# Subaru Hyper Suprime-Cam Survey of Cygnus OB2 Complex - I: Introduction,
Photometry and Source Catalog

Saumya Gupta1, Jessy Jose1, Surhud More2, Swagat R. Das1, Gregory J. Herczeg3,
Manash R. Samal4, Zhen Guo5, Prem Prakash1, Belinda Damian6, Michihiro
Takami7, Satoko Takahashi8,9, Katsuo Ogura10, Tsuyoshi Terai11, Tae-Soo
Pyo11,12
1Indian Institute of Science Education and Research (IISER) Tirupati, Rami
Reddy Nagar, Karakambadi Road, Mangalam (P.O.), Tirupati 517 507, India
2Inter University Centre for Astronomy and Astrophysics, Ganeshkhind, Pune
411007, India
3 Kavli Institute for Astronomy and Astrophysics, Peking University, Yi He
Yuan Lu 5, Haidian Qu, Beijing 100871, China
4Physical Research Laboratory (PRL), Navrangpura, Ahmedabad 380 009, Gujarat,
India
5 Centre for Astrophysics Research, University of Hertfordshire, Hatfield AL10
9AB, UK
6 Christ (Deemed to be University), Bangalore, India
7 Institute of Astronomy and Astrophysics, Academia Sinica 11F of Astronomy-
Mathematics Building, National Taiwan University, Taiwan, R.O.C
8 Joint ALMA Observatory, Alonso de Córdova 3107, Vitacura, Santiago, Chile
9 NAOJ Chile, National Astronomical Observatory of Japan, Alonso de Córdova
3788, Office 61B, Vitacura, Santiago, Chile, 7630492
10 Kokugakuin University, Higashi, Shibuya-ku, Tokyo 150-8440, Japan
11 Subaru Telescope, National Astronomical Observatory of Japan, National
Institutes of Natural Sciences, 650 North Aohoku Place Hilo, HI 96720, USA
12 School of Mathematical and Physical Science, SOKENDAI (The Graduate
University for Advanced Studies), Hayama, Kanagawa 240-0193, Japan
kcsaumya.gupta<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Low mass star formation inside massive clusters is crucial to understand the
effect of cluster environment on processes like circumstellar disk evolution,
planet and brown dwarf formation. The young massive association of Cygnus OB2,
with a strong feedback from massive stars, is an ideal target to study the
effect of extreme environmental conditions on its extensive low-mass
population.We aim to perform deep multi-wavelength studies to understand the
role of stellar feedback on the IMF, brown dwarf fraction and circumstellar
disk properties in the region. We introduce here, the deepest and widest
optical photometry of 1.5∘ diameter region centred at Cygnus OB2 in r2, i2, z
and Y-filters using Subaru Hyper Suprime-Cam (HSC). This work presents the
data reduction, source catalog generation, data quality checks and preliminary
results about the pre-main sequence sources. We obtain 713,529 sources in
total, with detection down to $\sim$ 28 mag, 27 mag, 25.5 mag and 24.5 mag in
r2, i2, z and Y-band respectively, which is $\sim$ 3 - 5 mag deeper than the
existing Pan-STARRS and GTC/OSIRIS photometry. We confirm the presence of a
distinct pre-main sequence branch by statistical field subtraction of the
central 18′ region. We find the median age of the region as $\sim$ 5 $\pm$ 2
Myrs with an average disk fraction of $\sim$ 9$\%$. At this age, combined with
AV $\sim$ 6 - 8 mag, we detect sources down to a mass range $\sim$ 0.01 - 0.17
M⊙. The deep HSC catalog will serve as the groundwork for further studies on
this prominent active young cluster.

###### keywords:

stars:low-mass – stars: pre-main-sequence – stars:imaging – methods:
observational – techniques: photometric – catalogues

††pubyear: 2021††pagerange: Subaru Hyper Suprime-Cam Survey of Cygnus OB2
Complex - I: Introduction, Photometry and Source Catalog–C

##  1 Introduction

The complete stellar life cycle is significantly shaped by its mass, which is
in-turn determined by the less understood evolutionary stages of star
formation and its related processes (Luhman 2012; Armitage 2015; Manara et al.
2017 and references therein). As low-mass stars ($<$ 1-2 M⊙) spend
comparatively longer time in the rudimentary stages than their massive
counterparts ($>$ 8 M⊙), comprehensive studies on low-mass star formation can
provide useful insight into the interesting underlying processes like
protoplanetary disk formation and evolution (Hartmann 2008; Williams & Cieza
2011; Armitage 2015), brown dwarf formation and the factors affecting them
(Basu 2017; Megeath et al. 2019). Moreover, since most of the stars form in
clusters, hence cluster environment plays a crucial role in stellar evolution
and related processes (Sicilia-Aguilar, Aurora et al. 2013; Samal et al. 2015;
Jose et al. 2016; Parker et al. 2021; Damian et al. 2021). For example, disk
evolution has been observed to be affected by various factors like viscous
accretion (Gorti et al. 2015; Ercolano & Pascucci 2017), stellar density
(Winter et al. 2018), external photoevaporation in diverse harsh environments
like ONC (O’dell et al. 1993), NGC 1977 (Kim et al. 2016), Cygnus OB2 (Wright
et al. 2012; Guarcello et al. 2016; Winter et al. 2019). Another intriguing
question which requires further investigation is the ambiguous uniformity of
Initial Mass Function (IMF) and its behavior in the low-mass and sub-stellar
regime. Although many recent and past studies suggest a uniform IMF across
various star forming regions in the Milky Way (Bastian et al. 2010; Offner et
al. 2014; Moraux 2016; Jose et al. 2017; Damian et al. 2021), variation has
been observed in the extreme environments like the Galactic Center (e.g. Lu et
al. 2013; Hosek et al. 2019), least luminous Milky Way satellites (Geha et al.
2013; Gennaro et al. 2018) and massive elliptical galaxies (van Dokkum &
Conroy 2010; Cappellari et al. 2012).

Since, both Galactic and extragalactic star formation principally occurs in
clusters and OB-associations (e.g Carpenter 2000; Lada & Lada 2003; Pfalzner
et al. 2012), an empirical model for low mass star formation developed by
eclectic inferences drawn from both Galactic as well as extragalactic studies,
is a pre-requisite to answer these fundamental questions. However, due to
observational constraints with the current technology, we can only start by
analysing the relatively distant young massive Galactic star forming regions
using powerful observing facilities. The nearby clusters (for e.g Gould Belt
regions), which are the focus of most of the studies (Dunham et al. 2015; Dzib
et al. 2018; Bobylev & Bajkova 2020; Kubiak et al. 2021; Damian et al. 2021)
are not the representative samples of extragalactic star-forming regions,
where most of the star formation occurs in the extreme cluster environments of
giant molecular complexes. The deep and wide field surveys of distant young
massive Galactic clusters are need of the hour as such clusters are less
dynamically evolved and hence, provide a robust sample of stars with similar
history of formation in extreme environments (e.g. Portegies Zwart et al.
2010; Longmore et al. 2014). The primary goal of this work is to obtain good
quality deep observations and use them to carry out an elaborate study of
Cygnus OB2, a young massive Galactic cluster with extreme environmental
conditions analogous to that of extragalactic star forming regions.

Cygnus OB2 (Right Ascension: 20:33:15, Declination: +41:18:54), located at
$\sim$ 1.6 kpc (Lim et al. 2019) from the Sun, is a typical analogue of the
extragalactic massive star forming regions located outside the solar
neighborhood. It is the central massive OB-association ( 2 – 10 $\times$ 104
M⊙ as determined by Knödlseder (2000); Wright et al. (2010)) embedded in the
giant Cygnus X molecular complex (Schneider et al. 2006; Reipurth & Schneider
2008) and harbors $\sim$ 220 OB-type stars (Comerón & Pasquali 2012; Berlanas
et al. 2020) along with tens of thousands of low mass stars (Albacete Colombo
et al. 2007; Drew et al. 2008; Wright & Drake 2009). The OB2 association has
an estimated age of $\sim$ 3 – 5 Myrs (Drew et al. 2008; Wright et al. 2010,
2015) and is affected by variable extinction, AV ranging between $\sim$ 4 - 8
mag (Wright et al., 2015). With a cluster environment impinged by high energy
radiation from massive OB-stars in the association, Cygnus OB2 is an ideal
laboratory to study the role of stellar feedback on the surrounding low-mass
stellar population in the region. The presence of globules and proplyds (see
Figure 20 in Appendix A for HSC r2-band images of the known proplyds from
Wright et al. (2012)) in the surrounding region (Schneider et al. 2012; Wright
et al. 2012; Schneider et al. 2016) and a reduced circumstellar disk fraction
in the vicinity of massive O-type stars (Guarcello et al., 2016) suggest the
effect of ongoing external photoevaporation on disk evolution. Approximately
1843 candidate young stellar objects (YSOs) have been identified based on
their NIR excess properties (Guarcello et al. 2013) within an area $\sim$
1${}^{{}^{\circ}}$ $\times$ 1${}^{{}^{\circ}}$ of Cygnus OB2. The GTC-OSIRIS
optical study by Guarcello et al. (2012) covers the central 40′ $\times$ 40′
region of the Cygnus OB2 with photometry of the sources reaching down to
$\sim$ 25 mag in r’-band, however photometric error exceeds 0.1 mag for $\sim$
40$\%$ of the total sources in the catalog. Similarly, previous studies
regarding the kinematics, structure as well as mass function of Cygnus OB2 are
confined to a stellar mass of $\sim$ $>$ 1 M⊙ (Wright et al. 2010, 2015;
Comerón & Pasquali 2012; Arnold et al. 2020). However, the low mass regime of
the region covered by $<$ 0.5 M⊙ stars, remains unexplored. Cygnus OB2 is
thus, a potential young massive cluster for which deep and wide-field optical
and NIR studies are essential. This paper is a step towards a detailed study
of one of the most massive star forming regions outside the solar
neighbourhood with detections reaching down to the sub-stellar regime ($\leq$
0.07 M⊙).

We present here the deepest (r${}_{2}\sim$ 28 mag) and the widest (1.5∘
diameter) (see Figures 1) optical catalog of one of the most massive Galactic
star forming regions i.e Cygnus OB2 along with the preliminary analysis for a
limited area using the presented HSC data. Thanks to the superb wide-field
imaging capabilities of Subaru Hyper Suprime-Cam (HSC), we have obtained high
quality deep optical photometry which is useful to give an insight into the
low mass star formation, proto-planetary disk evolution and the effect of
feedback from massive stars on the cluster properties like Initial Mass
Function (IMF), star formation efficiency and star to brown dwarf ratio.

