2210.11930
  * Pelayo-Baldárrago et al. (2023) Pelayo-Baldárrago M. E., Sicilia-Aguilar A., Fang M., Roccatagliata V., Kim J. S., García-Álvarez D., 2023, A&A, 669, A22
  * Portegies Zwart (2016) Portegies Zwart S. F., 2016, MNRAS, 457, 313
  * Portegies Zwart et al. (2010) Portegies Zwart S. F., McMillan S. L. W., Gieles M., 2010, ARA&A, 48, 431
  * Povich et al. (2019) Povich M. S., Maldonado J. T., Nuñez E. H., Robitaille T. P., 2019, ApJ, 881, 37
  * Prisinzano et al. (2022) Prisinzano L., et al., 2022, A&A, 664, A175
  * Reipurth & Clarke (2001) Reipurth B., Clarke C., 2001, AJ, 122, 432
  * Riaz et al. (2018) Riaz R., Vanaverbeke S., Schleicher D. R. G., 2018, MNRAS, 478, 5460
  * Robberto et al. (2020) Robberto M., et al., 2020, ApJ, 896, 79
  * Sarro et al. (2014) Sarro L. M., et al., 2014, A&A, 563, A45
  * Saurin et al. (2012) Saurin T. A., Bica E., Bonatto C., 2012, MNRAS, 421, 3206
  * Scholz et al. (2012) Scholz A., Muzic K., Geers V., Bonavita M., Jayawardhana R., Tamura M., 2012, ApJ, 744, 6
  * Scholz et al. (2013) Scholz A., Geers V., Clark P., Jayawardhana R., Muzic K., 2013, ApJ, 775, 138
  * Sicilia-Aguilar et al. (2004) Sicilia-Aguilar A., Hartmann L. W., Briceño C., Muzerolle J., Calvet N., 2004, AJ, 128, 805
  * Sicilia-Aguilar et al. (2005) Sicilia-Aguilar A., Hartmann L. W., Hernández J., Briceño C., Calvet N., 2005, AJ, 130, 188
  * Sicilia-Aguilar et al. (2006) Sicilia-Aguilar A., et al., 2006, ApJ, 638, 897
  * Sicilia-Aguilar et al. (2013) Sicilia-Aguilar A., Kim J. S., Sobolev A., Getman K., Henning T., Fang M., 2013, A&A, 559, A3
  * Sicilia-Aguilar et al. (2014) Sicilia-Aguilar A., Roccatagliata V., Getman K., Henning T., Merín B., Eiroa C., Rivière-Marichalar P., Currie T., 2014, A&A, 562, A131
  * Sicilia-Aguilar et al. (2019) Sicilia-Aguilar A., Patel N., Fang M., Roccatagliata V., Getman K., Goldsmith P., 2019, A&A, 622, A118
  * Silverberg et al. (2021) Silverberg S. M., Günther H. M., Kim J. S., Principe D. A., Wolk S. J., 2021, AJ, 162, 279
  * Slesnick et al. (2004) Slesnick C. L., Hillenbrand L. A., Carpenter J. M., 2004, ApJ, 610, 1045
  * Spearman (1987) Spearman C., 1987, The American Journal of Psychology, 100, 441
  * Stamatellos (2014) Stamatellos D., 2014, in The Labyrinth of Star Formation. p. 17 (arXiv:1302.3954), doi:10.1007/978-3-319-03041-8_3
  * Stamatellos & Whitworth (2009) Stamatellos D., Whitworth A. P., 2009, MNRAS, 392, 413
  * Suárez et al. (2019) Suárez G., Downes J. J., Román-Zúñiga C., Cerviño M., Briceño C., Petr-Gotzens M. G., Vivas K., 2019, MNRAS, 486, 1718
  * Vorobyov & Basu (2013) Vorobyov E. I., Basu S., 2013, Mem. Soc. Astron. Italiana, 84, 866
  * Vorobyov et al. (2017) Vorobyov E. I., Steinrueck M. E., Elbakyan V., Guedel M., 2017, A&A, 608, A107
  * Wang & Chen (2019) Wang S., Chen X., 2019, ApJ, 877, 116
  * Whitworth (2018) Whitworth A., 2018, arXiv e-prints, p. arXiv:1811.06833
  * Whitworth & Zinnecker (2004) Whitworth A. P., Zinnecker H., 2004, A&A, 427, 299
  * Winston et al. (2011) Winston E., Wolk S. J., Bourke T. L., Megeath S. T., Gutermuth R., Spitzbart B., 2011, ApJ, 743, 166
  * Winston et al. (2020) Winston E., Hora J. L., Tolls V., 2020, AJ, 160, 68
  * Winter (2019) Winter A., 2019, PhD thesis, University of Cambridge, UK
  * Winter & Haworth (2022) Winter A. J., Haworth T. J., 2022, European Physical Journal Plus, 137, 1132
  * Winter et al. (2018) Winter A. J., Clarke C. J., Rosotti G., Ih J., Facchini S., Haworth T. J., 2018, MNRAS, 478, 2700
  * Zapatero Osorio et al. (2017) Zapatero Osorio M. R., Béjar V. J. S., Peña Ramírez K., 2017, ApJ, 842, 65
  * de Zeeuw et al. (1999) de Zeeuw P. T., Hoogerwerf R., de Bruijne J. H. J., Brown A. G. A., Blaauw A., 1999, AJ, 117, 354

