The First Extensive Exploration of UV-bright Stars in the Globular Cluster NGC 2808

Globular clusters (GCs) are ideal astrophysical laboratories to test the theories of stellar evolution, especially the late evolutionary stages of low-mass stars. According to canonical stellar evolution models, the post-helium-core-burning (pHeCB) or post-horizontal branch (pHB) evolution of a star depends strongly on its envelope mass (Dorman et al. 1993, 1995). After the depletion of helium (He) in the core, horizontal branch (HB) stars with the highest envelope masses enter the asymptotic giant branch (AGB) phase, undergo thermal pulsations, and end up losing their envelopes to become extremely hot stars with constant luminosity. Known as post-AGB (pAGB) stars, these are short-lived (lifetime < 10⁵ yr) with luminosity $\mathrm{log}(L/{L}_{\odot })\geqslant 3.1$. The HB stars with slightly lower envelope masses (>0.02 M_⊙) ascend the AGB but do not undergo thermal pulsations in this phase. They eventually lose their envelopes and evolve toward higher temperatures with slightly lower luminosities ($\mathrm{log}(L/{L}_{\odot })\,\sim$ 2.65–3.1) than the pAGB stars. These are known as post-(early)-AGB (p(e)AGB) stars (Brocato et al. 1990) and have a lifetime of ≃10⁵ yr. After core He exhaustion, HB stars with the lowest envelope masses cannot ascend the AGB and hence directly evolve toward the white dwarf cooling curve with a slight enhancement in luminosity and are referred to as AGB-manqué stars (Greggio & Renzini 1990). The range of their luminosities is $\mathrm{log}(L/{L}_{\odot })\,\sim$ 1.8–2.65, with lifetimes of 20–40 Myr (Moehler et al. 2019). These late phases of low-mass stellar evolution are the least understood owing to uncertainties in the C/O core size (Charpinet et al. 2011; Constantino et al. 2015) and stellar winds in the red giant branch (RGB) phase that determine the envelope mass of HB stars (McDonald & Zijlstra 2015; Salaris et al. 2016). Due to the lack of detections of stars in these quickly evolving stages, the existing pHB models have not been tested extensively and have room for improvement.

A few pHeCB stars in various evolutionary stages are found in the ultraviolet (UV) images of GCs as highly prominent, luminous stars. Referred to as UV-bright stars (Zinn et al. 1972), these are observed to be brighter than the HB stars by 1 mag or more in the far-UV (FUV) with FUV–near-UV (NUV) color <0.7 mag (Schiavon et al. 2012). Originally, these were defined as stars brighter than the HB and bluer than the RGB. They were looked for as stars whose U-band magnitudes were brighter than those of any other star in the GC (e.g., Zinn et al. 1972). Since these searches were based on optical observations, they were biased toward the most luminous pAGB stars and unable to detect the less luminous p(e)AGB and AGB-manqué stars (Moehler 2001). Moreover, most of the stars detected were cooler than 30,000 K, although there were theoretical predictions of even hotter pAGB stars. The crowded cores of GCs posed yet another difficulty for ground-based optical observations.

The space missions, with the capability to obtain images in the UV, opened a whole new arena for the study of hot stars in GCs. The cooler stellar populations, such as main-sequence (MS) and RGB stars, are suppressed in the UV wavelengths, which helps to produce images with reduced stellar crowding in the central regions. The UV-bright stars, along with the hot extreme-HB (EHB) stars, contribute significantly to the UV luminosity of old stellar systems like GCs (Greggio & Renzini 1990, 1999; O'Connell 1999). Hence, these stars are speculated to be the reason for the UV-upturn phenomenon in elliptical galaxies (Greggio & Renzini 1990, 1999; Dorman et al. 1995; Brown et al. 1997, 2000). Thus, UV study rather than optical is critical to perform an accurate evaluation of the contribution of hot stars in late evolutionary stages to the UV luminosity of old systems. For a detailed review of hot stars in GCs, see Moehler (2001, 2010). Schiavon et al. (2012) presented a catalog of candidate pAGB, p(e)AGB, and AGB-manqué stars in 44 Galactic GCs, including NGC 2808, using Galaxy Evolution Explorer (GALEX) FUV and NUV observations. However, this study was limited by the spatial resolution (∼5'') of GALEX. Also, the membership information for these stars was not available then.

Moehler et al. (2019) combined photometric observations from various missions, such as the Ultraviolet Imaging Telescope (UIT; Stecher et al. 1997), GALEX, Swift Ultraviolet-Optical Telescope (UVOT), and Hubble Space Telescope (HST), to obtain a census of UV-bright stars in 78 GCs. The atmospheric parameters of the brightest pHB stars in the sample (including three stars from NGC 2808), derived from optical spectroscopic observations, were used to assess their evolutionary status. The numbers of theoretically predicted and observed hot pAGB stars for 17 GCs (excluding NGC 2808) were found to be comparable, though affected by poor statistics. The catalog of such stars in their list of clusters is yet to be published. Several optical spectroscopic studies of previously identified bright pHB stars have been performed to shed light on their chemistry and evolutionary status (Thompson et al. 2007; Chayer et al. 2015; Dixon et al. 2017, 2019).

Jain et al. (2019) studied NGC 2808 using the data obtained from the Ultra Violet Imaging Telescope (UVIT) aboard the Indian space satellite, AstroSat. They reported the detection of hot stars belonging to different classes, such as EHB, blue HB (BHB), red HB (RHB), blue hook (BHk), pAGB, and blue straggler stars (BSSs), from UV color–magnitude diagrams (CMDs), albeit without membership analysis. They focused on the photometric gaps in the UV CMDs and the multiple stellar populations in the cluster. The hot stellar populations of this cluster have also been explored using the UV and optical data from HST in the works of Brown et al. (2001, 2010, 2012), Dieball et al. (2005), Castellani et al. (2006), Dalessandro et al. (2011) and so on.