This paper is divided into the following sections: The Section 2 interprets
the Subaru Hyper Suprime-Cam observations, data reduction and catalog
generation using HSC pipeline. Section 3 presents the data quality in terms of
photometry, astrometry, completeness of the HSC data along with comparison
relative to already available optical photometry. In Section 4 we present the
data analysis and results obtained, aided with color-magnitude diagrams, age
analysis and disk fraction analysis. We then discuss and interpret the results
obtained with this data so far in Section 5 and encapsulate the entire work
along with our future plans, finally in Section 6.

##  2 Observations and Data Reduction

###  2.1 HSC Observations

Figure 1: RGB image of the 1.5 ∘ diameter region centred at Cygnus OB2 (RA:
20:33:15; Dec: +41:18:54) obtained with r2, i2 and Y-bands of Subaru HSC. The
inset white box covers the 40′ $\times$ 40′ (18.6 pc $\times$ 18.6 pc) region
observed by the past GTC/OSIRIS observations (Guarcello et al. 2013). The
inset green box covers 1′ $\times$ 1′ region ((RA: 20:32:12.7220; Dec:
+41:06:58.778)), further zoomed in the right corner of the image which gives a
vivid view of the abundance and high resolution of the point stellar sources
achieved by our observations of the target region.

Subaru is an 8.2 m class optical-infrared telescope built and operated by the
National Astronomical Observatory of Japan (NAOJ). With an 870 Megapixels
mosaic CCD camera comprising of 116 2k $\times$ 4k CCDs with a pixel scale
$\sim$ 0.17′′, the Hyper Suprime-Cam (HSC) instrument installed at the prime
focus of the telescope provides an excellent image quality over a wide field
of view (FOV; 1.8 $\deg^{2}$) (Miyazaki et al. 2012; Komiyama et al. 2017;
Furusawa et al. 2017; Miyazaki et al. 2018). We observed a region of 1.5∘
diameter centered at Cygnus OB2 (see Figure 1) with Subaru HSC in 4 broad-band
optical filters, namely, r2, i2, z and Y (Kawanomoto et al. 2018) on 17th
September’2017 (PI: J.Jose; Program ID: S17B0108N), using EAO (East Asian
Observatory) time111This EAO time for Cygnus OB2 observations was a
compensatory time given to us for the ToO event GW170817, which happened
during our scheduled night. Several long exposure and short exposure frames
(details given in Table LABEL:tab:_HSC_Observation_Specifications) were taken
to enhance the photometric accuracy of both faint as well as bright stars. The
excellent seeing conditions ($\sim$ 0.5′′ \- 0.7′′) atop Mauna Kea during the
observations (1.07 $\leq$ airmass $\leq$ 1.35) and superb optics of the camera
with a focal length $\sim$ 18320 mm have effectively enabled the otherwise
difficult pairing of a wide field of view with detailed spatial resolution
(see Figure 1). The mean FWHM values achieved in individual HSC filters are
indicated in Table LABEL:tab:_HSC_Observation_Specifications and Figure 2
Left. The achieved FWHM in individual filters is approximately uniform across
the observed FOV (Figure 2 Right).

Figure 2: Left: Histogram distribution for FWHM in each HSC-filter i.e Y, z,
i2 and r2. Right: Spatial distribution map of FWHM in z-band for the observed
region. The spatial map is obtained by binning the RA and Dec parameter space
into 10′ $\times$ 10′ bins across the entire observed region. The colorbar
indicates the mean FWHM of each bin.

Hitherto, HSC has primarily been used for extra-galactic observations (e.g.
Matsuoka et al. 2019; Ishikawa et al. 2020; Jaelani et al. 2020). However,
there is a dire lack of similar observations in Galactic stellar fields with
HSC. This study is a pioneering work to utilize the powerful and highly
sensitive imaging capabilities of Subaru Hyper Suprime-Cam for observations of
young Galactic star forming regions. A summary of the various procedures
followed and the modifications introduced in the default pipeline parameters
to reduce the observed HSC data is presented below.

Table 1:  Details about short and long exposure frames and FWHM in individual filters. Filters | HSC-Y | HSC-z | HSC-i2 | HSC-r2
---|---|---|---|---
Exposure Timeshort | 30s $\times$ 5 frames | 25s $\times$ 3 frames | 25s $\times$ 3 frames | 30s $\times$ 3 frames
Exposure Timelong | 200s $\times$ 3 frames | 300s $\times$ 4 frames | 300s $\times$ 10 frames | 300s $\times$ 16 frames
Mean FWHM | 0.61′′ | 0.68′′ | 0.62′′ | 0.53′′

###  2.2 Data Reduction and Catalog Generation

The observed raw data was downloaded from STARS (Subaru Telescope Archive
System) and reduced with the help of HSC Pipeline version 6.7. The entire
process of the data reduction by HSC pipeline (hscPipe) can be broadly
classified into (1) Single-visit Processing (2) Joint Calibration (3)
Coaddition (4) Coadd Processing/ Multiband Analysis. For details regarding the
following processes, refer to Bosch et al. (2017); Aihara et al. (2017, 2019).

The hscPipe initiates the data reduction with single-visit processing. The
detrending of the raw data includes overscan subtraction, bias correction,
dark current subtraction, flat-fielding, and fringe subtraction. The hscPipe
then performs Instrument Signature Removal (ISR) to mask and interpolate the
defects such as bad pixels, cross-talk, and saturated pixels. A few bright
sources short-listed using a 50$\sigma$ threshold value are used as reference
to model the Point Spread Function (PSF) using PSFEx software. The astrometric
and photometric calibration of these sources is performed with respect to the
Pan-STARRS DR1 PV3 reference catalog using the ‘Pessimistic B‘ matching
algorithm222refer https://dmtn-031.lsst.io/#pessimism-of-the-algorithm for
details. We discard the default ’Optimistic B’ algorithm as it is well-suited
for low density fields like extragalactic realms and has failure modes in
comparatively high density Galactic regions333See https://dmtn-031.lsst.io/,
which results in false matches and incorrect astrometry of the detected
sources. After performing sky subtraction and source measurements444The source
measurement step includes centroiding, shape measurements, aperture
corrections, etc., the previously generated PSF model is used to generate a
deeper catalog of stars using a 5$\sigma$ threshold. The above explained
process including the source extraction using 5$\sigma$ detection threshold,
is performed for each CCD during single visit processing. An internal
calibration is then carried out across different observing shots, termed as
visits. The astrometric and photometric calibrations are carried out by
matching the wcs and flux scale of each visit with the previously generated
matched list of reference bright stars and corresponding corrections are then
applied to each visit.

In the next step, the hscPipe coadds the images from various visits to create
a single deeper image and a PSF model is constructed for the coadded image.
The sky correction applied prior to the coadd process is turned off as it
contaminates our coadded images due to high amount of nebulosity present in
the region. The sky correction applied at this step merely writes a new
background model without modifying the photometry of detected sources. We
coadd the long exposure visits and short exposure visits separately for
individual filters, to obtain precise photometry for some of the bright
sources which get saturated in the long exposure images. Eventually, hscPipe
performs multiband analysis in order to generate the final photometric catalog
for each band. The source extraction is performed again, this time on the
coadded images using 5$\sigma$ threshold value to detect sources and
photometry is subsequently performed on the coadded images in each filter. As
a result of the source extraction, certain above-threshold regions called
footprints are generated each of which, comprises of one or more discrete
sources. These footprints, containing several peaks are merged together across
different filters. The overlapping footprints from different filters are then
combined. Within each of such combined footprints, the peaks close enough to
each other (that is, lying within 0.3′′ of the nearest peak) are merged as one
peak, otherwise are assigned as an individual new peak. This results in
consistent peaks and hence, footprints across individual filters. Each of the
peak corresponds to individual objects. The peaks within individual footprints
are further deblended in individual filters and the total flux is apportioned
into them.

The number of stellar sources detected during image coaddition relies upon the
footprint size as each footprint consists of several blended individual peaks.
The larger the size of the footprint, the more peaks or distinct objects it
can hold. As the hscPipe is designed primarily for sparse regions, the default
footprint size defined by the pipeline i.e 106 pixels is insufficient to
detect all stellar point sources in a comparatively dense Galactic star
forming region like Cygnus OB2. Hence, after performing rigorous checks with
several footprint sizes, we finally increased it to 1010 pixels for i2, z and
Y filters. The footprint size is increased to 1011 pixels for r2 filter
however, to ensure maximum detection inspite of it’s high sensitivity to the
extensive nebulosity present in the region. The modified footprint sizes in
individual filters aid in yielding an exhaustive catalog of point sources to
be detected in the images. Finally, hscPipe performs source measurements and
photometry for the detected sources and thus, both long exposure and short
exposure catalogs are obtained in r2, i2, z and Y bands. However, these
catalogs in individual filters are contaminated with plenty of
spurious555detections with no visible source present detections. Hence, we
have applied certain flags and external constraints to eradicate such spurious
detections, which we explain in the following section.

###  2.3 Point Source Selection

Table 2:  shows various flags applied with their description.

Flagging Condition | Description
---|---
deblend_nchild != 0 | Objects which consist of multiple childa peaks
deblend_skipped | Objects which contain multiple blended peaks
base_PixelFlags_flag_crCenter | Objects overlaps cosmic ray contaminated pixels
base_PixelFlags_flag_suspectCenter | Object overlaps a pixel with unreliable linearity correction
base_PixelFlags_flag_saturatedCenter | Object with saturated pixels
base_PixelFlags_flag_interpolatedCenter | Object with interpolated pixels from surrounding pixels

  * a

Each individual source peak obtained after deblending each footprint

We apply certain flags (see Table 2) and external constraints to remove the
spurious contamination from the obtained long and short exposure catalogs
(Section 2.2) with minimal loss of genuine point sources in individual
filters. For more details on catalog flags, please refer to Bosch et al.
(2017). Additionally, we select sources with photometric error $\leq$ 0.1 mag
in individual bands for both long and short exposure catalogs. We impose an
additional constraint of internal astrometric error $\leq$ 0.1′′ to remove
spurious sources without any loss of good point sources. This error in
astrometry of a source is with respect to its peak PSF position in different
visits (For more details please refer to Section 3.2). We consider only those
sources which have detection in at least two filters. Since the seeing
conditions during our observations varied between 0.5′′– 0.7′′, we have chosen
the upper limit of seeing i.e 0.7′′, as the maximum matching radius and best
match as the match selection criteria to cross match the sources between any
two bands using TOPCAT tool666http://www.star.bris.ac.uk/ mbt/topcat, in order
to avoid loss of any genuine counterparts (Mehta et al. 2018; Murata et al.
2020). The cross-matching radius, even if reduced (e.g 0.5′′) or increased
(e.g 0.8′′ or 1′′) varies the census of genuine sources atmost by a few
hundreds, which is a negligible amount when compared to the total number of
detected sources. Similary, the specified constraints of 0.1 mag in
photometric error and 0.1′′ in the internal astrometric error have been chosen
after checking and discarding several values ranging between 0.07 mag – 0.2
mag (in photometric error) and 0.08′′ – 0.5′′ (in astrometric error) as it
results either in loss of numerous faint point sources or an increment in
spurious detection by 5–10$\%$.

