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Issue
A&A
Volume 685, May 2024
Article Number L6
Number of page(s) 11
Section Letters to the Editor
DOI https://doi.org/10.1051/0004-6361/202449777
Published online 08 May 2024

© The Authors 2024

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is published in open access under the Subscribe to Open model. Subscribe to A&A to support open access publication.

1. Introduction

Post-asymptotic giant branch (PAGB) stars are the most luminous objects in globular clusters (GCs). They evolve from the top of the AGB and move leftward in the HR diagram at almost constant luminosity (Kwok 1982, 1993). They are rare in GCs (one or two per cluster is expected) due to the fact that PAGB stars have a very short lifetime (≤0.5 Myr; Moehler et al. 2019) compared to the age of GCs (10–12 Gyr; Harris 1996). Nevertheless, a handful of PAGB stars have been detected in more than 150 Galactic GCs (for details, see Moehler et al. 2019; Davis et al. 2022; Dixon 2024).

There are three major categories of PAGB stars observed in GCs based upon the evolution of their progenitors on the horizontal branch (HB), the core He burning phase. The first category is for HB stars with H-rich envelopes, which ascend towards the AGB; they have several thermal pulses at the tip of the AGB. Their post-AGB phase is treated as the normal PAGB phase (Greggio & Renzini 1990; Dorman et al. 1993; Moehler et al. 2019). The second category is for HB stars with H-poor envelopes but H-envelopes > 0.02 M⊙, which ascend towards the AGB, but never reach the AGB tip and leave the AGB phase early1 (Moehler et al. 2019). Their PAGB phase is known as post-early-AGB (PEAGB) phase (Greggio & Renzini 1990; Dorman et al. 1993; Moehler et al. 2019). They are less luminous than the normal PAGB stars (Dorman et al. 1993; Moehler et al. 2019). The third category of PAGB stars is for stars that evolved from HB stars with H-envelopes < 0.02 M⊙ (extreme-HB stars) (Dorman et al. 1993; Moehler et al. 2019). They never reach the AGB phase; rather, they remain hot and luminous during their post-HB evolution, and ultimately cool down through the white dwarf (WD) phase. These PAGB stars are known as AGB-manqué stars (Dorman et al. 1993; Gratton et al. 2010; Moehler et al. 2019).

In a cluster with a large binary fraction, a few red-giant-branch (RGB) stars in a binary system lose enough mass to their companion. They become inefficient in igniting He during the RGB phase and evolve off the RGB at the luminosity comparable to their RGB tip. These stars are called post-RGB stars (Lei et al. 2015; Kamath et al. 2016). They have similar luminosities to PEAGB stars and ignite He either on their post-RGB phase or the WD cooling track (Cassisi et al. 2003; Miller Bertolami et al. 2008; Lei et al. 2015).

Moehler et al. (2019) performed a comprehensive analysis of 78 Galactic GCs to identify the hot PAGB stars. They found 19 new PAGB stars in addition to 12 previously known PAGB/PEAGB stars. Prabhu et al. (2021) have detected five PAGB stars in the NGC 2808 using ultraviolet (UV) images of Ultraviolet Imaging Telescope (UVIT) on board AstroSat (Tandon et al. 2017). Davis et al. (2022) studied 97 Galactic GCs using optical filters and found 13 cooler (F and G type) PAGB stars among them. Dixon (2024) studied the CNO and s-process abundances of 17 previously known PAGB stars in the Galactic GCs to find evidence of the third dredge-up (3DU) among GC PAGB stars. Considering all the above surveys, a total of 42 unique PAGB/PEAGB/AGB-manqué stars have been observed so far only in ∼20 GCs when exploring more than 150 Galactic GCs. None of them has shown a binary signature (neither photometric nor spectroscopic). However, the low-mass PAGB stars, V29 in ω cen and K648 in M15, indicate that they have evolved in a binary system (Dixon 2024).

In this paper we report the discovery of a new hot PAGB star in Galactic GC E3 (ESO 37-1; Lauberts 1976) using UV images from UVIT and Gaia DR3 data. Cluster E3 (RAJ2000 = 09:20:57.07, DEJ2000 = −77:16:54.8; Harris 1996, 2010) is one of the faintest GCs in the Milky Way, and is likely to be the least massive one (2.9 × 103 M⊙; Sollima & Baumgardt 2017). It is a metal-rich cluster ([Fe/H]∼ − 0.7 dex; de la Fuente Marcos et al. 2015; Salinas & Strader 2015; Monaco et al. 2018) with a moderate reddening (E(B − V) = 0.29; Schlafly & Finkbeiner 2011). The cluster has the largest binary fraction (72%) among Galactic GCs (Milone et al. 2012).

2. Photometric and spectroscopic observations

Cluster E3 was observed in two far-UV (FUV: 1300–1800 Å) filters, F154W and F169M, of UVIT. The total exposure times of the F169M and F154W filters are 6047 s and 3546 s, respectively. The field of view (FoV) of UVIT is sufficient to cover the entire cluster (tidal radius = 8.49 arcmin, Harris 1996). However, we see only two FUV bright sources within the FoV of UVIT; one is within the half-light radius of the cluster, and the other is at the edge of the image (Fig. 1). The sources at the edges of the UVIT FoV are unreliable due to edge artefacts; hence, they were excluded during photometry. Finally, we detected eight sources in the FUV (red circles in Fig. 1).

thumbnail Fig. 1.

