# Globular Cluster UVIT legacy Survey (GlobUleS) III. Omega Centauri in Far-
Ultraviolet

Deepthi S. Prabhu Indian Institute of Astrophysics, Koramangala II Block,
Bangalore-560034, India  Pondicherry University, R.V. Nagar, Kalapet, 605014,
Puducherry, India  Annapurni Subramaniam Indian Institute of Astrophysics,
Koramangala II Block, Bangalore-560034, India  Snehalata Sahu Department of
Physics, University of Warwick, Coventry CV4 7AL, UK  Chul Chung Department of
Astronomy & Center for Galaxy Evolution Research, Yonsei University, Seoul
03722, Republic of Korea  Nathan W. C. Leigh  Departamento de Astronomía,
Facultad Ciencias Físicas y Matematicas, Universidad de Concepción, Av.
Esteban Iturra s/n Barrio Universitario, Casilla 160-C, Concepción, Chile
Department of Astrophysics, American Museum of Natural History, Central Park
West and 79th Street, New York, NY 10024-5192, USA 2  Emanuele Dalessandro
INAF-Astrophysics and Space Science Observatory Bologna, Via Gobetti 93/3
I-40129 Bologna, Italy  Sourav Chatterjee Tata Institute of Fundamental
Research, Mumbai 400005, India  N. Kameswara Rao Indian Institute of
Astrophysics, Koramangala II Block, Bangalore-560034, India  Michael Shara
Department of Astrophysics, American Museum of Natural History, Central Park
West and 79th Street, New York, NY 10024-5192, USA 2  Patrick Côté Herzberg
Astronomy and Astrophysics Research Centre, National Research Council of
Canada, 5071 W. Saanich Road, Victoria, BC V9E 2E7, Canada  Samyaday Choudhury
Space Telescope Science Institute, 3700 San Martin Dr., Baltimore, MD 21218,
USA  Gajendra Pandey Indian Institute of Astrophysics, Koramangala II Block,
Bangalore-560034, India  Aldo A. R. Valcarce  Departamento de Física,
Universidade Estadual de Feira de Santana, Av. Transnordestina, s/n,
44036-900, Feira de Santana, BA, Brazil  Millennium Institute of Astrophysics
MAS, Nuncio Monsenor Sotero Sanz 100, Of. 104, Providencia, Santiago, Chile
Gaurav Singh Indian Institute of Astrophysics, Koramangala II Block,
Bangalore-560034, India  Joesph E. Postma  Department of Physics and
Astronomy, University of Calgary, Calgary, AB T2N 1N4, Canada  Sharmila Rani
Indian Institute of Astrophysics, Koramangala II Block, Bangalore-560034,
India  Avrajit Bandyopadhyay Department of Astronomy, University of Florida,
Gainesville, FL 32601, USA  Aaron M. Geller  Center for Interdisciplinary
Exploration and Research in Astrophysics (CIERA) and Department of Physics and
Astronomy, Northwestern University,
1800 Sherman Ave., Evanston, IL 60201, USA  John Hutchings  Herzberg Astronomy
and Astrophysics Research Centre, National Research Council of Canada, 5071 W.
Saanich Road, Victoria, BC V9E 2E7, Canada  Thomas Puzia Institute of
Astrophysics, Pontificia Universidad Católica de Chile, Av. Vicuña MacKenna
4860, 7820436, Santiago, Chile  Mirko Simunovic Subaru Telescope,National
Astronomical Observatory of Japan, 650 N Aohoku Pl, Hilo, HI 96720, USA
Young-Jong Sohn  Department of Astronomy & Center for Galaxy Evolution
Research, Yonsei University, Seoul 03722, Republic of Korea  Sivarani
Thirupathi  Indian Institute of Astrophysics, Koramangala II Block,
Bangalore-560034, India  Ramakant Singh Yadav  Aryabhatta Research Institute
of Observational Sciences, Nainital, India

###### Abstract

We present the first comprehensive study of the most massive globular cluster
Omega Centauri in the far-ultraviolet (FUV) extending from the center to
$\sim$ 28% of the tidal radius using the Ultraviolet Imaging Telescope aboard
AstroSat. A comparison of the FUV-optical color-magnitude diagrams with
available canonical models reveals that the horizontal branch (HB) stars bluer
than the knee (hHBs) and the white dwarfs (WDs) are fainter in the FUV by
$\sim$ 0.5 mag than model predictions. They are also fainter than their
counterparts in M13, another massive cluster. We simulated HB with at least
five subpopulations including three He-rich populations with a substantial He
enrichment of Y up to 0.43 dex, to reproduce the observed FUV distribution. We
find the He-rich younger subpopulations to be radially more segregated than
the He-normal older ones, suggesting an in-situ enrichment from older
generations. The $\omega$ Cen hHBs span the same $T_{\rm eff}$ range as their
M13 counterparts, but some have smaller radii and lower luminosities. This may
suggest that a fraction of $\omega$ Cen hHBs are less massive than those of
M13, similar to the result derived from earlier spectroscopic studies of outer
extreme HB stars. The WDs in $\omega$ Cen and M13 have similar luminosity-
radius-$T_{\rm eff}$ parameters and 0.44 - 0.46 M⊙ He-core WD model tracks
evolving from progenitors with Y = 0.4 dex are found to fit the majority of
these. This study provides constraints on the formation models of $\omega$ Cen
based on the estimated range in age, [Fe/H] and Y (in particular), for the HB
stars.

