# HST observations of the globular cluster NGC 6402 (M 14) and its peculiar
multiple populations

Francesca D’Antona  INAF– Osservatorio Astronomico di Roma, Via Frascati 33,
00078 Monteporzio Catone (Roma), Italy  Antonino P. Milone  Dipartimento di
Fisica e Astronomia “Galileo Galilei”, Univ. di Padova, Vicolo
dell’Osservatorio 3, Padova, IT-35122  Christian I. Johnson  Space Telescope
Science Institute, 3700 San Martin Dr., Baltimore, MD 21218, USA  Marco Tailo
Dipartimento di Fisica e Astronomia “Galileo Galilei”, Univ. di Padova, Vicolo
dell’Osservatorio 3, Padova, IT-35122  Dipartimento di Fisica e Astronomia
“Augusto Righi”, Università degli Studi di Bologna, Via Gobetti 93/2, I-40129
Bologna, Italy  Enrico Vesperini  Department of Astronomy, Indiana University,
Bloomington, IN 47401, USA  Vittoria Caloi  INAF – IAPS Roma, Via Fosso del
Cavaliere, Roma, Italy, IT-00133  Paolo Ventura  INAF– Osservatorio
Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone (Roma), Italy
Anna Fabiola Marino  INAF-Osservatorio Astrofisico di Arcetri, Largo E.Fermi,
5. 50125, Firenze, Italy  Flavia Dell’Agli  INAF– Osservatorio Astronomico di
Roma, Via Frascati 33, 00078 Monteporzio Catone (Roma), Italy

(Received XXXX; Revised XXX; Accepted XXXX)

###### Abstract

We present Hubble Space Telescope (HST) photometric results for NGC 6402, a
highly reddened very luminous Galactic globular cluster (GC). Recent
spectroscopic observations of its red giant stars have shown a quite peculiar
behavior in the chemistry of its multiple populations. These results have
prompted UV and optical HST observations aimed at obtaining the cluster’s
“Chromosome map” (ChM), an efficient tool to classify GCs and characterize
their multiple populations. We find that the discontinuity in the abundance
distributions of O, Mg, Al and Na inferred from spectroscopy is more nuanced
in the ChM, which is mostly sensitive to nitrogen. Nevertheless, photometry in
optical bands reveals a double main sequence, indicating a discontinuity in
the helium content of the populations. The population with the largest
chemical anomalies (extreme) peaks at a helium mass fraction Y$\sim$0.31. This
helium content is consistent with results from the analysis of the
distribution of horizontal-branch stars and the spectrophotometry of the red
giants. The ChM and the color magnitude diagrams are compared with those in
NGC 2808, a prototype GC with helium abundances up to Y$\gtrsim$0.35, and both
confirm that NGC 6402 does not host stellar populations with such extreme
helium content. Further, the ChM reveals the presence of a group of stars with
larger metallicity, thus indicating that NGC 6402 is a Type II cluster. The
modalities of formation of the multiple populations in NGC 6402 are briefly
surveyed, with main attention on the Asymptotic Giant Branch and Supermassive
star models, and on possible clusters’ merging.

stars: evolution; Globular Clusters

††journal: ApJ

##  1 Introduction

In spite of being the tenth cluster in terms of luminosity (and mass) among
the Galactic globular clusters (GC), NGC 6402 (M 14) has not been subject to
close scrutiny like other massive GCs, being located close to the galactic
plane and highly reddened (E(B-V)$\simeq$0.6). The cluster has a moderately
high metallicity of [Fe/H]=$-1.13\pm 0.05$ (Johnson et al., 2019), which is
similar to that of NGC 2808, the cluster prototype for the study of multiple
populations (MPs). HST photometry from the Piotto et al. (2002) snapshot
survey showed that NGC 6402 is an example of a “second–parameter” cluster (for
a recent discussion, see Tailo et al., 2020), as its horizontal branch (HB)
morphology is too blue for its metallicity. In fact, the HB includes only a
few stars on the red side of the RR Lyr gap and extends to high Teff. The most
complete ground based photometry (B and V) down to the upper main sequence
(MS) is provided by Contreras Peña et al. (2013). The analysis and a catalogue
of 110 RR Lyr stars is given by Contreras Peña et al. (2018), who also
summarize the possible indications that this cluster has an extragalactic
origin.

The light element abundances in Galactic (but also in the extragalactic) GCs
display large variations, with typical anti–correlations indicating the
presence of two or more chemically distinct groups of stars (see e.g. Gratton
et al., 2019, for a recent comprehensive summary). While the elemental
abundances in some stars are similar to those of halo stars having the same
metallicity (population 1G), the majority of stars show abundance patterns
typical of gas processed at very high temperature (T$\sim$30–100 MK, depending
on the locus of processing) by proton capture reactions (population 2G111The
nomenclature here follows that of Milone et al. papers. 1G actually means
‘first generation’ to be considered as the generation of stars from which any
population with signatures of hot proton capture nucleosynthesis necessarily
follows (second generation or 2G), either within $\sim$106 yr (supermassive
star model) or within $\sim$108 yr (AGB model). Where confusion with previous
definitions arises we will clarify them.). The abundance of helium in the
standard halo and in the 1G of GCs is settled on the Big Bang composition
(Y$\sim$0.25 in mass fraction). However, it is larger in the p-processed gas
of the enriched populations and reaches values up to Y$\sim$0.35 in the
‘extreme’ groups present in a few massive clusters, such as $\omega$ Cen and
NGC 2808. In these clusters, the 2G itself is split into separate groups,
highlighted photometrically by splits of the MS due to the different values of
Y in each of them (Bedin et al., 2004; D’Antona et al., 2005; Lee et al.,
2005; Piotto et al., 2007; Tailo et al., 2016; Bellini et al., 2017), and, in
NGC 2808, by the grouping of different abundance anomalies revealed by high
dispersion spectroscopy (Carretta, 2015). A standard value of Y$\sim$0.35 is
quoted in the literature for the blue MS of NGC 2808 (e.g. D’Antona et al.,
2005), Y=0.37 is derived for the more complex case of $\omega$ Cen (e.g. Tailo
et al., 2016).

In recent years, photometry in the UV bands, especially in the HST bands of
the UV WFC3/UVIS filters F275W and F336W, complemented with the blue filter
F438W, has proven to be a powerful way of achieving information on the
multiple populations, thanks to the sensitivity of these filters to the C, N,
and O abundance variations. The results of the HST UV Legacy survey (Piotto et
al., 2015) permitted classifying GCs in terms of their “Chromosome Maps”
(ChMs, Milone et al., 2017), a pseudo-two color diagram where stars belonging
to the different populations cluster in different loci, as shown by the
comparison with the results of high dispersion spectroscopy (Marino et al.,
2019). Thus spectra and HST UV photometry are useful complementary tools to
investigate multiple populations and attempt to reach a full understanding of
their formation.

Both tools have shown that the most massive GCs exhibit the most complex
chemical patterns. C–N and Na–O anticorrelations are commonly present in all
GCs, but the most massive clusters also show Mg–Al, and sometimes even Mg–K
anticorrelation (e.g., Cohen & Kirby, 2012; Mucciarelli et al., 2015;
Carretta, 2021). A small fraction of Galactic GCs show significant iron
abundance variations, with very significant cluster-to-cluster differences in
the percentage of stars with higher metallicity and in the degree of iron
enhancement (see, e.g. Johnson et al., 2015, and references therein). These
“iron–complex” clusters, discovered by spectroscopy and by the split RGB in
the hk narrow-band photometry (e.g. Lee, 2015; Lim et al., 2015), have been
also identified by their remarkably complex ChM, as the higher metallicity
stars are located at the red side of the standard ChM loci, and they were
dubbed ‘Type II’ clusters (Milone et al., 2017). Most Type II clusters have HB
morphologies that extend to very high temperatures, which commonly identifies
these stars as descendants of the high–helium population (e.g. D’Antona &
Caloi, 2004, 2008). Finally, the more massive clusters contain a larger
fraction, up to more than 80%, of stars belonging to the anomalous 2G (see
Fig. 22 in Milone et al., 2017).

There is consensus that the gas forming the 2G has been exposed to high
temperatures, but the site and modalities of the consequent nuclear processing
are still debated. No models are fully consistent with the formation of
multiple populations (see, e.g. Gratton et al., 2019). Collecting data and
analysing the cluster-to-cluster differences in the chemical patterns helps to
discriminate among models and collect information on the formation process of
these fundamental galaxy constituents.

NGC 6402 also hosts “multiple populations”, as shown by Johnson et al. (2019),
who determined the chemical composition of 41 NGC 6402 giants by means of high
resolution spectra obtained with the Magellan-M2FS instrument. The Johnson et
al. (2019) analysis highlighted interesting peculiarities in the abundance
patterns of light elements, which prompted the present investigation. The
giants in the sample were shown to belong either to the P1 (1G), 12/35 giants
$\sim$34%, or to a very mildly polluted population (P2, which here we will
call 2G mild222The Johnson et al. (2019) work follows the nomenclature by
Carretta et al. (2018), who subdivides the stars in NGC 2808 into five groups
with increasing anomalies: P1, P2, I1, I2 and E. Roughly these groups
correspond to the ChM groups B (P1), C (P2), D (I1 and I2) and E (E) by Milone
et al. (2015) —see Sect. 5. Here we will use the term 1G (P1), 2G mild (P2)
and 2G extreme or E. Further nomenclature will be added in Sect. 3. , 14/35
giants $\sim$40%), or to a population with ‘extreme’ anomalies (E, 9/35 giants
$\sim$26%). The cluster is apparently lacking giants with ‘intermediate’ (I)
compositions between the 2G mild and 2G extreme or E group, and this may be
due to the precise modalities of formation. The gap in chemistry is a further
indication that the formation of MPs occurs discontinuously, in bursts. It may
also suggest that different polluters are at play in forming the gas of the E
and 2G mild populations. In fact Johnson et al. (2019) propose that the E
group is born in the gas processed in supermassive stars (hereinafter SMS,
Denissenkov & Hartwick, 2014), formed in the early phases of cluster formation
by merging of massive stars, and that the P2 (2G mild) group is formed much
later on, by AGB winds very diluted with re-accreting pristine gas, following
the model first proposed by D’Ercole et al. (2008); see also Calura et al.
(2019) for recent simulations.

We refer to Gratton et al. (2019) for a detailed summary of models proposed in
the literature, and limit a more detailed analysis to formation of the second
population in matter polluted by SMS (Denissenkov & Hartwick, 2014;
Denissenkov et al., 2015; Gieles et al., 2018) and to the AGB model (see, e.g.
D’Ercole et al., 2008; Bekki, 2011; D’Antona et al., 2016; Bekki & Tsujimoto,
2017; Ventura et al., 2018). These two models have qualitatively survived a
preliminary scrutiny, although with well recognized difficulty. The main
problems still hampering their validation are: i) for the AGB model, the issue
of the oxygen and sodium abundances in the extreme stars; ii) for the SMS
model, the formation itself of such objects, and the necessity of freezing
their H–burning stage to incomplete core hydrogen burning. Consequently,
observations which may help to understand whether two polluting sources are
needed in the complex formation of GCs, or at least for some of them, is an
issue which deserves attention and a deep analysis.

Recently attention has been also focused on the possible paths of formation of
iron–complex clusters, either along the same paths of formation of the MPs
(D’Antona et al., 2016; Lacchin et al., 2021; Wirth et al., 2021), or by
considering the possible merging between clusters differing in metallicity
(van den Bergh, 1996; Amaro-Seoane et al., 2013; Bekki & Tsujimoto, 2016;
Gavagnin et al., 2016; Khoperskov et al., 2018). As NGC 6402 will result to be
a Type II cluster, we will also ask whether this feature offers clues for the
formation model.

Figure 1: Left Panel. $m_{\rm F275W}$ vs. $m_{\rm F275W}-m_{\rm F814W}$ CMD of
NGC 6402 for stars in the central field. Right Panel. $m_{\rm F275W}$ against
the rms of the $m_{\rm F275W}$ measurements. HB non-variable stars, AGB stars,
and variable stars are colored blue, red, and aqua, respectively.

