Multiple stellar populations in Asymptotic Giant Branch stars of Galactic Globular Clusters

A peculiar feature of the chemical composition of stars belonging to Milky Way Globular Clusters (GCs) is the significant variation of light-elements such as helium, carbon (C), nitrogen (N), oxygen (O) and sodium (Na), observed only in a tiny fraction of the Galactic bulge ($\sim 1$%, Schiavon et al., 2017) and halo field stars ($\sim 3$%, Martell et al., 2011).

In few GCs, stars also show difference in magnesium (Mg) and aluminum (Al) content. The observed chemical variations are not random but follow trends defined by the anti-correlation C-N, O-Na, and Mg-Al. In particular, every GC includes two main stellar groups: 1G, composed of stars with halo-like chemical composition; 2G composed of stars depleted in C and O, and enhanced in N, Na and helium with respect to 1G. When observed in color-magnitude diagrams (CMDs) obtained by combining ultraviolet (UV) and optical observations, 1G and 2G stars lie on distinct sequences, called multiple stellar populations (MPs). The current framework of MPs in Galactic GCs largely derives from the study of the spectroscopic and photometric properties of red giant branch (RGB) stars (e.g. Milone et al., 2017; Lagioia et al., 2018; Marino et al., 2019). In a limited number of GCs it has also been possible to clearly identify MPs in fainter stars, thanks to the detection of split main sequences in CMDs (Anderson, 1997; D’Antona et al., 2005; Piotto et al., 2007; Milone et al., 2013, 2015a; Bellini et al., 2017b, e.g.).

The study of MPs at later evolutionary stages, is more problematic. In the case of horizontal branch (HB) stars, both age-metallicity and helium-mass loss degeneracy hamper a proper understanding of the impact that chemical variations have on the color distribution of core helium-burning stars in CMDs (see e.g. Sandage & Wildey, 1967; Fusi Pecci et al., 1993; Catelan et al., 2001; Tailo et al., 2020). This indetermination propagates to the subsequent evolutionary phase, the asymptotic giant branch (AGB), where the uncertain definition of the sub-populations distribution is further amplified by statistical fluctuations due to the fast evolutionary timescale of AGB stars (Greggio & Renzini, 1990).

A viable solution to this issue is provided by the direct spectroscopic determination of the atmospheric abundance of the light proton-capture tracing MPs (Sneden et al., 2000). In this context, early studies found evidence of significant difference in CN band strength between RGB and AGB stars in NGC 5904 (M 5) and NGC 6752, with the latter being biased toward the CN-weak populations Norris et al. (see 1981); Smith & Norris (see 1993). The same disproportion in CN-band distribution was also detected later in NGC 1851 AGB stars (Campbell et al., 2012). More recently, works based on high-resolution determination of abundance of Na, a light element not involved in internal mixing processes during the RGB evolution (Kraft, 1994; Carretta et al., 2009), confirmed the lack of Na-rich stars in the AGB of some GCs.

For instance, the Na content of 20 AGB stars of NGC 6752 analyzed by Campbell et al. (2013), was found to be lower than $\sim 0.2$ dex, corresponding to the abundance threshold separating 1G and 2G RGB stars (Carretta et al., 2012; Milone et al., 2013). Later on, through the analysis of new spectroscopic data of the same sample of stars, Lapenna et al. (2016) confirmed a relative lack of 2G members among NGC 6752 AGB stars, with none of them associated to the most Na- and helium-rich cluster population (Carretta et al., 2012; Milone et al., 2013). Interestingly, this finding seems to confirm the theoretical scenario predicted for the evolution of the hot HB stars of NGC 6752 (Villanova et al., 2009; Cassisi et al., 2014; Tailo et al., 2019b). Indeed, hot HB stars with tiny hydrogen-rich atmospheres, usually associated to the most helium-rich GC population(s) (e.g. D’Antona et al., 2002; Milone et al., 2018), would skip the early-AGB phase, characterized by a progressive expansion and cooling of the HB star envelope, and instead evolve to higher temperatures and luminosities until they reach the white-dwarf cooling sequence. The shell helium-burning phase of these stars is therefore called AGB-manqué (Greggio & Renzini, 1990).

A confirmation of this prediction would come from the recent spectroscopic analysis of the AGB stars of NGC 2808, a GC cluster known for its extended (and complex) HB morphology, linked to one of the largest internal helium variations observed among Galactic GCs ($\Delta$Y$\sim 0.124$, with Y = helium mass fraction, Milone et al., 2015a). Indeed, Marino et al. (2017) identified three groups of AGB stars with distinct Na abundance, following the typical Na-O anti-correlation trend observed for the cluster RGB stars, with the distribution skewed towards lower Na RGB values (see also Wang et al., 2016), thus implying that the extremely helium-enhanced cluster stars evolved as AGB manqué.

However, a similar outcome has been found in NGC 6121 (M 4) which, at the contrary of NGC 2808, is not populated by extremely hot HB stars (Marino et al., 2008; Villanova et al., 2012) and shows a rather small internal helium enrichment ($\Delta$Y$\sim 0.01$ Milone et al., 2018). As in the previous case, Marino et al. (2017) and Wang et al. (2017) found that the Na-poor and Na-rich cluster AGB star roughly cover the lowest two thirds of the [Na/Fe] abundance range occupied by the cluster RGB stars, thus suggesting that part of the 2G cluster stars could not reach the AGB phase (MacLean et al., 2016).