UVIT F169M filter image of E3. The half-light and tidal radius of E3 (Rh = 2.1′ and Rt = 8.49′, Harris 1996, 2010) are well within the field of view of UVIT. The red arrow indicates the probable post-AGB star. In the inset (upper right corner) the optical V-band image (Stetson et al. 2019) of the cluster (up to half-light radius) is shown. The PAGB star is easily distinguishable as one of the cluster’s brightest stars in both images.

We used the GC catalogue of Gaia DR3 (GCG21; Vasiliev & Baumgardt 2021) for cluster membership analysis (see details of the analysis in Appendix A). We found only one out of eight UVIT observed sources to be a cluster member, which is indicated by the red arrow in Fig. 1. The source is bright in FUV and optical bands (Table 1) and lies well within the half-light radius of the cluster. In Fig. 2 we show all the Gaia observed cluster member sources (grey dots) and the UVIT observed cluster member source (blue asterisk) on the vector-point diagram (left panel) and the parallax versus PMRA (middle upper panel) and parallax versus PMDEC (middle lower panel). We find that the proper motion and the parallax values of the UVIT observed source are in good agreement with the Gaia observed cluster member sources (Fig. 2). The Gaia BP−RP versus G colour-magnitude diagram (CMD) (right panel of Fig. 2) suggests that the source is an evolved PAGB star in the GC E3.

Table 1.

Observation details of the PAGB star.

thumbnail Fig. 2.

Diagrams showing the kinematics and photometric analysis of the cluster member sources with the Gaia data. The left panel shows the vector-point diagram of the cluster member sources from the Gaia catalogue (Vasiliev & Baumgardt 2021, grey dots) and the UVIT observed cluster member source (blue asterisk). The middle panel shows the parallax vs proper motion in RA (top) and Dec (bottom) for the Gaia-observed cluster members having parallax S/N (plx/e_plx) > 5 (grey dots) and the UVIT observed cluster member source (blue asterisks). The right panel shows BP−RP versus MG CMD in the absolute magnitude plane. The GaiaG magnitudes (grey dots) are scaled to absolute magnitudes using distance modulus, m − M = 14.50 (Baumgardt & Vasiliev 2021). The BaSTI-IAC isochrone of age 11 Gyr, [Fe/H] = −0.70 dex is overplotted as a red solid line. The zero-age HB (ZAHB) and terminal-age HB (TAHB) loci are shown as solid pink and dashed lines, respectively. The black dashed line shows different subcategories of PAGB and post-HB stars, as defined in Bond (2021).

2.1. Spectroscopic observations of the PAGB star

The spectroscopic observations of the PAGB star were obtained at two epochs (17 February 2023 and 26 March 2023) with a high-resolution (R ∼ 28 000) CHIRON2 spectrograph (Tokovinin et al. 2013) installed on the SMARTS 1.5 m telescope at the CTIO observatory, Chile. The observation details are given in Table B.1, and the reduction procedure of the spectra is explained in Appendix B.

2.1.1. Radial velocities

We measured the radial velocities (RVs) using our own implementation (Hełminiak et al. 2019) of the TODCOR technique (Zucker & Mazeh 1994). The procedure is described in Appendix C. The barycentric RVs were estimated as 40.20 ± 0.57 km s−1 and 34.66 ± 0.85 km s−1 for the spectra observed at the first and second epochs, respectively. These values are quite high with respect to the mean RV of the cluster (12.6 km s−1; Monaco et al. 2018). However, the change in velocities between two epochs is quite substantial; this signals the possible binarity of the star. Since the cluster has a large binary fraction (Milone et al. 2012), it is possible that the identified PAGB star is evolving in a binary system. In Appendix D we present the performed simulations for possible binary configurations of the PAGB star with constraints from the RVs. The simulations create binary models with different primary mass values in the range 0.2–0.8 M⊙. We find the period of the binary models is spread around 39.12 days (51% of the models) and 17.83 days (16.4% of the models) (Fig. D.1). This suggests a close orbit of the system. The mass ratio3 (q) of the system lies in the range of 0.2–1.5. Milone et al. (2012) calculated photometric binary fractions for E3 and found that around 40% of the cluster members have a binary with q > 0.5. We do not see another companion in the spectra, so q > 1.5 (a conservative upper limit) is unlikely. Since the source is close to the half-light radius, it is likely to have a heavier companion. Hence, we suggest q ≥ 1.0 for the binary system. However, further spectroscopic monitoring is required to confirm the binarity and characterise the companion.

2.1.2. Atmospheric parameters and abundances

The atmospheric parameters (Teff and logg) of the PAGB star were derived from CHIRON spectra using a relation involving the ionisation balance between Si II and Si III, for a set of Teff and logg pairs from TLUSTY model grid BSTAR2006 (Lanz & Hubeny 2007). The procedure of atmospheric parameter estimation is described in Appendix E. We find K, logg = 2.37 ± 0.20, and logεSi = 7.31 ± 0.05 from the spectral analysis of the PAGB star.

Using the above parameters derived from the spectra of the PAGB star, we derived abundances (ε) of all elements detected in the spectrum. The chemical composition analysis of the individual elements is given in Appendix F, and the abundance value of each element is given in Table F.1. The derived individual abundances of metals in the star are two to five times lower than in the Sun (Table F.1), suggesting that the star is metal poor. The [Fe/H] abundance (−0.7 ± 0.2 dex) matches the cluster metallicity (Monaco et al. 2018). Unlike this star, many PAGB binaries show depletion of iron (van Winckel 2003). However, in a recent study to understand depletion in binary RV Tauri stars (and a few binary PAGB stars), Gezer et al. (2015) found that iron depletion is prevalent in binaries with an accretion disk or with evidence of a former disk. The binaries without a disk do not show any depletion. Since we do not find any signature of an accretion disk (or depletion), the identified PAGB star might be a case where the evolution in a binary does not involve the formation of an accretion disk.