(Galaxy:) globular clusters: individual (NGC 5139) — (stars:)
Hertzsprung–Russell and C–M diagrams — stars : horizontal-branch — (stars):
white dwarfs — ultraviolet: stars

††journal: ApJ Letters

##  1 Introduction

Galactic globular clusters (GCs) harbor stars hot enough to be significant
emitters of ultraviolet (UV) light (see Moehler, 2001, 2010, for detailed
reviews). Studying these stars can help elucidate several problems in topics
such as the late stages of low-mass stars’ evolution (Moehler et al., 2019),
stellar dynamics eg., Ferraro et al. 2012; Leigh et al. 2013, the “UV-upturn”
seen in the spectra of elliptical galaxies (Greggio & Renzini, 1990; Dorman et
al., 1993, 1995) and so on. The identification of UV-bright stars is best done
using UV images, as crowding due to populous cooler stars are suppressed in
the central cores, at these wavelengths.

Omega Centauri ($\omega$ Cen; or NGC 5139), being the most massive GC in the
Galaxy mass = 3.5 $\times$ $10^{6}$$M_{\odot}$; Baumgardt & Hilker 2018
contains the largest known population of very hot horizontal branch stars HBs;
D’Cruz et al. 2000 and exotic blue straggler stars BSSs; Ferraro et al. 2006;
Mucciarelli et al. 2014. Stars with a wide range in metallicity ($-$2.2
$\lesssim$ [Fe/H] $\lesssim$ $-$ 0.6 dex) and helium (He) abundance (Y up to
0.4 dex) have been reported through spectroscopic measurements (Moehler et
al., 2011; Moni Bidin et al., 2012; Latour et al., 2021, and references
therein) and through isochrone-fitting and population synthesis of color-
magnitude diagrams CMDs; Norris 2004; Piotto et al. 2005; Lee et al. 2005; Joo
& Lee 2013; Tailo et al. 2016. The presence of He-core white dwarfs (WDs) has
also been suggested in the studies of Calamida et al. (2008) and Bellini et
al. (2013).

The previous far-UV (FUV) study of this cluster was conducted decades back
using the Ultraviolet Imaging Telescope UIT, Landsman et al. 1992; Whitney et
al. 1994, 1998 and the Hubble Space Telescope HST, D’Cruz et al. 2000.
However, these datasets are incomplete due to the limited spatial resolution
of UIT ($\sim$ 3′′) and field of view (FOV) of HST/WFPC2.

In this Letter, we present the first comprehensive FUV investigation of
$\omega$ Cen extending from its center to $\sim$ 28% of the tidal radius, rt =
48′ (Harris, 1996, 2010 edition, hereafter H96), carried out using the Ultra
Violet Imaging Telescope (UVIT) onboard AstroSat. For the first time, we
detect populations of HBs and WDs which are anomalously fainter in the FUV
band as compared to theoretical models as well as their counterparts in
another massive GC, M13.

##  2 Observations and Data Reduction

$\omega$ Cen was observed as a part of the Globular Cluster UVIT Legacy Survey
GlobULeS, Sahu et al. 2022 on 24 January 2021 in two FUV filters, F148W and
F169M, covering the entire 28$\arcmin$ diameter FOV of the instrument. A
detailed description of the UVIT and its calibration can be found in Tandon et
al. (2017, 2020). The CCDLAB software package (Postma & Leahy, 2017) was used
to create the science-ready images with exposure times of 6310.95 s (F148W)
and 6268.10 s (F169M). The astrometric calibration was performed using GALEX
NUV image (Bianchi et al., 2017) and the Gaia EDR3 data (Gaia Collaboration et
al., 2020) as references and the final accuracy was $\sim$ 0.5$\arcsec$.

We performed PSF photometry on these images as described in Sahu et al.
(2022). The source catalog was refined by removing three visibly saturated
stars, and those lying at the edge of the UVIT FOV. The final catalog contains
only the stars with PSF-fit errors less than 0.25 mag and those detected in
both the filters (N = 3697; obtained by matching the co-ordinates within a
maximum match radius of 1″). The UVIT image of the cluster in the F148W filter
and the magnitude vs. photometric error plots are shown in Fig. 1.

