Four stellar populations and extreme helium variation in the massive outer-halo globular cluster NGC 2419

ABSTRACT

Recent work revealed that both the helium variation within globular clusters (GCs) and the relative numbers of first- and second-generation stars (1G, 2G) depend on the mass of the host cluster. Precise determination of the internal helium variations and of the fraction of 1G stars are crucial constraints to the formation scenarios of multiple populations (MPs). We exploit multiband Hubble Space Telescope photometry to investigate MPs in NGC 2419, which is one of the most-massive and distant GCs of the Galaxy, almost isolated from its tidal influence. We find that the 1G hosts the ∼37 per cent of the analysed stars, and identified three populations of 2G stars, namely 2G_A, 2G_B, and 2G_C, which comprise the ∼20 per cent, ∼31 per cent, and ∼12 per cent of stars, respectively. We compare the observed colours of these four populations with the colours derived from appropriate synthetic spectra to infer the relative helium abundances. We find that 2G_A, 2G_B, and 2G_C stars are enhanced in helium mass fraction by δY ∼ 0.01, 0.06, and 0.19 with respect to 1G stars that have primordial helium (Y = 0.246). The high He enrichment of 2G_C stars is hardly reconcilable with most of the current scenarios for MPs. Furthermore, the relatively larger fraction of 1G stars (∼37 per cent) compared to other massive GCs is noticeable. By exploiting literature results, we find that the fractions of 1G stars of GCs with large perigalactic distance are typically higher than in the other GCs with similar masses. This suggests that NGC 2419, similarly to other distant GCs, lost a lower fraction of 1G stars.

1 INTRODUCTION

Nearly all globular clusters (GCs) are composed of two main groups of first- and second-generation stars (1G, 2G; Milone et al. 2017a) with different chemical compositions whose origin is still not understood (Gratton, Sneden & Carretta 2004; Marino et al. 2008, 2016; Carretta et al. 2009; Gratton, Carretta & Bragaglia 2012; Johnson & Pilachowski 2012, 2017, 2019, and references therein). According to many scenarios, 2G stars formed in the cluster centre out of the material polluted by more-massive 1G stars (e.g. Ventura et al. 2001; Decressin et al. 2007; D’Ercole et al. 2008, 2010). In these scenarios, GCs would lose the majority of their 1G, thus providing a significant contribution to the assembly of the Galaxy (e.g. D’Ercole et al. 2010; D’Antona et al. 2016). As an alternative, GCs would host a single stellar generation and stars with different chemical composition are the product of exotic phenomena that occur in the unique environment of proto GCs (e.g. De Mink et al. 2009; Bastian et al. 2013; Gieles et al. 2018).

NGC 2419 is one of the most-massive (⁠|$\mathcal {M}= 9 \times 10^{5}\, \mathcal {M_{\odot }}$|⁠; McLaughlin & van der Marel 2005) and metal-poor ([Fe/H] = −2.09, Mucciarelli et al. 2012) Galactic GCs. The large distance from the Galactic centre (d ∼ 87.5 kpc; Di Criscienzo et al. 2011b) makes it almost isolated from the tidal influence of the Milky Way. Based on Gaia data release 2 (DR2; Gaia Collaboration 2018) data, Baumgardt et��al. (2019) derive the orbit of NGC 2419 and inferred a perigalactic and apogalactic distances R_PER = 16.52 ± 2.68 kpc and R_APO = 90.96 ± 7.66 kpc. Baumgardt and collaborator adopted radial velocity R_v = −20.67 ± 0.34 km s⁻¹, μ_αcosδ = −0.02 ± 0.02 mas yr⁻¹, μ_δ = −0.57 ± 0.01 mas yr⁻¹.

Moreover, since its half-light relaxation time exceeds the Hubble time (Harris 1996, updated as in 2010), it would retain fossil information on the properties of multiple populations (MPs) at the formation. The possibility that NGC 2419 evolved in isolation, together with its extreme mass and metallicity, makes this cluster an ideal target to constrain the formation scenarios of MPs.

Recent work based on multiband photometry of 58 Galactic GCs have investigated the relation between MPs and fundamental parameters of the host clusters and revealed that the complexity of MPs increases with cluster mass. In particular, the maximum internal helium variation, which ranges from less than 0.01 to more than ∼0.12 in helium mass fraction, correlates with the mass of the host cluster, whereas the fraction of 1G stars with respect to the total number of cluster stars varies between |${\sim } 8{{\ \rm per\ cent}}$| and 67 per cent and anticorrelates with cluster mass (Milone 2015; Milone et al. 2017a, 2018).

In the context of the multiple-generation scenarios (D’Ercole et al. 2010; D’Antona et al. 2016, and references therein), we would expect that a cluster that formed and evolved in isolation has retained its initial mass and the fraction of 1G stars. As a consequence, NGC 2419 would exhibit similar helium spread as the other GCs with similar mass but a significantly larger frequency of 1G stars that would include up to ∼90 per cent of the cluster stars (e.g. Di Criscienzo et al. 2011a).

