# UOCS-IX. AstroSat/UVIT study of the open cluster NGC 2818: Blue Stragglers,
Yellow Stragglers, Planetary Nebula, and their membership

Sharmila Rani Indian Institute of Astrophysics, Bangalore, 560034, India
Pondicherry University, R.V. Nagar, Kalapet, 605014, Puducherry, India
Gajendra Pandey Indian Institute of Astrophysics, Bangalore, 560034, India
Annapurni Subramaniam Indian Institute of Astrophysics, Bangalore, 560034,
India  N. Kameswara Rao Indian Institute of Astrophysics, Bangalore, 560034,
India

###### Abstract

We present the first far-UV (FUV) imaging results of the intermediate-age
Galactic open cluster NGC 2818 that has a Planetary nebula (PN) within the
field using images taken from the Ultra-violet Imaging Telescope (UVIT) aboard
AstroSat. We identify cluster members by combining UVIT-detected sources with
Gaia EDR3 data. We detect four bright and hot blue straggler stars (BSSs) and
two yellow straggler stars (YSSs) based on their location in the optical and
FUV-optical color-magnitude diagrams. Based on the parameters estimated using
Spectral Energy Distribution (SED), we infer that BSSs are either collisional
products or might have undetectable white dwarf (WD) companions. Our
photometric analysis of YSSs confirms their binarity, consistent with the
spectroscopic results. We find YSSs to be formed through a mass-transfer
scenario and the hot components are likely to be A-type subdwarfs. A
comparison of the radial velocity (RV), Gaia EDR3 proper-motion of the PN with
the cluster, and reddening towards the PN and the cluster does not rule out
the membership of the PN. Comparing the central star’s position with
theoretical pAGB models suggest that it has already entered the WD cooling
phase, and its mass is deduced to be $\sim 0.66M_{\odot}$. The corresponding
progenitor mass turns out to be $\sim 2.1M_{\odot}$, comparable to the turn-
off mass of the cluster, implying that the progenitor could have formed in the
cluster. We suggest that the NGC 2818 might be one of the few known clusters
to host a PN, providing a unique opportunity to test stellar evolution models.

(Galaxy:) open clusters: individual (NGC 2818) — stars: yellow stragglers —
(stars:) blue stragglers — ultraviolet: stars — (stars:) Hertzsprung–Russell
and C–M diagrams

††software: GaiaTools (Vasiliev, 2019), Topcat (Taylor, 2011), Matplotlib
(Hunter, 2007), NumPy (van der Walt et al., 2011), Scipy (Oliphant, 2007;
Millman & Aivazis, 2011), Astropy (Astropy Collaboration et al., 2013, 2018)
and Pandas (McKinney, 2010)

##  1 Introduction

Open clusters (OCs) are ideal laboratories to probe the structure and history
of the Galactic disk. They are also test-beds to study the formation and
evolution of single and binary stellar populations. Dynamical interactions of
stellar populations in star clusters lead to binaries and the formation of
exotic stellar populations such as blue straggler stars (BSSs), yellow
straggler stars (YSSs), and cataclysmic variables. These systems, as well as
the end products of stellar evolution, such as hot white dwarfs (WDs), emit
the bulk of their energy in the ultraviolet (UV) regime. UV observations of
OCs are crucial to detect and understand the properties of the hot stellar
populations, as highlighted in Landsman et al. (1997) and Knigge et al.
(2008).

One of the intriguing products of stellar interactions in the OCs are BSSs
whose origin and evolution are still debated (Boffin et al., 2015). As these
stars appear brighter and bluer than the stars located in the MS turn-off
region of the cluster color-magnitude diagram (CMD), they are expected to be
more massive than the turn-off stars. To explain the mass gain and
rejuvenation of these objects, the main formation scenarios proposed are,
direct collisions or spiraling in of binary stars resulting in mergers (Hills
& Day, 1976), or mass-transfer activity in close-binary systems (McCrea,
1964). The dynamical evolution of hierarchical triple systems leading to the
merger of an inner binary via the Kozai mechanism (Iben & Tutukov, 1999;
Perets & Fabrycky, 2009) is another possible mechanism. Observational studies
of BSSs suggest that a combination of all the formation channels are
prevalent, and has a dependence on their environment, as they are found in a
variety of stellar environments such as OCs (Ahumada & Lapasset, 2007; de
Marchi et al., 2006), globular clusters (GCs) (Ferraro et al., 2012), the
Galactic field (Santucci et al., 2015), and dwarf galaxies (Santana et al.,
2012). Thus, studying BSSs can provide information about the dynamical history
of the cluster, the role of the dynamics on binary evolution, the frequency of
binary systems, and the contribution of binaries to cluster evolution. Member
stars that are redder than the BSSs and brighter than the sub-giants found in
the CMDs of OCs and GCs are considered as evolved BSSs, and are known as
yellow straggler stars (YSSs) ( See Sindhu et al., 2018 and references
therein).

There are only a few OCs in our Galaxy known to harbor Planetary nebulae
(PNe). PNe are classically considered to represent the late stages in the
stellar evolution of all the low as well as intermediate-mass stars with a
mass range of 0.8$-$8 $M_{\odot}$ (Weidemann, 2000). As the evolutionary
lifetime of PNe are short (around $10^{3}-10^{5}$ years, depending on the mass
of the progenitor) when compared to other evolutionary phases, especially when
the number of evolved stars present in OCs are small, PNe as members of OCs
are rare and are not expected in young OCs. Objects in this short-lived phase
are critically important to our understanding of the physical processes and
steps that transform stars into their remnants. They allow us to test the
theory of stellar evolution, including the physics of nucleosynthesis and the
relation between a star’s initial mass and its white dwarf (WD) remnant
(Kwitter et al., 2014). Moreover, the chemical composition of the PNe can
provide information about the dredge-up of chemical elements, which is
expected to depend on the star’s initial mass and composition. Finding a
planetary nebula (PN) as a member of an OC gives us an excellent opportunity
to better characterize and constrain its crucial parameters, such as distance,
reddening, and age.

NGC 2818, has the unique distinction of being one of the two galactic OCs
probably associated with a PN, and interestingly, the name NGC 2818 is
assigned to both an OC and a PN. Most importantly, the membership of the PN to
the OC is still debated. In this study, we analyze both the cluster and the
PN, NGC 2818.

Here we present the results of the UV imaging of NGC 2818 (both PN and OC) in
four far-UV (FUV) filters using the ultraviolet imaging telescope (UVIT) on
AstroSat. Our main aims are: (1) to identify and characterize the blue and
yellow straggler stars in the cluster to shed light on their formation and
evolution and (2) to characterize the central star of the PN (CSPN) to
investigate its association with the cluster. The age of this cluster is
estimated to be $\sim$800 Myr, and the reddening of the cluster is E(B$-$V) =
0.2 mag (Sun et al., 2021). This cluster is located at a distance of $3250\pm
300$ pc and the metallicity is found to be solar (Sun et al., 2021).

NGC 2818 is one of the OCs that shows an extended main-sequence turn-off
(eMSTO) phenomenon (Bastian et al., 2018), where the cluster MS is extended in
the CMD more than what is expected from a simple stellar population with
conventional evolutionary history. It has been demonstrated that stellar
rotation is the most probable cause of this phenomenon (Bastian & de Mink,
2009; Brandt & Huang, 2015; Niederhofer et al., 2015; Cabrera-Ziri et al.,
2016; Gossage et al., 2019). A spectroscopic study by Bastian et al. (2018)
showed that, in NGC 2818, stellar rotation is indeed linked to the stars’
position on the MSTO of the CMD made using the Gaia magnitudes (G) and color
(Gbp$-$Grp), such that rapidly rotating stars preferentially lie on the red
side of the eMSTO. However, the color range (Gbp$-$Grp) in optical CMD is
relatively small, whereas a larger color range is seen in UV colors, and it is
expected that the rotational effects are more prominently displayed in UV
colors mainly because of their sensitivity to surface (effective) temperature
changes. This study also explores the correlation between the colors derived
from UVIT FUV filters and stellar rotation.