Figure 1: Top :UVIT/F148W image of $\omega$ Cen. Bottom : Plot of PSF-fit
errors vs. magnitudes (not corrected for extinction) in the two filters. The
filter names, FWHM of the PSF and number of detections with fit error $<$ 0.25
mag (N∗) are indicated. The line indicates the median error in each filter.

The magnitudes were corrected for extinction by adopting $E(B-V)_{avg}$ = 0.12
mag (H96), $R_{V}$ = 3.1, and the Fitzpatrick reddening law (Fitzpatrick,
1999). The extinction coefficient values are 0.98 mag and 0.93 mag
respectively for the F148W and F169M filters111Calculated using the York
Extinction Solver (McCall, 2004).

##  3 Color-magnitude diagrams

The UV-optical color-magnitude diagram (CMD) of the cluster was constructed by
identifying the optical counterparts of the 3689 (out of a total of 3697) FUV-
detected sources using the HST-based catalog of Bellini et al. (2017a) (for
$r<$ core radius $r_{c}$ = $None$, hereafter inner region) and the catalogs of
Stetson et al. (2019) and Vasiliev & Baumgardt (2021) (for $$$<r<$$$; outer
region) as described in Appendix A. The optical magnitudes were converted from
Vega to AB system using appropriate conversion
factors222http://waps.cfa.harvard.edu/MIST/BC_tables/zeropoints.txt.

Fig. 2 shows the optical and FUV-optical CMDs of the cluster along with
various models and isochrone. For the HB, we used the Bag of Stellar Tracks
and Isochrones (BaSTI)333http://basti-iac.oa-abruzzo.inaf.it/ (Pietrinferni et
al., 2021) theoretical zero-age HB (ZAHB) and terminal-age HB (TAHB) models
with [$\alpha$/Fe] =$+$0.4 dex, and mass-loss parameter $\eta=0.3$, where,
overshooting is not applied and atomic diffusion effects are included. Three
models with the following metallicity and He abundance values were chosen:
[Fe/H] = $-$2.2 dex, Y = 0.247 dex (metal-poor, He-normal); [Fe/H] = $-$0.6
dex, Y = 0.257 dex (metal-intermediate, He-normal) and [Fe/H] = 0.06 dex, Y =
0.320 dex (metal-rich, He-enhanced). These choices were based on the values
reported in literature and as per the availability in the database. For the
BSS sequence, we used the BaSTI zero-age MS (ZAMS) isochrone of age = 0.5 Gyr,
with initial mass range $\sim$ 0.5 - 1.5 $M_{\odot}$ corresponding [Fe/H] avg
= $-$1.55 dex and primordial Y value. For the WD population, we used two DA
spectral type models with pure hydrogen (H) grid and thick H layers with
masses 0.5 $M_{\odot}$ and 0.6 $M_{\odot}$ (private comm. with Pierre
Bergeron).

Figure 2: Theoretical stellar evolutionary models overplotted on the optical
and FUV-optical CMDs. The BaSTI ZAHB and TAHB models for different
metallicities and He abundances are shown with continuous and dashed lines
respectively. The dotted lines represent the BaSTI ZAMS isochrone. The dash
dotted lines represent WD cooling sequences. The parameters corresponding to
all the models are indicated on the top panel of the figure.

The locations of the HBs, BSSs and WDs in the optical CMDs match well with the
model predictions (left panels of Fig. 2). In the FUV-optical CMDs (right
panels), the red HB and BSS sequences lie at the locations expected from the
models. It is well known that the hottest HBs, known as blue hook stars
(BHKs), appear fainter than canonical models in CMDs (Whitney et al., 1998;
D’Cruz et al., 2000). However, we find that all hot HBs (hHBs) with
$m_{F148W}-m_{F438W}\lesssim 2.0$ mag are fainter in the F148W band by about
$\sim$ 0.5 mag whereas no anomaly is observed in optical CMDs. The WDs too are
redder by comparable magnitude only in the FUV-optical CMDs (implying fainter
FUV magnitudes). A similar behavior is observed in the UVIT F169M filter (not
shown here). Any effect due to the instrument calibration or analysis
procedure was ruled out as described in Appendix B.

##  4 HB simulations

To check if the observed HB distribution originated from the extreme He-
enhancement, we produced synthetic CMDs shown in the top and middle panels of
Figure 3. Generally, the CMD synthesis of GCs should simultaneously reproduce
both the HB morphology and the main sequence (MS) to red-giant branch stars
(RGBs). We can derive reliable stellar parameters and subpopulations’ ratios
based on this. However, due to the observational limitations on MS to RGBs in
the FUV regime, we performed CMD synthesis only for HBs by referring to the
stellar parameters of Joo & Lee (2013) for $\omega$ Cen who reproduced both
sequences simultaneously. We adjusted three stellar parameters ${\rm
Y_{ini}}$, age, and [Fe/H] to find the best match to the observations. The
mass-loss parameter was adopted as $\eta=0.5$ for all the stellar populations.
The detailed descriptions for other parameters and the simulation are
summarized in Chung et al. (2017). Note that we did not include the evolved
phase of HBs (i.e., AGB manqué phase) in the model to avoid the highly
uncertain stellar evolution tracks after the He-core depletion.