Multiple stellar populations in NGC 2419 have been widely investigated both spectroscopically and photometrically. Based on high-precision photometry obtained from Wide Field Channel of the Advanced Camera for Survey (WFC/ACS) on the Hubble Space Telescope (HST), Di Criscienzo et al. (2011a) and Lee et al. (2013) found that the base of the red giant branch (RGB) of NGC 2419 exhibits a wide m_F475W − m_F814W colour broadening that is consistent with two stellar populations with an extreme helium difference of ΔY ∼0.17−0.19.

Spectroscopy revealed large star-to-star variation in magnesium and potassium, at variance with most GCs that have homogeneous [K/Fe] (Cohen, Huang & Kirby 2011; Cohen & Kirby 2012; Mucciarelli et al. 2012). Stars with different abundances of Mg and K exhibit different colours in the V versus u − V CMD (Beccari et al. 2013), in close analogy with what is observed in nearly all the GCs where stars with different light-element abundance populate distinct sequences in CMDs made with ultraviolet filters (Marino et al. 2008; Yong et al. 2008).

In this paper, we further investigate multiple stellar populations in NGC 2419 by extending to this cluster the same methods used by Milone et al. (2017a, 2018) to identify and characterize MPs of 58 GCs. The paper is organized as follows. Section 2 describes the data set and the data reduction. In Section 3, we present various photometric diagrams that we use to identify stellar populations in NGC 2419 and to derive the fraction of stars in each population. The chemical composition of the stellar populations is investigated in Section 4. Results are discussed in Section 5 where we also provide a summary of the paper.

2 DATA AND DATA ANALYSIS

To investigate multiple stellar populations in NGC 2419 we used archive images collected through 14 filters of the Ultraviolet and Visual Channel of the Wide Field Camera 3 (UVIS/WFC3) on board HST. These data are collected as part of the GO-11903 program (PI: J. Kalirai) with the main purpose of improving the UVIS photometric zero-points and as part of GO 15078 (PI: S. Larsen), which is a project focused on the dynamics of MPs in NGC 2419. The main properties of the data set are summarized in Table 1.

Photometry and astrometry have been obtained with the computer program Kitchen Sink 2 developed by Jay Anderson, which is similar to the software described by Anderson et al. (2008) to reduce images taken with the WFC/ACS but is optimized to work with images collected with various detectors of HST, including UVIS/WFC3.

Shortly, the software performs the fitting of appropriate point spread functions (PSFs) to all the observed sources and follows two distinct methods to measure stars with different luminosities. The magnitudes and positions of bright stars are measured in each exposure independently, and then averaged. To measure faint stars the software combines information from all the images that are placed into a common distortion-free reference frame. We used the solution provided by Bellini & Bedin (2009) and Bellini, Anderson & Bedin (2011) to correct the geometric distortion of the UVIS/WFC3 images. We refer to papers by Sabbi et al. (2016) and Bellini et al. (2017) for details on Kitchen Sink 2. Photometry has been calibrated to the Vega system as in Bedin et al. (2005) by using the updated zero-points of the UVIS/WFC3 filters provided by the STScI webpage.

The software by Anderson and collaborators provides various diagnostics of the photometric and astrometric quality that we used to select a sample of relatively isolated stars that are well fitted by the PSF and have small random mean scatter (rms) in magnitudes and positions. To do this, we applied the procedure by Milone et al. (2009) and Bedin et al. (2009). Finally, we corrected the magnitudes from the small variations of the photometric zero-point across the field of view as in Milone et al. (2012).

2.1 Artificial stars

We performed artificial-star (AS) experiments to infer the photometric uncertainties and to simulate the photometric diagrams by extending to NGC 2419 the procedure by Anderson et al. (2008).

In a nutshell, we first generated a list of coordinates and magnitudes of 100 000 stars. These stars have similar spatial distribution along the field of view as cluster stars and instrumental magnitudes, −2.5 log₁₀(flux), ranging from −13.8 to −4.0 in the F814W band. The other magnitudes are derived from the corresponding fiducial lines of RGB, subgiant branch, and main-sequence (MS) stars that we derived from the observed CMDs.

ASs are reduced by adopting exactly the same procedure used for real stars. The Kitchen Sink 2 computer program derives for ASs the same diagnostics of the photometric and astrometric quality calculated for real stars. We included in our investigation only the sample of relatively isolated ASs that are well fitted by the PSF and have small rms in magnitudes and positions and that are selected by using the same criteria that we adopted for real stars. The selected stellar sample includes 90.8 per cent of the total number of RGB stars brighter than m_F814W = 22.0, which is the sample of stars mostly analysed in our paper. The completeness level of 0.5 corresponds to m_F814W = 23.4 in the photometric diagram made with F343N, F336W, F438W, and F814W filters (see Section 3 for details).

3 MULTIPLE POPULATIONS IN NGC 2419

We show in Fig. 1 two diagrams that highlight different properties of stellar populations. The left-hand panel of Fig. 1 reveals that the m_F438W versus m_F438W − m_F814W CMD of NGC 2419 is not consistent with a simple population. Our conclusion is supported by the presence of a tail of stars with bluer colours than the bulk of RGB stars and by the fact that the colour width of the RGB is much larger than what we expect from photometric uncertainties alone, which are indicated by the error bars plotted on the right of the CMD. The fact that m_F438W − m_F814W is an efficient colour to identify RGB stars with the same luminosity but different effective temperature suggests that NGC 2419 hosts stellar populations with extreme helium abundance as previously noticed by Di Criscienzo et al. (2011a) and Lee et al. (2013).