2.2. Spectral energy distribution of the PAGB star

We performed the spectral energy distribution (SED) fitting of the PAGB star in the VO SED analyzer (VOSA; Bayo et al. 2008). The SED fitting procedure is described in Appendix G. We found that the best-fitting model grid has Teff = 18 000 K and logg = 2.25. The best-fitting model and observed fluxes are shown in Fig. G.1. VOSA also provides the bolometric luminosity (Lbol) and radius of the star (R) from their best-fit stellar atmosphere model grid based on the distance of the star and the total observed fluxes from the UV to IR bands. We found Lbol and R of the identified PAGB star as 2136 ± 150 L⊙ (log(L/L⊙) = 3.33 ± 0.03) and 4.61 ± 0.14 R⊙, respectively.

3. Evolutionary status of the PAGB star

In Fig. 3 we show all the previously observed PAGB stars (blue asterisks) in GCs with known Teff, Lbol, and logg values. The newly identified PAGB star in this paper is shown as a red asterisk. We find that the luminosity of the identified PAGB star is similar to most of the GC PAGB stars (log(L/L⊙)∼3.25; Dixon 2024). We show all the latest available PAGB evolutionary tracks with H-burning (upper left panel) and He-burning (lower left panel) prescriptions. The H-burning evolutionary tracks of initial masses 0.9, 1.0, and 1.25 M⊙ (dashed red, black, and green lines, respectively) are from Miller Bertolami (2016). The PAGB evolutionary tracks of Moehler et al. (2019) (solid lines) were generated from an initial mass of 0.85 M⊙, but they differ in their post-HB evolution based upon their location and mass on the HB phase. We find that the luminosity of evolutionary tracks varies upon their initial and/or final mass. The current mass of the identified PAGB star would be ∼0.51 M⊙ based upon the H-burning evolutionary tracks (upper left panel of Fig. 3).

thumbnail Fig. 3.

The log Teff versus log L (left panel) and log Teff versus logg (right panel) plots display PAGB stars that have been observed in GCs. The red asterisk indicates the newly discovered PAGB star in E3, and the blue asterisks indicate PAGB stars found in other GCs. In the upper left panel, the H-burning PAGB evolutionary tracks of Miller Bertolami (2016) and Moehler et al. (2019) with metallicity Z = 0.001 are shown as dashed and solid lines, respectively, and for different initial and HB masses (as shown in the legend at right). The PAGB tracks of Moehler et al. (2019) consider an initial mass of 0.85 M⊙ for all the evolutionary tracks. The lower left panel shows the post-RGB He-burning evolutionary tracks from Bloecker (1995) (green dotted line), Lei et al. (2015) (red dotted line), and Driebe et al. (1998) (black dotted line). The grey shaded region indicates a Teff range of 16 000–19 000 K. The current mass for each evolutionary track at ∼18 000 K is shown with an arrow of the same colour and style as the evolutionary track. In the right panel, PAGB stars are shown on the log Teff versus logg plane. The inset shows the zoomed-in view around the newly identified PAGB star.

The derived logg value of the star is lower than the other PAGB stars observed in Galactic GCs (right panel of Fig. 3). The evolutionary tracks on the logg versus log Teff plane suggest that the current mass of the identified PAGB star is ∼0.55 M⊙, which evolved from an initial mass of 1.0 M⊙ (Miller Bertolami 2016).

Hence, various evolutionary tracks on the Teff, Lbol, and logg plane suggest a current mass of the PAGB star in the range 0.51–0.55 M⊙ which has spent ∼1000 yr in the PAGB phase (1.0 M⊙ track; Miller Bertolami 2016). This mass range of the PAGB star indicates that the companion is also an evolved post-main sequence (of 0.5–0.8 M⊙ for q ≥ 1.0). The very close orbit of the system suggests that it would have gone into a common-envelope interaction that drastically shortened the orbital period (and ejected material into the ISM). In this case, the evolution of the star would have been interrupted compared to that of a single star. However, the star shows higher luminosity than would have resulted from interrupted evolution (black dotted line in the lower panel of Fig. 3, left panel), but a lower luminosity than would have resulted from a single star evolution (dashed lines in the upper panel of Fig. 3, left panel).

Recently, Davis et al. (2022) showed that PAGB stars are preferentially found in metal-poor clusters with blue or very blue HB stars. On the other hand, the identified PAGB star is in E3, a relatively metal-rich cluster containing red HB stars, which is one of the few cases of metal-rich clusters that contain PAGB stars (such as the famous blue star in 47 Tucanae). However, since the PAGB in E3 has a similar luminosity to the PAGB stars in metal-poor GCs, a binary configuration better supports its presence in a metal-rich and red HB cluster.

4. Evidence of third dredge-up in the PAGB star

PAGB stars, which undergo thermal pulses at the AGB-tip, bring up the processed materials to the surface (3DU process); as a result, the enhanced C, O, and other s-process elements could be found on the surface of PAGB stars. Recently, Dixon (2024) studied the CNO abundances of 11 PAGB stars observed in the Galactic GCs and found 4 of them have enhanced CNO abundances compared to the CNO abundance of their respective host cluster. They concluded that the increased C and O abundances during their 3DU enhanced the overall CNO abundance in those PAGB stars.