Figure 2: $m_{\rm F336W}$ vs. $m_{\rm F336W}-m_{\rm F438W}$ CMD (left) and
$m_{\rm F814W}$ vs. $C_{\rm F275W,F336W,F438W}$ pseudo CMD for stars in the
central field. Colors are the same as in Figure1

The HST UV observations of the central regions of NGC 6402 were planned to
further constrain the models, by adding the photometric information useful to
identify different stellar populations and combining this information with the
spectroscopic analysis. In this work we present the results of the UV
photometry of the core region of the cluster, its color magnitude diagrams,
and the ChM, and compare them with the most similar cluster in terms of mass
and metallicity, NGC 2808. We also present and compare with NGC 2808 the
observations of a deep color magnitude diagram in the bands F475W and F814W
obtained in parallel field exposures, and give a preliminary analysis of the
HB stellar distribution.

We show that NGC 6402 hosts less extreme populations than NGC 2808, as it
could also be evinced from the lack of extreme Mg depletion in the oxygen poor
giants. The maximum helium abundance in the E population results to be
Y$\sim$0.31, much smaller than the abundance required by present day massive
AGB models and by the SMS models so far analysed to be consistent with strong
oxygen reduction in the abundances. We briefly discuss the consequences of
these results.

##  2 Observations and data reduction

To investigate multiple stellar populations we exploit Hubble Space Telescope
(HST ) images of two fields of view in the direction of NGC 6402 as part of
GO-16283 (PI F. D’Antona). The primary field includes the cluster center and
has been observed through the F275W, F336W, F438W and F814W filters of the
Ultraviolet and Visual Channel of the Wide Field Camera 3 (UVIS/WFC3).
Parallel observations have been conducted with the Wide Field Channel of the
Advanced Camera for Surveys (WFC/ACS) through the F475W and F814W bands.
Additional information on the dataset is provided in Table 1.

Photometry and astrometry was carried out with the computer program KS2 by
using images corrected for the effects of poor charge transfer efficiency of
the UVIS/WFC3 and WFC/ACS detectors (Anderson & Bedin, 2010). The KS2 program
was written by Jay Anderson, and is the evolution of $kitchen\\_sink$,
originally developed to reduce two-filter ACS/WFC images (Anderson et al.,
2008). KS2 follows different recipes to derive stellar fluxes and positions.
The first method measures the stars in each exposure independently, by fitting
the appropriate effective point-spread function (PSF) models. The various
measurements are then averaged together to get the best estimates of
magnitudes and positions. This method provides the best measurements of bright
stars. To measure faint stars that have not enough flux to be properly
constrained by the PSF fit, KS2 combines the information from all exposures by
fixing the average stellar positions from all exposures. After subtracting
neighbor stars, it measures the faint stars by means of aperture photometry.
We refer to papers by Sabbi et al. (2016) and Nardiello et al. (2018) for
details on KS2.

Stellar positions have been corrected for geometric distortion by using the
solutions presented in Bellini & Bedin (2009) and Bellini et al. (2011).
Photometry has been calibrated to the Vega magnitude system by using the zero
points of the WFC/ACS and UVIS/WFC3 filters available at the Space Telescope
Science Institute web pages. Since we are interested in investigating multiple
populations, we selected the sample of well measured stars, which are
relatively isolated and well fitted by the PSF (see Milone et al., 2009, for
details). To do this, we exploited the diagnostics provided by the KS2
program, including magnitude rms, the fraction of flux in the aperture due to
neighbours and the quality of the PSF fit. Finally, the photometry was
corrected for differential reddening by using the method and computer program
described in Milone et al. (2012a).

Table 1: Description of the HST images used in the paper. All images are collected on February 6th-13rd 2021 as part of GO-16283 (PI F. D’Antona). CAMERA | FILTER | N$\times$EXPTIME
---|---|---
| Primary Field |
UVIS/WFC3 | F275W | 987s$+$988s$+$10$\times$1050s$+$
|  | 3$\times$1172s+1181s
UVIS/WFC3 | F336W | 11$\times$761s
UVIS/WFC3 | F438W | 2$\times$100s+10$\times$348s
UVIS/WFC3 | F814W | 10$\times$110s
| Parallel Field |
WFC/ACS | F475W | 350s$+$822s$+$2$\times$890s$+$
|  | 10$\times$990s$+$1046s$+$1091s
WFC/ACS | F814W | 35s$+$350s$+$10$\times$619s$+$719s

##  3 Photometric diagrams of NGC 6402

The differential-reddening corrected photometry has been used to build
photometric diagrams that are sensitive to multiple stellar populations.

###  3.1 The Color Magnitude diagrams

The left panel of Figure 1 shows $m_{\rm F275W}$ vs. $m_{\rm F275W}-m_{\rm
F814W}$ for stars in the central field. Thanks to the wide color baseline,
this CMD maximizes the effective-temperature differences among MS and RGB
stars with similar luminosities and provides an exquisite tool to identify
stellar populations with different helium abundances. The right panel of
Figure 1 shows the rms of the F275W magnitude determinations against $m_{\rm
F275W}$. The fact that some stars exhibit large rms values, when compared with
the bulk of stars of similar magnitude, is a signature of stellar variability.
The sample of candidate variables comprises 71 stars that are represented with
aqua triangles in both panels of Figure 1, including 65 candidate RR Lyrae,
two blue stragglers, two hot-HB stars, and two post-HB stars.

Two additional CMDs are provided in Figure 2 for stars in the central field. A
split RGB is clearly visible in the $m_{\rm F336W}$ vs. $m_{\rm F336W}-m_{\rm
F438W}$ CMD, which is the HST analogous of $U$ vs. $U-B$ and is mostly
sensitive to nitrogen variations (Marino et al., 2008). The $m_{\rm F814W}$
vs. $C_{\rm F275W,F336W,F438W}$ also reveals a broad RGB, thus confirming that
NGC 6402 hosts stellar populations with different light-element abundances.
Intriguingly, the AGB of NGC 6402 exhibits a wide $C_{\rm F275W,F336W,F438W}$
intrinsic spread, which is comparable with that of RGB stars with similar
luminosity. This fact demonstrates that, similarly to the RGB, the AGB of NGC
6402 hosts multiple populations.

Figure 3: Left panels show $\Delta_{C,{\rm F275W,F336W,F438W}}$ vs.
$\Delta_{\rm F275W-F814W}$ (top) and $\Delta_{\rm F336W-F438W}$ vs.
$\Delta_{\rm F275W-F814W}$ ChMs (bottom) of RGB stars in NGC 6402. The
corresponding Hess diagrams are plotted in the right panels.

###  3.2 The Chromosome map

The Chromosome map (ChM) is a pseudo two-color diagram of MS, RGB, or AGB
stars obtained from appropriate filter combinations that maximize the
separation among stellar populations in GCs (Milone et al., 2015; Marino et
al., 2017). However, the ChM differs from a simple two-color diagram because
the sequence of stars is verticalized on both colors.

Here, we derived two distinct ChMs of RGB stars based on the $m_{\rm F814W}$
vs. $m_{\rm F275W}-m_{\rm F814W}$, the $m_{\rm F814W}$ vs. $m_{\rm
F336W}-m_{\rm F438W}$ CMD, and the $m_{\rm F814W}$ vs. $C_{\rm
F275W,F336W,F438W}$ pseudo CMD by following the recipe by Milone et al. (2015,
2017, see their Section 3.1)333In a nutshell, to derive the $\Delta_{\rm
F275W,F814W}$ pseudo color of RGB stars, we divided the $m_{\rm F814W}$ vs.
$m_{\rm F275W}-m_{\rm F814W}$ CMD into 0.1-mag wide magnitude bins and
calculated the 4th and the 96th percentiles of the $m_{\rm F275W}-m_{\rm
F814W}$ color distributions of RGB stars in each bin. These quantities have
been associated with the median values of the F814W magnitude distribution of
the stars in each bin and have been linearly interpolated to derive the blue
and red boundaries of the RGB. The $\Delta_{\rm F275W,F814W}$ pseudo-color has
been derived by means of Equation 1 from Milone et al. (2017), which tranforms
the CMD into a ’verticalized’ diagram, where the blue and red RGB boundaries
translate into vertical lines with $\Delta_{\rm F275W,F814W}$=0 and
$\Delta_{\rm F275W,F814W}$=$-W_{\rm F275W,F814W}$, where $W_{\rm
F275W,F814W}=0.34$ mag is the RGB width calculated 2.0 F814W magnitudes above
the MS turn off. A similar approach has been adopted to derive the
$\Delta_{C\rm F275W,F336W,F438W}$ pseudo color but by using $m_{\rm F814W}$
vs. $C_{\rm F275W,F336W,F438W}$ pseudo CMD. In this case, the diagram has been
verticalized by assuming Equation 2 from Milone et al. (2017) and the $C_{\rm
F275W,F336W,F438W}$ RGB width of $W_{\rm F275W,F336W,F438W}=0.48$ mag. See
Milone et al. (2017) for details. . The $\Delta_{\rm{\it C}F275W,F336W,F438W}$
vs. $\Delta_{\rm F275W-F814W}$ ChM of RGB stars and the corresponding Hess
diagram are shown in the upper panels of Figure 3, whereas in the bottom
panels we plotted $\Delta_{\rm F336W-F438W}$ against $\Delta_{\rm
F275W-F814W}$. The ChM is shown again in the left panel of Fig.4. It
highlights the group of 1G stars, located around the origin of the map and
colored in green, and an extended 2G, where we identified four sub-populations
of 2GA, 2GB, 2GC and 2GD stars. Stars that are likely members of these groups
are colored orange, cyan, blue, and red, respectively. NGC 6402 is affected by
a large average reddening (E(B-V)=0.6, Harris, 1996) and by significant
reddening variations across the field of view. To verify that the multiple
populations identified on the ChM and the CMD are not artefacts due to
differential reddening, we checked that each population is distributed in the
entire field of view. Moreover, we divided the internal field into 39
quadrants and analysed the ChM of stars in each of them. All the five stellar
populations identified in Fig. 4 are present in the ChM of stars in each
quadrant, proving that they are real features of NGC 6402.

2GD stars define a tail of stars in the ChM with redder $\Delta_{\rm
F275W-F814W}$ values than the bulk of stars with similar $\Delta_{C,{\rm
F275W,F336W,F438W}}$ pseudo-colors. This region of the ChM is typically
populated by stars with enhanced iron and/or C$+$N$+$O abundance, and is a
distinctive feature of Type II GCs (Milone et al., 2017).

By extending the procedure by Zennaro et al. (2019, see their Section 3.3) to
the ChM plotted in Figure 4, we find that the 1G hosts 27.9$\pm$2.3% of the
studied RGB stars. The selected groups of 2G stars include 34.6$\pm$2.4%
(2GA), 16.1$\pm$2.0% (2GB), 12.9$\pm$1.4% (2GC) and 8.4$\pm$1.3% (2GD).

Figure 4: Reproduction of the $\Delta_{C,{\rm F275W,F336W,F438W}}$ vs.
$\Delta_{\rm F275W-F814W}$ ChM of Figure 3 (Left panel). Middle and left panel
show the sodium-oxygen and the magnesium-aluminum anticorrelations,
respectively, from Johnson et al. (2019). The dashed-dotted lines in the
middle panel separate the populations of P1, P2 and E stars defined by Johnson
and collaborators. 1G, 2GA, 2GB, 2GC and 2GD stars, selected from the ChM, are
colored aqua, orange, cyan, blue, and red, respectively. Stars for which both
photometry and spectroscopy are available are represented with large colored
symbols.

To infer the helium content of stellar populations, we adopted for NGC 6402
the method widely used by our group and used to constrain helium variations in
about 60 GCs (e.g. Milone et al., 2018; Lagioia et al., 2019). In a nutshell,
we derived the RGB fiducial lines of each population in the $m_{\rm F814W}$
vs. $m_{\rm X}-m_{\rm F814W}$, where X=F275W, F336W, and F438W. We defined
five equally-spaced F814W magnitude values in the interval between $m_{\rm
F814W}=14.8$ and 18.0. For each value we calculated the $m_{\rm X}-m_{\rm
F814W}$ color difference between each fiducial and the 1G ones. The comparison
between the observed colors and appropriate grid of synthetic spectra with
different abundances of He, C, N and O provides an estimate of the relative
abundances of these elements.

Results are listed in Table 2 and show that group 2GC is highly helium
enhanced, by $\Delta$Y$\sim 0.05$ with respect to the 1G and the 2GA, which
are both assumed to have pristine helium abundance (Y$\sim 0.25$).