The availability of both short exposure and long exposure photometry for the
sources has enabled us to deal with the saturated sources effectively. We
consider long exposure photometry in all the bands for those sources with
magnitude in Y-band $>$ 18 mag. In a similar fashion, sources with Y $\leq$ 18
mag are incorporated from short-exposure catalog in all the filters. However,
in addition to this, we also include short exposure photometry for sources
with 18 mag $\leq$ Y $\leq$ 22 mag and without any long exposure photometry
available for them. This is specifically done in order to include the sources
which lie close to bright stars and have been missed in the photometry from
long exposure. The particular threshold of Y $\leq$ 22 mag is chosen after
verifying that the sources with only short exposure photometry and Y $>$ 22
mag, are spurious detections and hence, discarded. This merging of short and
long exposure photometry can result in missing sources or repetition of
sources near the merging threshold i.e Y $=$ 18 mag and its corresponding
counterparts in other filters. Hence, to deal with this we take an average of
the long and short exposure magnitudes for the sources with 17.8 mag $\leq$ Y
$\leq$ 18.2 mag and their corresponding counterparts in other filters. An
important point to note here is that the long and short exposure photometry is
merged on the basis of the threshold values 18 mag or 22 mag taken in Y-band
and applied to the corresponding counterparts in other bands. Finally, we
perform an internal matching of the sources in the entire output catalog with
the upper value of astrometric uncertainity, i.e 0.1′′ as the matching radius
to avoid any repetition of sources. Any duplicates (0.5$\%$ of the total
sources) of the already detected sources in the catalog are removed in this
step.

Figure 3:  This flowchart summarizes the external conditions imposed after
applying flags mentioned in Table 2. These conditions ensure the maximum point
source detection and remove spurious sources from both long exposure and short
exposure catalogs separately, obtained after data reduction using hscPipe. The
short and long exposure photometry are then concatenated and merged based on
conditions mentioned above. For details please refer to Section 2.3.

To summarise, the output catalog thus procured, includes only those sources
which have detection in at least any 2 filters, photometric error $\leq$ 0.1
mag in all the filters and internal astrometric uncertianity $\leq$ 0.1′′. To
avoid any saturation effect due to bright stars, we incorporate the short
exposure photometry in all the filters (r2, i2, z and Y) as explained above.
The key steps in this process of point source selection are briefly shown as a
flowchart in Figure 3. We have finally secured 713,529 point sources all of
which have at least a 2-band detection. Approximately, 699,798 ($\sim 98\%$)
sources have Y-band photometry, 685,511 sources ($\sim$ 96$\%$) have z-band
photometry, 622,011 sources ($\sim$ 90$\%$) have $i_{2}$ band photometry and
358,372 sources ($\sim$ 50$\%$) have $r_{2}$ band photometry. Figure 4
presents a sample of our exemplary detection in different bands for a
particular region (RA: 20:34:10.4835 Dec: +40:57:48.783) of 2′ $\times$ 2′.
Almost all the visible sources, although faint, have been successfully
detected in the final HSC catalog. The adopted approach of selecting genuine
point sources as described in this section has yielded the deepest and the
widest comprehensive optical catalog of one of the most massive regions in the
Galaxy outside the solar neighborhood.

Figure 4:  A 2′ $\times$ 2′ area (RA: 20:34:10.4835 Dec: +40:57:48.783) in
different filters is overplotted with sources detected in each individual band
i.e Top Left: r2-band, Top Right: i2-band, Bottom Left: z-band and Bottom
Right: Y-band.

##  3 Data Quality

In the following sections, we discuss the data quality in terms of the
photometry, astrometry, limiting magnitude of detection, completeness of the
reduced HSC data with respect to the existing Pan-STARRS DR1777downloaded from
https://vizier.u-strasbg.fr/viz-bin/VizieR (Chambers et al. 2019) and
GTC/OSIRIS (Guarcello et al. 2012) optical data. We also perform a comparison
of the obtained HSC photometry with respect to Pan-STARRS DR1 photometry with
the help of magnitude offset plots and check the astrometric offset with
respect to Pan-STARRS DR1 and Gaia EDR3 data (Brown et al. 2016; Gaia
Collaboration et al. 2020).

###  3.1 Photometric Quality

Figure 5:  Scatter plots of HSC magnitudes versus error in individual HSC
filters. All the sources have error $\leq$ 0.1 mag. The discontinuity at Y =
18 mag in magnitude-error plot of Y-band (Top Left) is due to the merging of
long and short exposure photometry. Y = 18 mag is taken as the threshold
magnitude for this merging (see Section 2.3 for details on the merging
procedure.). The multiple branches observed in these plots are due to the long
and short exposure photometry merged to obtain the final catalog.  Figure 6:
A comparative magnitude versus error scatter plot for HSC (blue) with the
existing photometry from Pan-STARRS (Green) and GTC/OSIRIS (Guarcello et al.,
2012) (Red) in i2-band for an area of 30′ radius centred on Cygnus OB2. The
two branches observed in the HSC i2-band plot correspond to the long and short
exposure photometry.

The error versus magnitude plots shown in Figure 5 for the individual HSC
filters i.e r2, i2, z and Y-filter, summarize the accuracy of the obtained HSC
photometry. The plot illustrates that the photometric error is $\leq$ 0.05 mag
for sources with magnitudes down to $\sim$ 26.0 mag in i2-band, 27.5 mag in
r2-band, 24.7 mag in z and 24.0 mag in Y-band. Approximately 91$\%$ and 95$\%$
of the total sources have a photometric error $\leq$ 0.05 mag in Y and z-band
respectively. Similarly, 93$\%$ of the sources detected in i2-band and almost
90$\%$ of the detected sources in r2-band have an error $\leq$ 0.05 mag. A
comparative error versus magnitude plot is presented in Figure 6 for an area
of 30′ radius centred on Cygnus OB2 to juxtapose the accuracy of HSC
photometry with previous optical studies of the region such as with Pan-
STARRS, GTC/OSIRIS. Since GTC/OSIRIS observations are available for a limited
FOV (40′ $\times$ 40′), the chosen area (30′ radius centred at Cygnus OB2)
allows a fair comparison of photometric accuracy among the HSC, Pan-STARRS and
GTC/OSIRIS sources. The maximum detection limit within a photometric error
$\leq$ 0.1 mag attainable with Pan-STARRS and GTC/OSIRIS photometry is $\sim$
22.5 mag–24.0 mag (i-band), which is at least 3 mag shallower when compared to
the high accuracy attained by the HSC photometry down to the very faint sub-
stellar regime (i${}_{2}\sim$ 27.0 mag ; $\leq$ 0.07 M⊙) (see Section 3.3 and
Section 4.1 for details).

Figure 7:  Spatial distribution map generated by binning the entire observed
region into 10′ $\times$ 10′ bins in RA and Dec parameter space to signify the
variation of magnitude offset of HSC $i_{2}$-band photometry with respect to
Pan-STARRS DR1 i-band photometry across the area of observations. The colorbar
indicates the mean offset of sources in each bin. Figure 8:  Scatter plots for
determining magnitude offset of HSC photometry with respect to Pan-STARRS
photometry in different individual bands. An offset of 0.03$\pm 0.06$ mag,
0.01$\pm 0.07$ mag, 0.01$\pm 0.03$ mag and 0.01$\pm 0.03$ mag is observed in
Y, z, $i_{2}$, $r_{2}$-band respectively for the range of magnitudes marked by
dashed black lines. The marked magnitude ranges have been selected to
calculate the mean magnitude offset in order to avoid the saturation of HSC
photometry towards the brighter end and unreliable photometry of Pan-STARRS
towards fainter end of sources. The blue sources lie within 3$\sigma$ range
from mean offset whereas grey sources lie beyond 3$\sigma$ range from mean
offset.

In order to assess the photometric quality, we check the offset between HSC
and the counterpart Pan-STARRS DR1 photometry in the individual filters. To
compare the photometry, we transformed the Pan-STARRS DR1 photometry from Pan-
STARRS filter system to HSC system using the equations given in Appendix B.
The sources with good quality Pan-STARRS photometry have been selected by
giving an error cut off $\leq$ 0.05 mag and number of stack detections $>$ 2
(Chambers et al. 2019). We observe a moderate uniformity in the magnitude
offset across the entire region as presented in the spatial distribution map
in Figure 7. Figure 8 shows the scatter plots of magnitude offset i.e HSC
magnitudes–Pan-STARRS magnitudes versus HSC magnitudes, in all HSC filters. A
mean offset of 0.01$\pm$0.07 mag is observed in z-band with respect to the
Pan-STARRS magnitudes. Similarly, other bands i.e r2, i2, Y-band exhibit an
offset of 0.01$\pm$0.03 mag, 0.01$\pm$0.03 mag and 0.03$\pm$0.06 mag
respectively, which agrees well with the offset estimated in other studies
between HSC and Pan-STARRS (Komiyama et al. 2018; Aihara et al. 2019). The
mentioned mean offsets have been calculated for sources within a certain range
of magnitudes (range marked by dotted black lines in Figure 8) in individual
bands, after discarding the sources lying beyond 3$\sigma$ level (represented
by grey colored dots in Figure 8) iteratively for 5 iterations.

###  3.2 Astrometric Quality

Figure 9:  Spatial plots signifying the variation of internal error in Right
Ascension (Left) and Declination (Right) across the entire region. The spatial
maps are obtained by binning the RA and Dec parameter space into 10′ $\times$
10′ bins across the entire observed region. The colorbar indicates the mean
uncertainity in RA (Left) and Dec (Right) of each bin. The observed internal
astrometric error ranges between 0.01′′ \- 0.03′′, with almost uniform
distribution throughout the region.

We present a graphical interpretation of the high precision astrometry of
point sources in the HSC catalog in Figure 9 and 10. Due to our strict
selection criteria (see Section 2.3), all the sources have both $\Delta$ RA
and $\Delta$ Dec $\leq$ 0.1′′. This astrometric uncertainity of each source is
attributed to the uncertainity in the position of its observed peak flux in
different exposures. Hence, the mentioned astrometric error threshold of 0.1′′
is a quality measure of the internal astrometric calibration relative to
different visits. The internal astrometric error, mainly ranging between
0.01′′–0.03′′ appears to be uniform across the observed region (see Figure 9)
with a mean value $\sim$ 0.016′′ for the detected sources. However, the census
of sources decreases rapidly with increasing internal astrometric error
(Figures 10 Top Left and Top Right).