In Fig. 4 we plot the abundance ratios of C/CNO versus C (left panel) and N/O versus O (right panel) abundances of the eight PAGB stars for which C abundances were reported in Dixon (2024) (blue asterisks for the PAGB stars having 3DU and black asterisks for those having no sign of 3DU) along with the abundances of the identified PAGB star in this paper (red asterisk). We find that the identified PAGB star has similar C and O abundances to those PAGB stars of other GCs that have undergone the 3DU. This suggests the discovered PAGB star also went to the 3DU while on its AGB evolution.

thumbnail Fig. 4.

Comparison between abundance ratios of PAGB star of E3 and other GCs. PAGB stars with 3DU evidence are shown as blue asterisks; those with no 3DU evidence are shown as black asterisks. The newly identified PAGB star of E3 is shown as a red asterisk. The left panel shows C/CNO versus C abundance plot, whereas the right panel shows N/O vs. O abundance plot.

5. Conclusion

We explore all the photometric and spectroscopic details of the new hot PAGB star discovered in GC E3. The proper motion and parallax of the star from Gaia DR3 support its membership, and the location of the star in the absolute CMD suggests that the star is in the PAGB phase. The radial velocities show a variation of ∼6 km s−1 between the two epochs, suggesting a binary nature of the star. A simulation of possible binary systems with the observed RV values of the PAGB star and the cluster mean RV suggest that the binary period of the star is around 39 days (51% of models) or 18 days (16% of models). The abundances were derived for the He, C, N, O, Ne, Al, Si, S, and Fe lines. The metallicity of the star ([Fe/H] = −0.7 dex) agrees with the cluster metallicity. We find the Teff, logg, logL, and radius of the PAGB star to be 17 500 ± 1000 K, 2.37 ± 0.20, 3.33 ± 0.03, and 4.61 ± 0.14 R⊙, respectively, using SED fitting of 30 photometric fluxes from UV to IR bands. A comparison of various PAGB evolutionary tracks with the observed star on the H–R diagram suggests that the current mass of the PAGB star is in the range 0.51–0.55 M⊙. A comparison of the observed C, N, and O abundances of the star with the abundances of the PAGB stars of other GCs that show 3DU suggest that the PAGB star has undergone the 3DU and enriched its C and O abundances. Future multi-epoch spectroscopic observations are necessary to constrain the period and better understand the binary nature of the identified hot PAGB star.

1

Either having one or two thermal pulses or without experiencing any thermal pulse.

3

The ratio of the companion mass to the PAGB mass.

4

The catalogue provides zero point corrected parallax values, as suggested by Lindegren et al. (2021).

5

specutils.readthedocs.io/en/stable/api/specutils.analysis.snr.html

6

https://www.nist.gov/pml/atomic-spectra-database

7

http://tlusty.oca.eu/Tlusty2002/tlusty-frames-cloudy.html

8

http://svo2.cab.inta-csic.es/theory/main/

Acknowledgments

We thank the referee for his/her constructive comments. We thank Prof. M. Parthasarathy for his valuable discussion during the initial phase of the project. The CHRION spectra were obtained with the help of the National Science Center (NCN), Poland, using grant no. 2021/41/N/ST9/02746. AM is also supported by this NCN grant. ACP and SP acknowledge the support of the Indian Space Research Organisation (ISRO) under the AstroSat archival Data utilization program (No. DS_2B-13013(2)/1/2022-Sec.2). MG was partially supported by the NCN through the grant UMO-2021/41/B/ST9/01191. DKO acknowledges the support of the Department of Atomic Energy, Government of India, under Project Identification No. RTI 4002. The research work at the Physical Research Laboratory is funded by the Department of Space, Government of India. This publication uses the data from the AstroSat mission of the ISRO, archived at the Indian Space Science Data Center (ISSDC).

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Appendix A: Cluster membership analysis using Gaia DR3

The GC catalogue of Gaia EDR3 (GCG21; Vasiliev & Baumgardt 2021) provides information about the source positions (RA, DEC), proper motions (PMRA, PMDEC), parallax,4 cluster membership probability, and photometric magnitudes in G, BP, and RP filters for sources observed in the 170 Galactic GCs. We found 479 Gaia observed sources of E3 within the UVIT FoV having cluster membership probability > 90%. We cross-matched the eight UVIT observed sources with the Gaia catalogue and found only one source to be a cluster member. The UVIT observed cluster member source has a membership probability of 99% and lies well within the half-light radius of the cluster. For parallax information, we selected only those cluster member sources with good parallax (S/N > 5) and found only 8 out of 479 cluster member sources. The mean proper motions and parallax of the cluster estimated by Vasiliev & Baumgardt (2021) are PMRA (μαcosδ) = − 2.727 ± 0.027 (mas/yr), PMDEC (μδ) = 7.083 ± 0.027 (mas/yr), and parallax () = 0.146 ± 0.013, respectively. We find that the proper motion and the parallax values of the UVIT observed cluster member source are in good agreement with the Gaia observed cluster member sources (Fig. 2). The details of the UVIT and the Gaia observations of the source are given in Table 1.