##  Appendix A Data quality comparison

In this section, we present two data quality plots of the HSC data used in the
present study. As can be seen from Figure 10 (Top), the completeness of the
data in r2-band is down to 24.5 mag ($\sim$ 0.03 M⊙). The majority of sources
have photometric error $\leq$ 0.05 mag as evident from Figure 10 (Bottom). The
three branches observed in the HSC r2-band plot correspond to the merged Pan-
STARRS photometry (used while generating the deep optical catalog as mentioned
in Section 2.2), long and short exposure photometry. More details about
merging of the short and long exposure catalogs will be presented in Das et
al., in preparation. We compare the proper motion and parallax distribution of
Gaia DR3 counterparts of the members identified in this study with that of the
previous studies. Figure 11 Top and Figure 11 Bottom suggest an excellent
concordance between the proper motion and distance estimates of the new and
literature-based cluster members. Also, we observe an unavoidable yet limited
scatter in the proper motions and distance values of the members identified in
this study as compared to the literature-based members. However, some scatter
is inevitable in all membership analysis and has been observed in previous
studies (Cantat-Gaudin et al. 2018; Pelayo-Baldárrago et al. 2022; Das et al.
2023) as well.

Figure 10:  (Top) Completeness of HSC r2 filter based on the peak (turnover
point) of distribution (Jose et al. 2017; Gupta et al. 2021) (Bottom) Error vs
magnitude for r2-filter. The three branches observed in the HSC r2-band plot
correspond to the merged Pan-STARRS photometry, long and short exposure
photometry.

Figure 11:  (Top) Proper motion RA vs Dec distribution (Bottom) Distance
distribution for cluster members identified by previous studies versus members
from the present study with Gaia DR3 counterparts. We observe a small scatter
in the proper motions and distance values of the members identified in this
study as compared to the literature-based members. However, some scatter is
inevitable in all membership analysis.

Figure 12:  ROC curve for the (Left) first RF classifier phase. (Center)
second RF classifier phase. (Right) third RF classifier phase.

Hyper-parameters for all the phases of RF classifier are as follows:
random state = 50
number of estimators = 188
min$\\_$samples$\\_$split: 5
max$\\_$leaf$\\_$nodes: 14
max$\\_$features: 0.6
max$\\_$depth: 16

We provide all the necessary details of the entire RF process like accuracy,
precision, recall, F1 score and CV Score for each phase in Table 4. We have
also included the roc curves for the three phases here.

Phase | Accuracy | Precision | F1 score | Recall | CV Score
---|---|---|---|---|---
Phase 1 | 0.98 | 0.98 | 0.95 | 0.93 | 0.98
Phase 2 | 0.98 | 0.80 | 0.70 | 0.60 | 0.98
Phase 3 | 0.98 | 0.72 | 0.70 | 0.62 | 0.98
Table 4:  Quality parameters of the three Random Forest classifier phases

##  Appendix B Field Subtraction Method for Validation

We consider a 10′ radius control field located towards the outskirts of the
HSC observed area of IC 1396 and perform statistical field decontamination of
the cluster field, located towards the center of the same area. An area of
only 10′ radius is chosen here for field subtraction due to the lack of a
suitable control field of larger area, devoid of young pre-main sequence
stars, as observed by their spatial distribution (Das et al., in prep). The
10′ radius control field considered for the field subtraction here is chosen
carefully towards the outskirts as it is devoid of any pre-main sequence
sources which is suggested by the spatial density map given in Das et al.
2023. We perform the field decontamination by dividing the r2 \- Y color and
r2 magnitude parameter space into 0.1 mag bins, followed by the subtraction of
the control field count from the cluster field count (Gupta et al. 2021;
Damian et al. 2021). The member selection using pre-main sequence locus
approach is then performed for the statistically subtracted sources located
above the 10 Myr isochrone. Subsequently, sources within 1 $\sigma$ limit of
the defined locus and r2 $\geq$ 22 mag are selected as members. However, we
find that whether or not prior field subtraction is performed, the statistics
of members as well as mass distribution remains approximately unaltered. We
would like to emphasize here that the sources by field subtraction are not the
actual cluster members but just the statistical members in the 10′ central
cluster field. Hence, we continue without field decontamination for pre-main
sequence based membership analysis as given in Section 3.4. This is because
the cluster members obtained within 1 $\sigma$ of the empirical pre-main
sequence locus are common in all the CMD combinations (as mentioned in Section
3.4). On the contrary, the candidate members selected from the field
decontamination by statistical method need not be common across all
combinations of different bands as they are not true members. Moreover, due to
the lack of a suitable control field of 22′ radius area, we are unable to
perform decontamination for the central cluster considered for our analysis.