Figure 10:  Histograms of internal error in Right Ascension (Top Left) and in
Declination (Top Right). Histograms of the observed offset in astrometry of
HSC with respect to Pan-STARRS (blue), astrometry of Pan-STARRS with respect
to Gaia EDR3 (black) and astrometry of HSC with respect to Gaia EDR3 (red) in
Right Ascension is shown in the Bottom left panel and in Declination is shown
in the Bottom Right panel (See Section 3.2 for details).

We perform an additional check of the astrometry of the detected HSC sources
with respect to the external data such as Pan-STARRS DR1 and Gaia EDR3
available for the observed area of Cygnus OB2. The histograms in Figure 10
Bottom Left and Bottom Right show the offset between HSC, Pan-STARRS DR1 and
Gaia EDR3 astrometry in the HSC FOV (1.5∘ diameter region centred at Cygnus
OB2). The absence of any visible offset between HSC and Pan-STARRS astrometry
is attributed to the astrometric calibration performed with respect to Pan-
STARRS PV3 DR1 data to develop a PSF model during the single-visit processing
(refer Section 2.2). However, a mean offset of $\sim 1.9\pm
2^{\prime\prime}\times 10^{-5}$ in Right Ascension and $\sim 6.6\pm
8^{\prime\prime}\times 10^{-6}$ in Declination is observed with respect to the
Gaia EDR3 astrometry for both HSC and Pan-STARRS data and is well in
accordance with the astrometric accuracy estimated in Aihara et al. (2019)
with these two data sets. We also present the spatial distribution of the
astrometric offsets of HSC with respect to the GAIA EDR3 and Pan-STARRS DR1
astrometry in Figure 21 and observe an excellent uniformity throughout the
observed region.

###  3.3 Completeness

Figure 11: Top: Histograms representing the detection limit of individual HSC
bands with Black: r2-band; Green: i2-band; Red: z-band and Blue: Y-band. The
limiting magnitudes in individual HSC filters are mentioned in the legend. The
dashed lines and the corresponding magnitudes denote the 90$\%$ completeness
limit attained in individual filters as indicated by the turn-over point
method (see Section 3.3 and Table 3 for details). Bottom: Histogram depicting
the completeness of r2-band (Black) ; i2-band (Green) and z-band (Red) with
respect to the Y-band (Blue) of HSC.  Figure 12:  Histogram plot representing
the completeness of Pan-STARRS r-band (Green) and GTC/OSIRIS r-band (Red) with
respect to the HSC $r_{2}$-band (Blue) for a comparable common area of 30′
radius centred at Cygnus OB2. The dashed lines represent the corresponding
90$\%$ completeness limits which are found to be 21.5 mag for Pan-STARRS, 23.5
mag for GTC/OSIRIS and 26.5 mag for HSC.

The analysis of the final data gives the 5$\sigma$ limiting magnitude i.e the
magnitude of the faintest star detectable with our observations in individual
HSC filters. The histogram shown in Figure 11 (Top) indicates the detection
limit of HSC photometry in different bands. In-spite of the high amount of
nebulosity and moderate extinction prevalent in Cygnus OB2 (Drew et al. 2008;
Wright et al. 2010; Guarcello et al. 2012), the limiting magnitude reaches
down to888magnitude values rounded off to nearest 0.2 mag 28.0 mag in r2-band,
27.0 mag in i2-band, 25.5 mag in z and 24.5 mag in Y-band. At a distance of
1600 pc, age $\sim$ 5 $\pm$ 2 Myrs (see Section 4.3) and an average extinction
AV ranging between 6 – 8 mag (refer Section 4.1), the mentioned detection
limit of 27.0 mag in i2-band corresponds to a stellar mass of 0.02 – 0.03 M⊙
(using isochrones of Baraffe et al. (2015)) i.e less than the Lithium-burning
limit. The final HSC photometry is $\sim$ 90% complete down to 26.5 mag, 25.5
mag, 24.0 mag and 23.5 mag in r2, i2, z and Y-band respectively, as indicated
by the turn-over point in the histogram (denoted by dashed lines in Figure
11). The turnover point in source count approach to evaluate the 90$\%$
completeness limit gives similar results to the artificial star-count method
(Jose et al. 2016, 2017; Damian et al. 2021; Das et al. 2021). Since Y-band
has the highest number of detections, we take it as reference and calculate
the number of counterpart sources in r2, i2 and z-band in each 0.5 mag bin to
assess the completeness of other HSC filters relative to Y-band. The
completeness of the photometry in various filters relative to Y-band attained
by this method is presented in Figure 11 Bottom. We provide a summary of the
useful quality parameters in individual HSC filters, for an age $\sim$ 5 $\pm$
2 Myrs and AV = 6 - 8 mag in the Table 3. The obtained HSC photometry is found
to be deeper by an order of 3 - 5 mag , when compared with the existing Pan-
STARRS and GTC/OSIRIS photometry (limited to $\sim$ 21.5 mag and 23.5 mag,
respectively in r-band), and thus provides a substantial sample of faint low
mass sources in Cygnus OB2.

Table 3:  Details of final HSC catalog in individual filters. (For more
details of the given parameters, please refer to Sections 3.1, 3.2, 3.3 and
4.1)

Filters | HSC-Y | HSC-z | HSC-$i_{2}$ | HSC-$r_{2}$
---|---|---|---|---
Number of sources | 699,798 | 685,511 | 622,011 | 358,372
Fraction of sources $\leq$ 0.05 mag error | 91% | 95% | 93% | 90%
Brightness limita (mag) | 14.0 | 14.2 | 15.3 | 15.6
Limiting magnitudeb,c (mag) | 24.5 | 25.5 | 27.0 | 28.0
Limiting magnitude upto 90% completeness (mag) | 23.5 | 24.0 | 25.5 | 26.5
Limiting mass (in M⊙)d | 0.02-0.03 | 0.03-0.04 | 0.03-0.06 | 0.15-0.30

  * a

Magnitude of the brightest object detected

  * b

Magnitude of the faintest object detected

  * c

Magnitudes rounded off to 0.2 mag

  * d

Mass corresponding to magnitude with 90% completeness for AV: 6 – 8 mag and
age: 5 $\pm$ 2 Myrs.

##  4 Data Analysis and Results

We present here some preliminary analysis based on the HSC data to illustrate
the significance of Cygnus OB2 as an ideal target for low-mass star formation
studies with the help of a few color-magnitude diagrams (CMDs) presented in
this section. We also perform a statistical field decontamination using a
peripheral control field to obtain a statistical estimate of member stars and
use that to obtain the approximate median age and average disk fraction of the
central 18′ region of Cygnus OB2.

###  4.1 Color-Magnitude Diagrams

Figure 13:  Hess plot of z-Y vs z Color-Magnitude Diagram (CMD) with HSC
sources detected in the entire area of 1.5∘ diameter centred at Cygnus OB2.
The Hess plot is obtained by binning the color and magnitude parameter space
into bins of size 0.01 mag and 0.03 mag respectively. The black arrow marks
the direction of reddening vector of $A_{V}$ = 6 mag.

Figure 14:  Left: i2-Y vs i2 CMD within the central 18′ radius of Cygnus OB2.
Isochrones of age 0.5, 3 and 10 Myr and evolutionary tracks for various masses
(Baraffe et al., 2015), which are corrected for an Av=6 mag and distance =
1600 pc are shown using solid curves. The previously known YSOs of the complex
(Guarcello et al. 2013) are overplotted as red dots. Right: r2-i2 vs r2 CMD
for the same 18′ radius region. The black arrow marks the direction of
reddening vector for AV = 6 mag.

Color-magnitude diagrams (CMDs) are integral to segregate the cluster members
from foreground and background contaminants (e.g Jose et al. 2017; Esplin &
Luhman 2020; Damian et al. 2021) and estimate the age, temperature and
spectral type of member stars in a star-forming cluster. We present the Hess
plot of the z-Y vs z Color-Magnitude Diagram (CMD) in Figure 13, plotted with
our optical catalog obtained for the entire 1.5∘ diameter area of Cygnus OB2.
A similar i2-Y vs i2 CMD in Figure 14 (Left) and r2-i2 vs r2 CMD in Figure 14
(Right) have been plotted for the sources lying in the central region of 18′
radius. This area has been particularly selected due to the high concentration
($\sim$ 50$\%$ of the total) of YSOs (identified previously by Guarcello et
al. (2013)) present in this region. Cygnus OB2 exhibits a distinct pre-main
sequence branch which is a prominent feature observed in CMDs of young
clusters (Jose et al. 2013; Jose et al. 2017; Panwar et al. 2018; Damiani et
al. 2019; Biazzo et al. 2019; Ksoll et al. 2020; Damian et al. 2021). In order
to analyse the approximate age of the cluster, we over-plot isochrones of age
0.5, 3 and 10 Myr and evolutionary tracks for various masses from Baraffe et
al. (2015) on the i2-Y vs i2 CMD. As per the past studies, an extinction of AV
= 4 – 5 mag has been observed towards the north-west of Cygnus OB2 along with
AV = 5.5 – 7.0 mag observed towards centre and south of the association
(Wright et al. 2015). Hence, we choose a mean value of extinction as AV = 6.0
mag in order to redden our isochrones. The isochrones have been reddened using
the extinction laws of Wang & Chen (2019) for Pan-STARRS filter system, taking
AV = 6.0 mag and 1600 parsecs as distance of Cygnus OB2 from the Sun (Lim et
al. 2019). Consequently, the transformation equations (given in Appendix B)
have been used to convert the obtained magnitudes of Baraffe isochrones (in
Pan-STARRS filter system) to HSC filter system.

The majority ($\sim 88\%$) of the previously detected YSOs (Guarcello et al.
2013), overplotted as red circles, are located within the 10 Myr isochrone
overplotted on the i2-Y vs i2 CMD in Figure 14 Left and thus, occupy the
characteristic pre-main sequence branch. The source population occupying the
young pre-main sequence branch consists of both cluster members as well as
background contaminants. We obtain a statistical estimate of the membership in
the central 18′ using the field decontamination process further in Section
4.2. The color of these sources (i.e i${}_{2}-Y\geq$ 2) reinforces the claim
that they constitute the pre-main sequence population present in the central
18′ radius region of Cygnus OB2.

Figure 15:  The comparative Hess diagrams of r2-Y vs r2 CMDs to emphasize
cluster membership for sources located within (Left) the inner 18′ radius of
Cygnus OB2 (RA: 308.2785; Dec: 41.7477) and (Right) a rectangular region of
the same area towards the outskirts of Cygnus OB2 (RA: 308.2655; Dec:
41.7497). The black arrow marks the direction of reddening vector for AV = 6
mag.