Dispersion in Mg-Al abundance has also been employed to explore MPs in the AGB stars of GCs with different HB morphology. For instance, Lapenna et al. (2015) found no Al-rich stars among the AGB stars of NGC 6266 (M 62), a result indicating the total lack of of 2G AGB stars and compatible with the large helium variation detected from main sequence stars color difference by Milone (2015). Conversely, in their spectroscopic analyses, García-Hernández et al. (2015) and Masseron et al. (2019) found a similar spread in the AGB and RGB stars of NGC 5024 (M 53), NGC 5272 (M 3), NGC 6205 (M 13), NGC 6341 (M 92), NGC 7078 (M 15), and NGC 7089 (M 2).

In principle, spectroscopic discrepancies might be reduced by claiming either zero-point offsets in the abundances obtained from different datasets or with different reduction techniques (see e.g. Campbell et al., 2017), or the adoption of arbitrary thresholds for the selection of typical abundances in 1G and 2G AGB stars (Marino et al., 2017). However, an effective solution to the “AGB problem”, namely the unexpected high fraction of 2G stars avoiding the AGB phase (Campbell et al., 2013), requires an homogeneous definition of the observational properties of these stars in large samples of GCs. In this regard, photometry represents an ideal tool because it provides the necessary multiplexing capability. For instance, Gratton et al. (2010) adopted a statistical approach to analyze the relation between the parameter $R_{2}=\mathrm{N_{AGB}/N_{HB}}$, namely the numerical fraction of AGB-to-HB stars in a GC (Caputo et al., 1989), and the minimum mass along the HB, for a sample of 21 clusters. They found that blue-extended HB-morphology clusters attain $R_{2}$ values smaller than the rest of GCs. This result would be consistent with the AGB-manqué prediction.

Another approach is represented by the study of MPs through the use of filter combinations that trace the different chemical content of stars through the variation of their flux at different wavelengths. The two main solutions adopted so far are the index or pseudo-color $C_{\rm F275W,F336W,F438W}$ = $(m_{\rm F275W}-m_{\rm F336W})-(m_{\rm F336W}-m_{\rm F438W})$, sensitive to C, N, O stellar content thanks to the specific pass-band of the F275W, F336W, and F438W filters, available at the UV and Visual (UVIS) channel of the Wide Field Planetary Camera 3 (WFC3) on board Hubble Space Telescope (HST Milone et al., 2015b), and $C_{\rm F336W,F438W,F814W}$ = $(m_{\rm F336W}-m_{\rm F438W})-(m_{\rm F438W}-m_{\rm F814W})$, sensitive to the content of N, O, and helium through the F814W filter. From the previous definitions it follows that the latter index is not as sensitive as the former to the presence of MPs. Its lower accuracy is, however, counterbalanced by two clear upsides: the existence of a corresponding ground-based version $C_{UBI}$ = $(U-B)-(B-I)$ (Marino et al., 2008; Monelli et al., 2013) and, as a consequence, the possibility of being used in the post-HST era (Lagioia et al., 2019a).

The measurement of the color spread of stars in both previous combinations, usually referred to as width, $W$, provides a general view of the total chemical variations in the host GCs, and can be employed for a direct comparison of the MP properties in GCs with different age, mass, and metallicity, as already done in extensive studies of MPs in Galactic and extra-galactic GCs, by using the width of RGB stars (Milone et al., 2017; Lagioia et al., 2019b). In principle, therefore, the same approach can also be adopted with AGB stars. Indeed, few recent works have clearly shown that AGB stars are spread over color intervals comparable to those observed for RGB stars, like in the case of NGC 7089 (Milone et al., 2015b), NGC 2808 (Milone et al., 2015a), and NGC 6121 (Lardo et al., 2017; Marino et al., 2019). Moreover, the direct comparison between AGB and RGB star width in any given cluster could provide a solid evidence of missing MPs in AGB phase (Marino et al., 2017).

The quantity $W$, although representing a direct evidence of GC internal chemical variations, cannot provide the necessary resolution for the study of the detailed chemical composition of a cluster. A powerful tool has been recently introduced to overcome this problem: the so-called chromosome map (ChM, Milone et al., 2015b, a, 2017). This photometric diagram correlates the spread of stars in two different color combinations, each one sensitive to different features of the spectrum of a star. The most comprehensive ChM compilation published so far (Milone et al., 2017) includes all the 57 GCs observed in the HST UV Legacy Survey (Piotto et al., 2015) and has provided the most detailed glimpse into the complex composition of Galactic GCs. In particular, the ChM combines the information of the $C_{\rm F275W,F336W,F438W}$ with the large-baseline color $m_{\rm F275W}-m_{\rm F814W}$, that is sensitive to metallicity and helium variations. In this context, the recent analysis by Marino et al. (2017) has shown that the ChM of the AGB stars of NGC 2808 present a degree of complexity comparable with that visible in the ChM of RGB stars (Milone et al., 2015b), with three distinct groups corresponding to as many different spectroscopic abundances. It is unfortunately not as easy to obtain the ChM of AGB stars as for the RGB for plain evolutionary reasons. Indeed, the AGB evolutionary timescale is about ten times faster than that of RGB stars brighter than HB stars (Greggio & Renzini, 1990). It follows that only a limited number of GCs can provide the necessary statistical significance for a detailed MP study.