In the right-hand panel of Fig. 1 we plotted m_F814W against C_{F336W, F343N, F438W} = (m_F336W − m_F343N) − (m_F343N − m_F438W), which is a pseudo-colour sensitive to the abundances of C and N, mostly through the NH and CN bands. The RGB is clearly split into a red and blue sequence, which include approximately 35 per cent and 45 per cent of RGB stars, respectively, plus a population of stars located between the two main RGBs that comprises about 20 per cent of stars.

The black crosses superimposed on both photometric diagrams of Fig. 1 mark the asymptotic giant branch (AGB) stars that we selected from the left-hand panel CMD. Although the C_{F336W, F343N, F438W} broadening of AGB stars is larger than the broadening expected from observational errors, these AGB stars span a smaller range of C_{F336W, F343N, F438W} than RGB stars with the same luminosity. This fact indicates that, although the AGB of NGC 2419 is not consistent with a simple population, those 2G stars with extreme chemical composition avoid the AGB phase in close analogy with what is observed in NGC 6752, NGC 6266, and NGC 2808 (Campbell et al. 2013; Lapenna et al. 2015; Wang et al. 2016; Marino et al. 2017).

3.1 The chromosome map of NGC 2419

The chromosome map (ChM) is a powerful tool developed to identify and characterize multiple stellar populations in GCs (Milone et al. 2015). It consists of a pseudo two-colour diagram of MS, RGB, or AGB stars derived from photometry in different filters that are sensitive to the specific chemical composition of the distinct populations (e.g. Marino et al. 2017; Milone et al. 2017b). The most-widely filters used to construct the ChM are F275W, F336W, F438W, and F814W of WFC3/UVIS but other optical and near-infrared bands, like F606W, F814W, F110W, and F160W have been also used to derive the ChM of low-mass MS stars (Milone et al. 2017a).

Milone et al. (2017b, 2018) constructed the ChMs for RGB stars in 58 Galactic GCs by plotting the pseudo-colour C_{F275W, F336W, F438W}, which is mostly sensitive to the nitrogen abundance of the stellar populations, as a function of m_F275W − m_F814W, which is very sensitive to helium. However, the ChM is not a simple two-colour diagram because the RGB is verticalized in both dimensions (see Milone et al. 2015, 2017b for details).

Unfortunately, the available F275W photometry of NGC 2419 is obtained from a single exposure of 400 s only and is too shallow to properly identify MPs along the RGB of this distant cluster. As a consequence, we build a ChM by using photometric bands that are different from those used by Milone and collaborators, but are sensitive to helium and nitrogen variations. Specifically, we combined the information from the photometric diagrams plotted in Fig. 1 and exploited the verticalized (F438W−F814W) colour, Δ_{F438W, F814W}, that is sensitive to helium, and the verticalized (F336W−F343N)−(F343N−F438W) pseudo-colour, |$\Delta _{C F336W,F343N,F438W}$|⁠, which is an efficient tool to identify stellar populations with different nitrogen abundance.

The resulting Δ_{CF336W, F343N, F438W} versus Δ_{F438W, F814W} ChM is illustrated in the left-hand panel of Fig. 2, while the corresponding Hess diagram is shown on the right-hand side. In Appendix A, we provide further details on the procedure to derive the ChM of NGC 2419 and compare the Δ_{CF336W, F343N, F438W} versus Δ_{F438W, F814W} ChM with the ‘classical’ ChM from Milone et al. (2017a) of the GCs 47 Tucanae and M 15 made with the F275W, F336W, F438W, and F814W filters. This figure immediately reveals that NGC 2419 hosts four main stellar populations clustered around (⁠|$\Delta _{F438W,F814W},\Delta _{C F336W,F343N,F438W}$|⁠) = (−0.2,0.2), (−0.3,0.5), (−0.4,0.9), and (−0.8,0.9). In the next subsections, we properly identify these four populations and determine their relative stellar fractions.

3.2 Distinguishing the four stellar populations

To identify the main stellar populations of NGC 2419, we used the procedure illustrated in Fig. 3 that is similar to that used by Milone et al. (2017a, 2018) to define 1G and 2G stars in 58 GCs.

Panel (a) of Fig. 3 reproduces the ChM of RGB stars plotted in Fig. 2. We identify 1G stars as those clustered around the origin of the reference frame, while 2G stars are those in the sequence that reaches large values of |$\Delta _{C F336W,F343N,F438W}$|⁠. Clearly, 2G stars include three stellar populations that we name 2G_A, 2G_B, and 2G_C, with the latter corresponding to the population with the most-extreme Δ_{F438W, F814W} values. The normalized |$\Delta _{C F336W,F343N,F438W}$| and Δ_{F438W, F814W} histogram distributions are shown in panels (a2) and (a3).