In the right panel of Fig. 2, we show the optical CMD of the cluster member sources (grey dots) in the absolute magnitude plane. The colours and magnitudes of the Gaia filters are dereddened using E(B−V) = 0.29 (Schlafly & Finkbeiner 2011) and the Cardelli et al. (1989) extinction law. The Gaia G magnitudes are scaled to the absolute magnitudes using the distance modulus, m−M = 14.50 (Baumgardt & Vasiliev 2021). The UVIT observed source (blue asterisk) is ∼2.0 mag brighter than the other cluster member sources and appears bluer in colour (BP−RP =−0.2 mag), which is the location of the blue evolved stars of GCs (Zinn et al. 1972; Moehler et al. 2019; Bond 2021). We marked various regions of PAGB stars, defined by Bond (2021) as red-PAGB (rPAGB), yellow-PAGB (yPAGB), blue-PAGB (bPAGB), and AGB-manqué stars, on the Gaia BP−RP versus G CMD (right panel of Fig. 2). The UVIT observed cluster member source can be found in the bPAGB region. Hence, we confirm that the source is an evolved PAGB star and a bona fide member of the GC E3.

Appendix B: Reduction of CHIRON spectra of the PAGB star

We reduced the spectra with the pipeline developed at Yale University (Tokovinin et al. 2013). Wavelength calibrations were performed using the ThAr lamp exposures taken during the scheduled calibration runs. We applied barycentric corrections separately using calculations from IRAF with the bcvcor task. We calculated the signal-to-noise ratio (S/N) of the two spectra using the snr5 module in SPECUTILS. We found a S/N of 40.6 and 25.6 for the spectra at the first and second epochs, respectively.

Table B.1.

Details of the spectroscopic observations of the PAGB star.

The optical spectrum of the star in the spectral ranges 4505−6602 Å shows about 50 stellar absorption lines. The identification of the lines is based on the National Institute of Standards and Technology (NIST) Atomic Spectra Database.6

Absorption lines of neutral species including H I (Hα and Hβ), He I, C I, N I, O I, and Ne I were identified. Singly ionised species including C II, N II, O II, Si II, S II, Mg II, and Fe II were detected. Higher ionisation is seen in Al III, Fe III, Si III, and S III.

The spectrum of the star also contains absorption features that have interstellar origin. There is a Na I doublet (λ5889.951, 5895.924) and several very weak diffuse interstellar bands (DIBs). Emission lines are not detected in the spectrum of the star, in contrast to many hot post-AGB stars, whose spectra consist of two components: the star’s absorption spectrum and an overlain emission spectrum from a low-excitation gas envelope (Mello et al. 2012). Comparing the spectra at the two epochs, we find static O I emission lines at 5577 Å, 6300 Å, and 6364 Å, which are most probably due to air-glow (Leinert et al. 1998), and therefore we did not consider them for our analysis. The complete continuum-normalised spectrum of the star in the spectral ranges 4 505−6 602 Å is presented at http://lnfm1.sai.msu.ru/ davnv/E3/atlasE3.pdf.

Appendix C: RV estimation from the spectra of the PAGB star

The RVs were measured on prominent absorption lines, including He lines, but avoiding Hα and Hβ as they had broad absorption lines (FWHM > 100 km s−1) affecting a precise RV estimate. We used a template with Teff = 20 000 K, logg = 4.5 dex, and solar metallicity to create the cross-correlation functions (CCF; Fig. C.1) using the TODCOR technique (Zucker & Mazeh 1994). The uncertainties were calculated using a bootstrap procedure (Hełminiak et al. 2012), which is sensitive to the S/N of a component and velocity of rotation. The RVs were estimated as 40.20±0.57 km s−1 and 34.66±0.85 km s−1 for the spectra observed at the first and second epochs, respectively. We also checked for the consistency of RV measurements using broadening functions (BFs; Rucinski 1999). The RVs were calculated using a rotational broadening model described in Moharana et al. (2023). The BF-RVs were consistent with the TODCOR-RVs within the errors. The final RVs were taken from TODCOR due to their high precision.

thumbnail Fig. C.1.

1D projections of the TODCOR cross-correlation functions (CCFs) for the spectra observed at two epochs. The vertical shaded regions represent the errors in the observation of the RVs. The first epoch (red) has a RV of 40.20 ± 0.57 kms−1 and the second epoch (blue) has a RV of 34.66 ± 0.85 kms−1.

Appendix D: Simulation of binary configurations

To check the possible binary configurations of the identified PAGB star, we made a grid of models constrained by the observed radial velocities. We used the binary modelling code PHOEBE2 (Conroy et al. 2020 and references therein). Since we had two epochs of RV observations only, we considered the following assumptions for a simplified modelling:

  1. The binary is edge-on. The inclination of the orbital plane is fixed at 87 degrees, and the orbital period is constrained to be less than 1000 days. For a wider orbit, we expect a high renormalised unit weight error (RUWE) parameter in Gaia DR3; however, the RUWE value of the PAGB star is 1.022 (< 1.4).

  2. Models with orbits smaller than the radius of the PAGB star (4.61 R⊙) or reaching the Roche limit will be rejected. We assume the secondary radius to be 1.00 R⊙.

  3. The centre of mass (COM) or the gamma velocity of the binary is fixed at 12.6 km/s (the cluster mean).

The model generation followed these steps:

  1. Setting up an initial model with random draws from a set of masses (Mpri = 0.2, 0.5, 0.6, and 0.8 M⊙), eccentricities (e = 0.0, 0.2, 0.5, and 0.8), mass ratios (q = 0.5, 1.0, and 1.5), and binary periods (P; randomly between 0−90 days). The mass ratios and binary periods are guess values that are needed in order to initialise the PHOEBE2 set-up. We generated an initial set-up of 480 models.

  2. We apply the constraints and then q, P, and time of periastron passage (Tp) to best fit the observed RV values. The optimisation was done using the Nelder-Mead method (Nelder & Mead 1965) for 500 iterations.