The layout of this paper is as follows. In section 2, we describe the
observations, data reduction, and analysis methods. In Section 3, we present
proper-motion-based membership information using Gaia EDR3 data for cluster
stars and PN. Section 4 presents the selection of BSSs and YSSs from the
observed UV and Optical CMDs, including the stellar rotation effects on CMDs.
In Sections 5 and 6, we describe the properties of BSSs, and YSSs derived from
the UVIT photometry along with GALEX, Gaia and ground-based photometry and
their evolutionary status. A detailed discussion of all results is provided in
Section 7. Finally, in Section 8, we summarize our main results and
conclusions.

##  2 Observational Data and Analysis

###  2.1 UVIT Data

In order to probe the nature of the exotic stellar populations in NGC 2818, we
use data acquired with the UVIT instrument on board the Indian multiwavelength
astronomy satellite AstroSat. UVIT produces images of the sky in far-UV (FUV),
near-UV (NUV), and visible, simultaneously, over a circular field-of-view of
28$\arcmin$ diameter with a spatial resolution of $\sim 1\farcs 5$ in both FUV
and NUV channels. More details about the telescope, its initial and new
calibration, and its results are described in detail by Tandon et al. (2017,
2020). The derived magnitudes of the stellar sources observed with the UVIT
filters are in the AB magnitude system.

The observations of NGC 2818 used in this work were made in two epochs, first
on 21st December 2018 (Prop: A05$\\_$196 $-$P.I: N. K. Rao), and the second on
11th June 2020 (Prop: A09$\\_$047 $-$P.I: N. K. Rao). In the first epoch, the
observations were carried out in three FUV filters (F154W, F169M, and F172M),
and in the second, observations were performed with deep exposures in four FUV
filters (F148W, F154W, F169M, and F172M). The observations are carried out in
several orbits in order to complete the allotted exposure times in given
filters. We utilize a customized software package, CCDLAB (Postma & Leahy,
2017), to correct for the geometric distortion, flat field, spacecraft drift
and create images for each orbit. Then, the orbit-wise images were co-aligned
and combined to generate science-ready images in order to get a better signal-
to-noise ratio. Further analysis was done using these final science-ready
images to obtain the magnitudes of the sources detected with UVIT. The details
of the UVIT observations of NGC 2818 used in this analysis are tabulated in
Table 1. In Figure 1, we show the UVIT image of the cluster taken in the FUV
F148W band where the orange color depicts FUV detections. This image exhibits
an extended structure displaying the beautiful PN NGC 2818, where the central
star can be seen in the FUV.

Figure 1: UVIT color image of OC NGC 2818 in FUV F148W channel. Here orange
color depicts the FUV detections. The extended structure in this image
represents the PN NGC 2818. North is up, and east is left in the image.

Figure 2: UVIT/FUV images of PN NGC 2818 in three filters: F154W, F169M, and
F172M.

[1pt]  Filter $\lambda_{mean}$ $\Delta\lambda$ ZP texp (sec) Aλ (Å) (Å) (AB
mag) (1st epoch) (2nd epoch) (mag) F148W 1481 500 18.09 - 1736 1.58 F154W 1541
380 17.77 1491 2877 1.55 F169M 1608 290 17.41 1715 1999 1.54 F172M 1717 125
16.27 1903 2878 1.51

Table 1: List of the FUV observations of NGC 2818 obtained with UVIT in two
epochs used in this work. The last column lists the extinction value computed
in each FUV filter using Fitzpatrick (1999) law of extinction.

###  2.2 Photometry

To extract the magnitudes of detected stars in all FUV images, we have carried
out the point spread function (PSF) photometry using the IRAF/NOAO package
DAOPHOT (Stetson, 1987). The steps taken to obtain the magnitude of the
sources are as follows: First, the stars are located in the image using the
DAOFIND task in IRAF. Further, we used the PHOT task to perform the aperture
photometry. To construct the model PSF using the PSF task, bright and isolated
stars are selected in the image using the PSTSELECT task. The average PSF of
the stars in all FUV images is $\sim 1\farcs 2$. The ALLSTAR task is used to
fit the model PSF to all the detected stars in the image to obtain the PSF-
fitted magnitudes. The PSF magnitudes were converted to aperture photometry
scale using the PSF correction further followed by aperture correction,
estimated using the curve of growth analysis by choosing isolated bright stars
in the field. Finally, the saturation correction, in order to account for more
than one photon per frame, was applied to the obtained magnitudes in UVIT
filters. All steps to perform the saturation correction are described in
detail in Tandon et al. (2017). The extracted instrumental magnitudes are
calibrated into the AB magnitude system using the zero points (ZP) reported in
the recently published calibration paper (Tandon et al., 2020). Figure 3 shows
the PSF-fit error (median) as a function of magnitude in four FUV filters for
profound observations. We have detected stars up to $\sim$ 22 mag with PSF-fit
errors less than 0.3 mag in all FUV filters and considered them for further
analysis in the paper.
To apply the extinction and reddening correction to the derived UVIT
magnitudes of all detected stars, we adopted the reddening, E(B$-$V) = 0.2 mag
mentioned in the Sun et al. (2021). The ratio of total-to-selective
extinction, $R_{V}$ = 3.1 for the Milky Way, was taken from Whitford (1958) to
calculate the extinction value in the visual band ($A_{V}$). We used the
Fitzpatrick extinction law (Fitzpatrick, 1999) to compute extinction
coefficients $A_{\lambda}$ for all UVIT filters, as listed in Table 1.

###  2.3 Other Catalogs

This cluster was previously observed in UV, optical, and Infrared (IR) all-sky
surveys with GALEX (Bianchi et al., 2017), SDSS (Alam et al., 2015), APASS
(Henden et al., 2015), 2MASS (Cutri et al., 2003), and WISE (Cutri et al.,
2021), respectively. In this work, we combined the UVIT data with the multi-
wavelength photometric catalog spanning a wavelength range from UV-IR. We used
the virtual observatory tool in VOSA to cross-match the UVIT-detected sources
with the above-mentioned photometric catalogs (Bayo et al., 2008).

Figure 3: PSF-fit errors (median) as a function of magnitude for our UVIT
observations of NGC 2818 in all FUV bandpasses.

Figure 4: In three panels from left to right, PM members of the cluster are
shown with cyan dots, and the remaining Gaia EDR3 sample marked with black
dots represents field stars. Left Panel: position in the sky; Middle Panel:
Vector Point Diagram (VPD); Right Panel: Gaia Optical CMD.

##  3 Membership Determination

We employed the Gaia early data release 3 (EDR3) catalog that provides data
with unprecedented precision to identify the cluster members. In particular,
it provides the complete 5-parameter astrometric solution (positions, proper
motions, and parallaxes) and magnitudes in its three photometric bands (G,
GBP, and GRP) with a limiting magnitude of about G$\sim$21 mag. To assign the
proper motion (PM) membership probability (Pμ) of all stars observed in the
cluster, we first downloaded all detections located within a 30$\arcmin$
radius from the cluster’s center. To include all possible members of the
cluster, we opted to use a radius bigger than that provided by Kharchenko et
al. (2013) catalog. Then, we applied the data quality criteria to select the
sources with a good astrometric solution. Stars are selected as follows: (i)
we removed those with parallaxes that deviate by more than 3$\sigma$ from the
expected parallax calculated using the previously known distance to the
cluster, where $\sigma$ is the error in parallax given in Gaia EDR3 catalog,
(ii) we also removed the sources with renormalized unit weight error (RUWE)
exceeding 1.2 as larger values of this parameter might lead to an unreliable
astrometric solution (Lindegren et al., 2018; Riello et al., 2021).