We emphasize the cluster membership of the sources in the pre-main sequence
branch with the aid of a comparative study between an 18′ radius circular
region towards the centre and an equal rectangular area towards the periphery
of Cygnus OB2 (RA: 308.2665; Dec: 41.7497), as shown in Figure 15. The Hess
plot of r2-Y vs r2 CMD (Figure 15 (Left)) is plotted for the sources in the
central 18′ radius region, which is prolific in pre-main sequence cluster
members and a similar Hess plot is plotted in Figure 15 (Right) for the
sources lying towards the outskirts of Cygnus OB2. The absence of a
distinguished pre-main sequence branch in the CMD of the sources towards the
periphery as compared to the central region, suggests that it is mainly
populated by the non-cluster members in the foreground or background. Hence,
in accord with the literature (Knödlseder 2000; Wright et al. 2010; Guarcello
et al. 2013; Wright et al. 2015; Guarcello et al. 2016), our optical data
analysis advocates that Cygnus OB2 is an active young star formation site rich
in pre-main sequence, low mass as well as sub-stellar population with a
suggested age $\leq$ 10 Myrs.

###  4.2 Field Star Decontamination

The background and foreground contaminants, also termed as field star
contaminants, generally lie in the line of sight of the observed target region
and can overlap with the young pre-main sequence population in the CMDs as
mentioned in Section 4.1. Hence, the identification of cluster members is
particularly crucial for an accurate estimation of various cluster parameters
like age, distance, disk fraction which can otherwise be biased by the
presence of field stars. Although, kinematic parameters like proper motion,
radial velocity and other methods such as spectroscopy and SED analysis
provide the most precise membership identification (Panwar et al. 2017; Dutta
et al. 2018; Herczeg et al. 2019; Bhardwaj et al. 2019; Jose et al. 2020; Das
et al. 2021), such data is available only for a handful of the sources with
Gaia eDR3 counterparts complete down to $\sim$ 20 mag, which is inadequate for
the low mass pre-main sequence members in Cyngus OB2. Hence, a statistical
field star subtraction using an appropriate control field is useful to obtain
a statistical estimate of the probable cluster members down to faint low mass
limits (r2 $\sim$ 28 mag) (eg. Jose et al. 2017; Kaur et al. 2020; Damian et
al. 2021).

We perform the statistical field decontamination for a cluster field of 18′
radius centred at Cygnus OB2, which encloses $\sim$ 50$\%$ of the known YSOs
in the region. In the absence of a control field external to the observed
region, we choose a rectangular control field located towards the outskirts of
the Cygnus OB2 (centred at RA: 308.2655; Dec: 41.7497) of an area equal to
that of the cluster field. This control field is the same as used above for
Figure 15 (Right). We observe a higher source density in the control field as
compared to the cluster field, which may either be due to differences in the
stellar density or could be attributed to the different extinction observed in
the two directions. Although, the CO maps and mid-IR images from MSX from
Schneider et al. (2006) and Reipurth & Schneider (2008) suggest an approximate
uniform extinction across the Cygnus OB2, the extinction mapping performed by
us using deep near-IR UKIDSS data (to be discussed in the forth-coming work.)
reveals moderate differential reddening across the region with the control
field being less extincted than the cluster field by 1 - 1.5 mag. To address
the stellar density fluctuation, we chose a box in the color magnitude diagram
where we do not expect to see any pre-main sequence stars in the cluster field
(such as the one shown in Figure 16 (Left)). We scale down the counts in the
color magnitude diagram of the control field by a constant factor $f$, such
that the number of detected objects in this box is consistent between the
cluster and the control field within Poisson fluctuations. We infer the
posterior distribution of the parameter $f$ using Monte Carlo Markov sampling
using the package emcee (Foreman-Mackey et al., 2013). We performed multiple
iterations over several smaller box areas (located over the entire r2
magnitude range and r2 \- i2 color $\leq$ 2) in the CMD of the control field,
and obtain a median likelihood value of 0.73 that is used to scale the bin
counts of the control field in the entire color magnitude diagram. This median
likelihood value scales down the overdensity of sources in the control field,
which can otherwise result in the over subtraction of the sources while
performing field decontamination of the cluster field.

We then perform the field subtraction using r2-i2 versus r2 CMD and divide the
color and magnitude parameter space into 0.1 and 0.2 mag bins. For each bin,
we first scale down the count of sources in the control field and then,
subtract the control field count from the cluster field count. The resultant
count thus obtained, is a floating point number which represents the average
number of sources to be selected randomly as the field subtracted sources in
each bin. Hence, in order to obtain an integer count, we randomly select an
integer value within the Poisson fluctuations of the average count obtained as
a result of subtraction. The derived integer count is considered as the number
of sources to be selected as field subtracted sources in the cluster field per
bin. We emphasize here that this field decontamination is purely statistical
and the resultant field subtracted sources may not be the confirmed members of
the cluster. The Figure 16 shows the Hess plots of r2-i2 versus r2 CMD for the
cluster and control field along with that for the field subtracted sources. We
observe that the field subtracted sources distinctly occupy the pre-main
sequence branch in the CMD with a few scattered sources, which can be
attributed to the statistical uncertainty in the field decontamination
process. We repeated the field subtraction with another control field located
in the outskirts of Cygnus OB2, and find that the statistics remain comparable
within 10$\%$ uncertainty. Hence, we consider the field subtracted sources for
further analysis to estimate the median age and disk fraction of the chosen
cluster field area as described in the following sections.

Figure 16:  Hess plots of r2-i2 versus r2 CMD for (Left) the cluster field,
(Middle) the control field and (Right) the field subtracted sources. For the
hess plot of control field (Middle), the control field data count per bin is
scaled by the median log likelihood value, i.e 0.73. A sample box area chosen
to calculate this log likelihood value is shown as the white box in the Hess
plot of the cluster field (Left). Several such box areas are considered to
calculate the median log likelihood value. The white arrow marks the direction
of reddening vector for AV = 6 mag.

###  4.3 Age distribution of Cygnus OB2

The information about the age of the sources, combined with an estimate of the
disk bearing sources (YSOs) in a cluster is helpful in constraining the star
formation history of the region. However, the age estimation can be biased if
the sample is contaminated with field stars. Hence, we use the statistically
subtracted sources obtained after the field decontamination process, described
above in Section 4.2, to estimate the age of the chosen cluster field area.
However, to eliminate any leftover contaminants due to statistical error in
the field decontamination process which may bias our age estimation, we
consider only those sources with 20.5 mag $\leq$ r2 $\leq$ 26.5 mag, in
accordance with the completeness limit of r2-band. The upper limit of 20.5 mag
corresponds to 1.4 M⊙ source (the upper mass limit in Baraffe isochrones) at
an age $\sim$ 5 Myrs. Since, approximately 90$\%$ of the total field
subtracted sources have mass less than the considered upper limit, it will not
modify our results significantly. To further refine our selection, we define
an empirical pre-main sequence (PMS) locus and select only those sources which
are within 1 $\sigma$ limits of this empirical locus. We refer to these
sources as the selected sources. The PMS locus is obtained by dividing the r2
magnitude range into 0.5 mag bins. For each bin then, we take the mean of the
r2 magnitude and median of the r2 \- i2 color of the sources inside the bin.
This mean magnitude and the median r2 \- i2 color in each magnitude bin thus,
defines the empirical PMS locus (see Damian et al. (2021) for details). The
Figure 17 (Left) shows the Hess plot of r2 \- i2 versus r2 CMD overplotted
with the finally selected sources (red sources) and the empirical PMS locus
(green solid curve) along with the 20 Myr Baraffe isochrone (black dashed
curve). We also present the color distribution in each magnitude bin which
defines the PMS locus in Figure 17 (Right).

Figure 17: Left: Hess plot of r2 \- i2 vs r2 CMD of the field subtracted
members in the central cluster field of 18′ region of Cygnus OB2. This is
overplotted with the selected sources (red dots) i.e within 1 $\sigma$ limits
of the empirical pre-main sequence (PMS) locus (green solid curve) and 20.5
mag $\leq$ r2 $\leq$ 26.5 mag. These selected sources are considered for the
age estimation. Also, the 20 Myr Baraffe isochrone corrected for an Av=6 mag
and distance = 1600 pc is shown as the black dashed curve. The white arrow
marks the direction of reddening vector for AV = 6 mag. Right: Histograms for
r2 \- i2 color distribution in each r2 magnitude bin of 0.5 mag (the legend in
each histogram shows the respective magnitude bin for which the histogram of
color distribution is plotted).

We determine the age of these selected sources by fitting the Baraffe
isochrones of various ages (available at an interval of log(t) = 0.01). The
age is then assigned to each source based on its distance to the different
isochrones. Since for any particular age, the available isochrones are a set
of few discrete points (color and magnitude values), the age estimation based
on the distance to these few points can be biased. Hence, we fit these
discrete points using linear regression model with fifth order polynomial
distribution to interpolate the isochrones. This interpolation generates a
larger set of discrete points for any particular age and the accuracy of these
predicted values (color and magnitude values) is $\geq$ 99$\%$ for all the
isochrones of different ages. The interpolation of the isochrones thus, helps
in improving the overall accuracy of this age estimation method. We then
proceed to find, for each source, the two nearest isochrones with ages, say t1
and t2 and distances D1 and D2 respectively, from the source. The age is then
calculated as the weighted average of the two ages t1 and t2. The inverse of
the distances D1 and D2 are used as weights in order to calculate the weighted
average (t) of the ages of the two isochrones as given in equation below:

$t=\frac{t_{2}D_{1}+t_{1}D_{2}}{D_{1}+D_{2}}$

The weighted average t is thus, assigned as the age of the source. The process
is repeated for all the selected sources. The median age of the field
decontaminated sources within 18′ is thus, obtained to be 6.5 $\pm$ 5 Myrs. We
further converge this distribution to within 2 $\sigma$ limits from the mean
age of the entire distribution after performing 8 iterations. The median age
for the 2 $\sigma$ converged sample turns out to be 5 $\pm$ 2 Myrs. The Figure
18 shows histogram plot for the age distribution of the sources for the un-
converged sources. Although for the above age calculation, we have reddened
the Baraffe isochrones for an AV = 6 mag, we derive similar results (median
age within 4 – 6 Myrs) for an extinction variation between AV = 4.5 - 7.5 mag
(Wright et al. 2010, 2015). This is expected because the reddening vector
stays parallel to the isochrones for optical wavelengths. Hence, a variation
in the extinction simply shifts the sources along the isochrones without thus,
introducing any significant modification in the derived ages. Also, the
derived age of the region remains within 4 - 6 Myrs for a distance variation
ranging between $\sim$ 1500 - 1700 pcs (distance to Cygnus OB2 = 1600 $\pm$
100 pcs (Lim et al. 2019)). The other possible factors like binarity, optical
variability, although add to the broadening of the color in CMDs of young star
forming regions, however, may not affect the true age spread as well as the
cluster parameters like IMF significantly (Jose et al. 2017; Damian et al.
2021). The above analysis thus, confirms the median age of the central 18′
region with that of $\leq$ 10 Myrs as estimated by the previous studies (Drew
et al. 2008; Wright et al. 2015; Berlanas et al. 2018).

