MULTIPLE STELLAR POPULATIONS OF GLOBULAR CLUSTERS FROM HOMOGENEOUS Ca by PHOTOMETRY. I. M22 (NGC 6656)^{* †}

In Table 3, we provide our photometric data for stars brighter than V = 19 mag. Figure 4 shows the color–magnitude diagrams (CMDs) of bright stars in the M22 field. Note that, for the sake of clarity, we show stars within 10 arcmin from the center of the cluster. As can be seen in the figure, the double RGB sequences of M22 can be clearly seen, especially the distinctive split in the RGB stars in the hk versus V CMD. Note that the m1 versus V CMD is from our previous study of the cluster (Lee et al. 2009a) taken during the Phase I period.

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Table 3.  Color–Magnitude Diagram Data

ID	R.A.	decl.	V	$b-y$	hk
96	279.502014	−24.007305	11.436	0.849	1.280
104	279.061249	−24.014750	11.895	0.717	0.901
106	279.059052	−24.033777	11.756	0.927	0.954
130	278.959198	−24.261583	11.649	0.895	1.178
146	279.027954	−24.347834	12.278	0.528	0.463
163	279.502747	−24.352249	11.570	0.836	1.186
197	279.064087	−23.805361	12.211	0.885	0.815
252	279.312927	−23.539223	11.941	0.308	0.409
285	279.184082	−23.980139	12.530	0.888	0.842
297	279.138306	−23.940722	12.655	0.942	0.830
301	278.767181	−24.275888	13.256	0.202	0.221

Note. Table 3 is presented in its entirety in the electronic edition of the Astrophysical Journal Supplement. A portion is shown here for guidance regarding its form and content.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Because M22 is located toward the Galactic bulge ($l=9\buildrel{\circ}\over{.} 9$, $b=-7\buildrel{\circ}\over{.} 6$), the contribution from the field-star contamination is naturally expected to be very large (see Lee et al. 2009a for detailed discussions). We attempted to remove the off-cluster field stars in our bright RGB sample by using multicolor CMDs following the method described in Lee et al. (2009a, 2009b), which turned out to be very successful, as discussed below.

In Figures 5(a) and (b), we show CMDs of the M22 field using all of the stars measured from V = 11.5 to 17.5 mag. In the figures, blue solid lines indicate the RGB boundary grids in the $(b-y)$ versus V and in the hk versus V CMDs. In order to prepare these RGB boundary grids, we made use of the fiducial sequence of the model isochrones by Joo & Lee (2013), which were kindly provided by S.-J. Joo, and we adopted the distance modulus and the foreground reddening value for M22 by Harris (1996). Then we added a small amount of color offset values, ${\rm{\Delta }}(b-y)\approx \pm 0.04$ mag and ${\rm{\Delta }}{hk}\approx \pm 0.07$ mag, in the transformed model isochrone sequences to make the final RGB boundary grids. Although our definitions of the RGB boundary grids for the $(b-y)$ and hk indexes appear to be arbitrary, our approach appears to work very satisfactorily, as shown below.

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The total number of RGB stars detected in the enclosed region in Figure 5(c), is 3571. When plotted in the hk versus V plane, it can be clearly seen that about 42% of RGB stars selected in the $(b-y)$ versus V plane do not belong to M22, that is, either the disk or the bulge populations with large hk index values. A comparison with the radial-velocity measurements by Lane et al. (2009) shows that 12 stars out of 307 stars in common turn out to be radial-velocity nonmember stars. If we take this at face value, the fraction of the inclusion of the off-cluster field population in our M22 RGB selection procedure is 3.9 ± 1.4%, which appears to be too low to dramatically change the results presented in this paper. Without the 12 radial-velocity nonmember stars, we have 2054 RGB stars, from V = 12.0 to 16.5 mag, in total.

The validity of our RGB selection procedure can be confirmed by the surface-brightness profile (SBP) of the RGB stars in M22. In Figure 6(d), we show the SBP of the red-clump stars in the Galactic bulge (the stars lie inside a cyan box in Figure 5(a)). As expected, the SBP of the bulge population is almost flat against the radial distance from the center of M22. Note that the mild fluctuation seen in the small r region, $\mathrm{log}(r$ arcsec⁻¹) ≲ 2, is due to the small number of bulge red-clump stars ($n\leqslant 15$) detected in this region.