We assumed five subpopulations to reproduce HB morphologies in two observed
CMDs. From G1 to G5, the stellar parameters for each subpopulation are
indicated above the top panel of Figure 3. The normal He G1 (${\rm
Y_{ini}=0.23}$) and slightly He-rich G2 (${\rm Y_{ini}=0.28}$) show reasonable
agreements with the observed blue HBs. In our simulation, the extremely hot
HBs mainly originated from G3 and G4 populations with ${\rm Y_{ini}=0.43}$ and
$0.38$, respectively. If we do not change ${\rm Y_{ini}}$, other values of age
or metallicity (i.e., extremely old or metal-poor populations) cannot
reproduce those HBs. In addition, as Figure 6 of Joo & Lee (2013) shows,
$\omega$ Cen hosts at least one extreme metal-rich MS to RGB sequence. To
explain this population, we added G5 population with ${\rm[Fe/H]=-0.4~{}dex}$
and ${\rm Y_{ini}=0.38~{}dex}$, and this subpopulation matches HBs around
$(F148W-F438W)\simeq 0.0$ as well. The fractions of the simulated
subpopulations from G1 to G5, adopted based on Joo & Lee (2013), are 0.49,
0.27, 0.10, 0.07, and 0.07 respectively.

The FUV-optical CMD and the radial distribution of the HB stars belonging to
different subpopulations is shown in the bottom panels of Figure 3. Here, the
older, He-normal subpopulations G1 and G2 were grouped together (purple
symbols in the bottom left panel) and the younger, He-rich G3, G4 and G5 were
combined as another sample (olive symbols). The He-rich, second-generation HB
stars clearly appear more segregated. The Kolmogorov-Smirnov test returned a
$p$-value of $\sim$ 1 $\times$ 10-5, indicating that the two subpopulations
are not drawn from the same distribution.

(a)

(b)

Figure 3: HB simulations and radial distributions of subpopulations : The top
panels show the observed optical and FUV-optical CMDs and the middle panels
show the simulated HB CMDs overplotted on the observed. Parameters suggested
from our best fit simulation for subpopulations from G1 to G5 are indicated in
the legend above. The triangles in the middle panels denote the simulated RR
Lyrae stars. The distance modulus and reddening adopted to reproduce the
observed CMDs are $(m-M)_{F148W}=15.5$ mag, $E(F148W-F438W)=1.2$ mag, and
$(m-M)_{F814W}=14.1$ mag, $E(F438W-F814W)=0.3$ mag, respectively. The bottom
right panel shows the radial distribution of observed HB subpopulations where
G1 and G2 are considered as a single group and G3, G4 and G5 as another,
indicated with purple and olive symbols respectively in the bottom left panel.

##  5 Characterization of hot populations

We used the spectral energy distribution (SED)-fitting technique to
characterize the hot stars that showed departure from the BaSTI tracks. The
SEDs were constructed and fitted with appropriate models using VOSA (VO SED
Analyser; Bayo et al. 2008) which generates synthetic photometric points for
the chosen filters. The best-fit parameters were estimated by comparing the
observed data with synthetic photometry using a $\chi^{2}$ minimization method
with the $\chi_{red}^{2}$ given by the relation,

$\chi_{red}^{2}=\displaystyle\frac{1}{N-N_{f}}\sum_{i=1}^{N}\Bigg{\\{}\frac{(F_{o,i}-M_{d}F_{m,i})^{2}}{\sigma_{o,i}^{2}}\Bigg{\\}}$
(1)

Here, N and ${\it N_{f}}$ are the numbers of observed data points and the
model parameters fitted respectively, ${\it F_{o,i}}$ is the observed flux,
${\it F_{m,i}}$ is the model flux, ${\it M_{d}}={\it(\frac{R}{D})^{2}}$ is the
multiplicative dilution factor (where $R$ and D are the radius and distance to
the star, respectively) and ${\it\sigma_{o,i}}$ is the observed flux error.
VOSA calculates two additional parameters, $Vgf$ and $Vgf_{b}$, as visual
goodness of fit indicators, useful when the observational flux errors are
underestimated444See Section 5.1.4 of VOSA documentation for details
http://svo2.cab.inta-csic.es/theory/vosa/helpw4.php?otype=star&what=intro#. We
used $D_{avg}$ = 5.426 kpc (Baumgardt & Vasiliev, 2021). To account for the
extinction, VOSA uses the Fitzpatrick reddening relation. The errors in the
fitted parameters were estimated using the statistical approach described in
the VOSA documentation.