In this work, we study the unexplored UV-bright member stars in NGC 2808. This is one of the massive and dense GCs with an age = 10.9 ± 0.7 Gyr (Massari et al. 2016), [Fe/H] = −1.14 dex, and located at a distance of 9.6 kpc (Harris 1996, 2010 edition, hereafter H96). We combine the archival UV data from the UVIT with the UV-optical observations from the HST (Brown et al. 2001; Piotto et al. 2015; Nardiello et al. 2018) and optical observations from Gaia (Gaia Collaboration et al. 2018) and ground-based telescopes (Stetson et al. 2019). The member stars in the inner (central region within $\sim 2\buildrel{\,\prime}\over{.} 7\times 2\buildrel{\,\prime}\over{.} 7$, covered by HST WFC3/UVIS) and outer (region outside the HST field of view, FOV) regions of the cluster are identified utilizing the proper motion–based membership information from the HST and Gaia catalogs, respectively. We present the catalog of UV-bright member stars in this cluster (from inner to outer regions) for the first time, along with their surface parameters derived through the analysis of their spectral energy distributions (SEDs). We also investigate the evolutionary status of these UV-bright stars and compare the observed number of hot p(e)AGB³ stars with the expected number derived from theoretical estimations. Though Jain et al. (2019) used the UVIT data to study the HB population, here we aim to focus on the UV-bright members of the cluster and parameterize them to shed light on the short-lived late evolutionary phases of low-mass stars.

The layout of the paper is as follows. Section 2 gives an account of the observations and adopted data reduction procedure. The cross-match of the different data sets and the UV-optical CMDs are presented in Section 3. Sections 4–6 describe the observed UV-bright stars and their SEDs and evolutionary phases, respectively. The results are discussed in Section 7, and a summary is presented in Section 8.

This work utilizes data from the UVIT on board AstroSat, India's first multiwavelength space observatory. The UVIT consists of twin telescopes, each of 38 cm diameter, one dedicated to FUV (λ = 1300–1800 Å) and the other to NUV (λ = 2000–3000 Å) and VIS (λ = 3200–5500 Å) passbands. The VIS data are used for drift-correcting the images. The UVIT has a circular FOV of $28^{\prime}$ diameter and consists of multiple filters in each passband. The FUV and NUV detectors operate in photon-counting mode, and the VIS detector operates in integration mode. Further details regarding the instrument and calibration can be found in Tandon et al. (2017).

We used the archival UVIT data for NGC 2808 in two FUV (F154W and F169M) and four NUV (N242W, N245M, N263M, and N279N) filters. The images were created using the CCDLAB software package (Postma & Leahy 2017) by correcting for the spacecraft drift, geometrical distortions, and flat-fielding. The images created for each orbit were then aligned and merged to create the final science-ready image in each filter. The final exposure times for the science-ready image in various filters are tabulated in Table 1. The UVIT image of NGC 2808 is shown in Figure 1, with blue corresponding to F154W detections and green to those in N242W.

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2.1. Photometry

Crowded-field photometry was performed on the UVIT images using the DAOPHOT software package of IRAF/NOAO (Stetson 1987) through the following steps. Stars in the images were located using the DAOFIND task, and their aperture photometry magnitudes were computed using the PHOT task. The model point-spread function (PSF) was generated using a few bright isolated stars in the image. It was then fitted to all of the detected stars, and the PSF-fitted magnitudes were obtained using the ALLSTAR task. The curve-of-growth technique was used to calculate the aperture correction value, which was then applied to the magnitudes. To get the final magnitudes in each filter, saturation correction was applied according to the method described in Tandon et al. (2017). The number of detected stars in various filters is presented in Table 1. The plots of magnitude versus PSF fit error for different filters are shown in Figure 2.

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The magnitudes in all filters were corrected for extinction by adopting a reddening value, E(B − V) = 0.22 mag (H96), and the ratio of total to selective extinction, R_V = 3.1. The corresponding extinction coefficient in the V band is A_V = 0.682 mag. The extinction coefficients presented in Table 1 were calculated using the reddening law of Cardelli et al. (1989).

3.1. Cross-match of the UVIT Data with the HST Data

In order to identify various stars detected in the UVIT images, we cross-matched them with the HST UV Globular Cluster Survey (HUGS) catalog (Piotto et al. 2015; Nardiello et al. 2018) in the inner region of the cluster (within $\sim 2\buildrel{\,\prime}\over{.} 7\times 2\buildrel{\,\prime}\over{.} 7$). The HUGS astrophotometric catalog consists of data in the WFC3/UVIS F275W (NUV), F336W (U), and F438W (B) filters, along with the ACS/WFC F606W (V) and F814W (I) filters. The catalog also provides cluster membership probabilities estimated based on stellar proper motions. We selected stars with membership probabilities greater than 90% as cluster members. As we are interested in the UV-bright population of this cluster, we chose stars that are expected to be bright in the UV, such as the pHB and HB stars and BSSs from the HST CMD, and identified their unique counterparts in the UVIT images as explained below.

The CMDs and color–color plane (CCP) using the HST data for the inner region of the cluster are shown in Figure 3, where the stars are color-coded according to their classification. The top right panel shows the 28 identified pHB member stars. The bottom right panel shows the 176 identified BSS members as per the procedure described in Raso et al. (2017). The division of HB into RHB, BHB, EHB, and B gap objects and BHk was done using the m_F275W − m_F438W versus C_{F275W,F336W,F438W} plane (Brown et al. 2016), as shown in the left panels. The classification adopted here is similar to that of Brown et al. (2016). The RR Lyrae stars were identified by cross-matching with the data from Kunder et al. (2013). Since the HST images have a much better spatial resolution, a simple cross-match with the UVIT data may yield wrong identifications due to crowding in the innermost region of the cluster. A case of multiple HST stars for a single UVIT detection is demonstrated in Figure 4, where we have overlaid the HST F275W and UVIT F154W images. The gray patch is the UVIT detection, whereas in black are the stars from the HST in a region of about 5'' × 5''. In order to avoid such wrong/multiple identifications, we used a python code that returns only those HST stars among the pHB, HB, and BSS stars, which have no neighbors within a 18 radius (maximum UVIT PSF) of them. As the crowding is maximum near the cluster center, no HST–UVIT cross-match was performed for the innermost region (radius < 30''). Finally, 491 stars were selected from the HST catalog, and these were then cross-matched with the UVIT-detected stars with a maximum match radius of 1''. All of the cross-matched stars were found to have a photometric error of <0.2 mag in all UVIT filters.