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Figures 6(a)–(c) show the SBPs of the Ca-w group, the Ca-s group, and all RGB stars in M22 (see below for details on the definition of the Ca-w and the Ca-s groups). With slightly different zero-point offset values for each group of stars, our SBPs for M22 RGB stars are in excellent agreement with the Chebyshev polynomial fit of M22 by Trager et al. (1995) up to more than 10³ arcsec from the center of the cluster. Our investigation of the SBPs of M22 RGB stars strongly suggests that contamination from the off-cluster field stars in our result is not severe, consistent with our previous result from the comparison of the radial-velocity measurements of M22 RGB stars.

As shown in Figures 4 and 5, M22 exhibits the distinctive double RGB sequences in the hk versus V CMD, which is mainly due to the difference in the heavy-element abundances between the two groups (see also Lee et al. 2009a; Marino et al. 2009, 2011). As in our previous works (Lee et al. 2009a, 2009b), we define the calcium-weak (Ca-w) group of stars with a smaller hk index and the calcium-strong (Ca-s) group of stars with a larger hk index at a given V magnitude.

In the left panel of Figure 7, we show 2054 RGB stars from Figure 5(d) on the ${\rm{\Delta }}{hk}$ versus V plane, where ${\rm{\Delta }}{hk}$ is defined to be the difference in the hk index of the individual RGB stars with respect to the hk index of the fiducial sequence of the Ca-w RGB group. As shown, the differences in the hk index between the mean values of the Ca-w and Ca-s depend slightly on V magnitude, which is naturally expected if the difference in the absorption strengths of the Ca ii H and K lines is mainly responsible for the separation in the hk index of the RGB stars. Because of this magnitude (more precisely, surface gravity) dependency on the ${\rm{\Delta }}{hk}$, we divide the M22 RGB stars into four different magnitude bins, and we show histograms of the ${\rm{\Delta }}{hk}$ distributions of RGB stars of each magnitude bin in the right panels of Figure 7, all of which appear to show double peaks. In order to separate the two different groups of RGB stars based on the ${\rm{\Delta }}{hk}$ distribution, we adopt the expectation maximization (EM) algorithm for the two-component Gaussian mixture distribution model. In an iterative manner, we derive the probability of individual RGB stars being in the Ca-w and Ca-s groups. In the left panel of Figure 7, stars with $P(w| {x}_{i})$ $\geqslant$ 0.5 from the EM estimator are denoted with blue dots, which corresponds to the Ca-w group, and $P(s| {x}_{i})$ > 0.5 with red dots, which corresponds to the Ca-s group. In the right panel of the figure, we show the distributions of the Ca-w and Ca-s groups with blue and red solid lines, respectively, and we show the number ratio n(Ca-w):n(Ca-s) for each bin. In total, the number ratio between the Ca-w and the Ca-s groups is n(Ca-w):n(Ca-s) = 68.8:31.2 (±3.3). Table 4 shows the summary of our results.

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Our observed number ratio between the two groups does not necessarily reflect the initial stellar number ratio or the initial mass ratio between the two groups because both groups have different initial chemical compositions, different masses at a given luminosity, and furthermore slightly different ages (e.g., Lee et al. 2009a; Marino et al. 2009, 2011; Joo & Lee 2013). In order to take care of the heterogeneous evolutionary effects between the two groups, we constructed an evolutionary population synthesis model using the theoretical model isochrones by Joo & Lee (2013). We populated 10⁷ artificial stars in each group using Salpeter's initial mass function (IMF), and we generated 50 different sets for each group. We then compared the number ratios between the two groups in the magnitude range of 12.0 $\leqslant$ V $\leqslant$ 16.5 mag, finding n(Ca-w):n(Ca-s) = 48.3:51.7 (±0.3), in the sense that RGB stars in the Ca-s group are slightly more numerous than those in the Ca-w group at a fixed total number of stars in both groups. Note that using other types of IMF does not affect the results presented here, which was also pointed out by Joo & Lee (2013). As an exercise, we calculated the number ratio using the universal IMF by Kroupa (2001), and we obtained n(Ca-w):n(Ca-s) = 48.4:51.6 (±0.3), in excellent agreement with that from Salpeter's IMF within the 0.1% level.