###  5.1 Hot HB stars

The SEDs of hHBs were fitted using six appropriate models whose parameters,
and available ranges are tabulated in Table 1. We employed three approaches
aiming to test different aspects. In the first approach, we fitted the SEDs
adopting the values listed in the last column of Table 1 and by fixing the
value of $A_{V}$ to 0.372 mag for $E(B-V)_{avg}$ = 0.12 mag. In the next
approach, to check for the effects due to radiative levitation observed in HBs
hotter than the Grundahl-jump $T_{\rm eff}$ $\sim$ 11 500 K; Grundahl et al.
1999, we allowed the metallicity parameter to vary up to the solar value
keeping $A_{V}$ and the other parameter ranges unchanged. The final approach
was meant to check for the effect of differential reddening reported in the
cluster (Calamida et al., 2005; Bellini et al., 2017b) wherein we included
$A_{V}$ as a fit parameter with a range 0.279 - 0.775 mag corresponding to
$E(B-V)$ = 0.09 - 0.25 mag, keeping all other parameter ranges as in the last
column of Table 1.

Table 1: Models and parameter ranges adopted to fit the SEDs of hot HB stars
and WDs

Model Parameter Available range Adopted range Hot HB stars [0.5ex]3.5cm1pt2pt
[0.5ex]3.5cm1pt2pt [0.5ex]3.5cm1pt2pt [0.5ex]3.5cm1pt2pt Kurucz ODFNEW/NOVERa
$T_{\rm eff}$ 3 500 to 50 000 K 10 000 to 50 000 K $\log g$ 0 to 5 dex 3 to 5
dex [Fe/H] $-$4.0 to 0.5 dex $-$2.5 to $-$0.5 dex TMAP Grid 2b $T_{\rm eff}$
20 000 to 150 000 K 20 000 to 100 000 K $\log g$ 4 to 9 dex 4 to 5.5 dex TMAP
Grid 4b $T_{\rm eff}$ 20 000 to 150 000 K 20 000 to 100 000 K $\log g$ 4 to 9
dex 4 to 5.5 dex H mass fraction 0 to 1 0 to 1 TMAP Tübingenb $T_{\rm eff}$ 30
000 to 1 000 000 K 30 000 to 100 000 K $\log g$ 3.8 to 9 dex 3.8 to 5.5 dex H
mass fraction 0 to 1 full range He mass fraction 0 to 1 full range Pacheco et
al. (2021) $T_{\rm eff}$ 10 000 to 65 000 K full range $\log g$ 4.5 to 6.5 dex
4.5 to 5.5 dex [Fe/H] $-$1.5 to 0.0 dex $-$1.5 dex log[He/H] $-$4.98 to 3.62
full range Husfeld et al. (1989) $T_{\rm eff}$ 35 000 to 80 000 K full range
$\log g$ 4.0 to 7.0 dex 4.0 to 5.5 dex YHe 0.0 to 0.7 dex full range WDs
[0.5ex]3.5cm1pt2pt [0.5ex]3.5cm1pt2pt [0.5ex]3.5cm1pt2pt [0.5ex]3.5cm1pt2pt
Koesterc $T_{\rm eff}$ 5 000 to 80 000 K full range $\log g$ 6.5 to 9.5 dex
full range Levenhagend $T_{\rm eff}$ 17 000 to 100 000 K full range $\log g$
7.0 to 9.5 dex full range a [$\alpha$/Fe] = 0.4 dex; Castelli & Kurucz (2003)
b Werner & Dreizler (1999); Werner et al. (2003); Rauch & Deetjen (2003) c
Koester (2010) d Levenhagen et al. (2017)

The top left panel of Fig. 4 shows the FUV-optical CMD highlighting the sample
of hHBs analyzed. Among the inner region stars, we chose all the 421 HBs bluer
than the knee point in the CMD (at color $\sim$ 2.0 mag), which are shown with
red circles and denoted as OC hHB-I. For these stars, the UVIT photometry in
two filters was combined with the photometric data in 18 HST WFC3/UVIS filters
from Bellini et al. (2017a). Among the outer sources, we chose the 150 extreme
HB (EHB; $T_{\rm eff}$ $\gtrsim$ 20 000 K) stars with confirmed cluster
membership obtained through a cross-match with the sample of Latour et al.
(2018) (shown with blue circles and denoted as OC EHB-O). The SEDs of these
stars were constructed by complementing the UVIT photometry with the data in
five optical filters from the catalog of Stetson et al. (2019). We thus
derived the physical parameters for a total of 571 hHBs, using the three
approaches mentioned above. Since the results were found not to differ much,
the discussions below are based on the first approach (also shown in the
figure).