Figure 18:  Histogram to represent the distribution of age among the selected
sources (represented as red dots in Figure 17).

###  4.4 Disk Fraction

Circumstellar disk evolution sets the timescale for planet formation and
hence, measuring the disk fraction, that is, the fraction of stars surrounded
by circumstellar disks for a certain cluster age, is an important parameter to
give an insight into the star and planet formation in a young cluster (Haisch
et al. 2001; Williams & Cieza 2011; Helled et al. 2014; Ribas et al. 2014).
Although in a young cluster, disk fraction depends upon various factors such
as the metallicity, stellar density, environmental factors like external and
internal photoevaporation (Yasui et al. 2016; Yasui 2021; Thies et al. 2010;
Guarcello et al. 2016; Reiter & Parker 2019), a general trend of disk fraction
declining with age is observed. It ranges between 60$\%$ \- 80$\%$ for
clusters like NGC 1333 (Ribas et al. 2014), NGC 2023, RCW36 (Richert et al.
2018) with an age $<$ 1 Myr (e.g ) to 5$\%$ \- 10$\%$ for clusters like
LowCent-Crux (Hernández et al. 2007), 25 Orionis (Pecaut & Mamajek 2016) with
age $\sim$ 10 Myrs. In this section we calculate the disk fraction for the
central 18′ region of Cygnus OB2.

In order to calculate the disk fraction, we consider the previously identified
YSOs by Guarcello et al. (2013) within the cluster field area of 18′ radius.
The previously identified YSOs are complete between 0.7 M⊙ – 2 M⊙ (Guarcello
et al. 2013), which corresponds to 18.5 mag $\leq$ r2 $\leq$ 22.5 mag at a
distance $\sim$ 1600 pc and AV $\sim$ 6 mag. Hence, for estimating the disk
fraction, we consider only those YSOs with optical counterparts within the
mentioned r2-band magnitude completeness range. The sample data used to
calculate the disk fraction thus consists of only those field subtracted
member sources which lie within 1 $\sigma$ limit of the pre-main sequence
locus (Section 4.3) and 18.5 mag $\leq$ r2 $\leq$ 22.5 mag. Figure 19 shows
the Hess plot of r2 \- i2 versus r2 CMD for the field subtracted sources. This
Hess diagram is overplotted with the YSOs (Red circles) along with the sample
selected to calculate the disk fraction (i.e the total number of candidate
members) (White crosses). We find that the ratio of the number of YSOs to that
of the total number of sources, also termed as the disk fraction, turns out to
be $\sim$ 9$\%$. This is however, a lower limit on the disk fraction as the
previously identified YSOs are limited by the Spitzer IRAC Channel 2
sensitivity. This reason accounts for the lower disk fraction ($\sim$ 9$\%$)
obtained by our analysis as compared to the 18$\%$ \- 40$\%$ estimated by
Guarcello et al. (2016). Cygnus OB2 has a lower disk fraction, in comparison
to other young clusters like NGC 2264, CepOB3-East and West, which could be a
result of external photoevaporation of circumstellar disks as a result of
massive stars in vicinity.

Figure 19:  Hess plot of r2 \- i2 versus r2 CMD for the field subtracted
sources. This Hess diagram is overplotted with the YSOs (Red circles) along
with the sample selected to calculate the disk fraction (i.e the total number
of sources) (White crosses).

##  5 Discussion

Rigorous studies of the low mass star formation in young massive Galactic
clusters using multi-wavelength data sets are crucial to understand and solve
some of the important yet unanswered questions such as the nature of IMF for
stellar masses $<$ 0.5 M⊙, the role of feedback driven cluster environment on
the evolution of circumstellar disks, proportion of sub-stellar objects etc.
The young massive association of Cygnus OB2 is a promising target for such
purpose with its substantial massive as well as pre-main sequence population
(Albacete Colombo et al. 2007; Wright & Drake 2009). This paper presents the
deepest and the widest optical photometry of Cygnus OB2 available as of yet.
We detect a total of 713,529 sources with reliable data quality for objects
detected down to the faint low mass end (Section 3). The preliminary data
analysis performed with the deep HSC catalog suggests the presence of two
sequences in various CMDs (Section 4.1), the rightward sequence occupied by
the PMS cluster members along with background contaminants. The previously
identified YSOs overplotted on i2-Y vs i2 CMD in Figure 14 (Left) occupy the
pre-main sequence branch in the CMD, mostly towards the right side of the
isochrones of age $<$ 10 Myrs, as expected for a young association like Cygnus
OB2 (e.g. Jose et al. 2017; Damian et al. 2021). We observe that the pre-main
sequence segregation in various CMDs (Figure 15) for the central region is
consistent with most of the star formation being significantly clustered
around the centre of this dynamically unevolved region (Wright et al. 2016;
Arnold et al. 2020). The isochrone fitting done in Figure 14 Left suggests
that $\sim$ $45\%$ of the total 713,529 sources detected in the region, lie
within age less than 10 Myrs and a significant fraction of these sources
($\sim 12\%$) lie below the evolutionary track of mass less than 0.08 M⊙.
However, we caution the readers that this is an upper limit of candidate pre-
main sequence population in the region as the estimated fraction is likely to
be contaminated by the reddened background sources. More qualitative
identification and classification of the YSOs in the entire HSC FoV of Cygnus
OB2, both disk and diskless will be done in a future follow-up study using
multi-wavelength photometry.

We perform the field decontamination of the central 18′ region to get a
statistical estimate of membership of the sources, using a control field
located towards the periphery, which may be mostly contaminated with
foreground and background stars. Approximately, 70$\%$ of the field
decontaminated sources distinctly occupy the PMS branch with age less than 10
Myrs (Figure 16). Since these statistically decontaminated members are used
further to calculate age and disk fraction in the cluster field, we refine the
membership with the help of an empirical PMS locus (see Section 4.3 for
details). The median age of the central 18′ region is $\sim$ 5 $\pm$ 2 Myrs.
The age obtained by our analysis agrees quite well with that estimated by
several other studies of the region. For example, Drew et al. (2008) analyse
200 A-type stars across the Cygnus OB2, using IPHAS photometry and find the
age to be $\sim$ 5 Myrs. Similarly, Wright et al. (2015) used a list of 169
massive OB stars to derive the age of the region as $\sim$ 4 - 5 Myrs using
rotating stellar evolutionary models from Ekström et al. (2012) while Wright
et al. (2010) use X-ray sources to obtain 3.5 - 5.2 Myrs as the average age of
the region. Recent studies by Berlanas et al. (2018); Comerón et al. (2020)
perform spectroscopy of $\sim$ 60 OB-type stars (observed with INT, ISIS,
OSIRIS instruments) and find that the age of the region ranges between 1 - 6
Myrs irrespective of the stellar model used for age estimation. We corroborate
this result by verifying our age estimation with Parsec isochrone models
(Bressan et al. 2012) in addition to the Baraffe models, for a mass range of
0.3 M⊙ \- 1.4 M⊙ and derive the median age $\sim$ 4.5 $\pm$ 2 Myrs. Cygnus OB2
is a part of the larger Cygnus X giant molecular cloud which formed
approximately 40 - 50 Myrs ago. The star formation towards Cygnus OB2 region
however, has mainly taken place in the last 10 - 20 Myrs with the last star
formation activity peaking around 3 - 5 Myrs ago (Reipurth & Schneider 2008;
Comerón & Pasquali 2012; Comerón et al. 2016; Berlanas et al. 2018; Comerón et
al. 2020). This may suggest the substantial pre-main sequence population with
the median age $\sim$ 5 Myrs in the region as obtained with our data analysis.

We obtain a disk fraction of $\sim$ 9$\%$ for this cluster field using the
already known YSOs in the region. There is a wide variety of disk fractions
measured in young clusters. An average disk fraction of 30$\%$ \- 50$\%$ is
observed in several young clusters (within age $\sim$ 3 – 6 Myrs) such as NGC
2264 (Sung et al. 2009), CepOB3b-East and West (Allen et al. 2012), AFGL
333/W3 (Jose et al. 2016), IC348/U (Richert et al. 2018) and NGC 2282 (Dutta
et al. 2015). However, recent studies of some nearby young clusters (Hernández
et al. 2010; Guarcello et al. 2016; Richert et al. 2018) show considerably
smaller disk fractions. For example, the recent study by Richert et al. (2018)
with 69 MYStIX and SFiNCs young clusters reveals that the disk fraction could
drop to values $\leq$ 15$\%$ for a cluster age $\geq$ 4 Myrs, which is
consistent with our results. The particularly low disk fraction obtained for
the central region of Cygnus OB2 and such other clusters which lie at the
lower end of the spectrum of disk fractions, may be attributed to either the
evolutionary effect or the feedback effect from the massive OB-type stars in
vicinity (Guarcello et al. 2016). In this work we cannot conclusively pinpoint
the exact reason, however, evolutionary effects or external photo-evaporation
could be some of the possible reasons for the observed low disk fractions.

The significant census of low mass and sub-stellar sources detected with deep
HSC photometry (r2 $\sim$ 28 mag) will serve as an excellent statistical
sample for further studies to test the effect of feedback driven environmental
conditions of Cygnus OB2 on low mass population across the region. To
conclude, we find from our preliminary analysis that in accordance with the
literature, Cygnus OB2 is a young active star-forming region (age $<$ 10 Myr)
with a substantial pre-main sequence population. The deep multi-wavelength
studies are essential to understand low mass star formation in the region and
will be the area of focus in our future works.

##  6 Summary and Future Works

This paper presents the deepest and the widest optical catalog of the young
feedback-driven OB association of Cygnus OB2.

1) A 1.5∘ diameter area of Cygnus OB2 was observed with Subaru Hyper Suprime-
Cam (HSC) in 4 filters namely r2, i2, z and Y. The observations were taken in
excellent seeing conditions ranging between 0.5′′–0.7′′. The observed raw data
was reduced using HSC pipeline version 6.7.

2) The final HSC catalog contains only those point sources which have at least
2-band detection and additionally, have internal astrometric error $\leq$
0.1′′ along with photometric error $\leq$ 0.1 mag in individual bands. A total
of 713,529 sources are detected with 699,798 sources having a must detection
in Y-band, 685,511 sources in z-band, 622,011 in i2 and 358,372 sources in
r2-band.