  3. The optimisation discarded a few models if they failed to adhere to any pre-defined constraints. This gave us the final 396 models with possible q and P values.

The possible q and P values for our final binary models are shown in the left panel of Fig. D.1. The best-fit binary periods are clustered around three values: 39.12±4.65 days (51.26 % of the models), 17.83±1.26 days (16.4 %), and 6.65±0.92 days (6.8%) (right panel of Fig. D.1). The mass ratio, q, varies between 0.2 and 1.5 (56 %; grey dashed lines); however, the average values are around 1.0 for periods < 100 days (blue, red, orange, and green solid lines for masses 0.2, 0.5, 0.6, and 0.8 M⊙, respectively). We do not see any favourable eccentricity, but it is hard to constrain it with two epochs of observations.

thumbnail Fig. D.1.

Orbital period and mass ratio values obtained from the best-fitting binary models. Left panel: Distribution of mass ratio (q) and orbital periods (P) with primary masses 0.2, 0.5, 0.6, and 0.8 M⊙ (blue, red, orange, and green dots, respectively). The solid lines are linear fits of the q and P values for the separate primary masses considered. The grey dashed lines denote the range of favourable q values for the system. 56.6 % of the models have mass ratios between 0.5 and 1.5. Right panel: Distribution of the period of the best-fit models. We see three significant period distributions at ∼6 d, ∼18 d, and ∼39 d, with the 39 d distribution being more probable (51%).

thumbnail Fig. D.2.

Possible Keplerian models for radial velocity variations constrained to the observations (black dots). The models are for PAGB mass 0.2 M⊙ (blue), 0.5 M⊙ (red), 0.6 M⊙ (orange), and 0.8 M⊙ (green) around the orbital periods 17.83±1.26 days (upper panels) and 39.12±4.65 days (lower panels). The dashed grey curves represent the possible RV of the secondary to maintain the COM velocity as 12.6 km/s (black dotted line).

In Fig. D.2 we provide the possible RV values for the primary (coloured solid lines) and companion stars (grey solid lines) for a period of 17.83 days (upper panels) and 39.12 days (lower panels). The maximum RV can reach ∼100 km/s for the PAGB star with masses 0.6 M⊙ (period = 17.83 days) and 0.8 M⊙ (period = 39.12 days) (Fig. D.2).

Appendix E: Atmospheric parameter estimation from the high-resolution spectra

To derive the parameters of the stellar atmosphere from the CHIRON spectra, we used the TLUSTY model grid BSTAR2006 (Lanz & Hubeny 2007) and accompanied programs for calculating synthetic spectra (SYNSPEC, ROTIN; see Hubeny et al. 2021).

Synthetic profiles of the Balmer lines fit the observations only at a certain relation between Teff and logg. In the case of Hα and Hβ lines, these relations are similar in shape, but shifted relative to each other: log gβ(Teff) = log gα(Teff) − 0.4. The higher members of the Balmer series do not fall in the observed range (4505−6602 Å). Therefore, as the final relation for logg–Teff, we took the average between Hα and Hβ with an uncertainty of 0.2 dex.

The observations allowed us to construct a second relation involving the ionisation balance between Si II and Si III, whose lines are quite strong in the spectrum. We adjusted the silicon abundance (εSi) for each line of Si IIλ6347, 6371 and Si IIIλ4552, 4567, 4572 for a set of pairs (Teff, logg) along the found relation logg(Teff). For the true values of Teff and logg, the abundances εSi derived from Si II and Si III must coincide. We find that the coincidence of εSi over all lines Si III/Si II occurs at Teff = 16950 ± 100 K, logεSi = 7.31 ± 0.03, and ξ = 1.5 ± 0.5 km s−1 (see Fig. E.1). A big uncertainty of the corresponding value of logg = 2.37 ± 0.20 leads to an increase in the temperature uncertainty, making it asymmetric K. All calculations were made with the BSTAR2006 models with scaled solar abundances Z/Z⊙ = 1/2 (BL models) and ξ = 2 km s−1. We also redid all the calculations with the Z/Z⊙ = 1/5 (BS models) and ξ = 2 km s−1 to know the effect of variations in the chemical composition in the models. We find that it does not affect the relation log g − Teff, but it reduces Teff by 300 K in the diagram Teff − logεSi and increases logεSi by 0.04 dex. Thus, the final results are K, logg = 2.37 ± 0.20, and logεSi = 7.31 ± 0.05.

thumbnail Fig. E.1.

Silicon ionisation balance. Red is for Si II; the solid line is for Si IIλ6347, the dashed line is for Si IIλ6371. Blue is for Si III; the solid, dashed, dash-dotted lines are for Si IIIλλ4552, 4567, 4572, respectively. The shaded regions show the estimated uncertainties for each line.

Appendix F: Chemical composition of the individual elements

Table F.1.

Element abundances determined for the identified PAGB star. The abundances are estimated as logε = 12 + log(nX/nH) and [X/H]=log(nX/nH)−log(nX⊙/nH⊙). The solar values logε⊙ are from Asplund et al. (2009); σL is the standard deviation; is the final uncertainty, accounting for inaccuracies in the model parameters; N is the number of averaged lines.

Helium. He Iλλ4713, 4922, 5016, 5048, 5876 lines are considered. We removed the He Iλ4922 line from the averaging, because it is blended with some broad absorption feature and shows logεHe lower by 0.2 dex in comparison with the other lines. The rest of the lines agree well with each other. Figure F.1 shows the He I line profiles and fragments of the synthetic spectrum.

thumbnail Fig. F.1.