Figure 8 shows the mean theoretical luminosity functions (LFs) for the Ca-w and Ca-s groups. Note that the abscissa of the figure is M_V, and the gray shaded area corresponds to M22 RGB stars with 12.0 $\leqslant$ V $\leqslant$ 16.5 mag. As can be seen, the theoretical LFs for the RGB stars in both groups are very similar. If we consider the evolutionary effect, the intrinsic or the true number ratio between the two groups becomes n(Ca-w):n(Ca-s) = 70.2:29.8 (±3.3). Note that our new RGB number ratio is in good agreement with our previous rough estimate of the number ratio between the two groups, ≈0.70:0.30 (Lee et al. 2009a).

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As discussed by Lee et al. (2009a) and Marino et al. (2009, 2011), the double RGB sequences in M22 are due to the difference in chemical abundances between the Ca-w and the Ca-s groups, in particular the difference in the calcium abundance measured with the Ca filter and in heavy elements, which was first hinted at by the high-resolution spectroscopy of seven RGB stars by Brown & Wallerstein (1992) and confirmed later by Marino et al. (2009, 2011) with an expanded sample of RGB stars of the cluster. A more detailed discussion on the difference in the chemical abundances between the two groups will be given below. Also worth emphasizing is the fact that the differential reddening effect and the contamination from the off-cluster populations cannot explain the double RGB sequences in M22 (Lee et al. 2009a). Assuming the conventional interstellar reddening law for the extended Strömgren photometry system by Anthony-Twarog et al. (1991), E(hk) = −0.16 × $E(b-y)$ ≈ −0.12 × $E(B-V)$, the mean hk difference between the two RGB groups, ${\rm{\Delta }}{hk}$ = 0.09 mag, can be translated into ${\rm{\Delta }}(b-y)=-0.56$ mag, ${\rm{\Delta }}(B-V)=-0.75$ mag, and ${\rm{\Delta }}V=-2.33$ mag, in the sense that the metal-rich Ca-s RGB stars become bluer and brighter due to the foreground reddening. Indeed, this is not the case.

The Strömgren v passband includes the CN band at λ 4215 Å, and, as a consequence, the m1 index [= $(v-b)-(b-y)$] is capable of distinguishing the difference in the CN absorption strengths. In fact, the bimodal distribution in the m1 index of M22 RGB stars was known for decades, and it has been frequently attributed to the bimodal distribution in the CN abundances (Norris & Freeman 1983; Anthony-Twarog et al. 1995; Richter et al. 1999; Lee et al. 2009a). It is widely accepted that the variation in lighter-element abundances, such as C, N, and O, is thought to result from chemical pollution by the intermediate-mass AGB stars (see, for example, Ventura et al. 2001). The potential trouble with the m1 index is that the split between the double populations at the lower RGB sequence is not readily distinguishable in the m1 versus V CMD, most likely due to the strong surface-gravity sensitivity on the CN band strength, in the sense that the CN band strength is inversely correlated with the surface gravity of stars (see, for example, Tripicco & Bell 1991; Cannon et al. 1998), as shown in Figure 4.

On the other hand, as Lee et al. (2009a) discussed extensively, the hk index is a measure of calcium abundances of individual stars, so the difference in the hk index at a given luminosity indicates heterogeneous calcium and other heavy-element abundances between the double RGB populations in M22, which is confirmed by the high-resolution spectroscopic study of RGB stars in the cluster (Brown & Wallerstein 1992; Marino et al. 2009, 2011). Calcium and heavy elements can only be supplied through supernovae explosions of massive stars, and the origin of the split in the hk index is intrinsically different from that in the m1 index in M22 if the m1 index most sensitively depends on the CN abundances, as previous investigators perceived frequently. It is important to note that, however, because the Strömgren v passband includes numerous metallic lines, the m1 index also sensitively reacts to the difference in the heavy metal abundances.