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3.2. Cross-match of the UVIT Data with the Gaia and Ground-based Optical Data

3.3. CMDs

We constructed the UV-optical and UV CMDs for the inner and outer regions with the cross-matched members. The updated Bag of Stellar Tracks and Isochrones (BaSTI) theoretical zero-age HB (ZAHB) and terminal-age HB (TAHB; end of He-burning phase) models from Hidalgo et al. (2018) were fitted to the HB sequence of the cluster CMD. These models were generated in the UVIT, HST/WFC3, and HST/ACS filters by choosing metallicity [Fe/H] = −0.9 dex, He abundance = 0.249, solar scaled [α/Fe] = 0.0, and no convective overshoot. These models take into account the effects due to atomic diffusion at the hotter end of the HB, as is evident from the close match with the CMDs.

Figure 5 shows the CMD of the cluster for the inner region using the HST data. Stars that are used for the cross-match with the UVIT data are shown, along with the ZAHB and TAHB models. The gray dots represent stars with more than 90% membership probability.

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Figure 6 shows the optical and FUV-optical CMDs for all of the members detected in the F154W UVIT filter. To plot these CMDs, we converted the F438W and F606W magnitudes from the VEGA system to the AB system.⁴ The filled and open symbols represent the stars located in the inner and outer regions of the cluster, respectively. In the FUV, we have mainly detected the hotter part of the HB (BHB and EHB), BHk, pHB, and a few BSSs. Three RR Lyrae variables are also identified. In the m_F154W − m_F606W versus m_F154W plot (shown in the right panel), the BHB stars have a relatively tight distribution in magnitude, whereas the EHB, B gap, and BHk stars show a spread in the m_F154W magnitude with respect to the ZAHB track. Many of them are also found to be fainter than the ZAHB model. One of the detected BSSs, located in the outer region, is very bright in the F154W filter. The RHB stars are hardly detected, as they are not hot enough to emit in FUV wavelengths. The detected pHB stars are found to be brighter than the TAHB with a spread of about 2 mag in the F154W filter and 4 mag in the FUV-optical color. We discuss these UV-bright stars in detail in the next section.

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Similarly, Figure 7 shows the optical and NUV-optical CMDs for stars detected in the N245M UVIT filter. In the N245M filter, apart from the abovementioned sequences, we have detected the cooler RHB population as well. The RHB stars form a tight sequence when compared to the rest of the HB sequence and are located close to the ZAHB track. On the other hand, the other HB phases show a large spread, with many of them located above and below the ZAHB track. The BHk sequence has the largest statistically significant spread in the N245M magnitude, as is evident from the m_N245M − m_F606W versus m_N245M CMD (right panel). The bright BSS is found to be slightly fainter than the faintest BHB star.

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The UV CMDs for all of the stars common in the UVIT filters F154W and N245M are shown in Figure 8. In the m_F154W − m_N245M versus m_N245M CMD (left panel), the HB stars show a progressive reduction in the N245M magnitude as a function of m_F154W − m_N245M color. In the case of the m_F154W − m_N245M versus m_F154W CMD, the HB stars with color <0.0 mag have a horizontal sequence. The hot BHB, EHB, B gap, and BHk stars get mixed up in these CMDs. The bright BSS is found to be slightly fainter than the BHB stars, with an m_F154W − m_N245M color of ∼0.0 mag.

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Table 2 tabulates the number of stars belonging to different categories detected in each UVIT filter. In the outer region, since cluster members were selected based on Gaia data with an approximate limiting magnitude of V ≃ 20.5 mag, we have zero stars belonging to the optically faint B gap and BHk categories. We plan to perform a separate detailed study of the HB stars and BSSs presented in this section in the near future.

Table 2.  Number of pHB Stars, BSSs, and Different Categories of HB Stars in NGC 2808 Detected in Each UVIT Filter in the Region Covered by HST

Filter	NpHB	NBHk	NBgap	NEHB	NBHB	NRR Lyrae	NRHB	NBSS
F154W	11(7)	53(0)	12(0)	48(21)	147(65)	3(0)	2(0)	4(3)
F169M	11(7)	52(0)	12(0)	49(21)	146(64)	2(1)	1(0)	3(1)
N242W	11(7)	49(0)	11(0)	45(21)	146(66)	4(1)	119(124)	9(28)
N245M	11(7)	48(0)	12(0)	45(20)	146(66)	2(1)	65(23)	5(10)
N263M	11(7)	23(0)	8(0)	29(17)	140(66)	3(1)	38(4)	4(1)
N279N	11(7)	40(0)	10(0)	40(17)	147(64)	5(1)	103(49)	8(2)

Note. In parentheses are the numbers of these stars detected in the outer region of the cluster.

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The main aim of this study was to identify and characterize the pHB stars in the inner and outer regions of the cluster. Among the UVIT-detected stars in the outer regions, some bright stars were found to be nonmembers based on the list of possible members from Gaia Collaboration et al. (2018). We reassessed the membership of these stars in the outer region using methods presented in Singh et al. (2020), who also used the Gaia DR2 data. Two stars were found to have a membership probability of ∼90%. One star was found to have ∼40% membership probability, and this was studied by Moehler et al. (2019) using optical spectroscopy. We included these three stars along with the other pHB stars for further study.