We made use of a probabilistic Gaussian mixture model (GMM) method to select
cluster members and infer the intrinsic parameters of the distributions of
both member and non-member stars. In this method, the distribution of sources
in the vector-point diagram ($\mu_{\alpha},\mu_{\delta}$) is modeled as a
mixture of two Gaussian distributions, one for the cluster members and another
one for the field sources. The details of this method are well described in
Vasiliev (2019). The Gaussian probability distribution corresponding to the
sum of two distributions is

$f(\mu|\overline{\mu_{i}},{\sum_{i}})=\sum_{i=1}^{2}w_{i}\frac{exp\big{[}-1/2(\mu-\overline{\mu_{i}})^{T}\sum_{i}^{-1}(\mu-\overline{\mu_{i}})\big{]}}{2\pi\sqrt{det\sum_{i}}}$
(1)

$w_{i}\geq 0,\indent\sum_{i=1}^{2}w_{i}=1$ (2)

where $\mu$ is individual PM vector; $\overline{\mu_{i}}$ are field and
cluster mean PMs; $\scriptstyle\sum$ is the symmetric covariance matrix; and
$w_{i}$ are weights for the two Gaussian distributions. Full details of this
method for the n-dimensional case are described in (Vasiliev, 2019).

The initial guess for cluster PM $\mu_{\alpha}$ and $\mu_{\delta}$ values and
internal velocity dispersion are taken from (Cantat-Gaudin et al., 2020). We
utilized GaiaTools111https://github.com/GalacticDynamics-Oxford/GaiaTools to
maximize the total log-likelihood of GMM and measure the mean PM and standard
deviation of both the Gaussian distributions. The membership probabilities
(MPs) of all the selected stars are calculated using the same technique
simultaneously. The equations used to maximize the log-likelihood of GMM and
estimate the MP of the $i^{th}$ star belonging to the $k^{th}$ component are
given in appendix A in Vasiliev (2019).

The PM mean and standard deviations of the cluster distribution are computed
to be $\mu_{\alpha}$ = -4.417 mas/yr and $\mu_{\delta}$ = 4.540 mas/yr, with
$\sigma_{c}$ = 0.045 mas/yr. In Figure 4, we show the position of stars in the
sky, in the PM space known as vector point diagram (VPD), and in an optical
CMD created using Gaia filters. Cyan dots in all the plots depict the member
stars belonging to the cluster, and black dots represent the field stars. 718
stars are identified as most likely cluster members with Pμ>50$\%$ and
considered for subsequent analysis. This method works well for a
distinguishable distribution of PM for the field and cluster stars in the VPD.
But, in this case, the PM of cluster stars are located well within the PM
distribution of the field stars, suggesting a non-trivial identification of
cluster members from field stars. Therefore, it is possible that stars with a
lower membership probability than the above-mentioned limit might also be
members of the cluster.

###  3.1 Is PN a member of the cluster?

The membership of the PN with OC has been debated in several studies in the
past. Tifft et al. (1972) found that PN NGC 2818 is a member of the OC of the
same name. Dufour (1984) presented the results of photometric as well as
spectroscopic observations of the nebula to analyze its physical properties
and chemical composition. He suggested that the nebula is probably associated
with the star cluster. Pedreros (1989) analyzed this cluster using CCD UBV
photometric data and assumed a physical association of the nebula with the
cluster. Surendiranath et al. (1990) also suggested the association of the PN
with the cluster from their CCD photometry of the cluster. However, Mermilliod
et al. (2001) derived accurate heliocentric radial velocities for 12 cluster
red giants to obtain a mean heliocentric radial velocity of Vhel = +20.7 $\pm$
0.3 kms-1, significantly different from the PN velocity of $-$1 $\pm$ 3 kms-1
(Meatheringham et al., 1988), suggesting that they are unrelated. Recently,
(Vázquez, 2012) reanalyzed the complex kinematics and morphology of the nebula
using high-resolution Hubble Space Telescope (HST) archive imaging and high-
dispersion spectroscopic data and determined a systemic heliocentric velocity
of PN to be +26$\pm$2 kms-1 in closer agreement with the OC, suggesting its
membership. Moreover, based on its RV, H$\alpha$ surface brightness, and
radius, Frew et al. (2016) concluded that the PN might be a cluster member.

The Gaia EDR3 trigonometric parallax for the central star of the nebula (CSPN)
is 0.0319$\pm$0.21 mas, but it can be noted that the uncertainty in it is more
than its value. So, it can not be used to obtain the distance to the nebula.
The best estimate of the statistical distance is given by (Frew et al., 2016)
as 3000$\pm$800 pc not too far from cluster distance of 3250$\pm$300 pc
estimated by Sun et al. (2021). (Cantat-Gaudin et al., 2020; Cantat-Gaudin &
Anders, 2020) obtained the members of the several OCs, including NGC 2818,
using Gaia DR2 PM data, and suggested that it is a non-member of the cluster.

In our membership analysis, we have obtained the membership of the CSPN using
the Gaia EDR3 PM data. The PM in RA and DEC of the CSPN as listed in Gaia EDR3
catalog is $\mu_{\alpha}$ = $-3.712\pm 0.185$ mas/yr and $\mu_{\delta}$ =
$4.94\pm 0.18$ mas/yr. Its Pμ is estimated to be $\sim$11$\%$, indicating non-
membership. Nevertheless, it can be noted from the location of the CSPN shown
with the red star symbol in the VPD that it is lying close to the PM
distribution of the cluster members (Cyan dots), implying that it is quite
likely a member of the cluster. Statistically, it is lying within 3$\sigma$ of
the mean PM of the cluster. We expect that the future Gaia data release (Gaia
DR4) might give more precise and accurate PM measurements that can re-confirm
its association with the cluster. Further, assuming both cluster and nebula at
the same distance, we computed their true velocity using their already
available RV and PM information. We found that the true velocity of the
cluster and nebula turn out to be approximately the same (VC = $99.7kms^{-1}$
& VPN = $98.7kms^{-1}$), implying that the values of the space velocity are
similar.

####  3.1.1 Reddening towards the PN

Several estimates of extinction/reddening towards the cluster have been made
since the initial investigation by Tifft et al. (1972) of E(B$-$V) of 0.22
mag, reconfirmed by Surendiranath et al. (1990) and recently refined by Sun et
al. (2021), to 0.20 mag. However, there are a few independent estimates of
extinction towards the PN NGC 2818. Dufour (1984) estimated it from the Balmer
lines $H\alpha/H\beta$ ratio as 0.24$\pm$0.02 mag. Gathier & Pottasch (1988)
list a value of 0.20 mag, and Frew et al. (2016) estimated a value of
0.17$\pm$0.08 mag. We presently estimate E(B$-$V) value using free-free
continuum flux and the nebular $H\beta$ flux. The flux density, $S_{\nu}$ at 5
GHz of the entire nebula, is measured by Zhang (1995) as 33 mJy. The total
$H\beta$ flux is estimated by Gathier & Pottasch (1988) as $logF(H\beta)$ as
-11.40 ($ergcm^{-2}s^{-1}$). Following Pottasch (1984), the expected ratio of
$S_{\nu}$ to F($H\beta$) is given as

$\frac{S(_{\nu})}{F(H\beta)}=2.51\times 10^{7}\times
T_{e}^{0.53}\times(\nu)^{-0.1}\times YJy/ergcm^{-2}s^{-1}$

where $T_{e}$ is the electron temperature; $\nu$ is frequency in GHz; Y = (1 +
$\frac{n(He^{+})}{n(H^{+})}$). The value of $\frac{n(He^{+})}{n(H^{+})}$ is
$\sim 0.13$ assuming all He is in $He^{+}$ form. Dufour (1984) derived the
$T_{e}[OIII]$ of 14,500$\pm$500 K. From the above relation, the $logF(H\beta)$
expected from the radio continuum is -11.07. The equation from Milne & Aller
(1975) used to compute the reddening is following:

$E(B-V)=\frac{1}{1.46}log\frac{F(H\beta)_{exp}}{F(H\beta)_{obs}}$

Inserting the expected and observed $logF(H\beta)$ values in the above
equation, we obtain the value of E(B$-$V) $\sim$0.23 mag. Thus, the
extinction/reddening towards this cluster and nebula is of similar value.

