11institutetext:  Universidade de São Paulo, IAG, Rua do Matão 1226, Cidade
Universitária, São Paulo 05508-900, Brazil 22institutetext: UK Astronomy
Technology Centre, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, UK
33institutetext: IfA, University of Edinburgh, Royal Observatory, Blackford
Hill, Edinburgh, EH9 3HJ, UK 44institutetext: Instituto de Astrofísica,
Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago ,
Chile 55institutetext: Millennium Institute of Astrophysics, Av. Vicuña
Mackenna 4860, 782-0436 Macul, Santiago, Chile 66institutetext: Departamento
de Ciencias Fisicas, Facultad de Ciencias Exactas, Universidad Andres Bello,
Av. Fernandez Concha 700, Las Condes, Santiago, Chile 77institutetext: Vatican
Observatory, V00120 Vatican City State, Italy 88institutetext: Instituto de
Alta Investigación, Sede Esmeralda, Universidad de Tarapacá, Av. Luis Emilio
Recabarren 2477, Iquique, Chile 99institutetext: Università di Padova,
Dipartimento di Fisica e Astronomia, Vicolo dell’Osservatorio 2, I-35122
Padova, Italy 1010institutetext: INAF-Osservatorio Astronomico di Padova,
Vicolo dell’Osservatorio 5, I-35122 Padova, Italy 1111institutetext:
Universidade Federal do Rio Grande do Sul, Departamento de Astronomia, CP
15051, Porto Alegre 91501-970, Brazil

# Gemini/Phoenix H-band analysis of the globular cluster AL 3 ††thanks:
Observations collected at the Gemini Observatory, Proposals GS-2006A-C9 and
GS-2008A-Q-23-5, and at the European Southern Observatory (ESO), Proposal
64L-0212(A).

B. Barbuy 11 H. Ernandes 112233 S. O. Souza 11 R. Razera 11 T. Moura 11 J.
Meléndez 11 A. Pérez-Villegas 11 M. Zoccali 4455 D. Minniti 6677 B. Dias 88 S.
Ortolani 991010 E. Bica 1111

(Received; accepted )

###### Abstract

Context. The globular cluster AL 3 is old and located in the inner bulge.
Three individual stars were observed with the Phoenix spectrograph at the
Gemini South telescope. The wavelength region contains prominent lines of CN,
OH, and CO, allowing the derivation of C, N, and O abundances of cool stars.

Aims. We aim to derive C, N, O abundances of three stars in the bulge globular
cluster AL 3, and additionally in stars of NGC 6558 and HP 1. The spectra of
AL 3 allows us to derive the cluster’s radial velocity.

Methods. For AL 3, we applied a new code to analyse its colour-magnitude
diagram. Synthetic spectra were computed and compared to observed spectra for
the three clusters.

Results. We present a detailed identification of lines in the spectral region
centred at 15555 Å, covering the wavelength range 15525-15590 Å. C, N, and O
abundances are tentatively derived for the sample stars.

###### Key Words.:

Stars: Abundances, Atmospheres – Galaxy Bulge – Globular clusters: individual:
AL 3, NGC 6558, HP 1

††offprints: B. Barbuy

##  1 Introduction

The globular clusters AL 3, NGC 6558, and HP 1 share the characteristics of
having a metallicity of [Fe/H]$\sim$-1.0 and of being located in the Galactic
bulge. They are old and could represent the earliest stellar populations in
the Galaxy (Ortolani et al. 2006; Barbuy et al. 2018a; Kerber et al. 2019).

The star cluster AL 3 was discovered by Andrews & Lindsay (1967) and was also
cataloged as BH 261 by van den Bergh & Hagen (1975), reported as a faint open
cluster. It is reported in the ESO/Uppsala catalogue (Lauberts 1982) as ESO
456-SC78. Ortolani et al. (2006) showed that the star cluster shows B, V, I
colour-magnitude diagrams (CMD) typical of a globular cluster. It is centred
at J2000 $\alpha$ = 18h14m06.6s, $\delta$ =
$-$28o$38^{\prime}06^{\prime\prime}$, with Galactic coordinates l = 3.36o, b =
$-$5.27o, and located at 6$\aas@@fstack{\circ}$25 and 2 kpc from the Galactic
centre, hence in the inner bulge volume. The cluster has a depleted red giant
branch (RGB), similarly to low-mass Palomar clusters, indicating it to have
been stripped along its lifetime. This cluster has not been further observed
so far.

The NGC 6558 cluster is located in a window, identified by Blanco (1988), with
equatorial coordinates (J2000) $\alpha$ = 18h 10m18.4s, $\delta$ = -31∘ 45’
49” and Galactic coordinates l = 0.201∘, b = -6.025∘. It was analysed in terms
of CMD by Rich et al. (1998). Rossi et al. (2015) obtained a proper-motion-
cleaned CMD and presented a proper motion analysis, from which a study of its
orbits was given in Pérez-Villegas et al. (2018, 2020).

The globular cluster Cl Haute-Provence 1 or HP 1, also designated BH 229 and
ESO 455-SC11, was discovered by Dufay et al. (1954). It is located at J2000
$\alpha$ = 17h31m05.2s, $\delta$ = $-$29o$58^{\prime}54^{\prime\prime}$, with
Galactic coordinates l = 357.42o, b = 2.12o.

In the present work, we studied individual stars of these clusters in a
limited region of the spectrum in the H-band corresponding to the wavelength
region of the Phoenix spectrograph at the Gemini South telescope, centred at
15555 Å, and covering 15520-15590 Å, with a high spectral resolution of
R$\sim$75,000. This region was chosen for containing prominent lines of CN,
CO, and OH.