From our analysis, we find a total of 34 UV-bright member stars in this cluster that could be classified as pHB stars. Of these, 18 stars have FUV and NUV flux measurements from the UVIT and are marked with purple triangles in the UV-optical and UV CMDs in Figures 6–8. All of these stars satisfy the observational criteria for them to be classified as UV-bright stars as laid out in Schiavon et al. (2012); i.e., they are brighter than the ZAHB by more than 1 mag in the FUV, and the FUV−NUV color is less than 0.7 mag. The UVIT magnitudes and magnitude errors for these stars are presented in the Appendix. Figure 9 shows the spatial locations of all 34 observed UV-bright stars marked over the UVIT F154W image. Here 11 out of the 18 UVIT-detected pHB stars (shown by red circles) lie in the HST FOV, and they have been uniquely cross-matched. This can be seen in Figure 10, where we have overlaid the HST F275W and UVIT F154W images for these stars. We also note that similar unique cross-matches are achieved for all stars shown in the CMDs. The remaining 16 UV-bright stars (marked with blue circles in Figure 9) are located in the crowded innermost region of the cluster and hence could not be resolved by the UVIT. Among these, only four stars have FUV and NUV photometric measurements from the HST Space Telescope Imaging Spectrograph (STIS) instrument (Brown et al. 2001), whereas all 16 have NUV-optical data from the HUGS catalog.

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These multiwavelength photometric data for the UV-bright stars were used to determine their evolutionary status by estimating various parameters.

In order to estimate the parameters such as effective temperature (T_eff), luminosity (L), and radius (R) of the UV-bright stars, their SEDs were constructed with the available photometric data points. For this purpose, a virtual observatory functionality, the VO SED Analyser (VOSA; Bayo et al. 2008), was used. VOSA generates synthetic photometry for the chosen theoretical models using the transmission curves of the required photometric filters. The best-fit parameters of the SEDs were estimated by comparing the observed and synthetic photometric points using a χ² minimization method. The ${\chi }_{\mathrm{red}}^{2}$ value is calculated using the relation

$$\begin{eqnarray}&&{\chi }_{\mathrm{red}}^{2}=\displaystyle \frac{1}{N-{N}_{f}}\displaystyle \sum _{i=1}^{N}\left\{\displaystyle \frac{{\left({F}_{o,i}-{M}_{d}{F}_{m,i}\right)}^{2}}{{\sigma }_{o,i}^{2}}\right\},\end{eqnarray} \tag{ 1 }$$

where N is the number of photometric points, N_f is the number of fitted parameters for the model, F_o,i is the observed flux, F_m,i is the theoretical flux predicted by the model, ${M}_{d}={\left(\tfrac{R}{D}\right)}^{2}$ is the multiplicative dilution factor (where R is the radius of the star and D is the distance to the star), and σ_o,i is the error in the observed flux. We assumed a distance of D = 9.6 kpc and E(B − V) = 0.22 mag (H96) for all stars in the cluster. VOSA uses the Fitzpatrick reddening relation (Fitzpatrick 1999) to account for the extinction in the observed photometric points.

For all UV-bright stars except two, we used the Kurucz stellar atmospheric models (Castelli et al. 1997; Castelli & Kurucz 2003), and log g, [Fe/H], and T_eff are the possible free parameters for fitting the SED. In these models, the ranges of admissible values for the free parameters are 0.0–5.0 for log g, −2.5–0.5 for [Fe/H], and 3500–50,000 K for T_eff. For the remaining two stars, i.e., stars 3 and 32 in Table 3, the Tübingen NLTE Model Atmosphere Package (TMAP Tübingen; Werner & Dreizler 1999; Rauch & Deetjen 2003; Werner et al. 2003) was used, as the Kurucz model parameter space was inadequate to fit the SEDs of these stars. The free parameters in these models include T_eff in the range 30,000–1,000,000 K, log g ranging from 3.8 to 9, and H, He mass fractions in the range 0–1.