The expected distribution of the photometric errors is represented with grey points, while the corresponding |$\Delta _{C F336W,F343N,F438W}$| kernel-density distribution is plotted with a grey line. The adopted average Δ_{F438W, F814W} value of the grey points is chosen arbitrarily while the adopted average |$\Delta _{C F336W,F343N,F438W}$| value, |$\Delta _{C F336W,F343N,F438W}^{0}$|⁠, is determined by using the procedure by Milone et al. (2018, see their section 2.1).

In a nutshell, we assumed various possible values for |$\Delta _{C F336W,F343N,F438W}^{0}$|⁠, |$\Delta _{C F336W,F343N,F438W}^{i, 0}$| that range from −0.200 to 0.100 in steps of 0.001. For each choice of |$\Delta _{C F336W,F343N,F438W}^{i, 0}$| we derived the corresponding |$\Delta _{C F336W,F343N,F438W}$| kernel-density distribution of the errors, |$\phi ^{\rm i}_{\rm err}$|⁠, and the observed kernel-density distribution, |$\phi ^{\rm i}_{\rm obs}$|⁠. We compared the distributions |$\phi ^{\rm i}_{\rm err}$| and |$\phi ^{\rm i}_{\rm obs}$| for |$\Delta _{C F336W,F343N,F438W} \lt (\Delta _{C F336W,F343N,F438W}^{i, 0} + \sigma)$|⁠, where σ is defined as the 68.27th percentile of the |$\Delta _{C F336W,F343N,F438W}$| distribution of the errors, and calculated the corresponding χ². Both distributions are normalized in such a way that their maximum values, calculated in the interval with |$\Delta _{C F336W,F343N,F438W} \lt (\Delta _{C F336W,F343N,F438W}^{i, 0} + \sigma)$|⁠, correspond to one. We adopted as |$\Delta _{C F336W,F343N,F438W}^{0}$| the value of |$\Delta _{C F336W,F343N,F438W}^{i, 0}$| that provides the minimum χ².

The grey dashed horizontal line is plotted at the |$\Delta _{C F336W,F343N,F438W}$| level corresponding to the 1.5σ deviation from |$\Delta _{C F336W,F343N,F438W}^{0}$| and is used to separate the bulk of 1G stars (red points) from 2G stars (blue points). The observed kernel-density distribution of |$\Delta _{C F336W,F343N,F438W}$| and the error distribution corresponding to the minimum χ² are represented with black and grey lines, respectively, in panel (a2) of Fig. 3. For completeness, we show the observed Δ_{F438W, F814W} kernel-density distribution in panel (a3).

To identify a sample of bona-fides 2G_C stars, we extended to 2G stars the procedure described above. In this case we used the distribution of Δ_{F438W, F814W} to separate the bulk of 2G_C stars from the remaining 2G stars. Finally, we exploit the |$\Delta _{C F336W,F343N,F438W}$| to separate the majority of 2G_B stars from 2G_A stars.

The four groups of 1G, 2G_A, 2G_B, and 2G_C stars are coloured red, yellow, green, and cyan, respectively, in Fig. 3(b) and will be used in the next subsection to estimate the relative fraction of stars in each population.

3.3 Population ratios

To estimate the fraction of stars in each population identified in Section 3.2, we extended the method by Milone et al. (2012) and Nardiello et al. (2018) to the ChM of NGC 2419. The procedure is illustrated in Fig. 4. Briefly, we calculated the average values of Δ_{F438W, F814W}, and |$\Delta _{C F336W,F343N,F438W}$| for the stars of each population (coloured dots in Fig. 4) and used these points as centres of four regions, namely R1, R2_A, R2_B, and R2_C. Each region is an ellipse and is similar to the ellipse that reproduces the distribution of photometric uncertainties.

By solving these four equations, we calculate the total numbers of 1G, 2G_A, 2G_B, and 2G_C stars and find that the corresponding fraction of stars with respect to the total number of analysed RGB stars are 37 ± 1 per cent, 20 ± 1 per cent, 31 ± 1 per cent and 12 ± 1 per cent, respectively. As a consequence, the whole 2G comprises 63 ± 1 per cent of the total number of analysed stars.

To compare NGC 2419 with the other GCs, we plot in the left-hand panel of Fig. 5 the fraction of 1G stars as a function of the absolute visual magnitude, M_V (from Harris 1996, updated as in 2010), for the 58 clusters studied by Milone et al. (2017a, 2018) and for NGC 2419. The fraction of 1G stars correlates with M_V with a Spearman’s rank correlation coefficient, r = 0.71 ± 0.07. However, although NGC 2419 follows the general trend, its fraction of 1G stars is larger than that of most clusters with similar luminosity.

The right-hand panel of Fig. 5 shows that the fraction of 1G stars does not exhibit significant correlation with the perigalactic distances, R_PER, of the host GC from (from Baumgardt et al. 2019 based on Gaia DR2 data, r = 0.34 ± 0.12). Similarly, we verify that there is no significant correlation with the apogalactic distance (from Baumgardt et al. 2019 based on Gaia DR2 data, r = 0.31 ± 0.13) and with the distance from the Galactic centre (from the 2010 version of the Harris 1996 catalogue, r = 0.00 ± 0.13). However, we note that the clusters with large perigalactic distances R_PER > 3.5 kpc exhibit, on average, larger fractions of 1G than those of the remaining clusters with similar masses as shown in the left-hand panel of Fig. 5.