In Sect. 2, we examine the list of atomic and molecular lines in the region.
In Sect. 3, the observations are described. In Sect. 4, the CMD is analysed.
In Sect. 5, the stellar parameters are given. In Sect. 6, the C, N, O
abundances are derived. Conclusions are drawn in Sect. 7.

##  2 Spectroscopy in the H-band: Atomic and molecular lines

The H-band will be intensely observed in the near future, given the new
instruments placing emphasis on the near-infrared region, such as the James
Webb Space Telescope (JWST), and new spectrographs on ground-based telescopes
such as MOONS@VLT (presently CRIRES@VLT is available) and MOSAIC@ELT. The
project APOGEE (Apache Point Observatory Galactic Evolution Experiment), with
observations at a resolution of R$\sim$22,000 carried out at the 2.5-metre
Sloan Foundation Telescope at the Apache Point Observatory in New Mexico
(APOGEE-2N), and the 2.5-metre du Pont Telescope at Las Campanas Observatory
in Chile (APOGEE-2S), as described in Majewski et al. (2017) has shown the
power of the H-band.

Given the short wavelength range covering only 70 Å of the Phoenix
spectrograph, we faced the challenge of identifying the lines in moderately
metal-poor stars of the Galactic bulge, for which only a few lines are
available. Because the available lamps did not include lines in this region,
and experience proved that sky lines yielded a better wavelength calibration,
and given the short wavelength range, it is not straightforward to identify
the lines.

For this reason, we proceeded to a line identification, in the spectra of the
reference stars Arcturus and $\mu$ Leo, and created a shortened version of a
line list, containing only detectable lines.

Meléndez & Barbuy (1999, hereafter MB99) worked on a list of atomic lines in
the J and H bands. The list of lines mostly corresponded to the detectable
lines. That previous line list needed to be largely completed. Upon checking
the lines detectable in the wavelength range 15520-16000 Å, this was done by
verifying the line lists from APOGEE (Shetrone et al. 2015) and VALD (Piskunov
et al. 1995, Ryabchikova et al. 2015). We note that astrophysical oscillator
log gf strengths were applied to the APOGEE line list, and these should be
suitable for abundance derivation. Through a line-by-line check of its
detectability in the Arcturus spectrum, we identified lines of Mg I, Si I, Ca
I, Ti I, Mn I, and Ni I, and we were not able to find detectable lines from
the species C I, O I, Sc I, V I, Cr I, Co I, Cu I, Y I, and Y II. The spectra
computed including all lines of all these elements are entirely equivalent to
the one computed with the shortened line list, therefore to ensure
practicality when identifying which lines really contribute to a feature, we
created a table containing the detectable lines only. In this table, available
upon request, we report the oscillator strengths from MB99, APOGEE, VALD, and
adopted values, where in order of preference we adopted NIST and MB99.

Molecular electronic transition lines of CN A${}^{2}\Pi$-X${}^{2}\Sigma$, and
vibration-rotation CO X${}^{1}\Sigma^{+}$, OH X${}^{2}\Pi$ lines were included
in the synthetic spectra calculations. The line lists for CN were made
available by S. P. Davis, the CO line lists were adopted from Goorvitch
(1994), and the OH line list was made available by S. P. Davis and A. Goldman
(Goldman et al. 1998). For more details on CN, CO, and OH molecular lines, we
refer the reader to Meléndez & Barbuy (1999), Meléndez et al. (2001), and
Meléndez et al. (2002). TiO $\phi$-system b1$\Pi$-d1$\Sigma$ lines are also
present in the region. The line list by Jorgensen (1994) is included in the
calculations as described in Schiavon & Barbuy (1999) and Barbuy et al.
(2018a). The adopted dissociation potential of OH is 4.392 eV, D0 = 11.092 eV
for CO and D0 = 7.65 eV for CN (Huber & Herzberg 1979). The PFANT code
employed here for calculations of synthetic spectra is described in Barbuy et
al. (2018b), and it is available together with the atomic and molecular line
lists.111http://trevisanj.github.io/PFANT

We identified the lines in the reference stars Arcturus and $\mu$ Leo. For the
reference star Arcturus, the spectrum atlas from Hinkle et al. (1995) is used,
and for the metal-rich reference giant star $\mu$ Leo, APOGEE spectra are
used, and their studies are be presented elsewhere.

The adopted stellar parameters for Arcturus and $\mu$ Leo are from Meléndez et
al. (2003) and Lecureur et al. (2007), and they are reported in Sect. 5.

Table 1:  Log book of observations. Proposals GS-2006A-C9 on 15-16/07/2006, and GS-2008A-Q-23 on 10/04/2008 and 22/05/2008 Object | Date | LST | Exp. | Seeing |
---|---|---|---|---|---
|  | h:m | (m) | (”) |
NGC 6558-11 | 15-07-2006 | 22:00 | 2x25 | 0.6 |
NGC 6558-64 | 16-07-2006 | 14:48 | 3x30 | 0.7 |
NGC 6558-11 | 16-07-2006 | 16:33 | 2x20 | 0.5 |
NGC 6558-42 | 16-07-2006 | 19:13 | 2x30 | 0.7 |
NGC 6558-97 | 16-07-2006 | 20:25 | 3x20 | 0.6 |
NGC 6558-73 | 16-07-2006 | 21:38 | 2x30 | 0.9 |
HP 1-4 | 15-07-2006 | 13:42 | 3x30 | 0.6 |
HP 1-6 | 15-07-2006 | 20:12 | 3x30 | 0.6 |
HP 1-5 | 16-07-2006 | 13:03 | 3x30 | 0.8 |
HP 1-3 | 16-07-2006 | 18:02 | 2x30 | 0.6 |
AL 3-3 | 10-04-2008 | 15:58 | 4x15 | — |
AL 3-6 | 22-05-2008 | 15:09 | 4x15 | — |
AL 3-7 | 22-05-2008 | 16:21 | 4x15 | — |

##  3 Observations

The spectra of red giant stars of the bulge globular clusters NGC 6558, AL 3,
and HP 1 were observed with the Phoenix spectrograph installed on the 8m
Gemini South telescope. The program was tri-national from Brazil (PI: B.
Barbuy), Chile (PI: M. Zoccali), and Australia (PI: J. Meléndez).