All the aforementioned findings represent a clear signature that chemical variations are also a common property of AGB stars, and offer a compelling motivation for the extension of the MP analysis to a larger sample of clusters, which is the purpose of the present work. For this reason, we decided to analyze the observational properties of the AGB stars of all the clusters observed in the HST UV Legacy Survey (Piotto et al., 2015), in the same photometric bands adopted for the study of MPs along the RGB (Milone et al., 2017).

Section 2 of the present paper describes the methodology for the selection of the AGB and RGB samples in each analyzed cluster, the identification of AGB stars belonging to the metal-rich population (hereafter called anomalous) in type II GCs, and the measurement of the color spread, or width, of the selected sample in specific photometric indices. Section 3 reports the computation of appropriate evolutionary models for the comparison between observed width and theoretical predictions. Section 4 illustrates the relation existing between the AGB and RGB width. Section 5 show the procedure for the construction of the ChM of clusters with well populated AGB samples, and the analysis of population ratios. Section 6 describes the relation between the frequency of AGB stars and chemical enrichment in GCs. Finally, Section 7 provides a summary of the analysis and a description of the contribution of this work to the MP phenomenology in GCs.

The dataset analyzed in this work comprises a total of 58 clusters, including the 57 GCs observed in the UV Legacy Survey of Galactic GCs (Piotto et al., 2015), and the distant Galactic cluster NGC 2419 (Zennaro et al., 2019). All the 57 UV Legacy Survey GCs have been observed in the WFC3/UVIS broad-bands F275W, F336W, and F438W, and complemented with the F606W and F814W observations collected for the ACS Survey of Galactic GCs (Sarajedini et al., 2007). A complete description of the image database, exposure times, and reduction techniques is reported in Piotto et al. (2015); Milone et al. (2018) and Nardiello et al. (2018). Details about database and reduction procedure of NGC 2419 data are provided in the recent paper by Zennaro et al. (2019), to which we refer the interested reader.

In a nutshell, the photometry of every cluster has been derived by analyzing the images with the suite Kitchen Sync 2 (see Sabbi et al., 2016; Bellini et al., 2017a), originally developed by J. Anderson for the analysis of ACS images (Anderson et al., 2008). The suite is comprised of FORTRAN routines which recursively analyze the pixel values on the images and apply a local-peak finding algorithm. In each analyzed image, a selection of relatively bright stars is used to model a grid of spatially-variable point spread functions (PSF), which represent the best-fit model for stars detected at different locations on the chip.

The position and flux of stars with different luminosity are determined with two different approaches. For bright stars, position and flux are independently determined in each single exposure and then averaged, while for faint stars an average position is computed from all the images where a star is detected, and then the flux is determined at that position by using the best-fit PSF.

Finally, stellar positions are corrected for geometrical distortion by using the solution of Bellini & Bedin (2009) and Bellini et al. (2011). Instrumental magnitudes are calibrated to the VEGAMAG system as in Bedin et al. (2005).

A selection of well-measured stars has been performed by using the parameters of photometric quality produced by the reduction software as in Milone et al. (2009). The photometry of clusters affected by significant differential reddening has been also corrected as in Milone et al. (2012a). Finally, the cluster membership has been established on the basis of relative proper motions as done in Milone et al. (2018).

To qualitatively investigate the typical effects of changing the abundances of He, C, N, and O on the colors and magnitudes of AGB stars, we combined isochrones and synthetic spectra of AGB stars with appropriate chemical compositions. We used the evolutionary code ATON 2.0 (Ventura et al., 1998; Mazzitelli et al., 1999; Ventura et al., 2009) to calculate 12 Gyr-old isochrones with [Fe/H]$=-1.5$, [$\alpha$/Fe]$=0.4$ but different RGB mass loss, helium content and C, N, and O abundance (see D’Antona et al., 2002; Tailo et al., 2019b, 2020, for details).

We first investigated the effect of helium and mass-loss variations on the AGBs. We calculated an isochrone with pristine helium content (Y$=0.25$), [C/Fe]=0.0, [N/Fe]=0.0 and [O/Fe]=0.4 and RGB mass loss $\mu=0.30M_{\odot}$. Moreover, we derived two helium-enhanced isochrones with Y$=0.28$ with the same C, N and O content as above and different mass losses of $\mu=0.30M_{\odot}$ and $\mu=0.45M_{\odot}$. Finally, we computed three isochrones with Y$=0.28$, [C/Fe]=$-$0.5, [N/Fe]=1.21 and [O/Fe]=$-$0.1 and $\mu=0.30,0.45,0.60M_{\odot}$.

To account for the effect of C, N and O variations on the studied isochrones, we extended the procedure by Milone et al. (2012b, 2018) to the AGB. We identified five points along each isochrone with [C/Fe]=0, [N/Fe]=0 and [O/Fe]=0.4 and extracted their $T_{\rm eff}$ and gravity ($g$). We used ATLAS12 and SYNTHE computer programs (e.g. Castelli, 2005; Kurucz, 2005; Sbordone et al., 2007, 2011) to calculate a spectrum with [C/Fe]=0.0, [N/Fe]=0.0, and [O/Fe]=0.4 (reference spectrum) and a spectrum with enhanced nitrogen [N/Fe]=1.21 and depleted carbon and oxygen ([C/Fe]$=-0.5$ and [O/Fe]$=-0.1$). All spectra are computed over the wavelength interval between 2000 Å and 10,000 Å and are convoluted with the throughput of the F275W, F336W, F438W WFC3/UVIS filters and the F606W and F814W ACS/WFC filters used in this paper.