Both 2GB and 2GC are enriched in nitrogen with respect to the 1G by more than
1 dex and depleted in carbon and oxygen by $\sim$0.4 and 0.8 dex,
respectively. On the contrary, population 2GA shares similar C and O
abundances as the 1G but is enriched in [N/Fe] by $\sim$0.6 dex. We did not
infer the chemical composition of 2GD stars, due to the enhanced metallicity
of these stars. Since variations in iron significantly affect the stellar
colors (and it would be challenging to disentangle the effect of helium and
iron), we are not able to provide robust determinations of both helium and
metallicity for these stars. Nevertheless, given the extreme $\Delta_{C,{\rm
F275W,F336W,F438W}}$ pseudo-color, it would be reasonable to suggest that
these 2GD stars have extreme chemical composition, hence high helium and
nitrogen content, and are depleted in oxygen and carbon. If this hypothesis is
correct, 2GD stars are the RGB counterparts of a fraction of blue-MS stars.

Table 2: Chemical composition of stellar populations relative to 1G stars. We assumed all population [Fe/H]=$-1.10$ and adopted for the 1G Y=0.25, solar C and N content and [O/Fe]=0.3.  Pop. |  $\Delta$Y |  $\Delta$[C/Fe] |  $\Delta$[N/Fe] |  $\Delta$[O/Fe]
---|---|---|---|---
2GA | 0.000$\pm$0.010 | 0.00$\pm$0.20 | 0.60$\pm$0.15 |  $-$0.10$\pm$0.10
2GB | 0.037$\pm$0.007 |  $-$0.40$\pm$0.20 | 1.10$\pm$0.10 |  $-$0.80$\pm$0.15
2GC | 0.051$\pm$0.009 |  $-$0.40$\pm$0.20 | 1.20$\pm$0.15 |  $-$0.80$\pm$0.15

####  3.2.1 Comparison with Johnson et al. (2019).

As discussed in the introduction, the first evidence of multiple populations
in NGC 6402 was provided by Johnson et al. (2019), who analyzed 41 giant stars
by using high resolution spectra collected with Magellan-M2FS. They inferred
chemical abundances of eleven elements and identified three main stellar
populations based on their position in the [Na/Fe] vs. [O/Fe] plane. The
middle panel of Figure 4 reproduces the sodium-oxygen anti-correlation by
Johnson and collaborators and highlights the three populations of P1, P2, and
E stars identified by these authors.

To further constrain the chemical composition of stellar populations
identified along the ChM, we exploit eleven stars for which both photometry
and spectroscopy from Johnson et al. (2019) are available (large colored
symbols in Figure 4).

Results are listed in Table 3 where we show for each population with available
spectroscopic targets, the average elemental abundance, the random mean
scatter and the number of spectroscopic targets. We find that 1G stars have
nearly solar sodium content and are enhanced in both oxygen and magnesium. On
the contrary, 2GC are depleted in both [O/Fe] and [Mg/Fe] and enhanced in
[Na/Fe], with respect to the 1G.

The comparison between spectroscopic and photometric results provides the
opportunity to associate the populations identified in this paper and by
Johnson et al. (2019). Clearly the 1G corresponds to the population P1 by
Johnson and collaborators, while their population E is composed of stars in
the groups 2GB, 2GC and 2GD.

It would be tempting to associate the 2GA stars identified on the ChM with the
P2 by Johnson et al. (2019), as they exhibit moderate enhancement in N and Na,
respectively, with respect to the 1G. Unfortunately there are no elemental
abundances for 2GA stars. Moreover, the only P2 star with available photometry
seems located on the 1G of the ChM despite it is sodium enhanced by more than
0.2 dex with respect to the bulk of 1G stars. More data are needed to
establish whether the 2GA is composed of 1G stars or if the analysed P2 stars
has large photometric and/or spectroscopic uncertainties.

Table 3: Chemical composition of 1G, 2GB, 2GC and 2GD stars of NGC 6402 inferred from the chemical abundances derived by Johnson et al. (2019). | Population | mean | r.m.s | N
---|---|---|---|---
$\rm[O/Fe]$ | 1G | 0.58 | 0.19 | 6
| 2GB |  $-$0.40 | — | 1
| 2GC |  $-$0.35 | 0.32 | 3
| 2GD | 0.03 | — | 1
$\rm[Mg/Fe]$ | 1G | 0.38 | 0.06 | 7
| 2GC | 0.19 | 0.07 | 3
$\rm[Al/Fe]$ | 1G | 0.45 | 0.06 | 7
| 2GB | 1.27 | — | 1
| 2GC | 1.10 | 0.06 | 3
| 2GD | 0.90 | — | 1
$\rm[Si/Fe]$ | 1G | 0.30 | 0.08 | 7
| 2GB | 0.35 | — | 1
| 2GC | 0.38 | 0.02 | 3
| 2GD | 0.66 | — | 1
$\rm[Na/Fe]$ | 1G |  $-$0.01 | 0.11 | 7
| 2GB | 0.53 | — | 1
| 2GC | 0.57 | 0.02 | 3
| 2GD | 0.71 | — | 1
$\rm[Ca/Fe]$ | 1G | 0.29 | 0.05 | 7
| 2GB | 0.42 | — | 1
| 2GC | 0.38 | 0.01 | 3
| 2GD | 0.33 | — | 1
$\rm[Fe/H]_{I}$ | 1G |  $-$1.14 | 0.04 | 7
| 2GB |  $-$1.10 | — | 1
| 2GC |  $-$1.14 | 0.04 | 3
| 2GD |  $-$1.05 | — | 1
$\rm[Fe/H]_{II}$ | 1G |  $-$1.15 | 0.04 | 7
| 2GB |  $-$1.11 | — | 1
| 2GC |  $-$1.14 | 0.04 | 3
| 2GD |  $-$1.06 | — | 1
$\rm[Cr/Fe]$ | 1G | 0.04 | 0.07 | 7
| 2GB | 0.13 | — | 1
| 2GC | 0.13 | 0.07 | 3
| 2GD | 0.06 | — | 1
$\rm[La/Fe]$ | 1G | 0.28 | 0.02 | 7
| 2GB | 0.33 | — | 1
| 2GC | 0.32 | 0.14 | 3
| 2GD | 0.18 | — | 1
$\rm[Eu/Fe]$ | 1G | 0.32 | 0.06 | 6
| 2GB | 0.36 | — | 1
| 2GC | 0.41 | 0.02 | 2
| 2GD | 0.31 | — | 1

###  3.3 Parallel-field photometry

The $m_{\rm F814W}$ vs. $m_{\rm F475W}-m_{\rm F814W}$ CMD corrected for
differential-reddening of stars in the parallel field is plotted in Figure 5a.
Clearly, NGC 6402 exhibits a split MS in the magnitude interval $20.0<m_{\rm
F814W}<22.5$ and the two sequences seem to merge together along the MS turnoff
and the SGB. To further demonstrate that the double MS is not due to reddening
variations, we verified that red- and blue-MS stars are distributed along the
entire field of view, and that the double MS is evident in the CMDs of stars
of each of the nine quadrants that compose the field of view.

To estimate the fraction of stars in the blue and red MS we adopted the
procedure illustrated in Figure 5. In a nutshell, we selected the region of
the CMD where the MS split is evident (panel a) and derived the fiducial lines
of the red and blue MS (red and blue line, respectively, in panel b). These
two lines are used to verticalize the MS, in such a way that the fiducial
lines of the blue and the red MS translate into two vertical lines with color
residuals $\Delta_{\rm F475W,F814W}$=0 and $\Delta_{\rm F475W,F814W}$=1,
respectively (panel c, see Milone et al., 2015, for details). Finally, the
$\Delta_{\rm F475W,F814W}$ histogram distribution plotted in panel d is fitted
with a function provided by the sum of two Gaussian curves, by means of least
squares. From the area of the two Gaussian components (red and blue curves in
panel d of Figure 5) we infer that 65.2$\pm$2.3 % of stars belong to the red
MS, while the blue MS is composed of the remaining 34.8$\pm$2.3 % of MS stars.

Figure 5: This figure illustrates the procedure to estimate the fraction of
blue- and red-MS stars. Panel a shows the $m_{\rm F814W}$ vs. $m_{\rm
F475W}-m_{\rm F814W}$ CMD of stars in the parallel field while Panel b is a
zoom in of stars in the F814W interval where the split MS is more clearly
visible. The red and blue lines superimposed on the CMD are the fiducials of
the corresponding MSs. The verticalized $m_{\rm F814W}$ vs. $\Delta(m_{\rm
F475W}-m_{\rm F814W})$ diagram of panel-b stars is shown in the panel c) and
the corresponding $\Delta(m_{\rm F475W}-m_{\rm F814W})$ histogram distribution
is illustrated in panel d. The best fit bi-Gaussian function is superimposed
on the histogram (gray thick line) and the two components are colored blue and
red. Figure 6:  Procedure to estimate the helium abundance of the blue MS in
NGC 6402. Left panel shows the $m_{\rm F814W}$ vs. $(m_{\rm F475W}-m_{\rm
F814W})$ diagram for MS stars in the parallel field. Red and blue lines
represent the fiducials of the red and blue MS, respectively, while the best-
fit isochrones with Y=0.25 and Y=0.315 are colored black and orange,
respectively. Upper-right panel reproduces the verticalized $m_{\rm F814W}$
vs. $\Delta(m_{\rm F475W}-m_{\rm F814W})$ diagram. Here we added isochrones
with Y ranging from Y=0.29 to Y=0.36 in steps of 0.005 (green lines). The
shaded blue and red areas enclose the regions within $\pm$1-$\sigma$ color
from the corresponding fiducial. Bottom-right panel shows the $\chi^{2}$ value
against the helium abundance of the isochrone used to fit the blue MS. See
text for details.

In monometallic GCs the $m_{\rm F475W}-m_{\rm F814W}$ color split of MS stars
is due to helium variations. To infer the average helium difference between
blue-MS and red-MS stars we compared the observed MSs with appropriate
isochrones from the ATON database (Tailo et al., 2016, 2020) with different
helium abundances by using the procedure illustrated in Figure 6.

We adopted for all isochrones the same iron abundance, [Fe/H]=$-1.1$, and
[$\alpha$/Fe]=0.3 as in Johnson et al. (2019). The isochrone with Y=0.25 that
provides the best fit with the observed MSTO, SGB, and red MS is derived as in
Tailo et al. (2020) and corresponds to age of 12.50$\pm$0.75 Gyr, distance
modulus of (m$-$M)0=14.76 mag, and reddening of E(B$-$V)=0.62 mag.

To derive the helium abundance of the blue MS, we defined a grid of six
reference magnitude values in the interval where the split MS is clearly
visible. Specifically, reference magnitudes range from $m_{\rm F814W}=$20.4 to
$m_{\rm F814W}=$21.4 in steps of 0.20 mag. To infer the relative helium
content of the two MSs, we first calculated the $m_{\rm F475W}-m_{\rm F814W}$
color difference between the fiducial lines of the red and blue MS
corresponding to the six magnitude values. Then, we considered a grid of
helium-enhanced isochrones with Y ranging from 0.250 to 0.385 in steps of
0.005. We derived the color differences between best-fit isochrone with Y=0.25
and each helium enhanced isochrone and compared these color differences with
the observed ones by means of $\chi^{2}$ minimization. The best estimate for
the helium content of blue-MS stars corresponds to the helium abundance of the
isochrone that provides the minimum $\chi^{2}$ and corresponds to
Y=0.315$\pm$0.010. To estimate the uncertainty, we enhanced the color
separation between the two MSs by $\pm$1-$\sigma$, where $\sigma$ is the error
on the color determination, and derived the corresponding helium values by
using the procedure above. The uncertainty corresponds to the average of the
absolute differences between these helium determinations and the best helium
estimate.

The high helium content of the blue MS indicates that it is the counterpart of
population 2GB, 2GC and 2GD stars. On the contrary, 2GA stars share similar
helium content as the 1G (Y$\sim$0.25) and are likely associated with the red
MS. These conclusions, based on the chemical compositions of MS and RGB stars,
are corroborated by the fact that the fraction of 1G$+$2GA stars ($\sim 63$%)
is consistent with the fraction of red-MS stars ($\sim 65$%).

###  3.4 Multiple populations along the Horizontal Branch

To investigate multiple populations along the HB, we exploited the $m_{\rm
F275W}$ vs. $m_{\rm F275W}-m_{\rm F814W}$ CMD of Figure 7, which is very
sensitive to the effective temperature and the luminosity of HB stars. We
identified 629 candidate HB stars, including 65 RR Lyrae stars and 27 and 538
stars redder and bluer, respectively, than the RR Lyrae instability strip. The
corresponding HB ratio is HBR=0.81444The HB ratio (Lee et al., 1994; Mackey &
van den Bergh, 2005), is defined as (B$-$R)/(B$+$V$+$R), where B, R and V are
the numbers of stars bluer and redder than the instability strip, and the
number of variables in the HB, respectively. and is larger than that derived
by Contreras Peña et al. (2013, HBR=0.45).