Good fits, with $Vgf_{b}$ $<$ 15 (Rebassa-Mansergas et al., 2021), were
achieved for about 97% of the hHBs. The middle left panel of Fig 4 shows the
Hertzsprung–Russell (H-R) diagram for these stars along with the same ZAHB
models as in Fig. 2, early and late hot-flasher (EHF & LHF) models (Cassisi et
al., 2003) and a 0.44 $M_{\odot}$ He-core DA-type WD model with $Y_{ini}$ =
0.4 dex, $Z$ = 0.0005 dex progenitor (Althaus et al., 2017). Most of the stars
cooler than log $T_{\rm eff}$ $\sim$ 4.2 lie within the range of the ZAHB
models. A significant fraction within log $T_{\rm eff}$ $\sim$ 4.2 to 4.5 are
fainter than any of the ZAHB models. Their luminosity decreases with $T_{\rm
eff}$ reaching a minimum at log $T_{\rm eff}$ $\sim$ 4.4 which then increases
further. The hHBs within the log $T_{\rm eff}$ $\sim$ 4.5 to 4.65 are lying on
the EHF and LHF tracks. The ones hotter than log $T_{\rm eff}$ $\sim$ 4.6
follow the 0.44 $M_{\odot}$ WD model. In the bottom left panel, the log (R/R⊙)
of hHBs are plotted as a function of the log $T_{\rm eff}$, where the low-
luminous hHBs of $\omega$ Cen are found also to be smaller in size.

Figure 4: Comparison of the FUV-optical CMD, H-R diagram, log $T_{\rm eff}$ vs
log ($R/R_{\odot}$) plots for $\omega$ Cen (OC) and M13 with focus on the hHB
population and WDs. The -I (-O) denotes stars within the inner (outer) region.
The parameters corresponding to ZAHB models in the middle left panel are as
follows - ZAHB 1 : [Fe/H] = $-$2.20 dex, Y = 0.247 dex; ZAHB 2 : [Fe/H] =
$-$0.6 dex, Y = 0.257 dex; and ZAHB 3 = [Fe/H] = 0.06 dex, Y = 0.32 dex. LHF
is a late hot flasher model with [M/H]=$-$1.018 dex, Y = 0.250 dex, MZAHB =
0.490 $M_{\odot}$ and EHF is an early hot flasher model with [M/H] = $-$1.90
dex, Y = 0.247 dex and MZAHB = 0.502 $M_{\odot}$.

###  5.2 WDs

The top right panel of Fig. 4 shows the FUV-optical CMD highlighting the WD
sample chosen for SED-fitting. There are 77 (68) WD candidates from the inner
(outer) region represented by red (blue) star symbols and denoted as OC WD-I
(OC WD-O), whose SEDs were fitted using models and parameters tabulated in
Table 1. While inspecting the SEDs, we found about 8 outer WDs showing UV
excess. Their SEDs could not be fit with single WD model and hence were not
considered further. We also excluded the fits with $Vgf_{b}$ $>$ 15\. The SED
parameters for the rest of the sample (135 stars) are shown in the H-R diagram
on the middle right panel of Fig 4 along with two He-core models of masses
0.44 $M_{\odot}$ and 0.46 $M_{\odot}$ with He-rich ($Y_{ini}$ = 0.4 dex), $Z$
= 0.0005 dex progenitors (Althaus et al., 2017) 555Note that the adopted He-
core WD models do not result from binary evolution see Althaus et al. 2017 for
details.. Most stars lie in between the range of the models. The bottom right
panel shows the (log $R/R_{\odot}$) of the WDs as a function of the log
$T_{\rm eff}$, where the two populations of the WDs match well, except for a
small number of cooler and larger WDs in the outer $\omega$ Cen.

##  6 Comparison of hot populations in Omega Centauri and M13

To further understand the peculiarities seen in the properties of hot stellar
populations of $\omega$ Cen, we compared them with those of another massive
GC, M13 (or NGC 6205). M13 has [Fe/H] = $-1.53$ dex (H96) similar to the
[Fe/H] avg of $\omega$ Cen with $\Delta$Ymax $\sim$ 0.05 dex (Dalessandro et
al., 2013; Milone et al., 2018) and age $\approx$ 13 Gyr (Denissenkov et al.,
2017). M13 was also observed using UVIT as part of GlobULeS and the detailed
study has been carried out by Kumar et al. 2022 . We obtained the final
photometric data and the SED-fit results of HBs (in the range 11 500 K $\leq$
$T_{\rm eff}$ $\leq$ 20 000 K; iHBs) and WDs from the authors. These are
highlighted in yellow, black and light green symbols among the rest of the M13
FUV sources (cyan) on the FUV-optical CMDs (top panels of Fig. 4). The
$\omega$ Cen populations with $m_{F148W}-m_{F438W}\lesssim 2$ are clearly
fainter in the FUV, when compared to those of M13, whereas the locations of
redder stars match well.