As an example, the uppermost panel of Figure 13 compares the spectra of two AGB stars with Y=0.25, $\mu=0.30M_{\odot}$, $T_{\rm eff}=4875$K and $\log{g}=1.76$. The red spectrum is representative of 1G star and has [C/Fe]=0.0, [N/Fe]=0.0 and [O/Fe]=0.4, whereas the C, N, O content of the blue spectrum resembles 2G stars ([C/Fe]=$-$0.5, [N/Fe]=1.21 and [O/Fe]=$-$0.1). We calculate the magnitude difference between each point of the two spectra as -2.5 times the logarithm of their flux ratio and plot this quantity as a function of the wavelength. For comparison, we over-plotted the transmission curves of the five filters used in this paper. Clearly, the 2G spectrum provides F336W magnitude fainter than the 1G ones, mostly due to the NH band around 3,600 Å. 2G stars also exhibit brighter F275W and F438W magnitudes, as a consequence of the strength of the OH and CH molecular bands, respectively. Hence, C, N, and O variations in the spectra of AGB stars show a qualitative behavior similar to that observed in RGB stars (e.g. Milone et al., 2012b).

Synthetic spectra are convoluted with the throughput of the five filters used in this paper to derive the corresponding magnitudes. The magnitude differences between the comparison and the reference spectrum are added to the corresponding magnitudes of the isochrones with 1G-like chemical composition to derive the corresponding isochrones enhanced in N and depleted in C and O.

The photometric width as standard measurement of the amount of internal chemical variations gives us the ability to compare the properties of MPs across the entire parameter-space spanned by GCs. In this regard, recent works have demonstrated that a significant correlation exists between the spread of RGB in the indices $C_{\rm F275W,F336W,F438W}$ and $C_{\rm F336W,F438W,F814W}$, and cluster’s metallicity and mass (Milone et al., 2017; Lagioia et al., 2019a). For this reason we decided to study the relation between the AGB and RGB width.

In the top panel of Figure 14, we plot $W^{\rm AGB}_{C\,{\rm F275W,F336W,F438W}}$ vs. $W^{\rm RGB}_{C\,{\rm F275W,F336W,F438W}}$ of the 35 clusters, listed in Table 1, for which the measurement of the relative quantities is available. In the diagram, each point has been color-coded according to the corresponding cluster’s metallicity [Fe/H] (Harris, 1996, 2010 update), mapped to the color scale reported in the legend. We see that the two represented quantities follow, on average, a positive correlation. In order to provide a reference for the comparison, we overplotted three lines representing the identity relation $W^{\rm AGB}=W^{\rm RGB}$ (dashed line), and the relations $W^{\rm AGB}=1.5\,W^{\rm RGB}$ and $W^{\rm AGB}=0.5\,W^{\rm RGB}$ (top and bottom dotted lines). We observe that the majority of GCs (27 out of 35 GCs) have AGB width smaller than the RGB width, and that among them, 7 GCs have $W^{\rm AGB}<0.5W^{\rm RGB}$, with the remarkable cases of NGC 2419, NGC 5139 ($\rm\omega\,Cen$), and NGC 6752, the three GCs with the smallest AGB/RGB width ratio. On the other hand, NGC 6341 and NGC 5927 are the only two clusters lying above the $W^{\rm AGB}=0.5\,W^{\rm RGB}$ line. Their relatively large error bars, however, do not allow to draw strong conclusions. The color distribution seems to suggest the presence of a mild monotonic trend between the AGB intrinsic width and metallicity, with the most metal-rich clusters having on average larger width values.

The bottom panel displays the scatter plot of $W^{\rm AGB}_{C\,{\rm F336W,F438W,F814W}}$ vs. $W^{\rm RGB}_{C\,{\rm F336W,F438W,F814W}}$. As before, we also overplotted the same three reference lines. We observe that all the clusters lie within the region defined by the $W^{\rm AGB}=1.5\,W^{\rm RGB}$ and $W^{\rm AGB}=0.5\,W^{\rm RGB}$ lines, with the clusters quite uniformly distributed above and below the identity relation line. Only two clusters, namely NGC 6341 and NGC 6752, have AGB/RGB width ratios larger than 1.5. While the first cluster shows a behavior similar to that observed in the previous case, that of NGC 6752 is reversed. However, we highlight the fact that the AGB width estimate of this cluster has been derived from a relatively low number of stars (11) and, as a consequence, it is poorly constrained, as also indicated by its large error bars. Therefore, again, no firm conclusion can be achieved about these two GCs. We finally notice the absence of any trend with metallicity in this color combination.

The relation between AGB and RGB width visible in both the diagrams clearly indicates that none of the observed clusters have a mono-populated AGB sequence. The trend visible in the top panel shows that, on average, the AGB width is smaller than the RGB width. In the hypothesis that in each cluster all the stellar populations in the RGB evolve to the AGB, we would expect to observe AGB widths comparable with or larger than those of the corresponding RGB stars. The displayed trend instead, indicates that the AGB width is on average smaller than the RGB width. This finding clearly suggests that in the majority of clusters a significant fraction of 2G stars does not evolve to the AGB, as predicted by the AGB-manqué scenario. Our finding, based on a large sample of GCs, provides a robust evidence of the existence of this phenomenon.