Figure 7: $m_{\rm F275W}$ vs. $m_{\rm F275W}-m_{\rm F814W}$ CMD of HB stars in
NGC 6402, with RR Lyrae marked by green triangles (top). Bottom panels show
the histogram color distribution of HB stars. Vertical lines separate the two
main groups of HB stars. See text for details.

The histogram distribution of $m_{\rm F275W}-m_{\rm F814W}$ of HB stars
(bottom panel of Figure 7) is clearly bimodal with a narrow peak centered at
$\rm m_{F275W}-m_{F814W}\sim$0.8 and a much broadened one around $\rm
m_{F275W}-m_{F814W}=3.4$. Both peaks have colors that differ from those of the
Grundahl et al. (1999) and the Momany et al. (2004) jumps (hereafter G- and M-
jumps), which are located around $\rm m_{F275W}-m_{F814W}\sim 2.4$ and $\rm
m_{F275W}-m_{F438W}\sim 1.2$. These jumps are universal features of HB
morphology and are due to modifications of the stellar atmospheres (e.g. Brown
et al., 2016, 2017). The fact that the two peaks in the HB color distribution
appear independent from the G- and M- jumps indicate that they are not related
to atmospheric phenomena but can be safely associated to multiple populations.

Although the identification of the five populations of NGC 6402 along the HB
is beyond the scope of this paper, we tentatively associate multiple
populations along the RGB and the HB as follows. We notice that 354 out of 629
HB stars are bluer than $\rm m_{F275W}-m_{F814W}=2.0$. Hence, about the
55$\pm$2% of HB stars can be tentatively associated with the red HB peak and
the remaining 45$\pm$2% to the blue peak. It is tempting to speculate that the
red HB peak is composed of 1G and 2GA) while the helium-rich populations (2GB,
2GC and, possibly, 2GD) evolve into the blue HB peak. Notice anyway that these
fractions of HB stars are slightly but significantly different from the
fractions of RGB stars with pristine helium abundances (62$\pm$2%) and the
fractions of helium rich stars (38$\pm$2%).

Table 4: Properties of 1G and 2GE stars along the HB of NGC 6402. Columns are: population ID, helium abundance (Y), average mass loss ($\mu$), mass loss spread ($\delta$), stellar mass at the tip of the RGB ($\rm M_{\rm Tip}$) and average HB mass ($\rm\bar{M}_{HB}$).  ID | Y | $\rm\mu/M_{\odot}$ | $\rm\delta/M_{\odot}$ | $\rm M_{Tip}/M_{\odot}$ | $\rm\bar{M}_{HB}/M_{\odot}$
---|---|---|---|---|---
1G | 0.250 | $0.240\pm 0.022$ | $0.006\pm 0.002$ | 0.841 | $0.601\pm 0.022$
2GC | 0.315 | $0.280\pm 0.024$ | $0.005\pm 0.002$ | 0.757 | $0.481\pm 0.024$

####  3.4.1 Mass loss of multiple populations

Figure 8: Upper panel: $\rm m_{F275W}-m_{F814W}$ vs. $\rm m_{F275W}$ CMD of
the HB stars in NGC 6402. The contour plots represent the best fit simulation
of the 1G and the extreme 2G, respectively for red and blue. The two bottom
panels represent the histograms of the colour distributions of observed
(black) and simulated stars as direct comparison with the part of the HB the
two simulations overlap in the CMD.

Work based on both theory and high-resolution spectroscopy reveals that the
reddest HB tail is composed of the bulk 1G stars, while the bluest portion of
the HB is populated by the 2G stars with extreme helium content (e.g. D’Antona
et al., 2002; Marino et al., 2011). Based on this evidence (Tailo et al.,
2019, 2020, 2021) identified 1G stars and 2G stars with extreme chemical
composition in 56 Galactic GCs and measured the RGB mass loss. In the
following, we extend to NGC 6402 the method introduced by Tailo and
collaborators to identify 1G and 2GC stars along the HB and infer their RGB
mass losses.

In a nutshell, the method consists of comparing the observed color
distributions of the reddest and bluest HB stars with the colors of a grid of
synthetic HB stars. Simulated HBs have different average mass loss ($\mu$) and
mass loss spread ($\delta$) values. Specifically, $\mu$ ranges from 0.200 $\rm
M_{\odot}$ to 0.310 $\rm M_{\odot}$ in steps of 0.003 $\rm M_{\odot}$ and
$\delta$ varies from 0.002 $\rm M_{\odot}$ to 0.012 $\rm M_{\odot}$ in steps
of 0.001 $\rm M_{\odot}$.

We assumed for all simulations [Fe/H]=$-$1.1, [$\alpha$/Fe]=0.3 and age of
12.5 Gyr. We adopted Y=0.25 for 1G stars and Y=0.315 for the 2GC. Further
details on the procedure are provided by Tailo et al. (2020, 2021).

The simulation of 1G stars that provides the best match with the histogram
distribution of the reddest HB stars is derived by means of $\rm\chi^{2}_{d}$
minimization and corresponds to $\rm\mu=0.240\pm 0.022\,M_{\odot}$ and
$\rm\delta=0.006\pm 0.002\,M_{\odot}$. Similarly, we obtain for 2GC stars
$\rm\mu=0.280\pm 0.024\,M_{\odot}$ and $\rm\delta=0.005\pm 0.002M_{\odot}$.
Results are listed in Table 4 and plotted in Figure 8, where we superimposed
the contours of the best-fit synthetic CMDs on the observed CMD (upper panels)
and compare the observed and simulated histograms of the colors of 1G and 2GC
HB stars.

Interestingly, the amount of mass lost by 1G stars in NGC 6402 is comparable
with the mass loss of 1G stars in clusters with similar metallicity. Indeed,
as shown in the top panel of Figure 9, NGC 6402 follows the same trend in the
[Fe/H] vs. $\rm\mu_{1G}$ plane discovered by Tailo et al. (2020, 2021). We
also find that 2GC lose more mass than the 1G, in analogy with what is
observed in nearly all massive GCs. This result is shown in the bottom panel
of Figure 9, where NGC 6402 is represented by the purple diamond, and the dots
show the extra mass loss $\rm\Delta\mu_{e}$ in the sample of GCs studied by
Tailo et al. (2020).

Figure 9:  Diagrams of the mass lost during the RGB evolution, $\rm\mu_{1G}$,
versus [Fe/H] (top) and of the extra–mass loss of the 2G, $\rm\Delta\mu_{e}$,
versus the cluster mass Log($\rm M/M_{\odot}$) (bottom), from Tailo et al.
(2020, 2021). $\rm\mu_{1G}$ and $\rm\Delta\mu_{e}$ are i solar masses. NGC
6402 is marked with purple diamonds. The black dashed line in the top panel is
the best fit least squares straight line of all points.

Actually, the bottom panel of Fig. 9 shows that the extra mass loss
($\Delta\mu_{e}=0.040\pm 0.012\,M/M_{\odot}$) for NGC 6402 is relatively small
with respect to that of the other massive clusters. The result depends on the
helium content Y=0.315 assumed for 2GC stars: for a smaller value of Y,
$\Delta\mu_{e}$ would be larger and fit better with the trend defined by bulk
of the other clusters. We take this as an indication that Y=0.315 may
represent an upper limit to the possible helium of this extreme population.

Table 5: Fractions of populations in different samples Name | J2019 |  HST Parallel field | HST ChM | Tot ChM | HB
---|---|---|---|---|---
1G | P1 | 0.34 |  |  | 1G | 0.280 |  |  |
|  |  |  red MS | 0.652 |  |  | 0.626 | red | 0.55
2G mild | P2 | 0.40 |  |  | 2GA | 0.346 |  | ($m_{\rm F275W}-m_{\rm F814W}>2$) |
2G extreme | E | 0.26 |  blue MS | 0.342 | 2GB | 0.161 | 0.374 | blue | 0.45
|  |  |  |  | 2GC | 0.129 |  | ($m_{\rm F275W}-m_{\rm F814W}<2$) |
|  |  |  |  | 2GD | 0.084 |  |  |

##  4 Summary on the fraction of different populations from different data

Table 5 compares the information gathered on the different populations. The
results from the spectroscopic sample in Johnson et al. (2019) are given in
the second column. The HST parallel field data include 65% stars in the red MS
and 35% stars in the blue MS. The red MS includes both the P1 and P2
populations. The comparison with the ChM data is quite consistent, if we add
together the 1G and 2GA data (see Fig. 4) and collect as a generic extreme E
group all the other populations, including the 2GD with probably higher
metallicity. In general, we may say that the E group is larger than found in
Johnson et al. (2019), a result not so surprising when accounting for the fact
that the spectroscopic sample is quite small. The HB data are subdivided into
“red” and “blue”, at the right and left side of the color mF275–m${}_{\rm
F814}=$2 (Fig. 7). The resulting fractions are perhaps a bit more surprising,
because here we have an even larger –45%– fraction of stars belonging to the
blue side of the HB, which should be assigned to the E populations. A possible
explanation of the higher percentage of blue HB stars may be that our fraction
of red HB stars is too small, as testified by the fact that our RR Lyr group
is much less represented than in Contreras Peña et al. (2018). At first sight,
we could attribute the different fraction to the fact that our RR Lyr sample
is obtained at the center of the cluster, while the RR Lyrae in the whole
catalogue are spread all over the cluster: it is plausible that the 1G stars
are less concentrated than the 2G stars, as we know to occur in several GCs
(see e.g. Sollima et al., 2007; Bellini et al., 2009; Lardo et al., 2011;
Milone et al., 2012c; Simioni et al., 2016; Dalessandro et al., 2019;
Dondoglio et al., 2021); Dalessandro et al. (2019) find a spatial segregation
of the 2G in about half of a sample of 20 clusters, correlated with the
current half mass relaxation time $t/t_{rh}$. NGC 6402, with an age $t$=12.5
Gyr derived here, and $t_{rh}\sim 2.5\times 10^{9}$yr (Harris, 1996) has
$t/t_{rh}\sim 5$, in the range where segregation should still be present, and
deserves a study of the spatial distribution of the two populations. Anyway,
the parallel field is 6’ far from the cluster center, well out of the central
region, but it shows a proportion of 1G+2G mild and 2G extreme stars
consistent with those derived from the core data from which the ChM is
derived. Thus, further investigation is needed to understand the meaning of
the results concerning the HB. We conclude that the HST sample contains about
35% of stars belonging to the extreme and probably also intermediate
populations, while another $\sim$35% of stars belong to the mild 2G.

Figure 10: Left. ChM of RGB stars in NGC 2808. The red dashed-dot line
separates the bulk of 1G stars from the 2G. Middle. $C_{\rm
F275W,F336W,F438W}$ vs. $m_{\rm F275W}-m_{\rm F814W}$ diagram of HB stars in
NGC 2808. Candidate RR Lyrae stars are marked with green circles. The vertical
dashed line separates the red and the blue HB. We indicated the position of
the M- and G- jumps and the gap associated with the RR Lyrae instability
strip. Right. Optical, $m_{\rm F814W}$ vs. $m_{\rm F475W}-m_{\rm F814W}$, CMD
of NGC 2808 stars zoomed on the MS and the SGB. The red, middle and blue MS
are indicated by the black arrows. The letters A–E in all panels indicate the
five main populations of NGC 2808.

##  5 Comparison with NGC 2808

In this section we directly compare the photometric diagrams of NGC 6402 and
NGC 2808, which is one of the most-studied GCs in the context of stellar
populations. Such comparison is possible because NGC 2808 and NGC 6402 share
similar metallicities, ages, and masses.

NGC 2808 hosts populations with extreme contents of helium and light elements
that have been investigated along various evolutionary sequences, including
the MS, RGB, HB, and even the AGB (e.g. D’Antona et al., 2005; Piotto et al.,
2007; Carretta et al., 2009; Marino et al., 2014, 2017; Lagioia et al., 2021).
In the following, we discuss multiple populations in NGC 2808 along the RGB
stars, the MS, and the HB by using the same photometric diagrams available for
NGC 6402.