Table 3.  Results of the SED Analysis of UV-bright Stars in the Cluster

ID	R.A.	Decl.	Model	Teff	ΔTeff	$\tfrac{L}{{L}_{\odot }}$	${\rm{\Delta }}\tfrac{L}{{L}_{\odot }}$	$\tfrac{R}{{R}_{\odot }}$	${\rm{\Delta }}\tfrac{R}{{R}_{\odot }}$	${\chi }_{\mathrm{red}}^{2}$	Nfit	Phot. Used
	(deg)	(deg)		(K)	(K)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
Star 1	137.96181	−64.84165	Kurucz	27,000	500	50.80	0.27	0.33	0.01	7.58	11	FUV, NUV, opt.
Star 2	138.02575	−64.84307	Kurucz	21,000	500	352.95	1.53	1.42	0.07	8.21	10	FUV, NUV, opt.
Star 3	138.06046	−64.86146	TMAP	80,000	3750	2857.45	0.88	0.28	0.03	3.31	8	FUV, NUV, opt.
Star 4	138.05040	−64.84379	Kurucz	39,000	500	781.10	0.95	0.61	0.02	4.51	9	FUV, NUV, opt.
Star 5	138.04719	−64.87492	Kurucz	27,000	500	59.54	0.25	0.35	0.01	2.34	10	FUV, NUV, opt.
Star 6	138.06813	−64.86459	Kurucz	12,500	125	108.50	1.11	2.20	0.04	6.86	11	FUV, NUV, opt.
Star 7	138.05264	−64.86779	Kurucz	22,000	500	85.73	0.44	0.64	0.03	3.36	9	FUV, NUV, opt.
Star 8	138.04842	−64.84887	Kurucz	16,000	500	117.20	0.96	1.41	0.09	6.44	10	FUV, NUV, opt.
Star 9	138.04760	−64.85790	Kurucz	17,000	500	109.80	0.78	1.21	0.07	3.50	10	FUV, NUV, opt.
Star 10	138.03820	−64.87028	Kurucz	22,000	500	106.20	0.62	0.71	0.03	5.78	10	FUV, NUV, opt.
Star 11	137.96088	−64.85092	Kurucz	26,000	500	79.93	0.32	0.44	0.02	3.94	9	FUV, NUV, opt.
Star 12	138.02716	−64.86694	Kurucz	25,000	500	102.60	0.87	0.54	0.02	0.10	7	FUV, NUV, opt.
Star 13	138.01470	−64.85891	Kurucz	15,000	500	128.83	2.02	1.68	0.11	0.09	7	FUV, NUV, opt.
Star 14	138.01349	−64.86046	Kurucz	27,000	500	86.65	0.09	0.42	0.02	4.86	7	FUV, NUV, opt.
Star 15	138.01173	−64.86674	Kurucz	26,000	500	131.15	0.22	0.56	0.02	1.59	7	FUV, NUV, opt.
Star 16	138.03578	−64.86580	Kurucz	23,000	500	54.90	0.04	0.47	0.02	1.39	5	NUV, opt.
Star 17	138.03122	−64.85554	Kurucz	25,000	500	41.40	0.02	0.34	0.01	8.76	5	NUV, opt.
Star 18	138.03010	−64.86050	Kurucz	22,000	500	211.00	0.07	1.00	0.05	6.01	5	NUV, opt.
Star 19	138.02244	−64.87728	Kurucz	45,000	500	633.00	0.10	0.41	0.01	1.33	5	NUV, opt.
Star 20	138.01776	−64.87794	Kurucz	27,000	500	72.00	0.03	0.39	0.01	1.98	5	NUV, opt.
Star 21	138.01103	−64.87463	Kurucz	24,000	500	49.30	0.08	0.41	0.02	3.75	5	NUV, opt.
Star 22	138.00244	−64.87014	Kurucz	22,000	500	102.00	0.69	0.69	0.03	0.02	5	NUV, opt.
Star 23	138.00133	−64.86623	Kurucz	50,000	500	113.00	0.02	0.14	0.00	4.61	5	NUV, opt.
Star 24	137.99932	−64.85673	Kurucz	50,000	500	97.80	0.13	0.13	0.00	3.77	5	NUV, opt.
Star 25	137.99187	−64.87307	Kurucz	35,000	500	56.10	0.18	0.20	0.01	0.33	5	NUV, opt.
Star 26	137.99182	−64.85956	Kurucz	27,000	500	67.70	0.32	0.38	0.01	0.11	5	NUV, opt.
Star 27	137.96443	−64.86377	Kurucz	50,000	500	988.00	1.22	0.42	0.01	0.26	5	NUV, opt.
Star 28	137.85352	−64.87929	Kurucz	26,000	500	65.36	0.97	0.39	0.02	2.58	15	FUV, NUV, opt.
Star 29	137.92453	−64.70158	Kurucz	32,000	500	145.80	1.09	0.39	0.01	2.66	15	FUV, NUV, opt.
Star 30	138.08369	−64.84865	Kurucz	25,000	500	98.59	1.03	0.52	0.02	2.89	13	FUV, NUV, opt.
Star 31	138.00728	−64.79293	Kurucz	23,000	500	251.00	2.12	0.99	0.04	4.49	14	FUV, NUV, opt.
Star 32	137.99974	−64.89071	TMAP	100,000	5000	3010.25	1.20	0.18	0.02	9.06	12	FUV, NUV, opt.
Star 33	138.02306	−64.89646	Kurucz	26,000	500	53.26	0.51	0.36	0.01	2.39	11	FUV, NUV, opt.
Star 34	138.09187	−64.87727	Kurucz	24,000	500	119.91	0.75	0.63	0.03	4.40	11	FUV, NUV, opt.

Note. Columns (1)–(3) show the ID, R.A., and decl. of the objects, respectively. The model used for the SED fit is shown in column (4). The estimated parameters, such as temperature, luminosity, and radius (in solar units), of the stars and the errors in these parameters are tabulated in columns (5)–(10). The errors in the parameters are derived as half the grid step around the best-fit value. Columns (11)–(13), respectively, show the reduced χ² value corresponding to the fit, the number of photometric points used for fitting, and the corresponding photometric bands. Stars 1–11 have photometry from the UVIT and HUGS. Stars 12–15 have data points from the HST STIS and HUGS. Stars 16–27 have photometry only from HUGS. Stars 28–34 have photometric points from UVIT, GALEX, Gaia, and ground-based optical data. In the last column, opt. stands for optical.

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To fit SEDs using Kurucz models, we fixed the [Fe/H] value at −1.0 dex, close to the value for the cluster. Additionally, we constrained the log g to range from 3 to 5 for the Kurucz models and 3.8 to 6 for the TMAP models. This is the observed range of log g values for stars in pHB evolutionary phases from previous studies (Moehler et al. 2019). The important parameters obtained from the SED analysis are tabulated in Table 3. For the two stars fitted with TMAP models, the best-fit values of the H and He mass fractions are 0.7383 and 0.2495 for star 3 and 0.8 and 0.2 for star 32. However, we note that SED fitting is not the optimal method to estimate the above parameters. We do not quote the log g values obtained from the SED fits, as the SED fitting technique does not provide accurate values of this parameter.

The SEDs for stars 1–11 contain the UVIT (FUV, NUV) and HST (NUV, optical) photometric data points. Stars 12–26, lying within the inner region of the cluster, could not be resolved by the UVIT. Hence, only the HST photometry was used to construct the SEDs of these stars. Four stars among these, namely, stars 12–15, have HST/STIS photometry (FUV, NUV) from Brown et al. (2001), apart from the NUV and optical HUGS data. For stars 27–34, which lie outside the HST FOV, we utilize the UVIT, GALEX (Schiavon et al. 2012), Gaia, and ground-based optical data for SED generation. Examples of SED fits for stars 3 and 28 are shown in Figure 11. The SEDs for the other UVIT-resolved stars are shown in the Appendix. The residuals shown in these plots were calculated for each data point as follows:

$$\begin{eqnarray}&&{\rm{R}}{\rm{e}}{\rm{s}}{\rm{i}}{\rm{d}}{\rm{u}}{\rm{a}}{\rm{l}}=\displaystyle \frac{{F}_{o}-{F}_{m}}{{F}_{o}},\end{eqnarray} \tag{ 2 }$$

where F_o and F_m are the observed and model fluxes corresponding to the photometric points.

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Figure 12 shows a histogram of the temperature distribution of the UV-bright stars in the cluster. The values range from 12,500 to 100,000 K with a maximum number of stars having a temperature between 20,000 and 30,000 K.