In the top panels of Figure 9, we show the CMDs of M22 again. For the m1 versus V CMD, we show stars with $(b-y)$ $\geqslant$ 0.45 mag to prevent the degeneracy of the location of the HB and the RGB stars in the m1 versus V CMD. We also show the Padova model isochrones with [Fe/H] = −1.8 dex, comparable to that of the Ca-w group, and −1.5 dex, comparable to or slightly more metal-rich than that of the Ca-s group, with a fixed [CNO/Fe] ratio (Bressan et al. 2012). From the figure, it is palpable that the bifurcation in the RGB sequences on the m1 versus V CMD is mainly due to the difference in the metal abundance. In addition, the higher mean [CNO/Fe] ratio in the Ca-s group⁴ may intensify the difference in the m1 index between the two groups.

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A comparison of M22 with two Galactic GCs, M55 and NGC 6752 (J.-W. Lee 2015, in preparation), may help to elucidate the nature of the double RGB sequences. Note that the metallicity of M55 is [Fe/H] = −1.9 dex, equivalent to the Ca-w group in M22, whereas that of NGC 6752 is −1.5 dex, equivalent to the Ca-s group in M22. It is well known that the HB morphologies of both clusters are different. M55 contains only the blue HB (BHB) population, whereas NGC 6752 contains the BHB and the extreme blue HB (EBHB) populations. The CN distributions of both clusters are also different. M55 appears to show a unimodal CN distribution (Kayser et al. 2008), in sharp contrast to the bimodal CN distribution of NGC 6752 (Norris et al. 1981).

In the bottom panels of Figure 9, we show the composite CMDs of M55 and NGC 6752. In order to make these composite CMDs, we tweaked the color indexes and the visual magnitude of individual stars in NGC 6752 to match those in M55: ${\rm{\Delta }}(b-y)$ = 0.034 mag, ${\rm{\Delta }}m1$ = −0.008 mag, ${\rm{\Delta }}{hk}$ = −0.001 mag, and ${\rm{\Delta }}V$ = 0.654 mag. In the m1 versus V CMD, we do not plot the HB stars in M55 and NGC 6752 to avoid confusion with the RGB stars. We emphasize that these composite CMDs can successfully reproduce the photometric characteristics of M22. Especially, the CMDs of M22 and the composite GCs show a remarkable resemblance in the HB morphology and the double RGB sequences, both in the m1 and the hk indexes, suggesting that the double RGB sequence in the m1 index of M22 is likely due to the difference in the mean heavy-metal abundance. If so, the origin of the RGB split in the m1 index is the same as that of the hk index in M22.

Nonetheless, using the hk index as a metallicity indicator has advantages. As Anthony-Twarog et al. (1991) noted, the hk index is about three times more sensitive to metallicity than the m1 index is, for stars more metal-poor than the Sun, and it has half the sensitivity of the m1 index to interstellar reddening. The annoying trouble with the m1 index is that it loses sensitivity to metallicity changes in the regime below [Fe/H] ≈ −2 dex, especially for stars with higher surface gravity.

We also carried out the HST WFC3 photometry for the central part of M22. In Figure 10, we show the preliminary results from HST WFC3 observations of the cluster (PI: J.-W.Lee and PID: 12193) using the similar passbands that we used in our ground-based observations.

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The left panel of the figure shows the $({m}_{{\rm{F}}467{\rm{M}}}-{m}_{{\rm{F}}547{\rm{M}}})$ versus ${m}_{{\rm{F}}547{\rm{M}}}$ CMD, which is equivalent to the ground-based $(b-y)$ versus V CMD, near the the SGB and the faint RGB regions of M22. Similar to the ground-based $(b-y)$ versus V CMD, the split in the RGB or SGB cannot be readily seen in the figure.