From the comparison of distance, RV, PM, and extinction/reddening values of
the cluster and nebula, we suggest a physical association of the PN with the
OC.

##  4 Color Magnitude Diagrams

Figure 5: Optical CMD of the NGC 2818, created using Gaia EDR3 photometry. All
filled symbols denote the stars with P${}_{\mu}\geq 50\%$. Blue-filled stars
and yellow-filled stars are the selected blue and yellow straggler stars used
for further cross-match with UVIT data, respectively. The stars detected in
all FUV images are outlined with cyan-colored square and star symbols. The
over-plotted green solid line represents the non-rotating MIST isochrone of
solar metallicity and an age of 775 Myr, set at reddening, E(B$-$V)=0.2 mag
and distance modulus, (m$-$M)V = 12.56 mag.

###  4.1 Classification of Exotic sources

This section describes the classification and identification of exotic
sources, such as BSSs and YSSs, expected to emit in the FUV. As mentioned in
Section 3, we considered the probable cluster members with Pμ>50$\%$ and
created the PM-cleaned optical CMD (Gbp \- Grp vs. G) using the Gaia filters
shown in Figure 5. In this CMD, stars outlined with cyan color depict the
various identified star populations in FUV images. Rain et al. (2021)
presented a new proper-motion-cleaned catalog of BSSs in galactic OCs using
Gaia DR2 data. We cross-matched the Gaia EDR3 cluster members with the BSS
catalog to classify this population in the cluster. Out of five identified
BSSs in NGC 2818 by Rain et al. (2021), we detected four BSSs. The remaining
one BSS, not detected by us, is found to be a non-member of the cluster in our
membership catalog and also falls outside the FoV of NGC 2818 observed with
UVIT in two epochs. Jadhav & Subramaniam (2021) also produced a catalog of
BSSs in OCs using Gaia DR2 data with a Pμ>70$\%$, and they found two BSS
candidates in this cluster. The difference in the above-mentioned catalogs
could be due to the adopted age criteria, selection method, and different
membership probability cut-offs used in the two studies.

We obtained the MESA Isochrones & Stellar Tracks (MIST) for the UVIT and Gaia
EDR3 filters from an updated MIST online
database222https://waps.cfa.harvard.edu/MIST/interp_isos.html to identify and
classify distinct evolutionary sequences in the cluster (Choi et al., 2016;
Paxton et al., 2018). We considered isochrones with [$\alpha$/Fe] = +0.0,
metallicity, Z = 0.017210 (Sun et al., 2021), not incorporating initial
rotation. Cluster parameters such as age, extinction, and distance modulus,
adopted to fit the isochrone to the observed optical CMD, are 775 Myr, AV=0.6
mag, and (m$-$M)V=12.56, respectively (Sun et al., 2021). The overplotted
isochrone (solid green line) over the observed optical CMD is displayed in
Figure 5. We notice that the isochrone appears well-matched to the observed
CMD along the main-sequence, sub-giant branch (SGB), but it is not reproducing
the observed position of the red clump. To account for this mismatch along the
red clump, (Bastian et al., 2018) suggested that there might be a problem in
the calibration of the models for the red clump or the conversion between
theoretical properties of the isochrones (temperature, gravity, and
luminosity) to observational space in Gaia filters is off.
We also selected the YSSs based on their location in the optical CMD, as they
have colors in between the turn-off (TO) and RGB and appear brighter than the
SGB. We have chosen two such stars marked with yellow colored filled symbols
shown in Figure 5.

###  4.2 FUV-optical CMDs

This section presents the FUV-optical CMDs generated by cross-identifying
common stars between optical and our FUV detections. We cross-matched the
sources detected in the UVIT FUV filters with the Gaia EDR3 with a maximum
separation of 1$\farcs$3, which is the typical FWHM of the PSF for the UVIT
filters. To plot the FUV-optical CMDs, first, we made the magnitude system
adopted by Gaia similar to that of UVIT. That is, we transformed the Vega
magnitude system used in the Gaia photometric system to the AB system using
the photometric zero points reported in the Gaia EDR3
documentation333https://gea.esac.esa.int/archive/documentation.

We have created and shown the FUV-optical CMDs for cluster members in Figure 6
using F148W and F169M filters. We note that a similar trend of detected
stellar populations is observed in the other two filters (F154W & F172M). The
error bars displayed in all FUV CMDs are estimated as the median of the stars’
errors at a chosen magnitude range. The FUV-optical CMDs are also over-plotted
with updated MIST isochrones (Choi et al., 2016) to compare the locations of
the distinct sequences predicted by the theoretical models with the observed
ones. In all FUV images, hot and bright stars such as BSSs, YSSs, and MS are
detected. We have detected 4 BSSs out of 5 previously known in the literature
(Rain et al., 2021). Four detected BSSs are confirmed RV and PM members. Two
YSSs are also identified in all FUV images. We note that these stars are well-
separated and brighter than the theoretical isochrone presenting the SGB
sequence in all FUV-optical CMDs, in turn confirming their classification as
YSSs. RGB and Red clump stars are too faint to be detected in the FUV.
The FUV-optical CMDs show a large scatter along MS, as shown in Figure 6,
unlike optical CMD. The overlaid isochrones in all FUV-optical CMDs help to
trace the MS scatter. We note that a few MS stars are brighter than
theoretical MSTO not reproduced by isochrones. These might have high
rotational velocities accounting for this feature. Some of them may be
binaries or potential BSSs. One BSS is found to be very hot and bright in all
FUV-optical CMDs compared to the other three BSSs. This BSS can be an exciting
candidate to characterize, as it might have a hot WD companion. As two YSSs
are detected in all FUV images and found to be bright in all FUV-optical CMDs,
these stars also might have a hot companion, which leads to their detection in
the FUV images. These are intriguing targets further to understand their
formation and evolution in the clusters.

Figure 6: FUV-optical CMDs using F148W and F169M passbands of NGC 2818 of
confirmed members cross-identified using UVIT FUV and Gaia EDR3 catalog. The
error bars (median) are shown in gray color on the left side of each panel.
The rest of the details are the same as in Figure 5.

###  4.3 Extended MS turn-off in FUV CMDs

In order to check the sensitivity of UVIT colors to the $T_{eff}$ affected by
the rotational velocity, we plot (Gbp$-$Grp) vs. (F172M$-$G) color as shown in
Figure 7, which indicates a linear relation. The range of Gaia color is only
0.4 mag whereas F172M$-$G spans about 3.0 mag, which makes F172M$-$G color
more sensitive and responsive to rotational velocity. F172M$-$G color is
preferred over F169M$-$G because the band F172M allows only continuum light,
and no chromospheric or transitional emission lines are seen in late-type
stars in FUV.

Figure 7: F172M$-$G vs. Gbp$-$Grp color-color plot of all stars detected with
UVIT color-coded by their measured Vsini values. Stars with black color
symbols do not have estimated Vsini values.