The $\omega$ Cen hHBs are on an average less luminous than their counterparts
in M13 and the latter also fall within the range of the ZAHB models as seen in
the left middle panel. In the log $T_{\rm eff}$ vs log ($R/R_{\odot}$) plot, a
few of the $\omega$ Cen hHBs (mostly near log $T_{\rm eff}$ $\sim$ 4.4) are
found to have smaller radii than their M13 counterparts. This could explain
their lower luminosities. The above may also imply that a fraction of hHBs in
$\omega$ Cen are less massive than those of M13. The WDs in both clusters
occupy similar positions in the H-R diagram and the log $T_{\rm eff}$ vs. $R$
plot on the middle and bottom right panels respectively.

##  7 Discussion and Summary

The first comprehensive FUV study of $\omega$ Cen reveals that the HBs bluer
than the knee point in the FUV-optical CMD and the WDs are fainter in the FUV
by about $\sim$ 0.5 mag than canonical expectations and in comparison with
populations of another cluster having similar properties, namely, M13. Moni
Bidin et al. (2012), by deriving color-temperature relations, found analogous
results uniquely for $\omega$ Cen hHBs in the $U$ band while detecting no
anomaly in the $B$ and $V$ bands. The authors were unable to fully account for
this.

We simulated the HB and compared it with observations to estimate He-
enhancements, metallicities, and ages of subpopulations. We find that at least
five subpopulations with three He-rich ones are needed to explain the observed
HB CMDs. As well known, it would be challenging to determine metallicity and
age using HB CMDs only. However, in terms of HB morphology, we conclude that a
considerable amount of He-enhancement is inevitable to explain the hHBs in FUV
and optical CMDs. The fainter FUV magnitudes of hHBs could be due to the
sensitivity of FUV bands to the $Y_{ini}$ range (Chung et al., 2017). The
derived parameters of the subpopulations are also comparable to the studies by
Joo & Lee (2013). We find the He-rich younger subpopulations ($\sim$ 24%) to
be radially more segregated than the He-normal older subpopulations ($\sim$
76%), which is expected if the second-generation stars form from the ejecta of
intermediate-mass asymptotic giant branch stars (D’Ercole et al., 2008).
Bellini et al. (2009) reported similar results for He-rich MS stars. The
ranges in age, metallicity and He content that are needed to fit the observed
HB distribution provide constraints on the $\omega$ Cen formation models.

The properties of hHBs in $\omega$ Cen and M13 are in general comparable,
except for a small fraction of low luminous ones in $\omega$ Cen. Through
spectroscopic measurements, Moni Bidin et al. (2011) and Latour et al. (2018)
reported a mean mass lower than canonical expectations for EHB stars in
$\omega$ Cen (0.38 M⊙) and could not explain this conundrum.

The WDs in $\omega$ Cen and M13 have similar physical parameters. However,
unlike $\omega$ Cen, M13 is not known to host extreme He-rich stars that can
form He-core WDs from single stellar evolution. Chen et al. (2021) suggested
that the bright WDs in M13 are the result of slow cooling due to the residual
hydrogen-burning on the C/O WD surface. Hence, it is possible that some of the
FUV-detected WDs in $\omega$ Cen are such slowly cooling C/O WDs. Photometric
observations of WD pulsations in the future can shed more light in this
direction (Althaus et al., 2017).

We thank the anonymous referee for the helpful comments and suggestions. We
thank Andrea Bellini for making the HST photometric data available. We are
grateful to Pierre Bergeron & Leandro Althaus for making available the WD
models. DSP thanks Ranjan Kumar for sharing the results of M13 and Simone
Zaggia for the useful 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. AS
acknowledges support from SERB Power fellowship. C.C. acknowledges support
from the National Research Foundation of Korea (2022R1A2C3002992,
2022R1A6A1A03053472). NWCL gratefully acknowledges the generous support of a
Fondecyt Iniciación grant 11180005, as well as support from Millenium Nucleus
NCN19-058 (TITANs) and funding via the BASAL Centro de Excelencia en
Astrofisica y Tecnologias Afines (CATA) grant PFB-06/2007. NWCL also thanks
support from ANID BASAL project ACE210002 and ANID BASAL projects ACE210002
and FB210003. AARV acknowledges the funding from ANID, Millennium Science
Initiative, ICN12_009.