As illustrated in the left panel of Figure 10, the ChM of NGC 2808 reveals
that both 1G and 2G stars are not chemically homogeneous. 1G stars host two
main stellar populations (namely A and B), whereas the 2G is composed of at
least three distinct groups of stars (C, D and E). 1G stars share pristine
helium abundance (Y$\sim$0.25) and light-element abundances but are possibly
inhomogeneous in metallicity, with population-A stars being slightly more
metal rich than population-B stars. On the contrary, 2G stars are enhanced in
He, N, and Na and depleted in C and O. Specifically, population-C stars may be
very slightly enriched, by $\sim$0.005 dex in helium mass fractions (D’Antona
et al., 2016), while population-D and E stars have larger helium contents up
to Y$\sim$0.29, and Y$\sim$0.35, respectively.

NGC 2808 exhibits an extended HB that is well populated on both sides of the
RR Lyrae instability strip. The $C_{\rm F275W,F336W,F438W}$ vs. $m_{\rm
F275W}-m_{\rm F814W}$ diagram of HB stars is plotted in the middle panel of
Figure 10, where we marked the position of the G- and M-jumps. Work based on
high-resolution spectroscopy and on simulated HBs show that the red HB host
stars with different sodium contents but similar helium abundances. Hence, it
is composed of population A, B, and C stars (e.g. Marino et al., 2014;
D’Antona et al., 2016). Population-E stars mostly evolve into the bluest HB
tail, on the hot side on the M-jump. The HB region between the RR Lyrae and
the M-jump is mainly composed of population-D stars.

CMDs made with optical filters do not allow us to disentangle the five stellar
populations of NGC 2808. Nevertheless, the $m_{\rm F814W}$ vs. $m_{\rm
F475W}-m_{\rm F814W}$ CMD plotted in the right panel of Figure 10 reveals a
triple MS. In this diagram, the red MS is composed of stars of the populations
A, B, and C and is reproduced by isochrones with nearly pristine helium
content. The middle and the blue MS correspond to population-D and
population-E stars, respectively. From Milone et al. (2012b), the three MS
populations contain the following fractions of stars: 0.62$\pm$0.02 (red MS),
0.24$\pm$0.02 (middle MS) and 0.14$\pm$0.03 (blue-MS).

The comparison between NGC 2808 and NGC 6402 is illustrated in Figure 11. In
the upper-left panel we superimposed their $\Delta_{C{\rm F275W,F336W,F438W}}$
vs. $\Delta_{\rm F275W-F814W}$ ChMs in such a way that 1G stars of both
clusters share the same median values.

Clearly, the ChM of NGC 6402 is significantly less extended in both axis with
respect to the NGC 2808 map. In particular, there is no evidence for NGC 6402
counterparts of the most helium-rich stars of NGC 2808 (population E). We also
find that 1G stars of NGC 6402 roughly match the population B of NGC 2808,
while there is no evidence for population-A like stars. The group of 2GA stars
of NGC 6402 mostly overlaps the population C of NGC 2808 and the similarity
between these populations is corroborated by their chemical compositions.
Indeed, both 2GA stars of NGC 6402 and population-C stars of NGC 2808 share
similar He and O content as the 1G but are significantly enhanced in nitrogen.
Populations 2GB and 2GC are analogs of population-D stars in NGC 2808, as
demonstrated by the location on the ChM and the helium content $Y\sim 0.30$.
Intriguingly, NGC 2808 lacks a counterpart of the 2GD stars. These results are
confirmed from the comparison of the $\Delta_{\rm F336W-F438W}$ vs.
$\Delta_{\rm F275W-F814W}$ ChMs of NGC 2808 and NGC 6402 plotted in the
bottom-left panel of Figure 11.

The lack of stars with extreme helium content in NGC 6402 is corroborated by
the comparison of the $m_{\rm F814W}$ vs. $m_{\rm F475W}-m_{\rm F814W}$ CMDs
(bottom-left panel). Clearly, the red and middle MS of NGC 2808 match the red
and blue MS of NGC 6402, whereas NGC 6402 does not host the counterpart of the
blue MS (i.e. the population E) in NGC 2808. As expected, when we superimposed
on the CMD the isochrones with different helium contents that reproduce the
triple MS of NGC 2808, it results that blue-MS stars of NGC 6402 are not
consistent with the most helium rich isochrone (Y=0.36).

The comparison of the HBs of the two clusters is plotted in the upper-right
panel of Figure 11. Clearly, HB stars of both clusters follow the same
sequence in the $C_{\rm F275W,F336W,F438W}$ vs. $m_{\rm F275W}-m_{\rm F814W}$
plane (see Brown et al., 2016, for details). The HB of NGC 6402 exhibits a
shorter $m_{\rm F275W}-m_{\rm F814W}$ color extension compared to NGC 2808 and
shows no evidence for blue-hook stars, which are the progeny of stars highly
enhanced in helium. These facts corroborate the evidence that NGC 6402 does
not host stars with extreme helium content. At odds with NGC 2808, NGC 6402
does not show the red HB, thus NGC 6402 is a ‘second parameter’ cluster
belonging to the M 13 group. For a recent discussion of this problem see Tailo
et al. (2020) and references therein. Since the reddest HB tail is mostly
populated by 1G stars, we expect, in addition to metallicity, at least one
second parameter is responsible for the color of 1G stars. Age difference as
well as mass loss differences are possible second parameters. As an
alternative, stars on the red HB tail of NGC 6402 should be more helium rich
than the red-HB stars of NGC 2808 (D’Antona & Caloi, 2008).

Figure 11: Upper panels. Comparison of the $\Delta_{C,{\rm
F275W,F336W,F438W}}$ vs. $\Delta_{\rm F275W-F814W}$ (upper-left) and
$\Delta_{\rm F336W-F438W}$ vs. $\Delta_{\rm F275W-F814W}$ ChMs (lower-left) of
NGC 2808 (pink points) and NGC 6402 (black points). Right panels compares the
HBs of NGC 2808 (pink) and NGC 6402 (same colors as in Figure 1, top) and the
$m_{\rm F814W}$ vs. $m_{\rm F475W}-m_{\rm F814W}$ CMDs (bottom). We also
provide a zoom of the CMD on the upper MS, where we compare the observations
of NGC 2808 and NGC 6402 with isochrone with different helium abundances. See
text for details.

##  6 A summary of models

The issue of multiple populations includes chemical ‘anomalies’ of quite a
number of elements, with different problems highlighted by different stars in
different clusters. For some of these anomalies the contribution of some
particular polluters may be required555For instance, the s-process elemental
distribution in the metal poor star ROA 276 in $\omega$ Cen(Yong et al., 2017)
is well explained by the rotating models by Frischknecht et al. (2012, 2016).
. Nevertheless, most of the scenarios proposed to explain the light element
variations do not withstand a general scrutiny. We refer the reader to the
complete summaries available in the recent literature (e.g., Renzini et al.,
2015; Bastian & Lardo, 2018; Gratton et al., 2019) and discuss here the only
two remaining models which at least basically conform to the requirements of
the chemistry displayed in massive clusters, such as NGC 2808 and NGC 6402,
containing an “extreme” population. These are the super-massive star (SMS)
model, here considered in the basic formulation by Denissenkov & Hartwick
(2014) and Denissenkov et al. (2015) that also includes a qualitative
description in terms of a dynamical scenario (Gieles et al., 2018), and the
AGB model (Ventura et al., 2001). In the AGB stars the hot environment where
the light elements are processed by proton captures is not the stellar core,
but burning at the “hot bottom” of the convective envelope (HBB), from where
the elements are then transported by convection in the whole envelope and then
lost by stellar wind and planetary nebula ejection.
For the present work, the models are considered mainly to understand whether
the ejecta composition (with or without dilution with pristine gas) is
compatible both with the patterns of light element abundances in the giants
(Johnson et al., 2019) and with the helium content derived here for NGC 6402.
At the end of our analysis, we will conclude that neither model in its present
stage of development is compatible with the helium abundance of the extreme
2G, and suggest possible additional formation mechanisms.

###  6.1 The SMS model

The reason to propose that “supermassive” stars of about 104$\,{M}_{\odot}$
are at the origin of the elemental abundances found in the second population
of GCs, although the highest mass which can be formed by simple fragmentation
is 100 times smaller, is that such structures achieve the central temperature
of $\sim$75 MK, necessary to allow the reaction 24Mg(p,$\gamma$)25Al which
depleted 24Mg in the gas forming the extreme GC stars. This temperature is not
reached in the cores of standard massive stars. Another advantage is that the
p-captures by Mg isotopes in the SMS cores produce isotopic ratios compatible
with the ratios observed in five clusters (Da Costa et al., 2013), while
discrepant ratios are found when these reactions occur in the AGB HBB
environment (Ventura & D’Antona, 2009)666The correct isotopic ratios for
magnesium can be obtained in the AGB models by enhancing by a factor $\sim$3
the proton-capture rate by 25Mg at the temperatures $\sim$100 MK, in
particular the 25Mg(p, $\gamma$)26Alm channel, beyond the most recent
experimental determinations (Ventura et al., 2018). With this input, the AGB
nucleosynthesis also correctly predicts the total Mg depletion in different
clusters, and its trend with the metallicity. Larger Mg depletions are
observed in clusters of smaller metallicity (e.g. Mg is reduced by a factor
$\sim$10 in cluster NGC 2419 (Cohen & Kirby, 2012)). This trend is an
observational constrain not directly predictable in the case of SMS, as the
temperature at which nuclear activity takes place in the central regions is
almost unaffected by the metallicity, unlike the HBB conditions in massive AGB
stars.. Difficulties remain to explain the production of silicon by p–captures
on aluminum —a Si-Mg anticorrelation is present in NGC 2808 giants (Carretta,
2015)— as Si production occurs at the expense of the total depletion of Mg and
Na in the cores of SMS; further, potassium can not be produced (Prantzos et
al., 2017). Nevertheless, the SMS model also provides an advantage in the
description of the oxygen depletion and sodium enhancements (see in Sect. 6.2
the difficulties of the AGB model) as shown in the case of M 13 by Denissenkov
et al. (2015), whose 60$\times 10^{3}$$\,{M}_{\odot}$ model chemistry at
Ycore=0.38, diluted by 50% with pristine gas is able to reproduce the
abundance patterns O–Na and the isotopic Mg ratios.

Notice that for these same O–Na abundances, a small dilution by $\sim$10% with
pristine matter brings the O-Na abundances in the correct range to describe
the E stars in NGC 6402.

A further interesting feature of the SMS model is that it could help solve the
“uniqueness” problem of extreme composition stars being found only in a few
very massive old GC, because only those had the opportunity to host and evolve
SMS (see in Sect. 6.2 the alternative view of the AGB model).

Going beyond the nucleosynthesis results, we must remark that the possible
successes of the SMS site for nucleosynthesis of multiple populations has
strong constraints, namely:

  1. 1.

The protocluster must be able to form SMS of about the required mass of
$\sim$2–10$\times 10^{3}$$\,{M}_{\odot}$ (Denissenkov & Hartwick, 2014;
Prantzos et al., 2017). First, massive stars must sink to the cluster core due
to dynamical friction and then merge by multiple collisions. Models aimed at
explaining the possible presence of intermediate mass black holes in young
massive clusters have been developed (Portegies Zwart et al., 1999, 2004). The
process is constrained to occur within the very short main sequence timescale
of such objects.

  2. 2.

The core H-burning (main sequence) must be stopped very early, and at the
specific time required to avoid that the SMS ejecta have helium content larger
than the maximum helium observed in the extreme GC populations, roughly
constrained to be always Y$<$0.4. The hypothesis is that the SMS lose at early
times a great fraction of their mass, as a result of some instabilities and
stellar winds. No quantitative models are still available to support these
suggestions. The ejecta then mix with the gas of the environment and form the
second population stars, showing different degrees of p-capture processing.

For the purpose of this work, we put aside these problems, and keep the
chemistry of the diluted SMS gas as the basis for the formation of the E
population in NGC 6402, as depicted in Johnson et al. (2019). Note anyway that
the E population includes about 26% of the cluster mass, $\sim 3.5\times
10^{5}$$\,{M}_{\odot}$ if we refer to a present mass of 1.4$\times
10^{6}$$\,{M}_{\odot}$. Assuming now a dilution of roughly $\sim$40% with
pristine gas, we need anyway to process within SMS $\sim 2\times
10^{5}$$\,{M}_{\odot}$. Thus, either 20 SMS of 104$\,{M}_{\odot}$ each, or a
model such as the “conveyor belt” proposed by Gieles et al. (2018) is
necessary to achieve such a result. We must therefore consider that there are
still many unexplored aspects in the model.