Observed profiles of He I lines (dots) are superposed on the model spectra (red lines). The numbers represent the values of logεHe.

Carbon. The abundance εC is derived from two strong lines C IIλλ 6578, 6583. Figure F.2 shows the C II lines profiles superposed on model spectra.

thumbnail Fig. F.2.

C II line profiles. The plot symbols are the same as in Fig. F.1. The numbers represent the values of logεC.

Nitrogen. The observed spectrum contains several weak lines: N IIλλ4601, 4607, 4630, 5000, 5001, 5005, 5011, 5667, 5680. The abundances derived from the various lines do not agree well with each other; stronger lines require a higher abundance than weaker ones. It indicates a high microturbulence velocity ξ > 10 km s−1, but the observed width of the lines is small and almost completely determined by the instrumental profile that puts a limit on ξ < 5 km s−1. Figure F.3 shows the N II line profiles superposed on model spectra.

thumbnail Fig. F.3.

N II line profiles. The plot symbols are the same as in Fig. F.1. The numbers represent the values of logεN.

thumbnail Fig. F.4.

O II line profiles. The plot symbols are the same as in Fig. F.1. The numbers represent the values of logεO.

Oxygen. A few weak lines of O II are seen in the spectrum. We used O IIλλ4642, 4649, 4662, and 4676. Figure F.4 shows the O II lines profiles superposed on model spectra.

Neon. The abundance εNe is derived from Ne Iλλ6143, 6402, and 6507, which agree well with each other. There are two weaker lines Ne Iλλ6266, 6599, but they show a logεNe value that is 0.3 dex lower and 0.3 dex higher than the rest of the lines.

Aluminium. Two lines are used: Al IIIλλ5697, 5723.

Silicon. The silicon abundance is determined simultaneously with the atmospheric parameters (see above).

Sulphur. We considered lines S IIλλ5014, 5032, 5432, 5454, 5640, and 5647, although only the lines λλ5014, 5640, and 5647 are reliably present in the observed spectrum. These lines give logεS= 6.51, 6.26, and 6.59, respectively. The S IIλ5032 line is relatively weak, but it is in agreement with the above-mentioned εS. However, at this abundance the lines S IIλλ5432, 5454 must be present in the observations. The absence of these lines puts a limit logεS ≲ 5.5. In any case, there is a sulphur deficiency logεS < 6.59 ([S/H]<  − 0.53).

Iron. Only one Fe line Fe IIIλ5156 is visible in the spectrum and gives logεFe = 6.8. More weaker lines Fe IIλλ5018, 5169 and Fe IIIλ5127 are predicted by the model and agree with the observations within the uncertainties at the found abundance. The Fe lines are very weak in the spectra of early-type stars, making the estimate of metallicity based on iron a very difficult task. Therefore, we must rely on the CNO abundances as metallicity proxies (Mello et al. 2012). For the star, we found that Z(CNO) is equal to 0.005, compared to the solar value of 0.012.

The final uncertainty we estimated as where σT, σg, and σξ are uncertainties in logε, related to the uncertainties of Teff, logg, and ξ, respectively. The quantity σM is an estimate of the uncertainty associated with the difference between the real metallicity and the given metallicity of the BL models.

Appendix G: SED fitting of the PAGB star

Table G.1.

Telescopes and their filters used in the SED fittings of the UVIT observed PAGB star.

thumbnail Fig. G.1.

SED fit of observed fluxes in UVIT, GALEX, UVOT, UVBRI, Gaia DR3, APASS, DENIS, 2MASS, and WISE filters (30 photometric fluxes in total from UV to IR) for the PAGB star. The coloured solids are the observed fluxes, the black solids are the best-fitting model fluxes, and the grey solid is the best-fitting TLUSTY model grid spectra.

The SED fitting of the PAGB star was performed using 30 photometric fluxes observed in different filters ranging from the UV to IR bands (Table G.1) and the theoretical fluxes from the TLUSTY non-LTE O/B stellar atmosphere model7 (TLUSTY model; Hubeny & Lanz 1995; Lanz & Hubeny 2007; Hubeny et al. 2021). The SED fitting procedure was performed in VO SED Analyzer8 (VOSA; Bayo et al. 2008). We fitted the observed photometric fluxes with the TLUSTY model grids and found that the best-fitting model grid has Teff = 18 000 K and logg = 2.25. The best-fitting model and observed fluxes are shown in Fig. G.1.

All Tables

Table 1.

Observation details of the PAGB star.

In the text
Table B.1.

Details of the spectroscopic observations of the PAGB star.

In the text
Table F.1.

Element abundances determined for the identified PAGB star. The abundances are estimated as logε = 12 + log(nX/nH) and [X/H]=log(nX/nH)−log(nX⊙/nH⊙). The solar values logε⊙ are from Asplund et al. (2009); σL is the standard deviation; is the final uncertainty, accounting for inaccuracies in the model parameters; N is the number of averaged lines.

In the text
Table G.1.

Telescopes and their filters used in the SED fittings of the UVIT observed PAGB star.

In the text

All Figures

thumbnail Fig. 1.

UVIT F169M filter image of E3. The half-light and tidal radius of E3 (Rh = 2.1′ and Rt = 8.49′, Harris 1996, 2010) are well within the field of view of UVIT. The red arrow indicates the probable post-AGB star. In the inset (upper right corner) the optical V-band image (Stetson et al. 2019) of the cluster (up to half-light radius) is shown. The PAGB star is easily distinguishable as one of the cluster’s brightest stars in both images.
In the text
thumbnail Fig. 2.