3) We detect sources down to 28.0 mag, 27.0 mag, 25.5 mag and 24.5 mag in r2,
i2, z and Y-band respectively. Coupled with a distance of 1600 pc for an age
ranging between 5 $\pm$ 2 Myrs and extinction AV $\sim$ 6 – 8 mag, we achieve
$\sim$ 90% completeness down to a stellar mass $\sim$ 0.03 – 0.06 M⊙ and
$\sim$ 0.03 – 0.04 M⊙ i.e $<$ Lithium burning limit, in i2 and z-band
respectively. The corresponding mass completeness limit is down to $\sim$
0.02-0.03 M⊙ and $\sim$ 0.15-0.30 M⊙ in Y and r2-bands, respectively.

4) The median age of the central region of Cygnus OB2 ranges between 4 – 6
Myrs for an AV ranging between 4.5 – 7.5 mag and distance between 1500 – 1700
pcs. We obtain a disk fraction $\sim$ 9$\%$ in the central cluster, which is
however a lower limit given the restricted completeness of the already known
YSOs.

As the next step, we plan to adopt a multi-wavelength approach by combining
the presented HSC optical data with other existing data from UKIDSS, 2MASS and
Spitzer surveys to carry out a detailed analysis of the YSOs present in the
region. In addition to this we would use our deep optical photometry presented
in this paper, coupled with other data sets to evaluate cluster parameters
like IMF for very low mass stars ($<$ 0.1 M⊙) along with identification and
characterization of sub-stellar objects like brown dwarfs and understand the
role of feedback-driven environment of Cygnus OB2 on such parameters.

##  7 Data Availability

A sample table of the HSC catalog is presented in Table 4. The complete
catalog is provided as online material.

Table 4:  Sample table of HSC catalog data. The complete table is available as online material.  Source | RA | Dec | r2 | r${}_{2_{err}}$ | i2 | i${}_{2_{err}}$ | z | zerr | Y | Yerr
---|---|---|---|---|---|---|---|---|---|---
| (deg) | (deg) | (mag) | (mag) | (mag) | (mag) | (mag) | (mag) | (mag) | (mag)
1 | 308.69298 | 41.86609 | 25.728 | 0.019 | 23.568 | 0.006 | 22.090 | 0.008 | 21.434 | 0.008
2 | 308.83647 | 41.86581 | 24.790 | 0.010 | 22.666 | 0.003 | 21.175 | 0.004 | 20.515 | 0.004
3 | 308.70283 | 41.86674 | 26.425 | 0.044 | 24.641 | 0.018 | 22.859 | 0.015 | 22.154 | 0.016
4 | 308.84554 | 41.86651 | 25.894 | 0.028 | 22.267 | 0.002 | 20.231 | 0.002 | 19.183 | 0.001
5 | 308.79625 | 41.86680 | 24.398 | 0.007 | 22.314 | 0.002 | 21.279 | 0.005 | 20.026 | 0.002

## Acknowledgements

The authors thank the referee for the useful constructive comments which has
refined the overall structure and quality 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
gateful 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). The authors thank the
entire HSC staff and HSC helpdesk for their help. We would like to thank
S.Mineo, H.Furusawa, Y.Yamada and M.Kubo in HSC helpdesk team for useful
discussions regarding the data reduction. We thank NAOJ for providing access
to hanaco account which was used to perform some initial stages of data
reduction. We gratefully acknowledge the use of high performance computing
facilities at IUCAA, Pune for the HSC data reduction. We thank I.Baraffe for
providing us with isochrone models for an interval of log (Age) = 0.01,
through personal communication. We use Pan-STARRS and GAIA ED3 data for data
quality checks. 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). PP and
JJ acknowledge the DST-SERB, Gov. of India for the start up research grant
(No: SRG/2019/000664).