##  Appendix A Cross-match of UVIT detections with different catalogs

###  A.1 UVIT-HST cross-match

The optical counterparts of the FUV detections were identified by cross-
matching those within the core radius of the cluster ($r_{c}$ = $None$) with
the HST dataset from Bellini et al. (2017a). This astrophotometric dataset was
available in 18 WFC3/UVIS bands and 8 WFC3/IR bands for 478,477 stars.
However, we used only the WFC3/UVIS data since the IR photometry did not
include the information of the saturated stars, many of which belonged to the
HB. The saturated stars also did not have proper motion (PM) measurements in
the catalog. Hence, we did not perform a filtering of the sources based on
cluster membership. A direct cross-match of the UVIT and HST catalogs would
result in many spurious identifications because of the differences in the
spatial resolution and astrometric accuracy. Hence, we chose a subset of stars
from the HST dataset which included only the UV-bright stellar populations
such as HB, post-HB, BSSs and WDs. The HST photometry in Bellini et al.
(2017a) was measured with three methods, each of which worked best in
different magnitude regimes. Following the same selection criteria as the
authors, we used the results of method one photometry for HB, pHB and BSS
stars and those of method two for WDs. The UV color-magnitude plane
$m_{F275W}-m_{F336W}$ vs. $m_{F275W}$ was used to select the HB, pHB and BSS
stars and the WDs were selected from the $m_{F438W}-m_{F606W}$ vs. $m_{F438W}$
plane. This HST subset was cross-matched with the UVIT catalog with a maximum
match radius of $None$, using TOPCAT and about 963 stars were found to have
unique counterparts. We also manually verified that all the cross-
identifications were accurate. A counterpart could not be identified correctly
for one star at R.A. = 201.64700∘ and Decl. = $-$47.50401∘ in the UVIT catalog
(it is not included in HST catalog although it is visible in F555W image). So
this star is excluded.

###  A.2 UVIT-ground data-Gaia EDR3 cross-match

There were several UV-bright stars lying outside the HST FOV. In order to
analyze these stars and plot them in the UV-optical CMD, we used the ground-
based optical dataset in the $UBVRI$ filters from Stetson et al. (2019) and
the Gaia EDR3 EDR3-based catalog from Vasiliev & Baumgardt (2021). The latter
also included cluster membership probability estimates based on PM
measurements. For the cross-match, we first created a subset of stars from the
ground-based catalog, selecting only the population expected to be bright in
UV. This subset was matched with the UVIT detections with a maximum cross-
match radius of $None$. The number of stars common in both was about 2725. In
order to identify the cluster members among them, we matched this set further
with the Gaia EDR3-based catalog of Vasiliev & Baumgardt (2021). About 1771
stars were found to have membership probability more than $0.5$. However,
there were about 803 UV-bright stars which were not included in the Gaia EDR3
EDR3 catalog. Hence, their membership status is unknown. Finally, to plot all
the sources in similar color-magnitude plane, we transformed the Johnson-
Cousins $B$, $V$, and $I$ magnitudes of the stars in the outer region to the
corresponding HST WFC3/UVIS filters (namely, $F438W$, $F606W$, and $F814W$),
using the equations from Harris (2018).

##  Appendix B Checks for effects due to instrument calibration or analysis
procedure

We checked for various aspects that could possibly result in the bias observed
in the FUV-optical CMDs. Firstly, effects due to UVIT instrument-related
aspects such as changes in calibration, sensitivity and the slope of the
transmission window were inspected. These were ruled out as magnitudes
obtained from the recent observations of FUV-bright sources in the secondary
calibration source, open cluster NGC 188, and a previously studied GC NGC
2808, were consistent with earlier estimates. Next, we examined effects due to
data reduction and analysis procedures. We obtained similar magnitudes (within
$\sim$ 0.1 mag) with science-ready images produced using CCDLAB and the
official UVIT L2 pipeline, ruling out any issue due to the data-reduction
pipeline. Photometric analysis with IRAF was checked independently and found
to be consistent. Lastly, we looked for possible changes introduced due to the
transformation of optical magnitudes from the Vega to AB system. The bias was
found even when the filter with the smallest transformation factor (F606W) was
used, ruling out this possibility. In the top panels of Figure 5, we show the
CMDs constructed using the UVIT F148W and the HST F275W (NUV) and F336W (UV
wide) filters, consisting of the 963 UVIT-HST common detections. We find that
the hHBs and WDs show a deviation from model predictions in these CMDs also.
Additionally, the CMD constructed using only the HST filters F275W and F336W,
with the data from Bellini et al. (2017a), also shows the deviation,
supporting our analysis (bottom left panel of Fig. 5). In the bottom right
panel of Fig 5, we show the CMD with sources detected in both the UVIT FUV
filters.

(a)

(b)

(c)

Figure 5: Top panels : The UVIT/F148W$-$HST/F275W vs HST/F275W and
UVIT/F148W$-$HST/F336W vs HST/F336W CMDs showing the UVIT-HST common
detections (963 stars), along with the theoretical stellar evolutionary models
shown in Fig. 2. Bottom left : The F275W$-$F336W vs F275W CMD with the same
963 stars as above, is shown. Bottom right : The CMD consisting of all the
sources detected in both the UVIT F148W and F169M filters, along with
evolutionary models.

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