4 THE CHEMICAL COMPOSITION OF THE STELLAR POPULATIONS

To infer the chemical composition of the four stellar populations of NGC 2419, we combine photometry from this paper and chemical abundances inferred from spectroscopy in the literature. Specifically, we exploit the results by Mucciarelli et al. (2012), who analysed 49 giants by using medium-resolution spectra collected with the multiobject spectrograph DEIMOS@Keck. They find that NGC 2419 has homogeneous abundances of Fe, Ca, and Ti and discovered large star-to-star variations in Mg and K.

Chemical abundances from Mucciarelli and collaborators are available for eleven stars in the ChM of Fig. 2, including two 1G stars, one 2G_A star, six 2G_B stars, and two 2G_C stars (Fig. 6a). Panels (b) and (c) of Fig. 6 show that |$\Delta _{C F336W,F343N,F438W}$| anticorrelates with [Mg/Fe] and correlates with [K/Fe] while panel (d) of Fig. 6 reproduces the potassium–magnesium anticorrelation from Mucciarelli et al. (2012).

The comparison between the ChM and the chemical abundances indicates that 1G and 2G_A stars have similar magnesium abundance of [Mg/Fe] ∼ 0.4, while 2G_B and 2G_C are depleted in magnesium by ∼1 dex with respect to the remaining stars of NGC 2419. 1G stars have nearly solar potassium abundance, while the 2G_A is enhanced in [K/Fe] by ∼0.8 dex. The remaining stars exhibit extreme potassium contents up to [K/Fe] ∼ 1.4 dex for the six 2G_B stars and [K/Fe] ≳ 1.9 for the two 2G_C stars. As discussed by Mucciarelli et al. (2012) there is no evidence for significant variations of Ca, Fe, and Ti. The average elemental abundances for each population are provided in Table 2.

4.1 The helium abundance of multiple stellar populations

We estimated the relative helium abundance between 2G and 1G stars (δY_{2G, 1G}) by following the method by Milone et al. (2012, 2018) that is illustrated in Fig. 7. In a nutshell, we first derived the RGB fiducial lines of 1G and 2G stars in the CMDs m_F814W versus m_X − m_F814W, where X = F225W, F275W, F300X, F336W, F343N, F390W, F438W, F475W, F475X, F555W, F606W, F625W, and F775W. As an example, in the panels (a), (b), and (c) of Fig. 7 we show the fiducial lines corresponding to X = F275W, X = F343N, and X = F438W, respectively. We find that the 2G fiducials have bluer colours than the 1G fiducials in all the CMDs but for X = F336W and F343N, where 2G stars are redder than 1G stars.

We defined four equally spaced reference points in the magnitude bin with 18.0 < m_F814W < 20.8 and calculated the m_X − m_F814W colour difference between the fiducial of 2G and 1G stars for each reference point, Δ(m_X − m_F814W). The magnitude levels corresponding to these reference points (⁠|$m_{F814W}^{\rm ref} = 18.2, 19.0, 19.8, 20.6$|⁠) are represented with dotted lines in panels (a), (b), and (c) of Fig. 7 while in panel (d) we represent with coloured dots the Δ(m_X − m_F814W) values corresponding to the various X filters for the reference point with |$m_{F814W}^{\rm ref} = 19.8$|⁠.

We derived the gravity and effective temperature of 1G stars with luminosities that correspond to the reference points by using the best-fitting isochrones from the Darthmouth data base (Dotter et al. 2008). We assumed primordial helium content, Y = 0.246, iron abundance, [Fe/H] = −2.09 (Mucciarelli et al. 2012), and [α/Fe] = 0.40. The best fit between the isochrones and the data is provided by distance modulus and reddening of (m − M)₀ = 19.68 and E(B − V) = 0.07, respectively, and age of 13.0 Gyr, which are similar to the values listed by Harris (1996, 2010 update) and Dotter et al. (2010).

For each reference point we calculated a synthetic spectrum and a grid of comparison spectra with different chemical composition by using the computer programs ATLAS 12 and Synthe (Castelli 2005; Kurucz 2005; Sbordone, Bonifacio & Castelli 2007). We assumed [C/Fe] = −0.6, [N/Fe] = 0.6, [O/Fe] = 0.4, as inferred from high-resolution spectra of 1G stars in the metal-poor GC M 22 by Marino et al. (2011), and the values of effective temperature and gravity that we derived from the best-fitting isochrone and are provided in Table 3. The comparison spectra have [C/Fe] that ranges between −1.5 and 0.0 dex and [O/Fe] that ranges from −1.0 to 0.4 in steps of 0.1 dex. [N/Fe] varies from 0.30 to 2.00 in steps of 0.05 dex. The helium content of the comparison spectra ranges from Y = 0.246 to 0.470 in steps of 0.001 and the values of effective temperature and gravity are derived from the corresponding isochrone from Dotter et al. (2008). The magnesium content is fixed and corresponds to the average [Mg/Fe] abundances of 1G and 2G stars inferred from the data by Mucciarelli et al. (2012) and listed in Table 2.