###  6.2 The AGB model

The AGB model attributes the chemistry of multiple generations to star
formation in the gas expelled at low velocities by massive AGB and super–AGB
stars, collected into the central regions of the cluster and possibly diluted
with residual or re-accreted pristine gas.

From the point of view of chemistry of the different multiple populations,
D’Antona et al. (2016) have developed the idea that they are the result of
formation along the “timeline” of evolution of the different super-AGB and AGB
masses, having different ejecta composition. Application to the prototype
cluster NGC 2808 showed that the populations A, B, C, D, E by Milone et al.
(2015) should have formed in the order B E D C A. At first, the standard
population B forms, then the extreme population E, undiluted, at the time of
evolution of the masses which undergo super–AGB evolution, then the
intermediate population D, partially diluted with pristine gas, then the
population C, very diluted with pristine gas and thus showing only very mild
differences with respect to the standard B. The last population A was
suggested to be polluted by the ejecta of some Type Ia supernovae, whose
regular explosions eventually expel the re-accreting pristine gas and end the
second star formation epoch. Of course the details of the evolution of each
cluster determine the variety of chemical patterns found among different
clusters. In particular, the E population, whose chemistry indicates that it
forms before re-accretion, can be present only in clusters in which the
re–accretion of pristine gas is delayed enough, and models show that these are
the most massive clusters only (D’Ercole et al., 2016), in agreement with the
observations (e.g. Fig. 13 in Milone et al., 2018).

Figure 12: The Na–O data for NGC 2808 (black open circles) and for NGC 6402
(orange dots) are shown together with the average Na–O content in the ejecta
of AGBs and super–AGBs having Z=1.5$\times 10^{-3}$ shown as red squares. The
top right square refers to 7$\,{M}_{\odot}$, and the last square on the left
represents the abundances in the 4.5$\,{M}_{\odot}$ ejecta. The black lines
with triangles represent the abundances obtained by diluting the ejecta of the
7$\,{M}_{\odot}$ and of the 5$\,{M}_{\odot}$ with increasing amounts of a
pristine gas having the abundance [Na/Fe]=-0.15 and [O/Fe]=0.3. Actually
oxygen in the 1G of NGC 6402 looks much larger on average, with respect to the
Carretta 2015 determination of the 1G values in NGC 2808 and in many other
clusters (Carretta 2009a). The diagonal cyan lines show the helium content
along the dilution lines –see text.

Concomitantly, the helium content of the E populations must be equal to the
abundance in the pure ejecta of these stars, and all models agree that, for
general structural reasons, this must be in the range Y=0.34–0.38 (Ventura,
2010). Note that this prediction is confirmed by the indirect derivation of
the helium content in the “blue main sequence” of $\omega$ Cen (e.g. Tailo et
al., 2016) and NGC 2808 (D’Antona & Caloi, 2008) and it is one of the
successes of the AGB model: while the SMS model has to require that the main
sequence evolution stops at a very specific time, so that the average helium
after dilution is close to that required by observations, the AGB model
predicts this limit.

Another straightforward prediction of the AGB model is that the
nucleosynthesis, for the same degree of dilution, should be more advanced in
clusters of smaller metallicity (Ventura et al., 2013). Lower amounts of
metals imply lower opacities in the AGB envelopes, and a larger temperature at
the basis of the envelope where p-capture nucleosynthesis takes place. In
particular, at higher metallicity the ON chain and p-captures on Mg isotopes
are less efficient. This naturally produces the “vertical” Na–O relations of
the bulge clusters having the largest GC metals (Muñoz et al., 2020, and
references therein).

In this work, our attention must anyway consider the crucial issue not fully
solved in the models, namely the oxygen and sodium yields. A thorough
discussion is given in Renzini et al. (2015), and can be summarized by saying
that, in the range of the HBB temperatures of massive AGBs, the p-captures on
sodium destroy it, while at the same time p-captures on oxygen nuclei convert
it to nitrogen. The interplay between these two concomitant reactions is such
that sodium is depleted, if the star lives long enough to pursue a strong
oxygen depletion. Thus, strong mass loss (as in the super–AGBs) preserves
sodium, but does not destroy enough oxygen, while smaller rates of mass loss
(as in the massive AGBs) can deplete more oxygen, but preserve less sodium.
The resulting O-Na relation is shown by the (red) hook line in Figure 12. The
yields shown as red squares are from the extension of the work by Ventura et
al. (2013) to a metal mass fraction Z=1.5$\times 10^{-3}$ ([Fe/H]$\sim$–1.3)
(Dell’Agli et al., 2018) close to the metallicity of both NGC 2808 and NGC
6402. The upper right point red square results from the evolution of
7$\,{M}_{\odot}$, smaller masses follow until the 5$\,{M}_{\odot}$ model,
which is the mass of maximum oxygen depletion, while the 4.5$\,{M}_{\odot}$
model again displays larger sodium and oxygen abundances in the ejecta.

The yields in the range 5–7$\,{M}_{\odot}$ are close enough to the cooler
points of the E group in Johnson et al. (2019). The three most oxygen depleted
giants ([O/Fe]$\lesssim-0.4$) are out of the curves, as well as the E stars in
NGC 2808. In the context of the AGB model, an additional oxygen reduction is
attributed (D’Ercole et al., 2012; D’Antona et al., 2016) to anomalous “deep
mixing” in giants (D’Antona & Ventura, 2007), active when a high helium
content reduces the discontinuity in the hydrogen profile left by the maximum
deepening of convection at the first dredge up. Notice that this
interpretation requires that these stars are born with a high helium content,
such as the maximum helium yield of the massive AGB and super-AGB evolution
discussed above.

In summary, the yields are reasonable for the stars of the E group with lower
O–depletion, but require an additional hypothesis to describe the three most
extreme giants, according to today’s state of the art.

###  6.3 A mixed model

As discussed above, only SMS and AGB stars reach temperatures high enough to
account for the chemical composition of 2G extreme stars, even if with the
mentioned uncertainties. In addition, other dynamical events may concur to
determine the present day stellar content of NGC 6402. In particular we can
consider whether the cluster is the result of the merging of different
clusters (e.g. Sugimoto & Makino, 1989; van den Bergh, 1996; Amaro-Seoane et
al., 2013). Searle & Zinn (1978) were the first to argue that some fraction of
the galactic GCs has an external origin, and that the outer halo GC system is
due to the merger and accretion of ‘protogalactic fragments’777Today this
hypothesis has a part in the cosmological context of hierarchical structure
formation (e.g. Forbes et al., 2018). and Searle (1977) even argued that
merging of clusters could be possible within these fragments. Mergings
occurring in the galactic thick disk are modelled today (e.g. Khoperskov et
al., 2018); they may be relevant to understand the difference in metallicity
and the difference in age by many gigayears between the two populations of the
bulge clusters Terzan 5 (Ferraro et al., 2016) and Liller 1 (Ferraro et al.,
2021). Cluster mergers have also been explored as a possible solution to the
existence of iron-complex clusters and the iron-complex clusters as well (e.g.
Gavagnin et al., 2016).
In the case of NGC 6402, there are two aspects for which it is useful to
consider the merging hypothesis:

1) if the 2G extreme stars are manifactured by the SMS ejecta in one cluster
and the 2G mild stars are born from AGB polluted gas in another one, the
presence of the gap in abundances has a simple solution; this may help address
the primary SMS problem that very high stellar masses are required (see
Sect.6.1);

2) merging could explain the presence of a small fraction of (likely) metal-
richer stars identified in the ChM (group 2GD).

##  7 Discussion

Taken at face value, the high dispersion spectra observations give partially
contradictory results about how extreme the E composition stars are in NGC
6402. Magnesium abundances are reduced at most by $\sim$0.2 dex (see Fig. 8 in
Johnson et al., 2019), to be compared with the $\sim$0.5 dex of the E stars in
NGC 2808 (Carretta, 2015), so we should conclude that the E stars in NGC 6402
are not as extreme as in NGC 2808.

On the other hand, the oxygen abundances in the E sample of both clusters have
formally a similar logarithmic depletion (by $\sim 1.2$ dex) with respect to
the 1G (or P1) abundances, indicating a similarly “extreme” nuclear
processing. This result, anyway, is mostly due to the large difference between
the [O/Fe]1G$\sim$0.3 of NGC 2808 (Carretta et al., 2009; Carretta, 2015), and
the [O/Fe]1G$\sim$0.6 of NGC 6402 (Johnson et al., 2019) —see Fig. 12. The
zero point of the 1G is very important for the depletion models, as the ON
cycle depletes oxygen in proportion to its initial content, so that, in a
first approximation, stellar models having the same physical conditions (e.g.
HBB temperature) but different initial oxygen abundance, have about the same
logarithmic decrease in oxygen.

These contrasting results, together with the result of the present work, lead
us to assume, for the present analysis, that there is a zero point difference
between the 1G abundances by Carretta (2015) and by Johnson et al. (2019), and
that we can discuss the depletion of oxygen in NGC 6402 assuming that its 1G
abundance were a bare [O/Fe]$\simeq$0.3. With this assumption, the E stars in
NGC 6402 are not oxygen depleted as much as those in NGC 2808.

###  7.1 Helium in the extreme population of NGC 6402

The present work shows that the multiple populations hosted in NGC 6402 are
not so extreme as the multiple populations in the prototype cluster NGC 2808.
Three direct comparisons —simplified by the very similar metallicity of the
two clusters— show this:

  1. 1.

the ChM of NGC 6402 does not contain stars in the location of the E group in
NGC 2808 (Milone et al., 2015) (see Sect. 3);

  2. 2.

the comparison of the CM diagrams of the two clusters shows that the blue MS
of NGC 2808, identified with a population having Y$\sim$0.35-0.38 (D’Antona et
al., 2005; Piotto et al., 2007) is much bluer than the extreme MS in NGC 6402,
which can be fit with Y$\sim$0.31 (see Sect. 3.4.1);

  3. 3.

the HB of NGC 6402 does not include the well populated blue hook, generally
modelled as the site of post–RGB evolution of the high helium population
(D’Antona & Caloi, 2004; Lee et al., 2005; D’Antona & Caloi, 2008; Tailo et
al., 2015). If the reddest HB is modelled by assuming that it is populated by
1G stars with Y=0.25, the extreme HB can be fitted with stars having Y=0.31.
Consideration on the extra–mass loss needed to fit 2G HB stars (Tailo et al.,
2020) shows that this value Y=0.31 may be an upper limit to the helium content
of the hot HB stars (see Sect. 3.4.1);

We first investigate whether the AGB model and/or the SMS model are in
qualitative and/or quantitative agreement with this result.
The conclusions inferred in the context of the AGB scenario are illustrated in
Fig. 12: the three cyan lines mark the O–Na locus where the dilution provides
a helium abundance of Y=0.34, 0.31 and 0.29. It is clear that only gas diluted
with 40-50% of pristine gas has Y=0.31, and consequently its O abundance is
much larger than in the E stars of NGC 6402, and viceversa for the Na
abundance. The E stars oxygen is reproduced only by undiluted models (at
Y$\sim 0.35$), or by models assuming deep extra-mixing, which, anyway, also
requires a similarly high initial helium (D’Antona & Ventura, 2007). Further,
the Y=0.31 locus is in the middle of the O–Na region where there is a gap in
the Johnson et al. (2019) data.

In order to obtain consistency with the data, we need a much stronger
O–depletion in the yields (such as those obtained for smaller metallicity) but
preserving the sodium. This problem has never been solved in the models
(Renzini et al., 2015; D’Antona et al., 2016) and brings us back to a key
point of discrepancy in the AGB model.

For the SMS model, based on the results shown by Denissenkov et al. (2015) for
M 13 (their Figure 1 and Table 1), the location of giants with [O/Fe] in the
range from –0.5 to –0.1 is obtained by dilution with 10–20% of pristine gas,
from the pure ejecta having Y=0.384. Then, also in this case these stars
should have Y=0.357–0.37. We can not exclude that there could be a combination
of fine tuned SMS conditions (central temperature of H–burning —or SMS mass—
helium core abundance at the stop of the core evolution and gas shedding)
which allows a smaller helium content concomitant with the O–Na abundances of
the E population. Ad hoc computation of nucleosynthesis such as those
presented in Prantzos et al. (2017) could be useful to explore the range of
parameters and clarify whether the ‘mixed’ SMS+AGB model by Johnson et al.
(2019) can be considered feasible from the helium point of view.