The final suitable spectra include three stars of AL 3, two stars of NGC 6558,
and one star of HP 1, centred at 1.555 $\mu$m in the H band. Another three
stars in NGC 6558, and three in HP 1 were also observed; however, these showed
a low Signal-to-Noise (S/N), due to clouds or high airmass. The log of
observations is provided in Table 1.

This is the first spectroscopic work on AL 3, except for Gaia data (Gaia
Collaboration 2020). In Fig. 1, a 3 min $B$ exposure of AL 3 is shown for a
field extraction of 3.3’$\times$3.3’ (510$\times$510 pixels). The sample stars
of AL 3 are identified in the chart. Charts and identifications of the
observed stars in NGC 6558 and HP 1 are given in Barbuy et al. (2009, 2018)
and Barbuy et al. (2006, 2016), respectively.

Figure 1: AL 3: 3 min B image with the three sample stars identified.
Extraction of 3’$\times$3’. North is up and east is left.

###  3.1 Gaia cross-check

In order to verify the corresponding membership probability of observed stars
in AL 3, we performed the cross-match with Gaia Early Data Release 3 (EDR3;
Gaia Collaboration 2020). We selected stars within 20’ from the cluster centre
and used the renormalised unit weight error (RUWE) $\leq 2.4$ to ensure the
kinematics precision and the minimum match separation.

Having the high-precision EDR3 proper motions ($\mu_{\alpha}^{*}$ =
$\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$), we obtain the mean proper
motions for the cluster of $\mu_{\alpha}^{*}=3.59\pm 0.03$ mas yr-1 and
$\mu_{\delta}=-3.54\pm 0.04$ mas yr-1. These values are compatible with those
given in Baumgardt et al. (2019). We also computed the Gaussian membership
probability distribution of AL 3. We found that the stars AL3-6 and AL3-7 have
membership probabilities of 100%. Finally, the star AL3-3 has a relatively low
membership probability of $\sim$ 60%, but still, it could be considered a
member. Therefore, all three observed stars are probable members of AL 3.
Table 2 provides the Gaia EDR3 cross-match and the membership probabilities.

Table 2:  Gaia magnitudes, proper motions and membership probability. Star |  $\alpha$(J2000) |  $\delta$(J2000) | $G$ | $G_{RP}$ | $\mu_{\alpha}^{*}$ | $\mu_{\delta}$ | Memb
---|---|---|---|---|---|---|---
| deg | deg | mag | mag |  mas yr-1 |  mas yr-1 | %
AL3-3 | 273.5288067 | -28.6357960 | $14.186\pm 0.003$ | $13.323\pm 0.004$ | $3.78\pm 0.09$ | $-4.04\pm 0.07$ | 59
AL3-6 | 273.5247404 | -28.6346067 | $15.228\pm 0.003$ | $14.303\pm 0.011$ | $3.56\pm 0.06$ | $-3.64\pm 0.04$ | 100
AL3-7 | 273.5220767 | -28.6380356 | $13.924\pm 0.003$ | $13.062\pm 0.005$ | $3.58\pm 0.03$ | $-3.48\pm 0.03$ | 100

###  3.2 Radial velocity of AL 3

We were able to derive radial velocities for the sample stars. We used the low
S/N individual observations of each star (S/N$\sim$10.0) combined to increase
the signal-to-noise to S/N$\sim$18.0, and S/N$\sim$22.0 for AL3-3 and AL3-7,
respectively. Due to the stacking process, the most prominent features
identified are FeI 15,534.26, OH 15,542.10, TiI 15,543.758, TiO/NiI 15,55.25
blend, CN 15,555.25, and FeI 15,591.49. We also used the OH sky lines, as
listed in Table 2 by Meléndez et al. (2003). These features were used for
AL3-3, giving a radial velocity of -67.65 $\pm$ 3.65 kms-1. In the combined
spectrum of AL3-7, the same features result in a radial velocity of -68.93
$\pm$ 4.83 kms-1. The corresponding heliocentric velocities of -57.29 km.s-1
and -58.57 km.s-1 lead to a final mean heliocentric velocity of -57.93 km.s-1
$\pm$ 4.28 for AL 3. Figures 2 and 3 show the line identification and radial
velocity derivation.

The star AL3-6 shows a very noisy spectrum, and we verified that it was
observed under a high airmass of over 1.3, which also explains that it is
plagued with telluric features. For AL3-6, we obtained a different
heliocentric radial velocity, as shown in Fig. 4, of -29.57 $\pm$ 5.85 km.s-1,
compatible with the value given by Baumgardt et al. (2019) of -29.38 $\pm$
0.60 km.s-1.

The derived radial velocity is of crucial importance for the computation of
the cluster’s orbits - see Sect. 5. However, we obtained two different
figures: v${}_{\rm r}^{hel}$ = -57.93 and -29.57 km.s-1. In Fig. 4, we show
the spectrum of AL3-6 compared with that of AL3-7. Therefore, we obtained two
different radial velocities for AL 3, and consequently we considered both of
them for the calculation of orbits. Since we had already computed the orbits
for the lower value (from Baumgardt et al. 2019), we show the orbits for the
higher value here. Clearly, new observations of these stars in a more extended
wavelength range and with a higher S/N would be of great interest.