The corresponding colour differences have been derived from the convolution of each spectrum with the transmission curves of the WFC3/UVIS filters used in this paper. The best determinations of the relative helium content between 2G and 1G star are given by the chemical composition of the comparison spectrum that provides the best match with the observed colour differences and correspond to an helium difference δY_2G-1G = 0.07 ± 0.01, where the uncertainty is estimated as the rms of the four helium determinations divided by the square root of three. As an example, the black crosses plotted in panel (d) of Fig. 7 represent the colour differences corresponding to the spectra that provide the best fit with the observed colour difference between 2G and 1G stars for |$m_{F814W}^{\rm ref} = 19.8$|⁠.

The procedure described above has been also used to infer the relative abundances of He between 2G_A, 2G_B, 2G_C, and 1G stars. Results are listed in Table 3 for each value of |$m_{F814W}^{\rm ref}$|⁠, while in panels (f), (g), and (e) of Fig. 7 we show the observed difference between the colour of each population and the colour of 1G stars for |$m_{F814W}^{\rm ref} = 19.8$| and the corresponding colour differences inferred from the best-fitting spectra.

We conclude that 2G_A, 2G_B, 2G_C are enhanced in helium mass fraction by 0.01 ± 0.01, 0.06 ± 0.01, and 0.19 ± 0.02 dex, respectively, with respect to 1G stars. Fig. 8 compares the maximum helium variation that we derived for NGC 2419 with results for 58 GCs by Milone et al. (2018).

The procedure that we adopted to infer the helium content of the stellar populations also allows to constrain the relative abundances of C, N, and O (see Milone et al. 2015, 2017a for details). From the best-fitting spectra, we find that 2G_A are enhanced in nitrogen by 0.3 ± 0.1 dex and depleted in C and O by 0.3 ± 0.3 and 0.2 ± 0.2 dex, respectively, with respect to 1G stars. 2G_B stars exhibit higher [N/Fe] than the 1G (by 0.7 ± 0.1 dex), and lower [C/Fe] and [O/Fe] (by 0.6 ± 0.2 and 0.5 ± 0.1 dex, respectively). The 2G_C is enhanced in nitrogen by 0.7 ± 0.1 dex and depleted in carbon and oxygen by 0.7 ± 0.3 and 0.6 ± 0.2 dex, respectively, with respect to 1G stars.

5 SUMMARY AND DISCUSSION

We exploited HST images of the massive outer-halo GC NGC 2419 to investigate its multiple stellar populations by using photometry in 14 bands of UVIS/WFC3. The |$\Delta _{ C F336W,F343N,F438W}$| versus Δ_{F438W, F814W} ChM of RGB stars reveals that NGC 2419 hosts four main stellar populations of 1G, 2G_A, 2G_B, and 2G_C stars that comprise the 37 ± 1 per cent, 20 ± 1 per cent, 31 ± 1 per cent, and 12 ± 1 per cent of stars, respectively, of the total number of analysed stars.

Milone et al. (2017a, 2018) estimated the relative numbers of 1G and 2G stars in 58 Galactic GCs and find a significant anticorrelation between the fraction 1G stars and the mass of the host GC. The fraction of 1G stars in NGC 2419 (M_V = −9.42, Harris 1996 updated as in 2010) is larger than that of all the massive GCs with M_V < −9.0, the only exception is NGC 7078 (M_V = −9.19; Harris 1996 updated as in 2010), where 1G stars comprise 0.40 ± 0.02 per cent of the total number of stars.

Some scenarios on the formation and evolution of MPs predict that GCs were dominated by 1G stars at the formation and have lost a large number stars into the Galactic halo corresponding to ∼90 per cent of the total cluster mass. In particular, since 2G stars formed in the innermost cluster regions, the primordial GCs preferentially lost 1G stars (e.g. D’Ercole et al. 2008, 2010; D’Antona et al. 2016). The possibility that NGC 2419 evolved in isolation and is almost not affected by the tidal influence of the Galaxy suggests that it was not significantly affected by mass-loss due to tidal stripping.

The presence of a fraction of 1G stars that is larger than that of most GCs with similar masses makes it tempting to speculate that the interaction between the cluster and the Galaxy can affect its present-day ratio between 2G and 1G stars. Nevertheless, the evidence that the 2G includes more than 60 per cent of the total number of cluster stars of NGC 2419 is a challenge for the scenarios mentioned above that predict for this isolated cluster a fraction of 1G of ∼0.9 (e.g. Di Criscienzo et al. 2011b).

By comparing the results for NGC 2419 and for the 58 GCs homogeneously analysed by Milone et al. (2017a, 2018) we find no evidence for a strong correlation between the fraction of 1G stars and neither the distance from the Galactic centre nor with the perigalactic and the apogalactic distance. Nevertheless, we notice that clusters with large perigalactic distances host, on average, larger fractions of 1G stars than the remaining GCs. This fact suggests that the tidal interactions between the clusters and the Milky Way affects the present-day fraction of 1G stars.