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Figure 13 shows the trends in the best-fit parameters of the 18 UV-bright stars with UVIT photometry in the m_F154W − m_N245M versus m_F154W CMD. The left, middle, and right panels display the trends in T_eff, luminosity, and radius, respectively. Among the five stars with the brightest m_F154W magnitudes, the hottest stars are also the most luminous and have the smallest radii. The coolest among these five stars have $\mathrm{log}(L/{L}_{\odot })\,\sim$ 2.5 and R/R_⊙ ∼ 1.0. The star with the brightest m_F154W magnitude has log T_eff ∼ 4.6, with a fairly high luminosity ($\mathrm{log}(L/{L}_{\odot })\,\sim$ 3) and a smaller radius (R/R_⊙ ∼ 0.5). Most of the remaining pHB stars with m_F154W fainter than 15.5 mag have log T_eff in the range 4.3–4.5, with $\mathrm{log}(L/{L}_{\odot })\,\lesssim$ 2.2 and radii R/R_⊙ ≲ 0.5. The three coolest stars with m_F154W ∼ 16 mag have $\mathrm{log}(L/{L}_{\odot })\,\sim$ 2.0 and are relatively larger in size with R/R_⊙ ≳ 1.5.

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In order to evaluate the importance of FUV data points in the estimation of fundamental parameters, we fitted the SEDs of stars 1–15 and 28–34, excluding their available FUV photometric points. We found that the parameter values changed significantly for stars hotter than T_eff = 40,000 K with the underestimation of T_eff and L and the overestimation of R. This implied that FUV data are crucial to estimate the parameters of very hot stars. Hence, the results derived for hot stars without FUV data points are to be considered with lesser weight.

Since several previous studies (Bedin et al. 2000; Marino et al. 2017) adopted a reddening value of E(B − V) = 0.19 mag for this cluster, we also fitted the SEDs using this value to see by what amount the estimated parameter values change. With this reddening measure, we found that the effective temperature values decreased by 10% (e.g., in the case of the hottest star) to 20%, the bolometric luminosities decreased by about 20%–30%, and the radii increased by about 5%–10%.

The luminosities and temperatures derived from SED analysis were used to assess the evolutionary status of the observed UV-bright stars using the Hertzsprung–Russell (H-R) diagram. We used the pHB evolutionary tracks from Moehler et al. (2019), which are extended versions of the pAGB evolutionary models developed by Miller Bertolami (2016). The tracks correspond to [M/H] = −1 and a zero-age main-sequence (ZAMS) mass of M_ZAMS = 0.85 M_⊙ (age = 12 Gyr) assuming scaled-solar metallicity with initial abundances Z_ZAMS = 0.00172, Y_ZAMS = 0.24844, and X_ZAMS = 0.74984. In the models, the RHB, BHB, and EHB sequences were populated by regulating the mass loss on the RGB phase. Further details of the evolutionary tracks are presented in the Appendix.

Figure 14 shows the observed UV-bright stars in black (inner region) and magenta (outer region) inverted triangles plotted over the evolutionary tracks. It is evident from this figure that all of the UV-bright stars except the three most luminous ones have evolutionary masses <0.53 M_⊙. Most of these stars are observed to lie along/near the sequence with M_ZAHB = 0.5 M_⊙, which is a track evolving from the EHB phase. These are likely to be AGB-manqué stars, which directly descend the white dwarf cooling sequence after core He exhaustion. The hottest and most luminous UV-bright star (star 32 in Table 3) is located between the tracks with M_ZAHB = 0.75 and 0.85 M_⊙. Star 3, with slightly lower luminosity and T_eff, lies at the intersection of two post-RHB sequences with M_ZAHB = 0.65 and 0.75 M_⊙. From the models, the mass of this star then ranges from 0.527 to 0.544 M_⊙. Two stars (23 and 24) are found to be located outside the range of the model tracks.

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Moehler et al. (2019) considered the area defined by $\mathrm{log}(L/{L}_{\odot })\gt 2.65$ and 4.9 > log T_eff > 3.845 in the H-R diagram (region shaded in gray in Figure 14) to correspond to hot UV-bright p(e)AGB stars. Going by their definition, from Figure 14, we observe three stars lying inside this region and one star on the high-temperature boundary. Among the three stars that are inside the gray shaded region, two (stars 4 and 19) are quite unlikely to be p(e)AGB stars, as they are located close to the evolutionary track with M_ZAHB = 0.494 M_⊙. The remaining star (star 27) occupies a position where post-EHB (cyan) and post-BHB (olive green) sequences overlap, making it difficult to distinguish. Hence, only the hot and luminous star (star 3) seen on the boundary of the shaded region can be confirmed as a hot p(e)AGB star. In other words, the cluster has a maximum of two and a minimum of one detected hot p(e)AGB candidate based on the above definition. We have detected one star (star 32) hotter than the hot boundary of the shaded region. This star might have crossed the p(e)AGB stage and is probably evolving toward the white dwarf stage.

6.1. Comparison of Theoretically Expected and Observed Numbers of Hot p(e)AGB Stars

We now make a comparison of the observed number of hot p(e)AGB stars with the number of such stars anticipated from theoretical predictions. For this, we make use of the evolutionary flux method described in detail in Greggio & Renzini (2011). The following suppositions are made in this calculation: (a) GCs are simple stellar populations (SSPs), (b) the rate at which stars end up as remnants is equal to the rate at which stars leave the MS, and (c) the lifetimes of later stages of stellar evolution are considerably shorter than that of MS evolution. Under this premise, the number of stars, N_i, in a particular stage of evolution, i, in an SSP is given by the relation

$$\begin{eqnarray}&&{\text{}}{N}_{i}=B(t)\times {L}_{\mathrm{total}}\times {t}_{i}.\end{eqnarray} \tag{ 3 }$$

Here B(t) is the specific evolutionary flux, which is the number of stars entering (or exiting) a certain phase of stellar evolution per year per luminosity (L_⊙) of the sampled population; L_total is the total luminosity of the stellar population; and t_i is the duration of the evolutionary phase being analyzed. Assuming an age of ∼10 Gyr for the cluster and Salpeter's initial mass function, we can obtain an approximate value for the specific evolutionary flux of B ≃ 2 × 10⁻¹¹ stars yr^–1 L^–1_⊙.