Comparison of the CMD, F172M$-$G vs. Gbp (Fig. 8 upper right) with CMD of
Gbp$-$Grp vs. Gbp (Fig. 8 upper left) shows the sensitivity of F172M$-$G
color. The bend in the isochrone in F172M$-$G vs. Gbp CMD at a color of 4.0
indicates the beginning of eMSTO prominently (unlike Fig. 8, left panel), and
all the stars right of the isochrone show high rotational velocity. The MS
comprises stars with both high and low rotational velocities. However, the CMD
of F169M$-$G vs. Gbp exhibits some more aspects. From the comparison of
F169M$-$G color with F172M$-$G in Fig. 8, we find that the former is redder
than the latter. It can be due to the fact that the F169M flux in late-type
stars is smaller than at F172M. Moreover, the predicted colors using the
theoretical isochrones are following the same trend.
It is well known that MS stars later than about F2 would possess coronal and
transitional regions as evidenced in the FUV region by emission lines of C IV,
He II, Si IV, N V, N IV, etc. (Linsky & Haisch, 1979; Jordan & Linsky, 1987).
Prominent lines like C IV and He II occur in the F169M band region (unlike the
F172M band). The F154W and F148W would contain a few more emission lines in
addition to C IV and He II. Thus, the CMD of F169M-G vs. Gbp shows that the MS
stars are shifted bluewards to the isochrone, probably suggesting the presence
of transitional region lines. Even in the F169M$-$F172M vs. Gbp CMD shown in
the lower right panel of Figure 8, it is evident that most stars have bluer
colors than the theoretically expected ones from isochrones. It is to be noted
that all stars on the blue edge of the MS in CMD of F169M$-$G vs. Gbp
(15<Gbp<16, 5<F169M$-$G<6) show high rotational velocity in contrast to CMD of
F172M$-$G vs. Gbp (15<Gbp<16, 4<G172M$-$M<5). It is fairly well established
that high rotational velocities enhance the coronal and transitional line
emissions (Pallavicini et al., 1981; Linsky et al., 2020). Thus, it is
consistent with the suggestion that high rotation stars are on the blue side
because of high emission line activity in total contrast to the MS of
F172M$-$G vs. Gbp CMD. This phenomenon sets into stars redder than (Gbp$-$Grp)
$\sim$0.5 mag.

Figure 8: Optical (upper left), F172M-G vs Gbp (upper right), F169M-G vs. Gbp
(lower left), and F169M-F172M vs. Gbp (lower right) CMDs of NGC 2818 members
color-coded by measured Vsini values. The rest of the details are the same as
in Figure 5.

Figure 9: SEDs of four BSSs detected with UVIT. Extinction correction has been
incorporated in all the observed photometric fluxes from UV to IR. The BSS ID
adopted in this work is shown in each figure. The gray color presents the
best-fitting Kurucz model spectrum in all the plots. The data points that are
excluded in the SED fit are shown with the orange color-filled symbol. The
bottom panel in all the SEDs illustrates the residual between the observed
fluxes and model predictions.

Figure 10: Double-fit SEDs of YSSs. The meaning of all the symbols is
displayed in the legend. The star IDs and parameters of two components
obtained from the fit are shown on the top of both SEDs. The green color
represents the composite model flux along with the observed fluxes marked with
red symbols. Orange dotted-dash and blue dashed lines indicate Kurucz and
Koester models used to fit the star’s cooler and hotter components,
respectively. The middle panel presents the fractional residual (Orange dashed
line) corresponding to the single fit as well as the composite fit (Green
solid line). The fractional observational uncertainties in the flux are also
shown here. The values of $\chi_{red}^{2}$ and modified $\chi_{red}^{2}$
parameter, namely $vgf_{b}^{2}$ representing the best-fit are displayed in the
lower panel.

Figure 11: SED fit of the CSPN (left panel) and MS star (right panel) after taking into account the extinction correction. The black solid line represents the theoretical TMAP model fit to the observed fluxes shown with red symbols. The best-fit $T_{eff}$ value is displayed in the figure. The rest of the details are the same as in Figure 9 and 10. Table 2: Stellar parameters obtained from best SED fit of BSSs detected with UVIT in NGC 2818. Column 1 lists the star ID used in the paper. Columns 2 and 3 display the RA and DEC of all the stars considered for fitting, respectively. The $T_{eff}$, luminosities, and radii of all-stars, along with errors, are tabulated in columns 4, 5, and 6, respectively. Columns 7 and 8 lists the reduced $\chi^{2}$ value corresponding to the best fit and ratio of the number of photometric data points ($\frac{N_{fit}}{N_{tot}}$) used for the fit to the total number of available data points. Star ID | RA (deg) | DEC (deg) |  $T_{eff}$ (K) | $\frac{L}{L_{\odot}}$ | $\frac{R}{R_{\odot}}$ | ${\chi}_{red}^{2}$ | Vgf | $Vgf_{b}$ | $\frac{N_{fit}}{N_{tot}}$
---|---|---|---|---|---|---|---|---|---
BSS1 | 139.0306 | -36.59184 | $11,500\pm 250$ | $91.55\pm 17.54$ | $2.39\pm 0.22$ | 12.9 | 12.9 | 1.53 | 11/12
BSS2 | 139.0279 | -36.59178 | $9,000\pm 250$ | $32.99\pm 6.31$ | $2.31\pm 0.21$ | 3.1 | 3.1 | 0.88 | 12/12
BSS3 | 139.1633 | -36.43083 | $8,500^{+500}_{-250}$ | $52.28\pm 9.84$ | $3.30\pm 0.31$ | 4.8 | 4.8 | 1 | 19/19
BSS4 | 139.0276 | -36.6423 | $8,750\pm 250$ | $20.97\pm 3.94$ | $1.94\pm 0.18$ | 4.9 | 4.9 | 0.91 | 19/19
Table 3: Derived parameters of YS and MS stars from the composite SED fit. The different models used to fit the cooler (A) and hotter (B) components of the SEDs are presented in column 5. The rest of the columns have the same meaning as depicted in Table 2. Star ID | RA (deg) | Dec (deg) | Type | Model Used |  $T_{eff}$ (K) | $\frac{L}{L_{\odot}}$ | $\frac{R}{R_{\odot}}$ | ${\chi}_{red}^{2}$ | Vgf | $Vgf_{b}$ | $\frac{N_{fit}}{N_{tot}}$
---|---|---|---|---|---|---|---|---|---|---|---
YSS1 | 139.0523 | -36.57946 | A | Kurucz | $4,750\pm 125$ | $338.1\pm 63.25$ | $27.01\pm 2.49$ | 5.6 | 5.6 | 0.36 | 20/20
|  |  | B | Koester | $10,250\pm 250$ | $7.43^{+3.17}_{-2.36}$ | $0.864^{+0.105}_{-0.083}$ | 4.3 | 4.3 | 0.61 |
YSS2 | 138.9976 | -36.58243 | A | Kurucz | $5,000\pm 250$ | $78.91\pm 15.55$ | $10.93\pm 1$ | 3.5 | 3.5 | 0.71 | 16/16
|  |  | B | Koester | $10,000\pm 250$ | $4.72^{+1.76}_{-1.51}$ | $0.723^{+0.069}_{-0.069}$ | 2.4 | 2.4 | 0.81 |
MS | 139.0592 | -36.60989 | A | Kurucz | $6,000\pm 125$ | $18.35\pm 3.47$ | $3.98\pm 0.37$ | 7.3 | 7.2 | 0.99 | 18/18
|  |  | B | Kurucz | $9,000\pm 125$ | $10.79\pm 2.04$ | $1.36\pm 0.125$ | 7.3 | 7.2 | 0.99 |
Table 4: Derived parameters of PN NGC 2818 from the best SED fit. The notation of all columns is the same as described in Table 2 Star ID | RA | DEC | Model Used | $T_{eff}$ | $\frac{L}{L_{\odot}}$ | $\frac{R}{R_{\odot}}$ | ${\chi}_{red}^{2}$ | Vgf | $Vgf_{b}$ | $\frac{N_{fit}}{N_{tot}}$
---|---|---|---|---|---|---|---|---|---|---
| (deg) | (deg) |  | (K) |  |  |  |  |  |
PN NGC 2818 | 139.0061 | -36.62707 | TMAP(Grid3) | $190,000\pm 8080.40$ | $826.75\pm 225.21$ | $0.026\pm 0.002$ | 8.3 | 8.3 | 4.5 | 6/6

##  5 Spectral Energy Distribution Fits

It is well demonstrated in previous studies of exotic stellar populations,
such as BSSs in OCs, that they are products of stellar interactions. There
might be a chance of detecting a binary companion in the case of BSSs and
YSSs. SEDs of such systems can be used to obtain the parameters of the
multiple components. In this section, we present the multi-wavelength SEDs
constructed for the BSSs, YSSs, and CSPN identified with UVIT to derive their
atmospheric parameters like effective temperature ($T_{eff}$), luminosity (L),
and radius (R). We aim to probe the physical nature of these stars and
probable hot companions, if present, by estimating their stellar parameters
and placing them on the HR diagram. SEDs are generated with the observed
photometric data points spanning a wavelength range from FUV-to-IR and fitted
with selected theoretical models. We made use of the virtual observatory tool,
VOSA (VO Sed analyzer, Bayo et al., 2008) for SED analysis. The details of the
SED fitting technique are described in Rani et al. (2021). In addition to
$\chi_{red}^{2}$, VOSA calculates two extra parameters, Vgf and $Vgf_{b}$,
known as modified $\chi_{red}^{2}$ to estimate the goodness of fit in case the
observational flux errors are too small. The value of $Vgf_{b}$ should be less
than 15 to achieve a reliable SED fit (Rebassa-Mansergas et al., 2021).