Figure 2: AL 3-3: Radial velocity derivation. The solid black line is the
observed spectrum, the solid grey line is the noise spectrum, the solid red
line is the synthetic spectrum, the dashed red lines are those used to derive
the radial velocity, and the dashed black lines are the OH sky lines. Figure
3: AL 3-7: Radial velocity derivation. The solid black line is the observed
spectrum, the solid grey line is the noise spectrum, the solid red line is the
synthetic spectrum, the dashed red lines are those used to derive the radial
velocity, and the dashed black lines are the OH sky lines. Figure 4: AL 3-6:
Radial velocity derivation. The solid black line is the observed spectrum, the
solid grey line is the spectrum of star AL3-7, the dashed red lines are those
used to derive the radial velocity, and the dashed black lines are the OH sky
lines.

##  4 Colour-magnitude diagram of AL 3

Ortolani et al. (2006) presented $B$, $V$, and Cousins $I$ images of AL 3,
observed on 2000 March 6 using the 1.54m Danish telescope at the European
Southern Observatory (ESO) at La Silla. They derived a reddening of E(B-V) =
$0.36\pm 0.03$ and a distance of $6.0\pm 0.5$ kpc, based on the magnitude of
the horizontal branch (HB) of AL 3, and suggested a metallicity of
[Fe/H]$=-1.3\pm 0.3$ from a comparison of the CMD with the mean locus of the
cluster M5.

Rossi et al. (2015) described the observations with EFOSC at the NTT (ESO), La
Silla in May 2012. They reported a distance of $\sim 6.5$ kpc, in agreement
with Harris (1996, 2010 edition). Pérez-Villegas et al. (2020) adopted both
distances of 6.0 and 6.5 kpc and the radial velocity from Baumgardt et al.
(2019) for the calculation of orbits.

We carried out the isochrone fitting using the SIRIUS code (Souza et al. 2020)
on the same AL 3 data presented in Ortolani et al. (2006). The metallicity was
limited by using a Gaussian prior with the value of Ortolani et al. (2006). We
adopted the Dartmouth Stellar Evolution Database (DSED - Dotter et al. 2008),
with [$\alpha$/Fe]=0.4 and primordial helium. The asymptotic giant branch
(AGB) is also shown, based on BaSTI isochrones (Pietrinferni et al. 2006),
since they are not available in DSED. The result is in very good agreement
with results from Ortolani et al. (2006) within $1-\sigma$. We obtain a
reddening of $E(B-V)=0.38\pm 0.04$, a distance of d${}_{\odot}=6.0\pm 0.6$
kpc, and a metallicity of [Fe/H]$=-1.34\pm 0.18$. Our age determination
indicates an old age of $13.4^{+1.0}_{-1.2}$ Gyr, indicating that AL 3 is
another relic fossil. It is important to stress that our distance of 6.0 kpc
is also in agreement, within $1-\sigma$, with the value of 6.5 kpc from Harris
(1996, 2010), Rossi et al. (2015), and Baumgardt et al. (2019).

Finally, we note that the dispersion of the data could be due to differential
reddening, together with contamination and blends. The reddening of AL 3 is
relatively high, and the differential reddening is certainly an issue, as it
is in other bulge globular clusters with similar reddening. We expect an
amount of about 20% of differential reddening. In principle it can be
corrected, but the standard procedures for differential reddening correction
in this cluster cannot be applied due to the few bona fide reference stars in
the CMDs.

Figure 5 shows the solution of isochrone fitting. The solid blue line
represents the median solution, while the shaded regions indicate the
solutions within $1-\sigma$. The red stars are the three sample stars.
Finally, Figure 13 exhibits the corner plots showing the (anti)correlations
between the parameters.

Figure 5: AL 3 $V$ vs. $V-I$ CMD. The black dots are the stars within 120
pixel from the cluster centre (see Ortolani et al. 2006). The red stars are
the observed stars of the present work. The solid blue line represents the
median solution of the isochrone fitting, while the blue region reveals the
solutions within $1-\sigma$.

##  5 Stellar parameters

###  5.1 NGC 6558 and HP 1

Individual stars of NGC 6558 were analysed with high-resolution spectroscopy
by Barbuy et al. (2007, 2018b) and with moderate-resolution spectroscopy by
Dias et al. (2015). The stars NGC6558-42 and NGC6558-64 are studied here.

Similar studies of HP 1 were carried out in Barbuy et al. (2006, 2016) and
Dias et al. (2016). In the 2006 article, the bright red giants were labelled
with numbers 1 to 6, for the purpose of identifying them in the cluster chart.
In 2016, we adopted the identification numbers corresponding to the
photometric reductions relative to observations obtained at the New Technology
Telescope (NTT) at ESO, in 1994, as described in Ortolani et al. (1997). HP1-4
and HP1-5 are stars 2115 and 2939 in Barbuy et al. (2016). HP1-2 is the same
as in Barbuy et al. (2006). In our study, we only analysed HP1-5.

###  5.2 AL 3

The magnitudes and colours as follows are indicated in Table 3: B, V from
Ortolani et al. (2006), V, I from Rossi et al. (2015), JHK from the 2MASS
catalogue (Skrutskie et al. 2006),222
$\mathtt{http://ipac.caltech.edu/2mass/releases/allsky/}$;
$\mathtt{https://irsa.iapc.caltech.edu}$ and JHK from the VVV survey (Saito et
al. 2012).333$\mathtt{horus.roe.ac.uk/vsa}$

Effective temperatures were initially derived from $B-V$, $V-I$, $V-K$, and
$J-K$ using the colour-temperature calibrations of Alonso et al. (1999). V,I
Cousins were transformed to V,I Johnson using ($V-I$)C=0.778($V-I$)J (Bessell
1979). The $J,H,K_{S}$ magnitudes and colours were transformed from the 2MASS
system to California Institute of Technology (CIT), and from this to
Telescopio Carlos Sánchez (TCS), using the relations established by Carpenter
(2001) and Alonso et al. (1998). The conversion of JHK VVV colours to the JHK
2MASS system was done using relations by Soto et al. (2013).