In this analysis, we consider stars in the hot p(e)AGB phase of evolution, which corresponds to the gray shaded region in Figure 14. Each evolutionary track spans a duration, t, in this region. In order to estimate the expected number of hot p(e)AGB stars from Equation (3), we use the parameters for NGC 2808 listed in Table 4. The anticipated number of p(e)AGB stars in a cluster depends on how frequently a particular evolutionary track is followed in that cluster, which in turn depends on the fraction of stars in various parts of the HB. We calculate the number of p(e)AGB stars evolving along all of the evolutionary tracks starting from each branch of the HB, i.e., N^RHB, N^BHB, and N^EHB for stars evolving from the RHB, BHB, and EHB, respectively, using Equation (3) (Moehler et al. 2019). For this, we derive the fraction of RHB, BHB, and EHB stars with respect to the total number of HB stars in the cluster (f_RHB, f_BHB, and f_EHB) by combining the members of the HUGS and Gaia catalogs for complete spatial coverage. The values thus obtained are f_RHB = 0.47, f_BHB = 0.35, and f_EHB = 0.07. The final expected number of hot p(e)AGB stars in the cluster is then

$$\begin{eqnarray}&&N=({f}_{\mathrm{RHB}}.{N}^{\mathrm{RHB}})+({f}_{\mathrm{BHB}}.{N}^{\mathrm{BHB}})+({f}_{\mathrm{EHB}}.{N}^{\mathrm{EHB}}).\end{eqnarray} \tag{ 4 }$$

We obtain a range for N, since N^RHB, N^BHB, and N^EHB take a range of values depending on the duration in the p(e)AGB phase along each evolutionary track. Thus, for NGC 2808, we estimate the expected number of hot p(e)AGB stars in the gray shaded region of the H-R diagram as 1.27–3.80. The maximum observed number of p(e)AGB stars detected in this shaded region is two, which is in good agreement with the expected number of such stars.

Table 4.  Parameters for NGC 2808

Parameter	Value	Source
[Fe/H]	−1.14 dex	H96
Age	10.9 Gyr	Massari et al. (2016)
Integrated V magnitude, Vt	6.20 mag	H96
Distance modulus, ${\left(m-M\right)}_{V}$	15.59 mag	H96
Reddening, E(B − V)	0.22 mag	H96
Bolometric correction, BCV	−0.45 mag	Worthey (1994)

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We identify and characterize the sample of UV-bright member stars in NGC 2808 using the photometric data from the UVIT in combination with HST, Gaia, and ground-based observations. The detection of these stars is extremely important to build a statistically significant sample that can aid in understanding the late phases of evolution of low-mass stars and determining their contribution to the UV luminosity of old stellar systems. As highlighted earlier, observations in the UV wave bands are critical for this purpose. The UV-optical and UV CMDs constructed by combining the UVIT data with the HST (inner $2\buildrel{\,\prime}\over{.} 7\times 2\buildrel{\,\prime}\over{.} 7$ region of the GC), Gaia, and ground-based optical data (outside the HST FOV) reveal the sequences of hot members in the cluster. We do not use the UVIT data for stars within the innermost $1^{\prime}$ diameter region because of the possible effects of crowding. In the FUV filters, we detect mainly the pHB, BHB, EHB, BHk, and BSS populations, whereas in the NUV filters, the cooler RHB stars can also be spotted. The identification of the HB location is supported by the overlaid ZAHB and TAHB models.

Brown et al. (2001) observed the central $\simeq 1750\,{\mathrm{arcsec}}^{2}$ region of NGC 2808 using HST/STIS FUV/F25QTZ and NUV/F25CN270 filters. Although a direct comparison cannot be made between their and our UV CMDs (due to the differences in the filter characteristics and the FOV covered), some general features of the CMDs can be examined in detail. In their FUV − NUV versus FUV CMD, a gap between the BHB and EHB was found at an FUV − NUV color of ∼–1 mag. They also found a sparse subluminous population of stars below the end of the canonical ZAHB and explained them by invoking the late-hot flasher (BHk) scenario having enhanced He and C abundances due to flash mixing. The spread in the magnitudes of these stars was accounted for by the evolution of BHk stars to higher luminosities as the He-core burning progressed. We find a similar spread in the BHk magnitudes in our m_F154W − m_N245M versus m_F154W CMD shown in Figure 8. Brown et al. (2001, 2010) noted that some of these BHk stars are unusually redder, i.e., redder than expected from the models for normal BHk or EHB stars. A similar dispersion in the color of BHk stars is observed in our FUV − NUV versus FUV CMD. Brown et al. (2012) analyzed the UV spectra of two BHk stars with redder FUV − NUV colors and found that there is a large enhancement of Fe-peak elements in these stars that could serve as an explanation for their observed colors.

Brown et al. (2012) also discussed the results of UV spectral analysis of three unclassified objects, U1, U2, and U3, which are hotter than their canonical HB model. Based on their spectra and locations in the UV CMD, the possibilities of them being evolving pAGB stars or white dwarfs were disregarded. It was found that U1 and U2 have implausible effective temperatures (∼250,000 K), and U3 has T_eff = 50,000 K. These objects did not have any X-ray counterparts. The authors were unable to conclusively explain these unusually hot objects, although propositions such as the presence of an accretion disk in the objects, a change in extinction along the line of sight to the cluster, a nonstellar source, etc., were put forth. These objects, located within 30'' of the cluster center, are not resolved in the UVIT images. However, two of these objects, namely, U1 and U3, could be cross-matched with stars in the HUGS catalog having membership a probability >90%. These are found in the BHk and EHB positions, respectively, in the m_F275W − m_F438W versus m_F336W CMD shown in Figure 3. We detect similar objects in our UV CMDs in Figure 8 with bluer m_F154W − m_N245M colors (≲–1 mag) than the ZAHB model and roughly the same magnitudes as the HB. We plan to characterize the HB stars in our future study.