The Kurucz stellar atmospheric models are employed to create synthetic SEDs
(Castelli et al., 1997; Castelli & Kurucz, 2003) for BSSs and YSSs, which have
observed photometric data points covering a wavelength range from UV to IR.
The free parameters available in the Kurucz model are $T_{eff}$, metallicity,
and log g. To fit the observed SEDs of the stars, as mentioned earlier with
Kurucz models, we assumed $T_{eff}$, and log g as free parameters, and fixed
the value of metallicity [Fe/H] = 0.0, close to the cluster metallicity. We
adopted the range of $T_{eff}$ from 5,000-50,000 $K$ and log g from 3.5-5 dex
in the Kurucz models. We combined the photometric data points of UVIT (4
passbands) with GALEX (2 passbands), Gaia EDR3 (3 passbands) (Gaia
Collaboration et al., 2018), SDSS (3 passbands), APASS (2 passbands), 2MASS (3
passbands), and WISE (4 passbands) to generate the observed SEDs. VOSA makes
use of Fitzpatrick reddening law (Fitzpatrick, 1999; Indebetouw et al., 2005)
to compute the extinction in different passbands and correct for extinction in
observed fluxes for the provided $A_{V}$. VOSA utilizes the Markov chain Monte
Carlo (MCMC) approach to estimate the uncertainties in the stellar atmospheric
parameters obtained using the SED fit. We estimated the radius (R) of the star
using the scaling relation $M_{d}=\big{(}\frac{R}{D}\big{)}^{2}$, where D is
the distance to the cluster and $M_{d}$ is the scaling factor.

We conducted SED fitting analysis for four BSSs, two YSSs, and PN, as
described in the following subsections.

###  5.1 Blue Straggler Stars

The best-fitted SEDs for all BSSs are shown in Figure 9, where the lower panel
of each SED depicts the fractional residual between the observed and predicted
fluxes. The overplotted black solid line presents the synthetic Kurucz model
spectrum created using the parameters corresponding to the best-fit SED. The
star IDs adopted in this work are displayed on top of each SED. We observe
that the SEDs of all BSSs are seemed to be well-fitted with a single model, as
the residual is close to zero in all SEDs. Since the observed flux errors are
very small for all the filters used, the error bars (shown with black color)
are smaller than the data points. We list their parameters corresponding to
the best fit in Table 2. We obtain $Vgf_{b}$ values for all BSSs to be around
1, indicating the good SED fits, and all the derived fundamental parameters
are also reliable. The BSSs have a $T_{eff}$ range of 8,500$-$11,500 $K$, and
radii of 1.9$-$3.3 $R_{\odot}$. Now, here arises the two possibilities about
the nature of these stars: 1) either all BSSs are single stars, 2) or they are
binaries with a very faint companion, not able to detect by the UVIT
observations. If these stars are single, they are likely to be formed via the
merger of the component stars in a binary.

###  5.2 Yellow Straggler Stars

Figure 10 presents the SEDs of two stars classified as YSSs in this work. In
this figure, the lower panel represents the fractional residual, i.e., the
ratio of the difference between the observed and model flux
($F_{obs}-F_{model}$) and the observed flux at every given data point. We can
see in Figure 10 that both YSSs are showing significant UV excess as a single
model could not fit the entire SED. It can also be noticed in the fractional
residual plot showing a rise in flux in the UV wavelengths for a single
spectrum fit (shown as an orange dash-dotted line in the figure). To fit the
hotter component of the system, first, we gave excess for wavelength less than
3000 Å and fitted the cooler component that includes the optical and IR data
points with the Kurucz model by selecting $T_{eff}$ range from 3,500$-$50,000
$K$ and logg from 1.5$-$2.5 dex. From the single fit, the computed values of
$T_{eff}$ of the YSS1 and YSS2 are 4,750 $K$ and 5,000 $K$, respectively. The
radius of YSS1 and YSS2 is 27 R⊙ and $\sim$ 11 R⊙, respectively. From their
temperature and radii, we infer that they are in the giant phase of stellar
evolution. After obtaining the stellar parameters of the cooler component,
then we used Binary SED
Fitting444https://github.com/jikrant3/Binary_SED_Fitting code to fit the
hotter part of the SED. The full details of this code are well described in
Jadhav et al. (2021). As we expect the hotter component to be compact, we have
used the Koester WD model (Tremblay & Bergeron, 2009; Koester, 2010). In this
model, the range of free parameters $T_{eff}$ and logg is 5,000$-$80,000 $K$
and 6.5$-$9.5, respectively. The double fit of both stars is shown in Figure
10, where the Kurucz model fit is shown with an orange dash-dotted line, and
the Koester model fit with a light-blue dashed line. The composite fit is
marked with a solid green line. The fractional residual in both plots is close
to zero for all observed data points indicating how well the double component
fit reproduces the observed SED. This is even evident from the $vgf_{b}$
values (close to 1) computed from the SED fitting of both stars. The estimated
parameters of both YSSs from the best binary fit are tabulated in Table 3.
From the double fit, we estimate the $T_{eff}$ of the hotter companion of YSS1
and YSS2 are 10,250 $K$ and 10,000 $K$, respectively. The values of parameters
such as $T_{eff}$, luminosities, and radii of the stars are mentioned on the
top of each SED.

###  5.3 PN NGC 2818

As we have shown in the previous section, the PN NGC 2818 most likely has a
physical association with the cluster; it will be interesting to characterize
its central star to obtain information about its progenitor. We can clearly
see the CSPN in the FUV image, as shown in Figure 1, implying its very high
temperature. The magnitude of CSPN is a vital parameter to study its evolution
as it can be used to determine the stellar parameters. The magnitude of the
CSPN in optical filters was measured by Gathier & Pottasch (1988). As CSPN is
well observed in all FUV images, therefore we have calculated the magnitude of
the central star by performing the PSF photometry on the FUV images acquired
in 1st and 2nd epoch observations. We have subtracted the nebular background
in assessing the magnitude of the CSPN. The external extinction and distance
to the nebula are considered to be the same as that of the cluster. Four FUV
UVIT data points are combined with two optical photometric data points from
Gathier & Pottasch (1988) to construct the observed SED of the nebula. As the
central star seemed to be very hot, we have fitted its SED with the Tübingen
NLTE Model Atmosphere Package (TMAP) (Grid3) model used for hot stars (Rauch &
Deetjen, 2003; Werner et al., 2003). This model grid spans a range of
atmospheric parameters such as $50,000K\leq T_{eff}\leq 190,000K$, $5.0\leq
log{\it g}\leq 9.0$, and $0\leq X_{H}\leq 1$. It is important to note that we
took into account the external extinction while fitting its SED but did not
incorporate the internal extinction in the nebula. We have noticed that
$T_{eff}$ derived using the TMAP model fit to the observed SED corresponds to
their upper limit, which indicates that this star is likely to be hotter than
the estimated temperature from this model. The stellar parameters computed
from the best-fit SED of the nebula are summarised in Table 4.