## References

  * Aihara et al. (2017) Aihara H., et al., 2017, Publications of the Astronomical Society of Japan, 70
  * Aihara et al. (2019) Aihara H., et al., 2019, PASJ, 71, 114
  * Albacete Colombo et al. (2007) Albacete Colombo J. F., Flaccomio E., Micela G., Sciortino S., Damiani F., 2007, A&A, 464, 211
  * Allen et al. (2012) Allen T. S., et al., 2012, ApJ, 750, 125
  * Armitage (2015) Armitage P. J., 2015, arXiv e-prints, p. arXiv:1509.06382
  * Arnold et al. (2020) Arnold B., Goodwin S. P., Wright N. J., 2020, MNRAS, 495, 3474
  * Baraffe et al. (2015) Baraffe I., Homeier D., Allard F., Chabrier G., 2015, A&A, 577, A42
  * Bastian et al. (2010) Bastian N., Covey K. R., Meyer M. R., 2010, ARA&A, 48, 339
  * Basu (2017) Basu S., 2017, Perspectives on Low-Mass Star Formation (arXiv:1703.01542)
  * Berlanas et al. (2018) Berlanas S. R., Herrero A., Comerón F., Pasquali A., Bertelli Motta C., Sota A., 2018, A&A, 612, A50
  * Berlanas et al. (2020) Berlanas S. R., et al., 2020, A&A, 642, A168
  * Bhardwaj et al. (2019) Bhardwaj A., Panwar N., Herczeg G. J., Chen W. P., Singh H. P., 2019, A&A, 627, A135
  * Biazzo et al. (2019) Biazzo K., Beccari G., De Marchi G., Panagia N., 2019, ApJ, 875, 51
  * Bobylev & Bajkova (2020) Bobylev V. V., Bajkova A. T., 2020, Astrophysical Bulletin, 75, 267
  * Bosch et al. (2017) Bosch J., et al., 2017, Publications of the Astronomical Society of Japan, 70
  * Bressan et al. (2012) Bressan A., Marigo P., Girardi L., Salasnich B., Dal Cero C., Rubele S., Nanni A., 2012, MNRAS, 427, 127
  * Brown et al. (2016) Brown A. G. A., et al., 2016, Astronomy & Astrophysics, 595, A2
  * Cappellari et al. (2012) Cappellari M., et al., 2012, Nature, 484, 485
  * Carpenter (2000) Carpenter J. M., 2000, AJ, 120, 3139
  * Chambers et al. (2019) Chambers K. C., et al., 2019, The Pan-STARRS1 Surveys (arXiv:1612.05560)
  * Comerón & Pasquali (2012) Comerón F., Pasquali A., 2012, A&A, 543, A101
  * Comerón et al. (2016) Comerón F., Djupvik A., Schneider N., Pasquali A., 2016, Astronomy and Astrophysics, 586
  * Comerón et al. (2020) Comerón F., Djupvik A. A., Schneider N., Pasquali A., 2020, A&A, 644, A62
  * Damian et al. (2021) Damian B., Jose J., Samal M. R., Moraux E., Das S. R., Patra S., 2021, MNRAS, 504, 2557
  * Damiani et al. (2019) Damiani F., Prisinzano L., Pillitteri I., Micela G., Sciortino S., 2019, A&A, 623, A112
  * Das et al. (2021) Das S. R., Jose J., Samal M. R., Zhang S., Panwar N., 2021, MNRAS, 500, 3123
  * Drew et al. (2008) Drew J. E., Greimel R., Irwin M. J., Sale S. E., 2008, MNRAS, 386, 1761
  * Dunham et al. (2015) Dunham M. M., et al., 2015, The Astrophysical Journal Supplement Series, 220, 11
  * Dutta et al. (2015) Dutta S., Mondal S., Jose J., Das R. K., Samal M. R., Ghosh S., 2015, MNRAS, 454, 3597
  * Dutta et al. (2018) Dutta S., Mondal S., Joshi S., Jose J., Das R., Ghosh S., 2018, MNRAS, 476, 2813
  * Dzib et al. (2018) Dzib S. A., Loinard L., Ortiz-León G. N., Rodríguez L. F., Galli P. A. B., 2018, The Astrophysical Journal, 867, 151
  * Ekström et al. (2012) Ekström S., et al., 2012, A&A, 537, A146
  * Ercolano & Pascucci (2017) Ercolano B., Pascucci I., 2017, Royal Society Open Science, 4, 170114
  * Esplin & Luhman (2020) Esplin T. L., Luhman K. L., 2020, The Astronomical Journal, 159, 282
  * Foreman-Mackey et al. (2013) Foreman-Mackey D., Hogg D. W., Lang D., Goodman J., 2013, PASP, 125, 306
  * Furusawa et al. (2017) Furusawa H., et al., 2017, Publications of the Astronomical Society of Japan, 70
  * Gaia Collaboration et al. (2020) Gaia Collaboration Brown A. G. A., Vallenari A., Prusti T., de Bruijne J. H. J., Babusiaux C., Biermann M., 2020, arXiv e-prints, p. arXiv:2012.01533
  * Geha et al. (2013) Geha M., et al., 2013, ApJ, 771, 29
  * Gennaro et al. (2018) Gennaro M., et al., 2018, ApJ, 855, 20
  * Gorti et al. (2015) Gorti U., Hollenbach D., Dullemond C. P., 2015, ApJ, 804, 29
  * Guarcello et al. (2012) Guarcello M. G., Wright N. J., Drake J. J., García-Alvarez D., Drew J. E., Aldcroft T., Kashyap V. L., 2012, ApJS, 202, 19
  * Guarcello et al. (2013) Guarcello M. G., et al., 2013, The Astrophysical Journal, 773, 135
  * Guarcello et al. (2016) Guarcello M. G., et al., 2016, arXiv e-prints, p. arXiv:1605.01773
  * Haisch et al. (2001) Haisch Karl E. J., Lada E. A., Lada C. J., 2001, ApJ, 553, L153
  * Hartmann (2008) Hartmann L., 2008, Physica Scripta, T130, 014012
  * Helled et al. (2014) Helled R., et al., 2014, in Beuther H., Klessen R. S., Dullemond C. P., Henning T., eds, Protostars and Planets VI. p. 643 (arXiv:1311.1142), doi:10.2458/azu_uapress_9780816531240-ch028
  * Herczeg et al. (2019) Herczeg G. J., et al., 2019, ApJ, 878, 111
  * Hernández et al. (2007) Hernández J., et al., 2007, ApJ, 671, 1784
  * Hernández et al. (2010) Hernández J., Morales-Calderon M., Calvet N., Hartmann L., Muzerolle J., Gutermuth R., Luhman K. L., Stauffer J., 2010, ApJ, 722, 1226
  * Hosek et al. (2019) Hosek Matthew W. J., Lu J. R., Anderson J., Najarro F., Ghez A. M., Morris M. R., Clarkson W. I., Albers S. M., 2019, ApJ, 870, 44
  * Ishikawa et al. (2020) Ishikawa S., et al., 2020, The Astrophysical Journal, 904, 128
  * Jaelani et al. (2020) Jaelani A. T., et al., 2020, Monthly Notices of the Royal Astronomical Society, 495, 1291
  * Jose et al. (2013) Jose J., et al., 2013, MNRAS, 432, 3445
  * Jose et al. (2016) Jose J., Kim J. S., Herczeg G. J., Samal M. R., Bieging J. H., Meyer M. R., Sherry W. H., 2016, The Astrophysical Journal, 822, 49
  * 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
  * Kaur et al. (2020) Kaur H., Sharma S., Dewangan L. K., Ojha D. K., Durgapal A., Panwar N., 2020, ApJ, 896, 29
  * Kawanomoto et al. (2018) Kawanomoto S., et al., 2018, PASJ, 70, 66
  * Kim et al. (2016) Kim J. S., Clarke C. J., Fang M., Facchini S., 2016, ApJ, 826, L15
  * Knödlseder (2000) Knödlseder J., 2000, A&A, 360, 539
  * Komiyama et al. (2017) Komiyama Y., et al., 2017, Publications of the Astronomical Society of Japan, 70
  * Komiyama et al. (2018) Komiyama Y., et al., 2018, The Astrophysical Journal, 853, 29
  * Ksoll et al. (2020) Ksoll V. F., et al., 2020, arXiv e-prints, p. arXiv:2012.00524
  * Kubiak et al. (2021) Kubiak K., Mužić K., Sousa I., Almendros-Abad V., Köhler R., Scholz A., 2021, arXiv e-prints, p. arXiv:2102.05589
  * Lada & Lada (2003) Lada C. J., Lada E. A., 2003, Annual Review of Astronomy and Astrophysics, 41, 57
  * Lim et al. (2019) Lim B., Nazé Y., Gosset E., Rauw G., 2019, Monthly Notices of the Royal Astronomical Society, 490, 440
  * 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. R., Do T., Ghez A. M., Morris M. R., Yelda S., Matthews K., 2013, The Astrophysical Journal, 764, 155
  * Luhman (2012) Luhman K. L., 2012, Annual Review of Astronomy and Astrophysics, 50, 65
  * Manara et al. (2017) Manara C., Prusti T., Voirin J., Zari E., 2017, Proceedings of the International Astronomical Union, 12
  * Matsuoka et al. (2019) Matsuoka Y., et al., 2019, ApJ, 883, 183
  * Megeath et al. (2019) Megeath T., et al., 2019, BAAS, 51, 333
  * Mehta et al. (2018) Mehta V., et al., 2018, ApJS, 235, 36
  * Miyazaki et al. (2012) Miyazaki S., et al., 2012, in McLean I. S., Ramsay S. K., Takami H., eds, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 8446, Ground-based and Airborne Instrumentation for Astronomy IV. p. 84460Z, doi:10.1117/12.926844
  * Miyazaki et al. (2018) Miyazaki S., et al., 2018, PASJ, 70, S1
  * Moraux (2016) Moraux E., 2016, in EAS Publications Series. pp 73–114 (arXiv:1607.00027), doi:10.1051/eas/1680004
  * Murata et al. (2020) Murata R., Sunayama T., Oguri M., More S., Nishizawa A. J., Nishimichi T., Osato K., 2020, PASJ, 72, 64
  * O’dell et al. (1993) O’dell C. R., Wen Z., Hu X., 1993, ApJ, 410, 696
  * 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
  * Panwar et al. (2017) Panwar N., et al., 2017, MNRAS, 468, 2684
  * Panwar et al. (2018) Panwar N., Pandey A. K., Samal M. R., Battinelli P., Ogura K., Ojha D. K., Chen W. P., Singh H. P., 2018, The Astronomical Journal, 155, 44
  * Parker et al. (2021) Parker R. J., Nicholson R. B., Alcock H. L., 2021, MNRAS, 502, 2665
  * Pecaut & Mamajek (2016) Pecaut M. J., Mamajek E. E., 2016, MNRAS, 461, 794
  * Pfalzner et al. (2012) Pfalzner S., Kaczmarek T., Olczak C., 2012, A&A, 545, A122
  * Portegies Zwart et al. (2010) Portegies Zwart S. F., McMillan S. L., Gieles M., 2010, Annual Review of Astronomy and Astrophysics, 48, 431
  * Reipurth & Schneider (2008) Reipurth B., Schneider N., 2008, Star Formation and Young Clusters in Cygnus. p. 36
  * Reiter & Parker (2019) Reiter M., Parker R. J., 2019, MNRAS, 486, 4354
  * Ribas et al. (2014) Ribas Á., Merín B., Bouy H., Maud L. T., 2014, A&A, 561, A54
  * Richert et al. (2018) Richert A. J. W., Getman K. V., Feigelson E. D., Kuhn M. A., Broos P. S., Povich M. S., Bate M. R., Garmire G. P., 2018, MNRAS, 477, 5191
  * Samal et al. (2015) Samal M. R., et al., 2015, A&A, 581, A5
  * Schneider et al. (2006) Schneider N., Bontemps S., Simon R., Jakob H., Motte F., Miller M., Kramer C., Stutzki J., 2006, A&A, 458, 855
  * Schneider et al. (2012) Schneider N., et al., 2012, A&A, 542, L18
  * Schneider et al. (2016) Schneider N., et al., 2016, A&A, 591, A40
  * Sicilia-Aguilar, Aurora et al. (2013) Sicilia-Aguilar, Aurora Kim, Jinyoung Serena Sobolev, Andrej Getman, Konstantin Henning, Thomas Fang, Min 2013, A&A, 559, A3
  * Sung et al. (2009) Sung H., Stauffer J. R., Bessell M. S., 2009, AJ, 138, 1116
  * Thies et al. (2010) Thies I., Kroupa P., Goodwin S. P., Stamatellos D., Whitworth A. P., 2010, The Astrophysical Journal, 717, 577
  * Wang & Chen (2019) Wang S., Chen X., 2019, The Astrophysical Journal, 877, 116
  * Williams & Cieza (2011) Williams J. P., Cieza L. A., 2011, ARA&A, 49, 67
  * Winter et al. (2018) Winter A. J., Clarke C. J., Rosotti G., Ih J., Facchini S., Haworth T. J., 2018, MNRAS, 478, 2700
  * Winter et al. (2019) Winter A. J., Clarke C. J., Rosotti G. P., 2019, MNRAS, 485, 1489
  * Wright & Drake (2009) Wright N. J., Drake J. J., 2009, ApJS, 184, 84
  * Wright et al. (2010) Wright N. J., Drake J. J., Drew J. E., Vink J. S., 2010, ApJ, 713, 871
  * Wright et al. (2012) Wright N. J., Drake J. J., Drew J. E., Guarcello M. G., Gutermuth R. A., Hora J. L., Kraemer K. E., 2012, ApJ, 746, L21
  * Wright et al. (2015) Wright N. J., Drew J. E., Mohr-Smith M., 2015, Monthly Notices of the Royal Astronomical Society, 449, 741
  * Wright et al. (2016) Wright N. J., Bouy H., Drew J. E., Sarro L. M., Bertin E., Cuillandre J.-C., Barrado D., 2016, MNRAS, 460, 2593
  * Yasui (2021) Yasui C., 2021, arXiv e-prints, p. arXiv:2104.11764
  * Yasui et al. (2016) Yasui C., Kobayashi N., Saito M., Izumi N., 2016, AJ, 151, 115
  * van Dokkum & Conroy (2010) van Dokkum P. G., Conroy C., 2010, Nature, 468, 940

## Appendix A

We present in Figure 20, interesting images from HSC-$r_{2}$-band for a few
proplyds/globules/globulettes identified by Wright et al. 2012, with centre of
the regions mentioned in the sub-caption below.

Figure 20:  Images of proplyds/globules/globulettes in Cygnus OB2 in
$r_{2}$-band with their central co-ordinates Upper Left RA: 20:34:46.28; Dec:
+40:52:36.9 Upper Right RA: 20:34:14.4438; Dec: +41:07:39.961 Bottom Left RA:
20:33:12; Dec: +40:41:48.657 Bottom Middle RA: 20:34:47; Dec: +41:14:45 Bottom
Right RA: 20:34:53.6; Dec: +40:48:14.

##  Appendix B Transformation Equations

The transformation equations999During the data reduction the coefficients used
by the pipeline are as mentioned in the transformation equations used to
convert magnitudes from Pan-STARRS system to Subaru HSC system in individual
bands in order to plot the magnitude offsets are given below:

$\begin{split}Y_{HSC}&=Y_{Pan-STARRS}-0.001952+(0.19957(Y-z)_{Pan-STARRS})\\\
&+(0.216821((Y-z)^{2})_{Pan-STARRS})\end{split}$ (1)
$\begin{split}z_{HSC}&=z_{Pan-STARRS}-0.005585-(0.220704(z-Y)_{Pan-STARRS})\\\
&-(0.298211((z-Y))^{2}_{Pan-STARRS})\end{split}$ (2)
$\begin{split}i_{2_{HSC}}&=i_{2_{Pan-
STARRS}}+0.001653-(0.206313(i_{2}-z)_{Pan-STARRS})\\\
&-(0.016085(i_{2}-z)^{2}_{Pan-STARRS})\end{split}$ (3)
$\begin{split}r_{2_{HSC}}&=r_{2_{Pan-
STARRS}}+0.000118-(0.00279(r_{2}-i_{2})_{Pan-STARRS})\\\
&-(0.014363(r_{2}-i_{2})^{2}_{Pan-STARRS})\\\ \end{split}$ (4)

The reddening laws (Wang & Chen 2019) adopted by us to correct the Baraffe
isochrones for extinction in the Pan-STARRS are mentioned below:

$\frac{A_{r}}{A_{V}}=0.843\pm 0.006$

$\frac{A_{i}}{A_{V}}=0.628\pm 0.004$

$\frac{A_{z}}{A_{V}}=0.487\pm 0.003$

$\frac{A_{y}}{A_{V}}=0.395\pm 0.003$

These equations were used to convert the absolute Pan-STARRS magnitudes to
apparent magnitudes using distance = 1600 parseccs and AV = 6 mag. The
transformation equations mentioned above are then used to convert to HSC
photometric system to redden the isochrones appropriately.

## Appendix C

We present here the spatial distribution of astrometric offset of HSC data
with respect to Pan-STARRS DR1 and Gaia EDR3 data.

Figure 21:  Spatial plots signifying the variation of astrometric offset in
Right Ascension (Upper Left) and Declination (Bottom Left) between HSC and
Pan-STARRS data as well as HSC and Gaia EDR3 data (Upper Right and Bottom
Right) across the entire region. The spatial maps are obtained by binning the
RA and Dec parameter space into 10′ $\times$ 10′ bins across the entire
observed region. The colorbar indicates the mean uncertainity in RA (Left) and
Dec (Right) of each bin.