We emphasize that the displayed trend may include some spurious scatter due to the specific evolutionary conditions of each different cluster: mass loss has, indeed, an important effect on the color spread of AGB stars, as seen in the previous section. This implies that a precise evaluation of the chemical variations corresponding to every AGB width measurement can be obtained through the comparison between observations and theoretical models, suitably tailored to the specific properties of each analyzed cluster. However, a one-to-one comparison between the AGB and RGB width of each cluster is beyond the purpose of the present analysis.

The analysis of the AGB width presented in the previous section provides a strong indication about the presence of MPs along the AGB of the analyzed GCs, as well as of the partial depletion of MPs due to the evolution of the most chemically-enriched stars as AGB-manqué. To further investigate this phenomenon, we exploited the ChM of AGB stars. The construction of the ChM of the GCs analyzed in the present work, shown in Figure 15 for the template cluster NGC 2808, is based on the method introduced by Milone et al. (2015a) and extended to the AGB by Marino et al. (2017). In the figure, panel (a) displays the portion of the $m_{\rm F814W}$ vs. $C_{\rm F275W,F336W,F438W}$ pseudo-CMD of the cluster, zoomed on the AGB stars. AGB stars are represented as red points, while all the other visible stars, mainly composed by bright RGBs, as light-gray points. As described in Section 2.4, we excluded the brightest AGB cluster stars, which are shown as light-red points. Long-dashed horizontal lines delimit the selected luminosity interval. The left and right dashed black curves represent, respectively, the 4th and 96th percentile of the pseudo color-distribution of the AGB stars. They have been obtained by dividing the entire luminosity interval in 4 bins and then computing, for each bin, the color corresponding to the 4th and 96th percentile of the color distribution. We then applied a boxcar-average smoothing to the observed distribution points and finally fit the resulting pseudo-colors by a cubic spline along the central magnitude of the bins. We then performed a double-normalization by subtracting to the pseudo-color of each star, the corresponding value along the 96th percentile fit curve, and dividing the result by the distance between the point of the 4th and 96th fit curve at the same magnitude (see equation 1 and 2 in Milone et al., 2017). The ratio has been finally multiplied by the factor $W^{\mathrm{96th-4th,AGB}}_{C{\rm F275W,F336W,F814W}}$, corresponding to the intrinsic width of the AGB stars. This quantity is defined as the observed distance between the fit curves at a reference luminosity equal to 5 mag brighter than the main-sequence turn-off in F814W band, minus the contribution due to the photometric error, as described in the previous section.

The luminosity of the main sequence turn-off has been determined by applying the naive estimator method (Silverman, 1986). This procedure consists in subdividing a pre-selected F814W magnitude range centered on the turn-off region of the CMD, in a number of magnitude bins. For each bin the median color and magnitude of stars is computed. The same algorithm is applied in sequence by shifting the first bin magnitude by an fraction of the bin width. The magnitude and color of all median points are then boxcar-average smoothed. Finally the bluest color of the interpolating function is taken as the $m^{MSTO}_{F814W}$ value. We found $W^{\rm 4th-96th,AGB}_{C\,{\rm F275W,F336W,F438W}}=0.508$ mag. The result of the double normalization is a new quantity called ${\rm\Delta}_{C\,{\rm F275W,F336W,F438W}}$. The same procedure has been applied to the $m_{\rm F814W}$ vs. $m_{\rm F275W}-m_{\rm F814W}$ CMD displayed in panel (b). We found in this case $W^{\rm 4th-96th,AGB}_{\rm F275W,F814W}=1.487$ mag and obtained the new quantity ${\rm\Delta}_{\rm F275W,F814W}$.

Panel (c) displays the ChM, namely the ${\rm\Delta}_{C\,{\rm F275W,F336W,F438W}}$ vs. ${\rm\Delta}_{\rm F275W,F814W}$ diagram of the AGB stars of NGC 2808. A glance at the distribution of the stars immediately shows that in this cluster, the AGB stars are not evenly distributed but rather clustered in at least four distinct groups (see Marino et al., 2017, for comparison). In order to understand if the observed scatter can be accounted to the photometric error, we derived the ChM expected for a mono-populated cluster. In this case the scatter is mostly due to the observational errors. The center of the resulting distribution has been arbitrarily shifted at coordinates $({\rm\Delta}_{\rm F275W,F814W},{\rm\Delta}_{C\,{\rm F275W,F336W,F438W}})$ = $\sim(-1.65,-0.85)$. It appears as an ellipse flattened along the horizontal direction, with a major semi-axis of $\approx 0.025$ mag. We see that the vertical extension of the AGB ChM is $\sim 0.1$ mag, therefore about four times larger than that of the error distribution.