###  5.4 MS stars

We also have constructed the SEDs for the MS stars detected with UVIT, for
which rotational velocity information was available in the literature to
investigate their nature. Apart from that, we also have considered the MS
stars for SED analysis for which rotational velocity was not estimated
earlier, and their position in all FUV-optical CMDs was not matched with their
expected one. 31 MS stars with the known rotational velocity are identified
with UVIT in two epochs. Other than these stars, 6 MS stars are brighter than
MS turn-off in FUV CMDs. We have used the Kurucz models to fit their observed
SEDs to obtain their physical parameters and check their binarity. Out of 37
stars, we observed that only one MS star shows significant FUV excess, as
displayed in the right panel of Figure 11, whereas other stars show less or
mild UV excess that could not be fitted with a double component SED.
Chromospheric activity in the above star cannot account for UV excess as it is
exceptionally high compared to the model. The other possibility to explain
this excess is the presence of a hot companion that mainly emits at shorter
wavelengths. To account for the presence of the hot companion, we fitted the
entire SED with the Kurucz model using the binary fit task from VOSA. The
double component fit for this star is found to be satisfactory (Right panel of
Figure 11), and the best-fit parameters computed are tabulated in Table 3. The
radii of both components suggest that they are not quite on the MS. The cooler
companion is likely to be a sub-giant ($R/R_{\odot}\sim$ 4.0), whereas the hot
companion has a smaller radius ($R/R_{\odot}\sim$ 1.36) when compared to the
MS star of similar temperature ($R/R_{\odot}\sim$ 6.0). It might be possible
that this is a post-mass transfer system where the hotter component is the
donor, and the cooler component is still bloated after gaining mass. The
rotational velocity (Vsini) of this star is around 39 km/s.

##  6 Evolutionary Status

Placing the stars on the HR diagram provides information about their
evolutionary stage and helps in probing the nature of the hot companions in
the case of binary stars. To examine the evolutionary status of exotic stars
considered in this study, we have plotted the theoretical evolutionary
sequences starting from the MS to the moment the star has entered the tip of
the RGB stage. These tracks are taken from MIST models computed by Choi et al.
(2016); Paxton et al. (2018) and selected for the cluster age and metallicity
close to the cluster metallicity. The stellar parameters estimated from the
single SED fit for four BSSs are plotted in the HR diagram. The meaning of the
color and symbols are marked in Figure 12. We can notice in Figure 12 that
BSSs are lying bluer to the MS track, suggesting that these four stars belong
to the BS evolutionary phase.

The location of two YSSs on the HR diagram is near the theoretical RGB
sequence. It indicates that their progenitors’ (BSSs) have already evolved
into a giant phase where the contracting helium core is surrounded by the
hydrogen-burning shell. The hot companions of both YSSs seemed to be compact
in nature, as indicated by their estimated radii suggesting they might belong
to the WD or extremely low mass (ELM) WD or subdwarf stage of stellar
evolution. In addition to the MS tracks, we have presented the DA-type WD
cooling sequences with masses 0.5$M_{\odot}$ and 0.2$M_{\odot}$ taken from
Tremblay et al. (2011) in Figure 12. From comparing the position of the hot
companions of both YSSs with theoretical WD cooling tracks, we notice that
their location is not reproduced by them, implying that they still have not
entered the WD stage. While there are non-DA type WDs that are believed to
result from mergers, they are not expected to be found in OCs because the
merger process would take longer than the age of the cluster.

In order to find out where ELM WDs fall in the HR diagram, we have used the
field ELM WD catalog provided by Brown et al. (2016). They have estimated the
$T\rm{{}_{eff}}$ and log g values of the considered ELM WD sample in their
paper. To place them on the $T_{eff}$ vs. luminosity plot, SED fitting
technique is used to estimate the luminosity of all ELM WDs (Priv. Comm.
Vikrant Jadhav). The extinction correction has been incorporated in all the
stars. All field ELM WDs are marked as cyan-filled symbols in Figure 12. We
note that the hot companions of the YSSs are more luminous than the field ELMs
with a similar temperature.

As the location of the binary companions of YSSs is not reproduced by the WD
tracks as well as ELM WDs, we further suspect that they might belong to the
class of A-type subdwarfs (sdA) as they are lying near the general location of
subdwarfs in the HR diagram. sdA stars are supposed to occupy the location
between the dwarfs and WDs in the HR diagram; hence, they are more compact
than dwarfs, indicating a higher log g value. Brown et al. (2017) performed a
detailed study of sdA stars to investigate their physical nature and a
possible link to the ELM WDs. We used the field sdA catalog to locate their
positions on the HR diagram. As only effective temperatures of all sdA stars
were available in the catalog, we used the SED fitting technique to determine
their luminosities. The extinction in the visual band ($A_{V}$) for these
stars was estimated using the reddening map provided by Schlafly & Finkbeiner
(2011). We have taken care of the extinction correction in the observed fluxes
in different bands of all sdA stars. The distances to these stars are
available in the Gaia EDR3 catalog. We have used the distances reported in
Bailer-Jones et al. (2021), estimated using Gaia EDR3 catalog, and they all
fall within a range of $\sim$1.5 to 8 kpc. The sdA stars are displayed with
purple-filled symbols in the HR diagram. The hot companions of YSSs are found
to be hotter than the similarly luminous field sdAs and more luminous than the
similarly hot field sdAs.

From this comparison, we suggest that they are most likely to be sdA stars
formed through a binary mass transfer scenario. These binaries are probably a
post-mass-transfer system consisting of an A-type subdwarf candidate and a YS
star. We also checked the position of the hotter and cooler components of the
MS star on the HR diagram displayed with orange-color symbols. The hotter
component occupies a location bluer than theoretical isochrone, might be
evolving to the sdA type star, whereas the cooler component occupies the
location expected for sub-giants. The evolution of this star might be similar
to the YSS as the cooler component is evolving to the giant stage, whereas the
hotter component later might end up as sdA. Thus, we speculate that this
system might be a progenitor of the YSSs detected in this cluster.

Further, we have used the pAGB models computed by Miller Bertolami (2016) to
deduce the evolutionary state of the CSPN. We adopted the cluster metallicity
(Z=$\sim 0.02$ dex) to select the pAGB tracks. Tracks with a range of final
mass as shown in Figure 12 are presented from the beginning of the pAGB phase
when the H-rich envelope drops below $M_{env}=0.01M_{*}$ to the moment the
star has already entered its WD cooling sequence at $L_{*}=L_{sun}$. The
estimated parameters of the PN from the SED fit are plotted in the HR diagram
(Red filled symbol). From the comparison to these theoretical pAGB tracks, we
observe that CSPN is found to be located on the track (Black dash-dotted line)
corresponding to the final mass $0.657M_{sun}$. It can be noted from here that
the star has already entered the WD cooling phase.

Figure 12: HR diagram of the bright stars identified with UVIT. Various
evolutionary tracks are presented from the beginning of the MS to the moment
when a star has entered to the stage, followed by the WD cooling sequences.
All these tracks are generated for cluster metallicity and age. The pAGB
sequences with different final masses are shown here to compare the location
of the CSPN marked with a red star symbol. BSSs and YSSs are displayed with
blue-filled circles and yellow star symbols, respectively. The hotter
companions of YSSs are shown with magenta star symbols. In addition, Field ELM
WDs and A-type subdwarfs represented with cyan and purple symbols are also
placed in the HR diagram to compare the position of the hot companions of both
YSSs. Green color solid and dashed lines correspond to the DA-WD tracks with
different masses.