Spectroscopic investigation has revealed that NGC 2419 exhibits extreme star-star-abundance variation in Mg and K (Cohen et al. 2011, 2012) with an extended Mg–K anticorrelation (Mucciarelli et al. 2012). Such chemical composition is different from that of the majority of GCs that have homogeneous content of potassium (e.g. Carretta et al. 2013). From the analysis of eleven stars in the ChM that have been studied by Mucciarelli and collaborators by using medium-resolution HIRES@Keck spectra, we find that the abundance of potassium increases from [K/Fe] ∼ 0.1 to [K/Fe] ∼ 1.9 when moving from 1G to 2G_C stars. Moreover, 2G_B and 2G_C stars are significantly depleted in Mg, by ∼0.8 and 0.9 dex, respectively, with respect to 1G and 2G_A stars that have both [Mg/Fe] ∼ 0.5.

Previous evidence of a broad RGB is provided by Di Criscienzo et al. (2011a, see their fig. 9) and Lee et al. (2013) and is based on photometry in the F475W and F814W bands collected with WFC/ACS. From the comparison of the observed CMD and isochrones, these authors concluded that NGC 2419 hosts stars that are heavily enhanced in helium by ΔY ∼ 0.17–0.19. Di Criscienzo et al. (2015), based on the HB of NGC 2419 suggested a smaller helium enhancement of ΔY ∼ 0.11. The presence of stellar populations with large helium variations is qualitatively confirmed by Beccari et al. (2013) on the basis of the colour broadening in the V versus V − I CMD derived from data collected with the Large Binocular Telescope.

To further investigate the chemical composition of the four stellar populations of NGC 2419 and infer their relative helium abundances, we compared the observed colours of RGB stars with the colours derived from synthetic spectra with appropriate chemical composition. We find that 2G_A, 2G_B, and 2G_C stars are, respectively, enhanced in helium mass fraction by δY = 0.01 ± 0.01, 0.06 ± 0.01, and 0.19 ± 0.02, with respect to 1G stars that are assumed at primordial helium content (Y ∼ 0.246). The extreme helium abundance of 2G_C stars that we inferred from multiband photometry is consistent with the findings by Di Criscienzo et al. (2011b) and Lee et al. (2013).

Although helium is the second most-abundant element in stars, the relative helium content of stellar populations in GCs can be hardly derived from spectroscopy. To date, spectroscopic determination of helium in the MPs of GCs are limited to few stars in few GCs only and are based either on chromosphere lines of RGB stars (e.g. Dupree, Strader & Smith 2011; Dupree & Avrett 2013; Strader, Dupree & Smith 2015) or photospheric lines of horizontal branch stars with effective temperatures between ∼8500 and ∼11 500 K (e.g. Villanova, Piotto & Gratton 2009; Marino et al. 2014). Recent work has inferred the helium abundance of large sample of Galactic and extragalactic GCs (Milone et al. 2018; Lagioia et al. 2018, 2019) and concluded that the internal helium variations is typically smaller than ∼0.12 in helium mass fraction. Moreover, the maximum internal helium variation correlates with the mass of the host GC (e.g. Milone 2015; Milone et al. 2018). The fact that NGC 2419, which is one of the most-massive GCs of the Milky Way, is the cluster with the largest observed helium variation corroborates the conclusion that the complexity of MPs increases with cluster mass.

Several scenarios for the formation of MPs in GCs proposed that 2G stars formed by the ejecta of more-massive 1G stars. The nature of the polluters is still widely debated. AGB stars with masses of |${\sim } 3{\!-\!}8\, {\mathcal{ M}}_{\odot }$| (e.g. Ventura et al. 2001; D’Antona et al. 2002, 2016; Tailo et al. 2015), fast-rotating massive stars (FRMSs; Decressin et al. 2007; Krause et al. 2013), and supermassive stars (Denissenkov & Hartwick 2014) are considered as possible candidates (see Renzini et al. 2015 for a critical review).

Stars with extreme helium abundance are a challenge for the AGB scenarios because they predict that the maximum helium content of 2G stars is smaller than Y ∼ 0.38, although Karakas, Marino & Nataf (2014) suggested that such stars with extreme helium content can form from the ejecta of a previous generation of helium-rich AGB stars. On the contrary, the presence of stars with extreme helium abundance is consistent with the FRMS and supermassive stars scenarios (e.g. Prantzos, Charbonnel & Iliadis 2017). As an example, Chantereau, Charbonnel & Meynet (2016), based on the FRMS scenario, predict that about 10 per cent of present-day GC stars have Y > 0.40, which is qualitatively consistent with what we observe in NGC 2419. Nevertheless, the lack of stars with very high helium content (Y > 0.50) is in contrast with the predictions by Chantereau and collaborators.

ACKNOWLEDGEMENTS

We thank the anonymous referee for suggestions that significantly improved the manuscript. 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), and the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie (Grant Agreement No. 797100, beneficiary: Marino). APM and MT acknowledge support from MIUR through the FARE project R164RM93XW ‘SEMPLICE’ (PI: Milone).