The density diagram plotted in panel (d) further confirms the presence of discrete stellar populations. It shows indeed two main groups of stars at coordinates $\approx(-0.30,0.15)$ and $\approx(-1.00,0.15)$, and two other less populated groups at $\approx(-0.40,0.25)$ and $\approx(-1.40,0.30)$. With the aim of properly assigning a membership to each star in the various groups, we built the histogram distribution of AGB stars along the y-axis and x-axis. The results are shown in panel (e) and (f), respectively. Each histogram has been obtained by splitting the horizontal and vertical intervals in bins of $0.10$ mag, and computing the number of clusters falling in each bin at steps equal to half bin width. This choice mitigates the arbitrary decision of a given bin width. In the histogram of panel (e), we can recognize three distinct sections, centered at ${\rm\Delta}_{C\,{\rm F275W,F336W,F438W}}$ = $\approx 0.06,0.21,0.40$ mag. The histogram of the last section shows a secondary split at $\approx 0.38$ mag, in agreement with the density map in panel (d). The histogram in panel (f) shows two main peaks at ${\rm\Delta}_{\rm F275W,F814W}$ = $\approx-0.30$ mag and $\approx-0.95$ mag. Therefore, we used the vertical histogram distribution to subdivide the ChM into three groups, that we named 1G (magenta points), ${\rm 2G_{a}}$ (azure points) and ${\rm 2G_{b}}$ (blue points). The nomenclature follows the subdivision adopted by Marino et al. (2017). For the sake of clarity, we used a different color code for the three groups of stars. We finally cross-matched the three AGB spectroscopic targets by Marino et al. (2017), and marked them with a black starred symbol in the ChM of panel (c). We see that these stars, which have different O and Na abundance, belong to the different groups identified in the AGB ChM, thus providing the definitive confirmation that 1G, ${\rm 2G_{a}}$, and ${\rm 2G_{b}}$, correspond to distint stellar populations with different light-element abundance

A detailed interpretation of the MP composition of the cluster AGB star can be obtained by comparing the present ChM with that obtained from the analysis of RGB stars (Milone et al., 2017). Since ChM are built from the measurement of the spread of stars in specific color combinations, such a comparison is ultimately connected to that of the widths. However, as already mentioned before, this implies a precise evaluation of the factors affecting the evolutionary path of post-HB stars, which is not the purpose of the present analysis. Notwithstanding, we decided to perform a crude comparison by assuming that the effect of the presence of 1G and 2G stars in the extension of the ChM of AGB and RGB stars is comparable. Therefore, we decided to scale-up the width of the RGB stars in $m_{\rm F275W}-m_{\rm F814W}$ and $C_{\rm F275W,F336W,F438W}$ (see Milone et al., 2017, Table 2) to that of the AGB stars derived in this work. The scaled RGB ChM is represented by the gray points plotted on background in panel (c).

Interestingly, we observe that the AGB ChM broadly reproduces the overdensities corresponding to the sub-populations observed in the RGB ChM. In particular we observe a similar elongation between the AGB and RGB 1G populations, with three AGB stars (${\rm\Delta}_{\rm F275W,F814W}\lesssim-0.5$ mag) attaining ${\rm\Delta}_{C\,{\rm F275W,F336W,F438W}}$ values bluer than the blue ${\rm\Delta}_{\rm F275W,F814W}$ tail of the RGB stars. On the other side ${\rm 2G_{a}}$ and ${\rm 2G_{b}}$ AGB stars appear to follow the same trend of the sub-groups C and D of the 2G RGB population (see Marino et al., 2017). We also notice the presence of a blue ${\rm\Delta}_{\rm F275W,F814W}$ tail in the ${\rm 2G_{b}}$ group, that overlaps the location of the extreme helium-enhanced cluster (E) population ($\mathrm{\delta\,Y}\geq 0.1$ Milone et al., 2015a). This appears to be in contrast with the predictions of evolutionary models of very helium-rich stars, which must avoid the AGB phase (e.g. Chantereau et al., 2016). Of course, spectroscopic investigation is mandatory to understand whether these AGB stars are the counterparts of RGB and MS stars with extreme helium abundances, or if they have intermediate helium content but have experienced severe RGB mass loss.

For reference we also computed the histogram distribution of the ChM of the photometric errors. The corresponding orange-shaded histograms appears to be spread over an interval visibly narrower than the sub-structures visible in both the ChM histogram distribution in panel (e) and (f).

We used the same procedure to build the ChM of all the other GCs with $\mathrm{N_{AGB}}>25$ in our database (see column 2 of Table 1). The heterogeneous F814W magnitude distribution of the AGB stars of NGC 104 and NGC 6637, in the CMDs used to build their ChM, did not allow to obtain reliable estimate of the AGB widths. For this reason, these two GCs have been excluded from the following analysis.

We ended up with a sample of 14 GCs including NGC 362, NGC 1261, NGC 1851, NGC 2419, NGC 5024, NGC 5139, NGC 5286, NGC 5986, NGC 6093, NGC 6388, NGC 6441, NGC 6715, NGC 7078  and NGC 7089. The ChMs of these GCs, sorted by increasing metallicity, are displayed in Figure 16. In the ChMs of type II GCs we also highlighted the anomalous AGB stars with the usual red starred symbol. As for NGC 2808, in each panel we plotted on background the scaled-up ChM of the corresponding cluster RGB stars. In passing we note that we have also derived the ChM of the RGB stars of NGC 2419 for the first time in this paper. For the sake of comparison, the probable 1G and 2G RGB members of each cluster Milone et al. (2017) have been colored, respectively, in light-green and magenta, except for NGC 2419 and NGC 6441, for which it is not possible to obtain a straightforward population classification of their RGB stars. In all the type II GCs diagrams, the anomalous RGB stars are represented as grey points.

In the majority of GCs, the distribution of the AGB stars does not appear clustered in separate groups, except for NGC 7078, NGC 1261, NGC 362 and perhaps NGC 6388, where we can recognize a subdivision that resembles that of the overlapped RGB ChM. We also notice that, similarly to what is observed in the RGB ChM, the anomalous AGB stars in type II GCs lie on the rightmost part of the diagram.