##  7 Discussion

We have conducted an observational study of OC NGC 2818 and the PN within its
field using FUV medium-resolution space-based imaging data from UVIT aboard
AstroSat. This paper aims to use the most accurate and complete Gaia EDR3 data
on stellar astrometry and photometry in the nearby intermediate age OC NGC
2818 to establish the membership probability of known stars and to deduce the
evolutionary state of exotic stars. Since the stars reside in the central area
of the cluster, we have confined ourselves with the consideration of the inner
part of the cluster with a radius of 30$\arcmin$ and selected 37508 stars
brighter than G = 21 mag. Using the GMM method to pick out the PM members, we
have chosen 718 stars as the cluster members with $P_{\mu}>50\%$ and
considered them further to identify their FUV counterparts with UVIT. FUV-
optical and FUV CMDs were generated for the cluster members and overlaid with
the MIST isochrones to compare the position of different observed evolutionary
sequences with theoretically expected ones. MIST isochrones are found to match
well with the observed sequences in FUV-optical CMDs, but in FUV CMDs,
especially F169M$-$F172M vs. Gbp, most of the detected stars in both filters
are lying blueward of their expected location from isochrones.

In all FUV images, we have identified four BSSs, two YSSs, and MS based on
their location in the optical as well as FUV-optical CMDs. Then, we performed
the SED analysis to deduce their physical properties to evaluate their nature.
The $T_{eff}$ of BSSs estimated from SED fit ranges from 8500$-$11500 $K$,
hinting that they are quite hot, consistent with the young age (700$-$800 Myr)
of the cluster. In the previous studies of BSSs in other OCs conducted using
UVIT data, the $T_{eff}$ range varies from cluster to cluster depending upon
its age. The temperature range of BSSs in OC M67 (4 Gyr) is 6250$-$9000 $K$
(Jadhav et al., 2019), in King 2 (6 Gyr) 5750$-$8500 $K$ (Jadhav et al.,
2021), in OC NGC 188 (7 Gyr) 6100$-$6800 $K$ (Gosnell et al., 2015). In
intermediate-age OCs such as NGC 7789 (1.6 Gyr) (Vaidya et al., 2022) and NGC
2506 (2.2 Gyr) (Panthi et al., 2022), BSSs span a temperature range from
7250$-$10250 $K$, and 7750$-$9750 $K$, respectively. The SEDs of all BSSs are
well-fitted with a single model, and we suggest that collisions leading to the
mergers might explain their formation in this cluster. Another plausible
possibility is that they might have a faint WD companion undetectable with
UVIT. If this is the case, then the second prominent scenario to explain their
existence in star clusters, i.e., mass transfer in close binaries, will
dominate over the previous one. Moreover, mass transfer in binaries will
dominate in OCs as they are less dense and compact than GC systems. Further,
spectroscopic analysis of these stars will help to confirm their nature.

Two YSSs, from their SED fits, are found to be binaries, and the location of
YSSs and their hot components in the HR diagram suggests that cool components
are already in the RGB phase. In contrast, hot components most plausibly
belong to sdA class. We infer from here that these two stars are post-mass-
transfer systems where BSS (accretor) has evolved into a giant stage and
became YSS, and the donor star into a sdA. In addition, a spectroscopic study
performed by Mermilliod et al. (2001) of RGB stars, including these two stars,
found that they are spectroscopic binaries, confirming our result. Their
radial velocities estimated by them also verify their membership. Hence, we
suggest that these two stars to be formed via a mass transfer scenario in the
cluster.

From the comparison of the distance, extinction, RV and PM values of the PN
with the cluster, it turns out that it is a most likely member of the cluster.
Bohigas (2003, 2008) estimated the $T_{eff}$ from the ionization modeling of
the nebula as $T_{eff}$ 149,000 $K$ and log g of 7.1 (however, this might also
be dependent on the distance assumed). Mata et al. (2016) gives the $T_{eff}$
as 160,000 $K$. Gathier & Pottasch (1988) estimate the HI Zanstra temp
175,000K and HeII Zanstra temp of 215,000K. Kohoutek et al. (1986) derived the
luminosity ($L_{*}=851L_{\odot}$) and radius ($R_{*}=0.038R_{\odot}$) of CSPN
using optical observations, and adopting the identical distance to the nebula
as that of the cluster (d=3.5 kpc). The atmospheric parameters of CSPN
determined using the SED fitting technique are more or less in agreement with
the previous estimations. Based on the comparison of the central star’s
location with the predicted ones from the theoretical models in the HR
diagram, the central star’s mass turns out to be 0.66 $M_{\odot}$. Cummings et
al. (2018) presented the WD initial–final mass relation (IFMR) for progenitor
stars of $M_{initial}$ from 0.85 to 7.5 $M_{\odot}$. In their Figure 5, they
displayed the comparison of the Initial–Final Mass Relation (IFMR) estimated
for the observed sample with the theoretical isochrones. For a WD with a mass
of 0.66 $M_{\odot}$, the initial mass of the progenitor is estimated to be
$\sim$2.1 $M_{\odot}$ (From their Fig. 5). In this work, the MSTO mass of this
cluster determined using isochrone fit is $\sim$2 $M_{\odot}$. The previously
reported turn-off mass for this cluster and the initial mass of the nebula’s
progenitor are $\sim$2.1 $M_{\odot}$, and $2.2\pm 0.3$ $M_{\odot}$,
respectively (Dufour, 1984). Our estimations are consistent with the previous
ones. From the comparison of the cluster turn-off mass and progenitor mass, we
infer that PN is quite likely a cluster member. Thus, this study showcases the
significance of using the FUV data to study the exotic populations and late
stages of the evolution of intermediate-mass stars in OCs.

##  8 Summary and Conclusions

The main results from this work can be summarized as follows:

  * •

In this study, we employed UVIT observations onboard AstroSat to identify BSSs
and YSSs in the open cluster NGC 2818, and also characterize the CSPN. We
further created the optical and UV-optical CMDs of member stars co-detected
using UVIT and Gaia EDR3 data in this cluster.

  * •

The PM members of the cluster are obtained using Gaia EDR3 data, and we found
that PN NGC 2818 might be a member of this cluster, consistent with the
previous studies.

  * •

As this cluster is young, hot and bright stars such as BSSs, YSSs, and MS are
detected in all FUV images.

  * •

To compare the observations with theoretical predictions, optical and UV-
optical CMDs are overlaid with non-rotating MIST isochrones generated for
respective UVIT and Gaia filters. The theoretical isochrones reproduce the
features of all CMDs quite well.

  * •

The FUV-optical CMDs prominently show the eMSTO phenomenon already reported in
this cluster, consistent with the previous studies.

  * •

We characterized the four detected BSSs in the cluster, and a single model
fits well to all the observed SEDs. We suggest from the single model fits that
these stars might have a faint WD companion that could not be detected with
UVIT’s detection limit or result from the merger of two close binaries.

  * •

We suggest the presence of two YSSs in this cluster based on their location in
the CMDs. Both YSSs were found to have excess flux in the UV, connected to its
binarity. They are confirmed spectroscopic binaries, and their hot companions
are compact objects, likely to be sdA stars. Based on these results, we
conclude that they are products of the binary mass transfer.

  * •

From comparing the position of the CSPN with the theoretical pAGB evolutionary
tracks, we found that it has entered the WD cooling phase, and its mass is
found to be $\sim 0.66M_{\odot}$. The mass of the progenitor corresponding to
the WD of mass $0.66M_{\odot}$ would be $\sim 2.1M_{\odot}$, similar to the
turn-off mass of the cluster, further confirming its membership.

## Acknowledgements

We thank the anonymous referee for the valuable comments and suggestions. AS
acknowledges support from SERB Power Fellowship. S. Rani wants to thank
Vikrant Jadhav for providing the field ELM WDs SED fit parameters catalog. S.
Rani thanks Sonith L. S. for the fruitful discussions. This publication
utilizes the data from AstroSat mission’s UVIT, which is archived at the
Indian Space Science Data Centre (ISSDC). The UVIT project is a result of
collaboration between IIA, Bengaluru, IUCAA, Pune, TIFR, Mumbai, several
centers of ISRO, and CSA. This research made use of VOSA, developed under the
Spanish Virtual Observatory project supported by the Spanish MINECO through
grant AyA2017-84089. This research also made use of the Aladin sky atlas
developed at CDS, Strasbourg Observatory, France (Bonnarel et al., 2000).

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