Diagrams showing the kinematics and photometric analysis of the cluster member sources with the Gaia data. The left panel shows the vector-point diagram of the cluster member sources from the Gaia catalogue (Vasiliev & Baumgardt 2021, grey dots) and the UVIT observed cluster member source (blue asterisk). The middle panel shows the parallax vs proper motion in RA (top) and Dec (bottom) for the Gaia-observed cluster members having parallax S/N (plx/e_plx) > 5 (grey dots) and the UVIT observed cluster member source (blue asterisks). The right panel shows BP−RP versus MG CMD in the absolute magnitude plane. The GaiaG magnitudes (grey dots) are scaled to absolute magnitudes using distance modulus, m − M = 14.50 (Baumgardt & Vasiliev 2021). The BaSTI-IAC isochrone of age 11 Gyr, [Fe/H] = −0.70 dex is overplotted as a red solid line. The zero-age HB (ZAHB) and terminal-age HB (TAHB) loci are shown as solid pink and dashed lines, respectively. The black dashed line shows different subcategories of PAGB and post-HB stars, as defined in Bond (2021).
In the text
thumbnail Fig. 3.

The log Teff versus log L (left panel) and log Teff versus logg (right panel) plots display PAGB stars that have been observed in GCs. The red asterisk indicates the newly discovered PAGB star in E3, and the blue asterisks indicate PAGB stars found in other GCs. In the upper left panel, the H-burning PAGB evolutionary tracks of Miller Bertolami (2016) and Moehler et al. (2019) with metallicity Z = 0.001 are shown as dashed and solid lines, respectively, and for different initial and HB masses (as shown in the legend at right). The PAGB tracks of Moehler et al. (2019) consider an initial mass of 0.85 M⊙ for all the evolutionary tracks. The lower left panel shows the post-RGB He-burning evolutionary tracks from Bloecker (1995) (green dotted line), Lei et al. (2015) (red dotted line), and Driebe et al. (1998) (black dotted line). The grey shaded region indicates a Teff range of 16 000–19 000 K. The current mass for each evolutionary track at ∼18 000 K is shown with an arrow of the same colour and style as the evolutionary track. In the right panel, PAGB stars are shown on the log Teff versus logg plane. The inset shows the zoomed-in view around the newly identified PAGB star.
In the text
thumbnail Fig. 4.

Comparison between abundance ratios of PAGB star of E3 and other GCs. PAGB stars with 3DU evidence are shown as blue asterisks; those with no 3DU evidence are shown as black asterisks. The newly identified PAGB star of E3 is shown as a red asterisk. The left panel shows C/CNO versus C abundance plot, whereas the right panel shows N/O vs. O abundance plot.
In the text
thumbnail Fig. C.1.

1D projections of the TODCOR cross-correlation functions (CCFs) for the spectra observed at two epochs. The vertical shaded regions represent the errors in the observation of the RVs. The first epoch (red) has a RV of 40.20 ± 0.57 kms−1 and the second epoch (blue) has a RV of 34.66 ± 0.85 kms−1.
In the text
thumbnail Fig. D.1.

Orbital period and mass ratio values obtained from the best-fitting binary models. Left panel: Distribution of mass ratio (q) and orbital periods (P) with primary masses 0.2, 0.5, 0.6, and 0.8 M⊙ (blue, red, orange, and green dots, respectively). The solid lines are linear fits of the q and P values for the separate primary masses considered. The grey dashed lines denote the range of favourable q values for the system. 56.6 % of the models have mass ratios between 0.5 and 1.5. Right panel: Distribution of the period of the best-fit models. We see three significant period distributions at ∼6 d, ∼18 d, and ∼39 d, with the 39 d distribution being more probable (51%).
In the text
thumbnail Fig. D.2.

Possible Keplerian models for radial velocity variations constrained to the observations (black dots). The models are for PAGB mass 0.2 M⊙ (blue), 0.5 M⊙ (red), 0.6 M⊙ (orange), and 0.8 M⊙ (green) around the orbital periods 17.83±1.26 days (upper panels) and 39.12±4.65 days (lower panels). The dashed grey curves represent the possible RV of the secondary to maintain the COM velocity as 12.6 km/s (black dotted line).
In the text
thumbnail Fig. E.1.

Silicon ionisation balance. Red is for Si II; the solid line is for Si IIλ6347, the dashed line is for Si IIλ6371. Blue is for Si III; the solid, dashed, dash-dotted lines are for Si IIIλλ4552, 4567, 4572, respectively. The shaded regions show the estimated uncertainties for each line.
In the text
thumbnail Fig. F.1.

Observed profiles of He I lines (dots) are superposed on the model spectra (red lines). The numbers represent the values of logεHe.
In the text
thumbnail Fig. F.2.

C II line profiles. The plot symbols are the same as in Fig. F.1. The numbers represent the values of logεC.
In the text
thumbnail Fig. F.3.

N II line profiles. The plot symbols are the same as in Fig. F.1. The numbers represent the values of logεN.
In the text
thumbnail Fig. F.4.

O II line profiles. The plot symbols are the same as in Fig. F.1. The numbers represent the values of logεO.
In the text
thumbnail Fig. G.1.

SED fit of observed fluxes in UVIT, GALEX, UVOT, UVBRI, Gaia DR3, APASS, DENIS, 2MASS, and WISE filters (30 photometric fluxes in total from UV to IR) for the PAGB star. The coloured solids are the observed fluxes, the black solids are the best-fitting model fluxes, and the grey solid is the best-fitting TLUSTY model grid spectra.
In the text

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