The temperatures resulting from photometry are of the order of 5000 K for the
three stars. These temperatures, however, are not compatible with another
indicator, which is the Hydrogen Brackett 16 line, centred at 15556.457 Å. A
fit of this line for both AL 3 stars was carried out iteratively, after
deriving their CNO abundances. The resulting temperatures, adopted in the
following analysis, are 4250 K and 4500 K for AL3-3 and AL3-7, respectively.
The fits to the hydrogen line are shown in Figure 6. For AL3-6, the low
quality of the spectrum does not allow the fit of the hydrogen line, in
particular due to strong telluric absorptions in the region. It appears to be
cooler and compatible with 4150 K. This incompatibly between photometric and
hydrogen-wing-derived temperatures is a main source of uncertainty in the
present study.

To derive the gravity, we used the PARSEC isochrones (Bressan et al.
2012).444http://stev.oapd.inaf.it/cgi-bin/cmd To inspect the isochrones, we
adopted a metallicity of [Fe/H]$=-1.0$, or overall metallicity Z$=0.00152$ (10
times below solar), and an age of 12 Gyr. Assuming a reddening of
$E(B-V)=0.36$ (Ortolani et al. 2006, and present results), leading to
$E(V-I)=0.478$ and A${}_{V}=1.12$, we transformed the apparent magnitudes to
absolute magnitudes, as well as the colours ($V-I_{corr}$ = $V-I$-$E(V-I)$),
and we identified the correspondence of the observed stars to the theoretical
isochrone.

The metallicity resulting from the CMD fitting is [Fe/H]=-1.34, which was
imposed as a prior. We inspected individual lines of Fe in the AL3-3 spectrum
and the fits are more compatible with [Fe/H]=-1.0. There is also the evidence
from other similar bulge globular clusters such as NGC 6558, NGC 6522, HP 1,
and Terzan 9, which are found to have [Fe/H]$\sim$-1.0 from high-resolution
spectroscopy. Bica (2016) showed that there is a peak in metallicity at
[Fe/H]$\sim$-1.0 in the bulge, which we also adopted for AL 3. An isochrone
fitting with this higher metallicity was tried, but appeared difficult to
converge. This is a second source of uncertainty of the present study. Final
adopted stellar parameters for program stars, and of the reference stars
Arcturus (Meléndez et al. 2003) and $\mu$ Leo (Lecureur et al. 2007), are
reported in Table 4.

Table 3:  AL 3: coordinates, magnitudes, and colours of sample stars. Star | 2MASS | $\alpha$(J2000) | $\delta$(J2000) | V | I | J | H | K | J | H | K |
---|---|---|---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  |  | 2MASS |  | VVV |
B11 | 18101902-3144506 | 18 10 19.01 | -31 44 50.64 | 15.902 | 14.275 | 13.136 | 12.440 | 12.280 | 13.017 | 12.397 | 12.248 |
B64 | 18101803-3145435 | 18 10 18.03 | -31 45 43.55 | 15.703 | 14.180 | 13.064 | 12.456 | 12.277 | 13.055 | 12.529 | 12.384 |
B73 | 18102150-3145268 | 18 10 21.50 | -31 45 26.77 | 15.709 | 14.187 | 13.128 | 12.449 | 12.316 | 13.047 | 13.047 | 12.313 |
F42 | — | 18 10 17.65 | -31 45 38.93 | 16.054 | 14.442 | — | — | — | — | — | — |
F97 | 18101520-3146014 | 18 10 15.21 | -31 46 00.67 | 16.037 | 14.467 | 13.183 | 12.481 | 12.338 | — | 12.503 | 12.378 |
HP1-2 | 17310585-2958354 | 17 31 05.60 | -29 58 34.00 | 16.982 | 14.332 | 12.210 | 11.268 | 10.969 | 14.588 | 13.675 | 13.368 |
HP1-4 | 17310538-2959199 | 17 31 05.30 | -29 59 20.00 | 17.070 | 14.281 | — | 11.67 | — | 11.258 | 11.392 | 10.688 |
HP1-5 | 17310729-2959021 | 17 31 07.20 | -29 59 02.00 | 17.131 | 14.395 | 11.901 | 10.869 | 10.595 | 12.021 | 11.285 | 10.898 |
AL3-3 | 18140691-2839087 | 18 14 06.90 | -28 38 09.0 | 14.524 | 13.204 | 12.214 | 11.631 | 11.469 | 12.211 | 11.714 | 11.544 |
AL3-6 | 18140592-2838049 | 18 14 05.80 | -28 38 06.0 | 15.563 | 14.203 | 12.763 | 12.272 | 12.256 | — | — | — |
AL3-7 | 18140529-2838168 | 18 14 05.30 | -28 38 19.0 | 14.313 | 12.963 | 11.878 | 11.296 | 11.170 | 11.920 | 11.472 | 11.195 |
Table 4:  Adopted stellar parameters for individual stars in NGC 6558, AL 3, and HP 1, and resulting C, N, O abundances. For NGC 6558, the stellar parameters are from Barbuy et al. (2007), and for HP 1 they are from Barbuy et al. (2016). Stellar parameters for the Sun, Arcturus, and $\mu$ Leo are also included.  Name | Teff | --log g | --[Fe/H] | vt | [C/Fe] | [N/Fe] | [O/Fe]
---|---|---|---|---|---|---|---
| (K) |  |  | km/s |  |  |
| Program stars
F42 |  -3800 |  -0.5 |  -$-$1.05 | 1.65 |  $-$0.5 | +0.8 | +0.5
HP1-5 |  -4525 |  -2.0 |  -$-$1.07 | 1.55 |  $-$0.1 | 0.8 | 0.5
AL3-3 |  -4250 |  -1.7 |  -$-$1.00 | 1.2 |  $-$0.1 | 0.0 | 0.0
AL3-6 | 4150 | 1.3 | -1.00 | 1.2 | +0.8 | +1.0 | +0.8
AL3-7 |  -4500 |  -1.5 |  -$-$1.00 | 1.2 |  $-$0.2 | -0.1 | 0.0
| Reference stars
Sun |  -5770 |  -4.44 |  -+0.00 | 1.0 | +0.00 | +0.00 | +0.00
Arcturus |  -4275 |  -1.55 |  -$-$0.54 | 1.65 | +0.11 | +0.40 | +0.43
$\mu$ Leo |  -4540 |  -2.3 |  -+0.30 | 1.3 |  $-$0.1 | +0.65 | +0.00
Figure 6: AL 3-3 and AL 3-7: Hydrogen Brackett 16 line computed for Teff =
4250, 4500, 4750, 5000 K (upper panels) and adopted values of 4250 K and 4750
K, respectively (lower panels). The dashed line is the observed spectrum
Figure 7: AL 3-6: Tentative fit to this low S/N spectrum, showing that it is
compatible with a high CNO abundance. Blue and black lines: Same observed
spectrum normalized in two different ways. Red and cyan lines: Synthetic
spectra computed with [C/Fe]=0.7 (red), 0.8 (cyan), [N/Fe]=+1.0, [O/Fe]=+0.8.