The study by Schiavon et al. (2012) did not include the full sample of pHB stars in NGC 2808 due to the limited spatial resolution of GALEX and the lack of membership analysis for these stars. There are 22 candidates in their list of UV-bright stars in NGC 2808. We find 15 stars to be in common between our sample and theirs.

The UV CMD presented in Brown et al. (2001) shows one pAGB candidate star with an FUV magnitude of 12.46 mag. This star is unresolved in the UVIT images and not included in the HUGS catalog, as it is saturated in the WFC3/UVIS filters. Hence, our analysis does not include this star. Brown et al. (2001) also found five pHB candidates from the UV CMD, of which four stars are common with our catalog. The fifth pHB candidate is not included in the HUGS catalog; hence, its membership cannot be assessed, even though it is detected in the UVIT images (R.A. = 1380235, decl. = −6486531).

In Table 5, we compare our estimates of T_eff with the values available in the literature for three UV-bright stars in the cluster. Brown et al. (2012) derived the T_eff for the AGB-manqué star AGBM1 using the HST/STIS UV spectrum. Moehler et al. (2019) estimated the T_eff values for the stars C4594 and C2946 using the medium-resolution optical spectra from the EFOSC2 instrument at the 2.2 m MPI/ESO telescope. From the table, it is evident that the T_eff values derived through SED analysis are in close agreement with spectroscopic estimations.

Moehler et al. (2019) calculated the theoretically expected numbers of hot p(e)AGB stars in 17 galactic GCs (excluding NGC 2808) and compared them with the observed numbers. The numbers matched more or less in the case of 14 clusters. In the remaining three clusters, the observed numbers of p(e)AGB stars were larger than the predicted values. The massive and dense GC NGC 5139 (ω Cen) has the maximum number of observed p(e)AGB stars (five), with the expected number in the range 1.3–13.5. Here we find that the number of such stars is between one and three (including the saturated pAGB candidate from Brown et al. 2001), which agrees well with the expected number for NGC 2808.

The pHB stars identified in this study will provide a good sample to explore the stellar evolutionary properties in this phase. From Figure 9, we see that there are seven member stars located in the outer region of the cluster that are ideal candidates for further follow-up spectroscopic studies. These are identified from the AstroSat/UVIT images and are in relatively less crowded regions of the cluster. This GC is known to host populations with a wide range of MS He abundances (Piotto et al. 2007; Milone et al. 2015). In addition, many of the UV-bright stars with T_eff > 25,000 K are likely to experience gravitational settling and/or weak winds that may alter their surface He (and metal) abundance (e.g., Dixon et al. 2017). These abundance uncertainties call for thorough spectroscopic investigation. Moreover, spectroscopy can provide accurate estimation of T_eff, log g, and radial velocity and its variation (if any); detailed chemical abundance information on the signs of third dredge-up (which will help to clearly distinguish between p(e)AGB and pAGB phases); and so on.

• 1.  
  We performed a comprehensive study of the UV-bright member stars in the GC NGC 2808 using the AstroSat/UVIT, HST, Gaia DR2, and ground-based optical data. The identification and detailed study of these stars are important to create a statistically significant sample for two main reasons: (i) to shed light on the rapid evolution of the late phases of low-mass stars, such as the pAGB, p(e)AGB, and AGB-manqué phases, and (ii) to assess the contribution of these stars to the total UV output of old stellar systems.
• 2.  
  Member stars in the inner and outer parts of the cluster are identified to create optical, UV-optical, and UV CMDs. The stars in the HB sequence are identified and compared with the ZAHB and TAHB models. A large number of hot HB stars are detected along with an FUV-bright BSS. These will be studied in detail in the future.
• 3.  
  We detected 34 UV-bright stars based on their locations in the UV CMDs. Among these, 27 stars are found to be located within the inner $2\buildrel{\,\prime}\over{.} 7\times 2\buildrel{\,\prime}\over{.} 7$ region of the cluster, and seven stars are in the outer region.
• 4.  
  We estimated parameters such as the T_eff, R/R_⊙, and L/L_⊙ of these stars through the SED fitting technique. Their effective temperatures range from 12,500 to 100,000 K, luminosities from ∼40 to 3000 L_⊙, and radii from 0.13 to 2.2 R_⊙. Our T_eff estimations from SED fitting are found to match well with the available spectroscopic estimations for a few stars from the literature.
• 5.  
  By comparing the derived parameters with theoretical models available for evolved stellar populations, the evolutionary status of these stars is probed. We find that most UV-bright stars have evolved from EHB stars with M_ZAHB = 0.5 M_⊙, and these are in the AGB-manqué phase. From the theoretical models, we observe that all except the three hottest and most luminous UV-bright stars have HB progenitors with M_ZAHB < 0.53 M_⊙.
• 6.  
  The expected number of hot p(e)AGB stars in NGC 2808 is estimated from stellar evolutionary models and found to agree well with the observed number.
• 7.  
  Seven pHB stars identified in the outer region are ideal for further spectroscopic follow-up studies. These stars are identified from the AstroSat/UVIT images. This work thus demonstrates the capability of the UVIT in detecting and characterizing the UV-bright stars.

We thank the anonymous referee for the encouraging comments and suggestions. We are thankful to S. Moehler for her valuable comments that helped in improving the manuscript. We thank Gaurav Singh for providing us the catalog of Gaia proper motion–based cluster members. D.S.P. thanks Sharmila Rani and Vikrant Jadhav for useful discussions. This publication utilizes data from the 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 Topcat (Taylor 2005); the Aladin sky atlas developed at CDS, Strasbourg Observatory, France (Bonnarel et al. 2000; Boch et al. 2014); Matplotlib; NumPy; SciPy; and pandas.

The details of the pHB evolutionary sequences from Moehler et al. (2019) used in the main text are presented in Table 6. The UVIT photometric magnitudes and magnitude errors for the UVIT-resolved pHB members are presented in Table 7. The SEDs for the UVIT-resolved stars other than the ones shown in the main text (stars 3 and 28), are displayed in Figure 15.

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