Footnotes

REFERENCES

APPENDIX A: THE |$\Delta _{C F336W,F343N,F438W}$| VERSUS Δ_{F438W, F814W} CHROMOSOME MAP

We introduced in this paper the |$\Delta _{C F336W,F343N,F438W}$| versus Δ_{F438W, F814W} ChM map that is similar to the classical |$\Delta _{C F275W,F336W,F438W}$| versus Δ_{F275W, F814W} map but is based on the F336W, F343N, F438W, and F814W stellar magnitudes. To derive this ChM, we used the method illustrated in Fig. A1 that is similar to the procedure by Milone et al. (2015, 2017a) but combines the information from the m_F438W versus m_F438W − m_F814W and the m_F814W versus C_{F336W, F343N, F438W} diagrams plotted in panels (a1) and (b1) of Fig. A1.

The red and blue lines superimposed on each diagram are the envelopes of the RGB and are derived by using a procedure is based in part on the naive estimator (Silverman 1986). We divided the RGB into F814W magnitude intervals of size δm that are defined over a grid of points separated by bins of fixed magnitude (s = δm/3). For each F814W interval, we computed the value of the 4th and the 96th percentile of the m_F438W − m_F814W and C_{F336W, F343N, F438W} distributions. The resulting red and blue RGB envelopes are derived by associating to these values the mean F814W magnitudes of RGB stars in each interval. Due to the small number of upper RGB stars, with m_F814W < 17.5, the envelopes in the region have been derived by hand.

To compare the ChMs of different clusters, we calculated the m_F438W − m_F814W and C_{F336W, F343N, F438W} difference between the red and blue fiducials shown in panels (a1) and (b1) of Fig. A1 at the magnitude level of two F814W magnitudes above the MS turn-off (m_F814W = 21.2). These quantities, which are indicative of the RGB width, are called as W_{F438W, F814W} and |$W_{C F336W,F343N,F438W}$|⁠, in close analogy with what done by Milone et al. (2017a). We plot the |$\Delta ^{\prime }_{C F336W,F343N,F438W}$| versus |$\Delta ^{\prime }_{F438W,F814W}$| ChM in panel (d) of Fig. A1, where |$\Delta ^{\prime }_{C F336W,F343N,F438W}$| = |$W_{C F336W,F343N,F438W} \Delta _{C F336W,F343N,F438W}$| and |$\Delta ^{\prime }_{F438W,F814W} = W_{F438W,F814W} \Delta _{F438W,F814W}$|⁠.

To compare the |$\Delta _{C F336W,F343N,F438W}$| versus Δ_{F438W, F814W} ChM used in this paper with the classical |$\Delta _{C F275W,F336W,F438W}$| versus Δ_{F275W, F814W} ChM, we exploit the photometry in the appropriate bands of NGC 7078 (M 15) and NGC 104 (47 Tucanae) from Milone et al. (2017a, 2018).¹

Left-hand panels of Fig. A2 show the classical ChM from Milone and collaborators, while the |$\Delta ^{\prime }_{C F336W,F343N,F438W}$|versus |$\Delta ^{\prime }_{F438W,F814W}$| that we derived with the procedure described above are plotted in the right-hand panels. We show only those stars for which photometry in all filters is available. In the upper panels, we used orange colour to represent 1G stars and yellow, blue, and red colours to represent the other three populations of M 15 identified by Nardiello et al. (2018) from the classical ChM. Similarly, in the lower panels we represent 1G and 2G stars of 47 Tucanae identified by Milone et al. (2017a) with orange and yellow colours, respectively. The group of 2G stars with extreme chemical composition (Milone et al. 2018) are coloured blue.

In both ChMs 1G stars (orange points in Fig. A2) are clustered around the origin of the reference frames, whereas 2G stars are those in the steep branches reaching high values of both |$\Delta _{C F275W,F336W,F438W}$| and |$\Delta ^{\prime }_{C F336W,F343N,F438W}$|⁠. In particular, 2G stars with extreme chemical compositions also exhibit the largest values of |$\Delta _{C F275W,F336W,F438W}$| and |$\Delta ^{\prime }_{C F336W,F343N,F438W}$|⁠.

Milone et al. (2017a, 2018) show that for a fixed variation of helium, C, N, and O the m_F275W − m_F814W RGB colour width depends on cluster metallicity, with metal-rich GCs having wider RGBs than cluster with low metallicities. We exploited the isochrones from Dotter et al. (2008) used by Milone and collaborators to verify that the same conclusion can be extended to the m_F438W − m_F814W RGB colour width. The comparison of the |$\Delta ^{\prime }_{C F336W,F343N,F438W}$| versus |$\Delta ^{\prime }_{F438W,F814W}$| ChMs of 47 Tucanae ([Fe/H] ∼ −0.79; Cordero et al. 2014) and M 15 ([Fe/H] ∼ − 2.37; Sneden, Pilachowski & Kraft 2000) of Fig. A2 with the ChM of NGC 2419 ([Fe/H] ∼ −2.09; Mucciarelli et al. 2012) reveals that the latter spans the widest range of |$\Delta ^{\prime }_{F438W,F814W}$| thus supporting the conclusion the NGC 2419 host stellar populations with extreme helium content.