##  6 CNO abundances

The atmospheric models were interpolated in the grid of models by Gustafsson
et al. (2008). The synthetic spectra were computed employing the PFANT code
described in Barbuy et al. (2018b). In order to derive the C, N, O abundances,
we fitted the CN, OH, and CO lines iteratively.

###  6.1 The cool red giant N6558-42

The cool red giant, NGC6558-42, shows strong lines and is a typical red giant.
For this reason, we show the fits to the spectrum of this star in detail in
Figures 8 and 9.

The star NGC6558-64 instead, which would have an effective temperature of 4850
K according to the analysis from optical spectra by Barbuy et al. (2018b),
could be as hot as 5500 K. This is seen from the profile of its Hydrogen
Brackett 16 line; however, this should be taken with caution due to defects in
the observed spectrum. For this reason, we could not converge on CNO
abundances for this star.

Figure 8: NGC 6558-42: Line identification in the range 15527-15555 Å. Dashed
line: Observed spectrum. Solid red line: Synthetic spectrum. Synthetic
spectrum computed with [C/Fe]=-0.5, [N/Fe]=0.8, [O/Fe]=+0.5. Figure 9: NGC
6558-42: Same as Fig. 8, in the range 15555-15587 Å.

###  6.2 AL-3 and HP 1

There is a clear contrast between the spectra of HP1-5, AL3-3, and AL3-7, that
have shallow lines, and AL3-6 and NGC6558-42, that show strong lines. Whereas
NGC6558-42 is a typical red giant, the stars AL3-3, AL3-7, and HP1-5 show weak
molecular lines. From the location of stars AL3-3 and AL3-7 in the CMD of Fig.
5, they should be AGB stars. In Fig. 10, we show the observed spectrum in the
selected wavelength regions containing CN, OH lines, and the CO bandhead at
15578 Å for stars AL3-3, AL3-7, and HP1-5. The molecular lines are very
shallow, due to a combination of warm temperatures and low metallicities.
Clearly, the CNO abundances derived for these stars are less reliable than for
the cool star NGC6558-F42. Their CNO abundances are compatible with being
close to solar, but given the shallowness of the lines, it is clear that the
molecular lines are not reliable for abundance measurements.

AL3-6 instead shows very strong CNO lines. Figure 7 indicates that [C/Fe]=
+0.7, 0.8, [N/Fe]=+1.0, [O/Fe]=+0.8 for this star. We show two different
renormalisations to illustrate the difficulty in analysing this spectrum.
Additionally, the computations with two different carbon abundances illustrate
the extreme sensitivity of the lines. Clearly, however, there is an urgent
need to observe this star in the optical and/or in a more extended wavelength
region in the H-band to obtain firm conclusions on the CNO abundances of AL 3.

Figure 10: HP 1-5, AL 3-3, and AL 3-7: Spectrum in selected wavelength regions
containing CN, OH lines and the CO bandhead. Synthetic spectra are computed
for the CNO abundances given in Table 4.

###  6.3 Errors

The main uncertainty in the derivation of CNO abundances in AL 3 stems from
the effective temperatures. Adopting a colour excess E(B-V)=0.36 the
photometric magnitudes results in temperatures of $\sim$5000 K. In order to be
compatible with the wings of hydrogen lines, we would have to adopt
E(B-V)=0.2, but the present fit of the CMD confirms the high reddening value.

Hydrogen wings that we adopted are a very good temperature indicator, and the
temperatures can be roughly derived for the two stars showing the line,
whereas for the cooler star AL3-6, the H line is not strong, indicating that
it is cooler than the other two stars. For this star, we adopted Teff = 4150
K, compatible with its almost absent hydrogen-profile and a temperature
compatible with its location in the RGB. With this temperature, we obtained
high CNO values and could not converge with lower values. We note that the CN,
CO, and OH dissociation equilibrium interplay gives a strong constraint on the
result, but at the same time, these are very sensitive to abundance
variations. We adopted effective temperature errors of $\pm$250 K for AL3-6,
and $\pm$150 K for AL3-3 and AL3-7, errors of $\pm$0.8 for the gravity, and
$\pm$0.3 for metallicity.