The ChMs of Fig. 16 clearly show that, in each GC, the observed color spread is not compatible with the presence of a single population. Moreover they show that the MPs in the AGB can be associated to the different groups visible in the RGB ChMs.

The study of the AGB frequency relative to HB stars plays an important role in the context of MPs. In particular, since AGB-manqé stars are the progeny of HB stars with mass lower than $\sim 0.5$$M_{\odot}$(Moehler et al., 2019; Prabhu et al., 2020), which are associated with the most helium-rich stellar component in a cluster (D’Antona et al., 2002; Tailo et al., 2020), differences in internal helium variations between clusters can affect the AGB/HB ratio. This prediction is quantified by the evolutionary parameter $\mathrm{R_{2}}$ (Caputo et al., 1989), namely the number ratio between AGB and HB stars, which is proportional to the ratio between the lifetime of stars in these two evolutionary phases. According to theoretical predictions, $\mathrm{R_{2}}$ should not be higher than about 0.2 (Cassisi et al., 2014).

To explore this phenomenon, we took advantage of a large database of homogeneously defined AGB samples in GCs, determined in the present work, and of the independent measurements of maximum internal helium variations, $\mathrm{\delta Y_{max}}$, obtained by (Milone et al., 2018). For each GC, we determined the frequency of AGB stars relative to HB stars, $\mathrm{(N_{AGB}/N_{HB})}$, by counting HB members in the corresponding $m_{\rm F606W}$ vs. $m_{\rm F606W}-m_{\rm F814W}$ CMD. The error of each frequency measurement has been estimated with the same method used in Section 2.3). With the purpose of limiting spurious outcomes due to the stochastic fluctuations, we decided to limit the following analysis to the 36 GCs in our database with $\mathrm{N_{AGB}}\geq 10$, for which we report the corresponding frequency values Table 3.

In the left panel of Figure 19 we plot of $\mathrm{(N_{AGB}/N_{HB})}$ and ${\rm\delta Y_{max}}$ for these GCs, where color, size and shape of each point map, respectively, metallicity (Harris, 1996, 2010 update), present-day mass (Baumgardt & Hilker, 2018), and cluster’s type (Marino et al., 2019), as indicated in the legend. The diagram shows a scattered distribution, with all the GCs having frequency values smaller than $\sim 0.2$ except NGC 6171, which has $\mathrm{(N_{AGB}/N_{HB})}\lesssim 0.3$. We observe that the bulk of GCs does not seem to follow any clear trend. It is necessary to consider that the AGB of type II GCs can suffer a significant depletion of anomalous population stars, as seen in Section 2.3. Hence, the resulting shortage of AGB stars in these GCs would importantly affect the observed AGB/HB frequency meaning in a way difficult to predict. This implies in turn that no strong conclusions can be derived for these GCs.

On the other side, if we limit our analysis to type I GCs with $\log(M/M_{\odot})\lesssim 6$, therefore excluding the two massive GCs NGC 2808, NGC 2419, which are the type I clusters with the highest internal helium variation ($\mathrm{\delta Y_{max}}>0.1$ Milone et al., 2018), and among the GCs with the most complex MP pattern (Milone et al., 2015a; Zennaro et al., 2019), the majority of points display an inverse monotonic trend, with smaller AGB frequencies attained by clusters with higher internal helium variations. This impression is confirmed by the high value of the Spearman’s coefficient ($\rho_{\rm s}=-0.727$) reported in the bottom right corner. Finally we notice that the distribution of points shows no correlation with the cluster metallicity.

Finally, we verified that the analysis of the AGB/RGB frequency shows a similar trend, resulting therefore in the same conclusions. For the sake of convenience we decided to not show the corresponding plot.

Another way of investigating AGB depletion and helium enrichment is through the analysis of the relation between observed frequency and minimum mass along the HB. Gratton et al. (2010) showed that a direct correlation exists between minimum mass along the HB and the numeric frequency of AGB stars relative to the RGB, with lower frequencies attained by clusters with smaller minimum HB mass. In the right panel of Figure 19 we plot $\mathrm{(N_{AGB}/N_{HB})}$ vs $\mathrm{M_{HB}^{2Ge}}$, where the latter quantity indicates the average mass of the HB stars belonging to the most helium-enriched population, recently determined by Tailo et al. (2020), available for 20 type I GCs in our database. Color and size of each points follows the convention adopted in the left panel. With the exception of the outlier NGC 6171, we observe a clear correlation, that confirms the expectation of the AGB-manqé scenario of lower AGB frequencies in clusters with smaller minimum mass in the HB (Prabhu et al., 2020). The mild monotonic trend is also indicated by the value of the Spearman’s coefficient, $\rho_{\rm s}=0.551$, In passing we also notice that clusters with higher total mass have, on average, smaller minimum HB mass, while no clear trend is visible with metallicity.

The two plots in Figure 19 indicate, in general, a mild correlation between frequency of AGB stars and internal helium variations in clusters, which is in turn directly related to the mass of their hottest HB stars. The lack of a strong evidence of correlation is potentially connected to the fact that the parameters ruling the distribution of HB stars are degenerate. For instance, at a given helium enrichment, we would expect more massive HB stars in slightly younger GCs, thus a smaller proportion of AGB-manqué. The same conclusion would also be true for clusters of the same age, but different metallicity.