Figure 13: The bottom left panel shows the Na–O data for NGC 2808 and for NGC
6402 together with the dilution curves of the models (see the caption of Fig.
12) and an ideal dilution curve (magenta line with stars) starting at
[O/Fe]$=-1.0$ and [Na/Fe]=0.55. The top panel shows the helium content along
the dilution curves as function of [O/Fe] and the right bottom panel shows the
[N/Fe] abundance along the dilution curve. The [N/Fe] of the ejecta having
[O/Fe]=-1 in this context is roughly 1.8, 0.6 dex larger than the [N/Fe] of
the model of 5$\,{M}_{\odot}$ used as comparison.

###  7.2 Helium and the oxygen and nitrogen abundances: what is required from
models

Fig. 13 shows what is needed by a successful model to conform to the results
obtained from the analysis of NGC 6402 HST data. Whatever the model (a
modified AGB or SMS model) the ejecta of at least some of these stars must
have a very low oxygen abundance (say $\sim$5% of the pristine one), a
reasonably large sodium abundance (e.g. [Na/Fe]=0.55, as chosen in the
figure), but, also, a helium abundance not exceeding Y$\sim$0.35 (as found in
the massive AGBs). Only in this case it is possible to have a helium abundance
of $\sim$0.315 by diluting with pristine gas, and still reproduce the location
in the O-Na plane of the bulk of the E stars in Johnson et al. (2019) sample,
as shown in the top panel.
New modelling is needed to understand whether the chemistry of the ejecta of
super-AGB, AGB and SMS can be made compatible with this requirement.

The bottom right panel of Fig. 13 shows instead the plausible run of nitrogen
in the same ideal model. Indeed, if oxygen is reduced to 1/20 in the
processing, more oxygen has been processed to nitrogen and the ejecta reach a
value [N/Fe]$\sim 1.8$, to be compared to the value of $\sim$1.3 corresponding
to a reduction of $\delta$[O/Fe]$\sim$0.4. This has an interesting consequence
on our understanding of the HST results, as we show in the next section.

###  7.3 The ChM and the “lack” of the intermediate population

The comparison between the ChM of NGC 6402 (black) with the ChM of NGC 2808
(red) is shown in Fig. 11, and highlights how powerful photometry can be at
providing a complementary vision to the high dispersion spectroscopic results.
The large gaps in [O/Fe], [Na/Fe], and [Al/Fe] distributions found in the
spectra suggest that at most 10% of the total population is contained in the
“intermediate” range (the I (or D) population). This is in partial agreement
with the UV photometry, as the ChM shows overdensities for the E group and for
the stars closer to the first population. In the D’Antona et al. (2016) scheme
for the timing of formation of the different MPs, the gap in abundances is
obtained if, after the formation of the moderately diluted 2G extreme E star
group, re-accretion of pristine gas is fast enough that the late forming stars
belong to the very diluted P2 (or 2G mild) group. On the other hand, Johnson
et al. (2019) interpret the gap as a possible evidence of delayed formation
for intermediate composition stars. Thus the birth of the second population
would consist of two distinct phases, an early one to form the 2G extreme
stars, and a very late one to form the P2 (or 2G mild) stars, and suggests the
possibility that there are two different classes of pollutors. The merging of
two clusters with very close initial abundance would provide a natural site
for this occurrence.

###  7.4 The group 2GD

The ChM in Fig. 3 and its comparison with NGC 2808 in the upper left panel of
Fig. 11 shows clearly that the extreme 2G in NGC 2808 extends beyond the
extreme 2G of NGC 6402. At the same time, it shows that NGC 6402 includes a
group of stars which are typical of Type II or iron–complex clusters. Lacking
spectroscopic evidence, we can speculate that $\sim$9% of the cluster stars
are enriched in metals. Notice that they are 2G stars, without a clear 1G
counterpart. Also NGC 2808 possibly hosts stars with higher metallicity (group
A in Fig. 11) but, on the contrary, they belong to 1G. This must be telling us
something about the pollution mechanism. In the D’Antona et al. (2016) model,
the higher metallicity groups are born from gas contaminated by the first SN
Ia explosions, before these explosions fully expel the gas out of the GC
putting an end to 2G star formation. The timing of this event helps to explain
why the iron-richer groups are often s-process rich, being polluted by the
ejecta of AGBs of smaller mass, where s-process enhancements are due to the
prolonged third dredge up phases. In the case of NGC 6402, the SN Ia pollution
must have occurred mainly on p-processed gas, while pollution took place
within a pristine gas region in NGC 2808.
As the 2GD group is mainly 2G, it is unlikely that it is a signature of
merging. Further speculation is beyond the scope of this work. The results
presented here for NGC 6402 call for additional efforts in the development of
new theoretical models.

###  7.5 The lack of a gap in the ChM

We remark here that the lack of a “gap” in the ChM map is not in contradiction
with a possible gap in some of the light elements abundances, because the
ordinate in the ChM mostly traces the nitrogen abundance, which can be more
continuous than Na or Al, if the p-processed gas comes from progenitors having
different nucleosynthesis patterns. From Fig. 13, if there are indeed yields
as low in oxygen to justify the low value of Y=0.315 for the E population,
necessarily their nitrogen abundance in the ejecta is much higher, up to a
factor 2.5 (or 0.4 in the log) larger than the nitrogen in ejecta which
deplete less oxygen, such as in the 5–7$\,{M}_{\odot}$AGBs models. The right
bottom panel of Fig. 13 shows then that stars with similar sodium abundance
(e.g.[Na/Fe]=0.2) may differ by up to 0.5 dex in nitrogen. Thus evolution of
stars with intermediate oxygen depletion (and different nitrogen) may result
in a continuous coverage of the ChM. Spectroscopy of stars in the less
populated region of the ChM would be very useful, because they can help to
discriminate between stars formed by ejecta with different compositions.

##  8 Conclusions

We have presented multi-band photometry of the massive GC NGC 6402 based on
multi-band HST observations collected as part of GO-16283 (PI. F. D’Antona).
Our photometric diagrams have been combined with results from high-resolution
spectroscopy (Johnson et al., 2019) to constrain the formation scenarios of
multiple populations in GCs.

The huge gap in the distribution of some light elements (O, Mg, Al and Na)
found by Johnson et al. (2019) is certainly one of the most-intriguing
properties of multiple populations in NGC 6402. One of the main objectives of
our work consists in exploring whether NGC 6402 lacks stellar populations with
intermediate chemical composition, based on a large stellar sample. To do
this, we exploit the ChM, which is the photometric diagram that has been
previously used to identify and characterize multiple populations in 57
Galactic GCs as part of the HST UV Legacy Survey of GCs (Piotto et al., 2015;
Milone et al., 2015, 2017). The main results of the new observations
concerning the ChM are the following:

  1. 1.

the ChM do not show stars with extreme chemical compositions as observed in
some massive GCs (e.g. NGC 2808 and $\omega$ Cen). Notably, NGC 6402 lacks the
E group stars of the prototype cluster NGC 2808;

  2. 2.

the ChM contains a group of 2G stars (dubbed 2GD) on the red side of the
diagram, indicating the presence of a small group of stars ($\sim 8$%) having
higher metallicity: NGC 6402 is then a “Type II” cluster, in the definition by
Milone et al. (2017);

  3. 3.

the ChM does not show any gaps. There is a region less populated in the middle
region, between the extreme groups (2GC and 2GA). When we locate on the ChM a
few giants in common with the spectroscopic sample, we find that there is an
extreme star also among the less extreme group 2GB.

Thus it is very important to broaden the spectroscopic investigation of this
cluster and study targets in the middle of the ChM.

An independent result of the observation was obtained in the parallel field
data: the color magnitude diagram shows indeed a split MS, confirming that we
are in the presence of a dichotomy in the helium abundance of the cluster
stars. Therefore, the spectroscopic gap is fully confirmed by the presence of
the MS gap. These results indicate that the cluster has undergone two stages
of 2G star formation, the first one from matter strongly contaminated with
p-processed elements and significantly rich in helium, the second one from
matter —not necessarily sharing the same heavy p-processing of the first
event— heavily diluted with pristine gas, so that both the helium content and
the abundances of light elements remain either standard or close to standard.

Already a simple superposition of the parallel field data of NGC 2808 and NGC
6402 shows that the blue MS of the latter cluster is much less extreme, and
thus its helium content is much smaller than the Y$\sim$0.35 attributed to the
prototype cluster. In fact, the analysis of the MS data provides Y$\sim$0.31
for this blue MS (and notice that also the ChM analysis provides a similarly
“low” Y=030 for the extreme stars). This helium content for the extreme
population is also consistent with the analysis of the HB.

The different samples examined give fractions of stars in the three main
groups defined by spectroscopy (1G, mild 2G and extreme 2G) reasonably
compatible with each other, apart from the HB stars, which has far too few
“red” stars, which should correspond to the 1G plus mild 2G sample. We will
address this problem in a future study.

We find that the determination of a helium content Y$\sim 0.31$ for the 2G
extreme stars is extremely useful, because it confirms the composition gap,
and allows a more demanding comparison between models and abundances. We
examine both the SMS model and the AGB model, and conclude that the present
O–Na abundance patterns of the AGB yield for the metallicity of this cluster
(Z=1.5$\times 10^{-3}$) are not compatible with Y$\sim 0.31$. Also SMS present
models seem not compatible with the data, but we leave some space to further
exploration of the parameters space (i:SMS mass —or core temperature of
nuclear processing— and ii: helium content at which the evolution of the SMS
is artificially stopped).

Concerning the AGB model, we conclude that models allowing for a larger oxygen
depletion preserving sodium are needed to be compatible with the data. Whether
and under which hypotheses this is possible is to be explored. Anyway, it is
difficult to maintain the hypothesis that the most extreme oxygen abundances
found in GCs are simply due to deep mixing in the high helium red giants,
favored by the small chemical discontinuity left by convection at the first
dredge up (D’Antona & Ventura, 2007).

One bonus of having established the degree of oxygen depletion necessary for
the 1G ejecta polluting the extreme star sample is the following: the
pollutors of the 2G population will probably cover a range of oxygen
depletion, from the most extreme value [O/Fe]$\sim-1$, to the moderate
depletion shown by the AGB models. Consequently, after dilution with pristine
gas, the gas forming the 2G mild stars may also cover a range of nitrogen
abundances able to smooth down any gap in the ChM.

## Acknowledgements

This work has received funding from the European Research Council (ERC) under
the European Union’s Horizon 2020 research innovation programme (Grant
Agreement ERC-StG 2016, No 716082 ’GALFOR’, PI: Milone,
http://progetti.dfa.unipd.it/GALFOR). APM acknowledges support from MIUR
through the FARE project R164RM93XW SEMPLICE (PI: Milone). APM has been
supported by MIUR under PRIN program 2017Z2HSMF (PI: Bedin). MT acknowledges
support from the European Research Council Consolidator Grant funding scheme
(project ASTEROCHRONOMETRY, G.A. n. 72293, http://www.asterochronometry.eu).
We thank the referee for suggestions and for a very careful reading of the
manuscript.