###  6.4 Orbits of AL 3

In order to investigate whether AL 3 belongs to the bulge, thick disc, or
halo, given its solar CNO abundances, we carried out the calculations of
orbits for the cluster. We employed a Galactic model that includes an
exponential disc made by the superposition of three Miyamoto-Nagai potentials
(Smith et al. 2015), a dark matter halo with a Navarro-Frenk-White (NFW)
density profile (Navarro, Frenk & White 1997), and a triaxial Ferrers bar. The
total mass of the bar is $1.2\times 10^{10}$ M⊙, an angle of $25^{\circ}$ with
the Sun-major axis of the bar, and a major axis extension of 3.5 kpc. We
assumed three pattern speeds of the bar $\Omega_{b}=40$, 45, and 50 km s-1
kpc-1. We kept the same bar extension, even though we changed the bar pattern
speed. Our Galactic model has a circular velocity $V_{0}=241$ km s-1 at
$R_{0}=8.2$ kpc (Bland-Hawthorn & Gerhard 2016; which is also compatible with
the Gravity Collaboration et al. (2019)), and we assumed a peculiar motion of
the Sun with respect to the local circular orbit of
$(U,V,W)_{\odot}=(11.1,12.24,7.25)$ km s-1 (Schönrich, Binney & Dehnen 2010).

To take into account the effects of the observational uncertainties associated
with the cluster’s parameters, we generated a set of of 1000 initial
conditions using a Monte Carlo method considering the errors of distance,
heliocentric radial velocity, and absolute proper motion components. With such
initial conditions, we integrated the orbits forward for 10 Gyr using the NIGO
tool (Rossi 2015).

In Fig. 11, we show the probability density map of the orbits of AL 3 in the
$x-y$ and $R-z$ projections co-rotating with the bar, using the two adopted
distances, 6.0 kpc (Ortolani et al. 2006) and 6.5 kpc (Baumgardt et al. 2019).
The yellow colour displays the space region that the orbits of AL 3 cross more
frequently. The black curves are the orbits using the central values of the
observational parameters. In Figure 12, we show histograms relating to the
number of probable orbits as a function of pericentric distance (rmin),
apocentric distance (rmax), maximum height above the plane (—Z—max), and
eccentricity ($e$). In Table LABEL:Orb_para, we give the median values of the
orbital parameters, and the errors provided in each column are derived
considering the 16th and 84th percentiles of the distribution. The orbital
parameters are similar for the three pattern speeds. From the apocentric
distance, we can see that AL 3 is mostly confined within $\sim 4$ kpc, and it
has a high probability to belong to the bulge component ($\sim 88\%$) when the
adopted distance is 6.5 kpc. However, a significant fraction of orbits can
reach apocentric distances up to $\sim 6$ kpc, indicating that AL 3 could
belong to the disc component, with a non-negligible probability ($\sim 12\%$).

In Fig. 12, we show histograms relating to the number of probable orbits as a
function of pericentric distance (rmin), apocentric distance (rmax), maximum
height above the plane (—Z—max), and eccentricity. If a distance of 6.5 kpc is
adopted, then it is clear that AL 3 is a very central cluster, with a maximum
height reaching at most $Z\sim 1.5$ kpc, and with a high eccentricity orbit.
This is typical of the very old, moderately metal-poor globular clusters of
the Galactic bulge, similar to NGC 6522, NGC 6558, and HP 1.

On the other hand, if a distance of 6.0 kpc is adopted, according to Ortolani
et al. (2006), the cluster reaches distances farther from the Galactic centre
with lower eccentricities (see left and bottom and top panels of Figures 11
and 12, respectively). The probabilities also change to an $\sim$60 %
probability of belonging to the bulge and $\sim$40% to the disc. With this
distance, the probability of being part of the disc increases significantly,
and maybe this result could be more consistent with the solar CNO abundances.

Figure 11: Probability density map for $x-y$ and $R-z$ projections of the set
of orbits for AL 3 for distances of 6.0 kpc (left panels) and 6.5 kpc (right
panels), using three different values of $\Omega_{b}=40,45,$ and $50$ km s-1
kpc-1. The orbits are co-rotating with the bar frame. Yellow corresponds to
the larger probabilities. The black lines show the orbits using the central
values.

Figure 12: Distribution of orbital parameters for AL 3, for distances of 6.0 kpc (top panels) and 6.5 kpc (bottom panels), with pericentric distance $r_{\rm min}$, apocentric distance $r_{\rm max}$, maximum vertical excursion from the Galactic plane $|z|_{\rm max}$, and eccentricity $e$. The colours show the different pattern speed of the bar, $\Omega_{b}=40$ (blue), 45 (orange), and 50 (green) km s-1 kpc-1. Table 5: Median orbital parameters and membership probability of AL 3. $\Omega_{b}$ | $\langle r_{\rm min}\rangle$ | $\langle r_{\rm max}\rangle$ | $\langle|z|_{\rm max}\rangle$ | $\langle e\rangle$ | $\mathcal{P}_{\rm bulge}$ | $\mathcal{P}_{\rm disc}$
---|---|---|---|---|---|---
(km s-1 kpc-1) | (kpc) | (kpc) | (kpc) |  | (%) | (%)
$d_{\odot}=6.0$ kpc
40 | $1.00^{+0.43}_{-0.61}$ | $3.94^{+0.52}_{-0.66}$ | $1.36^{+0.19}_{-0.15}$ | $0.60^{+0.20}_{-0.10}$ | 61.7 | 38.3
45 | $0.84^{+0.47}_{-0.45}$ | $3.97^{+0.55}_{-0.65}$ | $1.36^{+0.16}_{-0.13}$ | $0.66^{+0.14}_{-0.15}$ | 60.1 | 39.9
50 | $0.75^{+0.89}_{-0.34}$ | $3.98^{+0.72}_{-0.65}$ | $1.31^{+0.15}_{-0.10}$ | $0.68^{+0.12}_{-0.20}$ | 60.6 | 39.4
$d_{\odot}=6.5$ kpc
40 | $0.46^{+0.69}_{-0.36}$ | $3.34^{+0.69}_{-0.61}$ | $1.41^{+0.21}_{-0.19}$ | $0.75^{+0.18}_{-0.19}$ | 89.2 | 10.8
45 | $0.47^{+0.50}_{-0.36}$ | $3.39^{+0.76}_{-0.67}$ | $1.40^{+0.17}_{-0.17}$ | $0.76^{+0.17}_{-0.15}$ | 87.9 | 12.1
50 | $0.53^{+0.35}_{-0.40}$ | $3.42^{+0.75}_{-0.73}$ | $1.33^{+0.15}_{-0.17}$ | $0.74^{+0.17}_{-0.12}$ | 88.5 | 11.5