MPs are a common property of Galactic GCs. They have been widely characterized along main sequence, RGB and HB stars in large samples of clusters (e.g. Anderson, 1997; D’Antona et al., 2005; Piotto et al., 2007; Milone et al., 2017; Lagioia et al., 2019b; Marino et al., 2019; Dondoglio et al., 2021; Tailo et al., 2020). A coherent picture at later evolutionary stages is, however, still missing.

Recent spectroscopic analyses revealed that a lower fraction of 2G stars is found to populate the AGB of some clusters, like NGC 6752 (Campbell et al., 2013; Lapenna et al., 2016), NGC 6121 (Marino et al., 2017; MacLean et al., 2016, M 4), NGC 6205 (Lapenna et al., 2015, M 62) and NGC 2808 (Marino et al., 2017). Although no univocal consensus has been achieved on the interpretation of the results, the lack of a more or less significant fraction of 2G stars corresponds to the predictions of the AGB-manqué scenario (Greggio & Renzini, 1990), according to which the most helium-enriched stars have envelope masses too low in the HB phase, so they do not evolve towards the Hayashi track as a normal AGB star, but rather towards higher temperatures until they reach the white-dwarf cooling sequence.

In order to shed new light to this problem we decided to analyze the photometric properties of the AGB stars in the largest sample of GCs analyzed so far, composed by 58 objects observed by HST in UV and optical bands (Sarajedini et al., 2007; Piotto et al., 2015). Suitable combinations of filters allow to disentangle MPs in CMDs and study their properties in statistically significant samples of stars. Through a procedure that exploits CMDs in different color combinations we selected the most probable AGB candidates in every analyzed cluster. Then, we derived their properties through the analysis of their photometric features and comparison with theoretical models. Our methods and findings are summarized in the following:

1. 1.

   we investigated AGB stars in type II GCs and identified, for the first time, AGB stars associated with their metal-rich (anomalous) stellar populations. The fraction of anomalous AGB stars with respect to the total number of AGB stars is significantly lower than the corresponding fraction of stars in the anomalous RGB, with NGC 7089 and NGC 362 possible exceptions;

2. 2.

   we constructed the $m_{\rm F814W}$ vs. ${C_{\rm F275W,F336W,F438W}}$ CMD of the bright stars of 56 GCs with at least one AGB detection. We find that the AGB sequences of at least 48 clusters exhibit larger pseudo-color spread than that expected from photometric errors alone. Hence, they host multiple stellar populations. In eight clusters, namely NGC 7099, NGC 4590, NGC 5466, NGC 6218, NGC 6397, NGC 6496, NGC 6535, and NGC 6809, there is no evidence of intrinsic ${C_{\rm F275W,F336W,F438W}}$ broadening among AGB stars with similar luminosity. However, the small number of AGB stars in these clusters prevents us from any conclusion on the presence of MPs among their AGB. We conclude that in none of the studied clusters all 2G stars avoid the AGB phase;

3. 3.

   we used synthetic spectra with appropriate chemical composition and theoretical stellar models from the Roma database (Ventura et al., 1998; Mazzitelli et al., 1999) to derive, for the first time, isochrones of 1G and 2G AGB stars. We show that 2G stars define AGB sequences with smaller values of $C_{\rm F275W,F336W,F438W}$ and bluer ${M_{\rm F275W}-M_{\rm F814W}}$ colors than 1G stars with the same luminosity. The flux difference is mostly due to NH molecular bands that affect the spectral region covered by the F336W filter and the OH and CN molecules enclosed by the F275W and F438W filters, respectively. Since 2G stars are enhanced in N and depleted in C and O, they have fainter F336W and brighter F275W and F438W magnitudes than 1G stars with the same luminosity. Moreover, 2G stars are helium enhanced with respect to the 1G, hence they have colors bluer than 1G stars at the same luminosity. In addition to the content of helium, C, N, and O, the amount of mass loss experienced during the RGB phase affects the colors of AGB stars. In particular, an increase in mass loss can dramatically shift to the blue the AGB sequences;

4. 4.

   we measured the intrinsic width of AGB stars in the pseudo-colors ${C_{\rm F275W,F336W,F438W}}$ for 35 GCs with ${\mathrm{N}_{AGB}\geq 10}$, and compared it with the corresponding quantity obtained from RGB stars. We observe that the intrinsic width of AGB stars is on average smaller than that of RGB. This finding suggests that a substantial part of the RGB stars in these GCs does not evolve to the AGB;

5. 5.

   we constructed the ChM of 15 GCs with well populated AGB sequence and identified their 1G and 2G AGB stars: this allowed us to derive the fraction of 1G stars along the AGB. On average, AGB stars host fractions of 1G stars larger than in the RGB, and NGC 2808, NGC 5139, NGC 6715, and NGC 7078 and are the clusters with the most pronounced differences. This result is consistent with the AGB-manqué scenario where part of 2G stars skips the AGB phase (Campbell et al., 2013) due to their typical mass lower than that of 1G stars. Indeed, 2G stars are enhanced in helium (Lagioia et al., 2018; Milone et al., 2018) and lose more mass in the RGB phase compared to the 1G (Tailo et al., 2019a, 2020). This scenario is corroborated by the evidence from this paper and from Gratton et al. (2010) that the frequency of AGB/HB stars of the type I GCs correlates with the minimum mass of HB stars; the AGB frequency of type I GCs with $\log(M/M_{\odot})\lesssim 6$ also anti-correlates with the maximum helium abundance of 2G stars.