## References

  * Amaro-Seoane et al. (2013) Amaro-Seoane, P., Konstantinidis, S., Brem, P., & Catelan, M. 2013, MNRAS, 435, 809
  * Anderson & Bedin (2010) Anderson, J., & Bedin, L. R. 2010, PASP, 122, 1035
  * Anderson et al. (2008) Anderson, J., Sarajedini, A., Bedin, L. R., et al. 2008, AJ, 135, 2055
  * Bastian & Lardo (2018) Bastian, N., & Lardo, C. 2018, ARA&A, 56, 83
  * Bedin et al. (2004) Bedin, L. R., Piotto, G., Anderson, J., et al. 2004, ApJ, 605, L125
  * Bekki (2011) Bekki, K. 2011, MNRAS, 412, 2241
  * Bekki & Tsujimoto (2016) Bekki, K., & Tsujimoto, T. 2016, ApJ, 831, 70
  * Bekki & Tsujimoto (2017) —. 2017, ApJ, 844, 34
  * Bellini et al. (2011) Bellini, A., Anderson, J., & Bedin, L. R. 2011, PASP, 123, 622
  * Bellini & Bedin (2009) Bellini, A., & Bedin, L. R. 2009, PASP, 121, 1419
  * Bellini et al. (2017) Bellini, A., Milone, A. P., Anderson, J., et al. 2017, ApJ, 844, 164
  * Bellini et al. (2009) Bellini, A., Piotto, G., Bedin, L. R., et al. 2009, A&A, 507, 1393
  * Brown et al. (2016) Brown, T. M., Cassisi, S., D’Antona, F., et al. 2016, ApJ, 822, 44
  * Brown et al. (2017) Brown, T. M., Taylor, J. M., Cassisi, S., et al. 2017, ApJ, 851, 118
  * Calura et al. (2019) Calura, F., D’Ercole, A., Vesperini, E., Vanzella, E., & Sollima, A. 2019, MNRAS, 489, 3269
  * Carretta (2015) Carretta, E. 2015, ApJ, 810, 148
  * Carretta (2021) —. 2021, A&A, 649, A154
  * Carretta et al. (2018) Carretta, E., Bragaglia, A., Lucatello, S., et al. 2018, A&A, 615, A17
  * Carretta et al. (2009) Carretta, E., Bragaglia, A., Gratton, R. G., et al. 2009, A&A, 505, 117
  * Cohen & Kirby (2012) Cohen, J. G., & Kirby, E. N. 2012, ApJ, 760, 86
  * Contreras Peña et al. (2013) Contreras Peña, C., Catelan, M., Grundahl, F., Stephens, A. W., & Smith, H. A. 2013, AJ, 146, 57
  * Contreras Peña et al. (2018) —. 2018, AJ, 155, 116
  * Da Costa et al. (2013) Da Costa, G. S., Norris, J. E., & Yong, D. 2013, ApJ, 769, 8
  * Dalessandro et al. (2019) Dalessandro, E., Cadelano, M., Vesperini, E., et al. 2019, ApJ, 884, L24
  * D’Antona et al. (2005) D’Antona, F., Bellazzini, M., Caloi, V., et al. 2005, ApJ, 631, 868
  * D’Antona & Caloi (2004) D’Antona, F., & Caloi, V. 2004, ApJ, 611, 871
  * D’Antona & Caloi (2008) —. 2008, MNRAS, 390, 693
  * D’Antona et al. (2002) D’Antona, F., Caloi, V., Montalbán, J., Ventura, P., & Gratton, R. 2002, A&A, 395, 69
  * D’Antona & Ventura (2007) D’Antona, F., & Ventura, P. 2007, MNRAS, 379, 1431
  * D’Antona et al. (2016) D’Antona, F., Vesperini, E., D’Ercole, A., et al. 2016, MNRAS, 458, 2122
  * Dell’Agli et al. (2018) Dell’Agli, F., García-Hernández, D. A., Ventura, P., et al. 2018, MNRAS, 475, 3098
  * Denissenkov & Hartwick (2014) Denissenkov, P. A., & Hartwick, F. D. A. 2014, MNRAS, 437, L21
  * Denissenkov et al. (2015) Denissenkov, P. A., VandenBerg, D. A., Hartwick, F. D. A., et al. 2015, MNRAS, 448, 3314
  * D’Ercole et al. (2012) D’Ercole, A., D’Antona, F., Carini, R., Vesperini, E., & Ventura, P. 2012, MNRAS, 423, 1521
  * D’Ercole et al. (2016) D’Ercole, A., D’Antona, F., & Vesperini, E. 2016, MNRAS, 461, 4088
  * D’Ercole et al. (2008) D’Ercole, A., Vesperini, E., D’Antona, F., McMillan, S. L. W., & Recchi, S. 2008, MNRAS, 391, 825
  * Dondoglio et al. (2021) Dondoglio, E., Milone, A. P., Lagioia, E. P., et al. 2021, ApJ, 906, 76
  * Ferraro et al. (2016) Ferraro, F. R., Massari, D., Dalessandro, E., et al. 2016, ApJ, 828, 75
  * Ferraro et al. (2021) Ferraro, F. R., Pallanca, C., Lanzoni, B., et al. 2021, Nature Astronomy, 5, 311
  * Forbes et al. (2018) Forbes, D. A., Bastian, N., Gieles, M., et al. 2018, Proceedings of the Royal Society of London Series A, 474, 20170616
  * Frischknecht et al. (2012) Frischknecht, U., Hirschi, R., & Thielemann, F. K. 2012, A&A, 538, L2
  * Frischknecht et al. (2016) Frischknecht, U., Hirschi, R., Pignatari, M., et al. 2016, MNRAS, 456, 1803
  * Gavagnin et al. (2016) Gavagnin, E., Mapelli, M., & Lake, G. 2016, MNRAS, 461, 1276
  * Gieles et al. (2018) Gieles, M., Charbonnel, C., Krause, M. G. H., et al. 2018, MNRAS, 478, 2461
  * Gratton et al. (2019) Gratton, R., Bragaglia, A., Carretta, E., et al. 2019, A&A Rev., 27, 8
  * Grundahl et al. (1999) Grundahl, F., Catelan, M., Landsman, W. B., Stetson, P. B., & Andersen, M. I. 1999, ApJ, 524, 242
  * Harris (1996) Harris, W. E. 1996, AJ, 112, 1487
  * Johnson et al. (2019) Johnson, C. I., Caldwell, N., Michael Rich, R., Mateo, M., & Bailey, J. I. 2019, MNRAS, 485, 4311
  * Johnson et al. (2015) Johnson, C. I., Rich, R. M., Pilachowski, C. A., et al. 2015, AJ, 150, 63
  * Khoperskov et al. (2018) Khoperskov, S., Mastrobuono-Battisti, A., Di Matteo, P., & Haywood, M. 2018, A&A, 620, A154
  * Lacchin et al. (2021) Lacchin, E., Calura, F., & Vesperini, E. 2021, MNRAS, 506, 5951
  * Lagioia et al. (2019) Lagioia, E. P., Milone, A. P., Marino, A. F., & Dotter, A. 2019, ApJ, 871, 140
  * Lagioia et al. (2021) Lagioia, E. P., Milone, A. P., Marino, A. F., et al. 2021, ApJ, 910, 6
  * Lardo et al. (2011) Lardo, C., Bellazzini, M., Pancino, E., et al. 2011, A&A, 525, A114
  * Lee (2015) Lee, J.-W. 2015, ApJS, 219, 7
  * Lee et al. (1994) Lee, Y.-W., Demarque, P., & Zinn, R. 1994, ApJ, 423, 248
  * Lee et al. (2005) Lee, Y.-W., Joo, S.-J., Han, S.-I., et al. 2005, ApJ, 621, L57
  * Lim et al. (2015) Lim, D., Han, S.-I., Lee, Y.-W., et al. 2015, ApJS, 216, 19
  * Mackey & van den Bergh (2005) Mackey, A. D., & van den Bergh, S. 2005, MNRAS, 360, 631
  * Marino et al. (2011) Marino, A. F., Villanova, S., Milone, A. P., et al. 2011, ApJ, 730, L16
  * Marino et al. (2008) Marino, A. F., Villanova, S., Piotto, G., et al. 2008, A&A, 490, 625
  * Marino et al. (2014) Marino, A. F., Milone, A. P., Przybilla, N., et al. 2014, MNRAS, 437, 1609
  * Marino et al. (2017) Marino, A. F., Milone, A. P., Yong, D., et al. 2017, ApJ, 843, 66
  * Marino et al. (2019) Marino, A. F., Milone, A. P., Renzini, A., et al. 2019, MNRAS, 487, 3815
  * Milone et al. (2009) Milone, A. P., Bedin, L. R., Piotto, G., & Anderson, J. 2009, A&A, 497, 755
  * Milone et al. (2012a) Milone, A. P., Marino, A. F., Piotto, G., et al. 2012a, ApJ, 745, 27
  * Milone et al. (2012b) Milone, A. P., Piotto, G., Bedin, L. R., et al. 2012b, A&A, 537, A77
  * Milone et al. (2012c) —. 2012c, ApJ, 744, 58
  * Milone et al. (2015) Milone, A. P., Marino, A. F., Piotto, G., et al. 2015, ApJ, 808, 51
  * Milone et al. (2017) Milone, A. P., Piotto, G., Renzini, A., et al. 2017, MNRAS, 464, 3636
  * Milone et al. (2018) Milone, A. P., Marino, A. F., Renzini, A., et al. 2018, MNRAS, 481, 5098
  * Momany et al. (2004) Momany, Y., Bedin, L. R., Cassisi, S., et al. 2004, A&A, 420, 605
  * Muñoz et al. (2020) Muñoz, C., Villanova, S., Geisler, D., et al. 2020, MNRAS, 492, 3742
  * Mucciarelli et al. (2015) Mucciarelli, A., Bellazzini, M., Merle, T., et al. 2015, ApJ, 801, 68
  * Nardiello et al. (2018) Nardiello, D., Libralato, M., Piotto, G., et al. 2018, MNRAS, 481, 3382
  * Piotto et al. (2002) Piotto, G., King, I. R., Djorgovski, S. G., et al. 2002, A&A, 391, 945
  * Piotto et al. (2007) Piotto, G., Bedin, L. R., Anderson, J., et al. 2007, ApJ, 661, L53
  * Piotto et al. (2015) Piotto, G., Milone, A. P., Bedin, L. R., et al. 2015, AJ, 149, 91
  * Portegies Zwart et al. (2004) Portegies Zwart, S. F., Baumgardt, H., Hut, P., Makino, J., & McMillan, S. L. W. 2004, Nature, 428, 724
  * Portegies Zwart et al. (1999) Portegies Zwart, S. F., Makino, J., McMillan, S. L. W., & Hut, P. 1999, A&A, 348, 117
  * Prantzos et al. (2017) Prantzos, N., Charbonnel, C., & Iliadis, C. 2017, A&A, 608, A28
  * Renzini et al. (2015) Renzini, A., D’Antona, F., Cassisi, S., et al. 2015, MNRAS, 454, 4197
  * Sabbi et al. (2016) Sabbi, E., Lennon, D. J., Anderson, J., et al. 2016, ApJS, 222, 11
  * Searle (1977) Searle, L. 1977, in Evolution of Galaxies and Stellar Populations, ed. B. M. Tinsley, R. B. Larson, & G. D. Campbell, 219
  * Searle & Zinn (1978) Searle, L., & Zinn, R. 1978, ApJ, 225, 357
  * Simioni et al. (2016) Simioni, M., Milone, A. P., Bedin, L. R., et al. 2016, MNRAS, 463, 449
  * Sollima et al. (2007) Sollima, A., Ferraro, F. R., Bellazzini, M., et al. 2007, ApJ, 654, 915
  * Sugimoto & Makino (1989) Sugimoto, D., & Makino, J. 1989, PASJ, 41, 1117
  * Tailo et al. (2016) Tailo, M., Di Criscienzo, M., D’Antona, F., Caloi, V., & Ventura, P. 2016, MNRAS, 457, 4525
  * Tailo et al. (2019) Tailo, M., Milone, A. P., Marino, A. F., et al. 2019, ApJ, 873, 123
  * Tailo et al. (2015) Tailo, M., D’Antona, F., Vesperini, E., et al. 2015, Nature, 523, 318
  * Tailo et al. (2020) Tailo, M., Milone, A. P., Lagioia, E. P., et al. 2020, MNRAS, 498, 5745
  * Tailo et al. (2021) —. 2021, MNRAS, 503, 694
  * van den Bergh (1996) van den Bergh, S. 1996, ApJ, 471, L31
  * Ventura (2010) Ventura, P. 2010, in IAU Symposium, Vol. 268, Light Elements in the Universe, ed. C. Charbonnel, M. Tosi, F. Primas, & C. Chiappini, 147–152
  * Ventura & D’Antona (2009) Ventura, P., & D’Antona, F. 2009, A&A, 499, 835
  * Ventura et al. (2018) Ventura, P., D’Antona, F., Imbriani, G., et al. 2018, MNRAS, 477, 438
  * Ventura et al. (2001) Ventura, P., D’Antona, F., Mazzitelli, I., & Gratton, R. 2001, ApJ, 550, L65
  * Ventura et al. (2013) Ventura, P., Di Criscienzo, M., Carini, R., & D’Antona, F. 2013, MNRAS, 431, 3642
  * Wirth et al. (2021) Wirth, H., Jerabkova, T., Yan, Z., et al. 2021, MNRAS, 506, 4131
  * Yong et al. (2017) Yong, D., Norris, J. E., Da Costa, G. S., et al. 2017, ApJ, 837, 176
  * Zennaro et al. (2019) Zennaro, M., Milone, A. P., Marino, A. F., et al. 2019, MNRAS, 487, 3239