##  7 Conclusions

We analysed spectra of individual stars of the globular clusters AL 3, NGC
6558, and HP 1, obtained with the PHOENIX spectrograph at the Gemini South
telescope. With a high spectral resolution of R$\sim$75,000, in the H band
centred at 15555 Å, the wavelength coverage is short (15520 - 15590 Å).

In AL 3, this limited wavelength range means that it is difficult to use
atomic lines to deduce the stellar parameters effective temperature, gravity,
and metallicity. For this reason, we obtained the effective temperature from
the Hydrogen Brackett 16 line, gravity from photometric data, and isochrones.
The metallicity [Fe/H]$\sim$-1.3$\pm$0.3 was deduced from the observed CMD
given in Ortolani et al. (2006) and is confirmed in the present work through
analysis of the same CMD. We note that we adopted [Fe/H]=-1.0 for the analysed
stars, due to spectroscopic evidence. For NGC 6558 and HP 1, the stellar
parameters were adopted from previous analyses from optical spectra (Barbuy et
al. 2007, 2018), and Barbuy et al. (2006, 2016) respectively. Adopting these
stellar parameters, we computed the synthetic spectra in order to derive the
abundances of C, N, and O. Since they vary interdependently, the fit was done
iteratively, where particular attention was given to the CO bandhead. The
stars analysed in NGC 6558 and HP 1 show typical CNO abundances of red giants,
and confirm previous oxygen abundance derivation.

AL 3 is a more complex case: two stars analysed in AL 3 show solar CNO
abundance ratios, but based on very shallow lines, and the location of these
two stars in the CMD point to them being AGB stars. The star AL3-6 shows
instead very strong CNO abundances of the order of [C/Fe]=+0.8, [N/Fe]=+1.0,
[O/Fe]=+0.8. A strong CNO abundance indicated by this cooler star shows that
AL 3 appears to be an extremely interesting old cluster. In conclusion,
further investigation of this cluster are clearly needed. We also derived the
cluster’s radial velocity, which in turn allowed us to compute the cluster
orbits. For the two AGB stars, we found a higher velocity, whereas for the
third cooler star, the radial velocity is compatible with the value from
Baumgardt et al. (2019).

The orbital behaviour of AL 3 indicates that it is a typical inner bulge,
moderately metal-poor globular cluster if its distance to the Sun is 6.5 kpc
(Baumgardt 2019), but if the distance is 6.0 kpc (Ortolani et al. 2006 and
present work), there is an increased probability of AL 3 belonging to a diss
component. We derive a very old age for AL 3 of 13.4 Gyr, which would point
towards an old bulge cluster. Therefore, we conclude that the cluster AL 3
appears to be an extremely interesting cluster that should be further
investigated through more wavelength-extended spectra, and including larger
samples of member stars.

###### Acknowledgements.

BB, HE, RR, JM, and EB acknowledge grants from FAPESP, CNPq and CAPES -
Financial code 001. TM acknowledges FAPESP postdoctoral fellowship no.
2018/03480-7. APV acknowledges FAPESP postdoctoral fellowship no.
2017/15893-1. Support for MZ is provided by Fondecyt Regular 1191505, the
BASAL CATA Center for Astrophysics and Associated Technologies through grant
PFB-06, and ANID - Millennium Science Initiative Project ICN12_009, awarded to
the Millenium Institute of Astrophysics (MAS). S.O. acknowledges the partial
support of the research program DOR1901029, 2019, and the project BIRD191235,
2019 of the University of Padova.

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##  Appendix A Isochrone fitting - corner plot

The SIRIUS code performs the isochrone fitting through the construction of the
Markov chain Monte Carlo (MCMC) algorithms. The purpose of the MCMC method is
to obtain the posterior distribution of each parameter via the generation of
random samples. Figure 13 shows the corner plots, that is, a graphical
representation of the 4D parameter space of the isochrone fitting (age,
reddening, distance, and metallicity). The histograms represent the cumulative
best solutions (posterior distribution) for each parameter, while the 2D
density maps show the correlations between the parameters as well as the
region with the highest density. To represent the posterior distributions of
each parameter, we adopt the region of highest density as the central value
and the uncertainties calculated from the 16th and 84th percentiles.

Figure 13: Corner plots representing the 4D parameter space of the Markov
chain constructed through the Monte Carlo algorithm for the isochrone fitting.
To represent the solutions, we adopt the peak of the distribution as the best
value, and the uncertainties are computed using the $16^{th}$ and $84^{th}$
percentiles. More details are available in Souza et al. (2020).