On the other hand, the ${{hk}}_{\mathrm{STMAG}}$ [= $({m}_{{\rm{F}}395{\rm{N}}}-{m}_{{\rm{F}}467{\rm{M}}})-({m}_{{\rm{F}}467{\rm{M}}}-{m}_{{\rm{F}}547{\rm{M}}})$] versus ${m}_{{\rm{F}}547{\rm{M}}}$ CMD shows the distinctive split in the SGB and the RGB sequences of M22, confirming the results from our new ground-based observations discussed above. Note that the SGB split in M22 has already been known in other HST passbands by Marino et al. (2009, 2012), and the presence of the SGB split is likely due to variations in the CNO abundance (Cassisi et al. 2008). Especially, Marino et al. (2012) performed a low-resolution spectroscopic study for a large number of SGB stars in M22, finding that the elemental abundance trend of the faint SBG (fSGB) group is consistent with that of the s-process-rich group in their early study (Marino et al. 2011, i.e., Ca-s in this study), whereas the elemental abundance trend of the bright SGB (bSGB) is consistent with that of the s-process-poor group (i.e., the Ca-w group), demonstrating that the observed difference in the CNO abundance can account for the observed SGB split.

Milone et al. (2009) devised a rather clever but complicated method to estimate the number ratio between the fSGB and the bSGB in NGC 1851. However, there are at least three aspects that make it difficult for M22 to be analyzed using the method described by Milone et al. (2009). First, the spatial stellar number density in a fixed area on the sky (i.e., the number of stars/$\square \prime\prime$) of M22 is about 20 times smaller than that of NGC 1851. Therefore, the number of SGB stars detected in our HST observations for M22 is much smaller than that in NGC 1851 by Milone et al. (2009). The small number of stars makes it difficult to delineate a clear SGB fiducial sequence for M22. Second, the foreground interstellar reddening value of M22, $E(B-V)$ = 0.34, is much larger than that of NGC 1851, $E(B-V)$ = 0.02 (Harris 1996). Furthermore, a differential foreground reddening effect may exist across M22, although the differential reddening is not the main reason for showing the double RGB or SGB sequences in M22, as we have already discussed. Lastly, the curvature of the SGB stars and the location of the transition region between the SGB and the base of the RGB are different between the HST ${{hk}}_{\mathrm{STMAG}}$ and the F606W–F814W photometric systems. The essential idea of the method proposed by Milone et al. (2009) is to estimate the intrinsic or true number ratio between the two SGB populations, derived from the apparent number ratio by taking care of the evolutionary effect, as we have done for the RGB stars. It is also important to point out that their method is arbitrary and model dependent, as they have noted.

Before turning to the observed number ratio between the two SGB groups in M22, we investigate the methodological aspect by employing the evolutionary population synthesis models that we constructed for the RGB stars above. In the left panels of Figure 11, we show artificial CMDs around the SGB region of M22 for different photometric systems. In order to construct the evolutionary population synthesis models, we use the model isochrones by Joo & Lee (2013) with Salpeter's IMF. The photometric errors are estimated from the measurement errors around the SGB region in our HST observations. We populate 10⁸ artificial stars in each group. In the figure, blue dots denote the bSGB group, and red dots the fSGB in M22. For the sake of clarity, we only show a small fraction of stars in the figure. We then count the number of SGB stars for each group at a fixed color range (the vertically shaded areas) and at a fixed magnitude range (the horizontally shaded areas) returned from our calculations.

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The middle panels of Figure 11 show the distributions of SGB stars in the fixed color ranges for the different photometric systems, and the right panels show those in the fixed magnitude ranges. Similar to our RGB number ratio estimates, we calculate the differences in the magnitudes or in the color indexes against those of the fiducial sequences of the bSGB group. The first number ratios in each plot are those returned from the EM estimator assuming the two-component Gaussian mixture model, and the number ratios inside the parentheses are the input values used in our evolutionary population models. Note that these number ratios in parentheses reflect the evolutionary effect between the two SGB groups at given color or magnitude ranges. In the figure, our adopted ranges in each color index may be rather arbitrary, but we intend to maximize the available number of stars, maintaining the clear separation between the two SGB groups.

First, the SGB number ratio returned from the EM estimator between the two groups at the fixed (F606W − F814W) color is n(bSGB):n(fSGB) = 42:58, and that of the input value from the evolutionary population synthesis models is 39:61. On the other hand, the SGB number ratio determined at the fixed F606W magnitude appears to be more uncertain. We obtained n(bSGB):n(fSGB) = 63:37 with the input value of 56:43.

Next, the SGB number ratios determined from the $b-y$ versus V CMD appear to be the least reliable in our simulations. We obtain n(bSGB):n(fSGB) = 44:56 for the fixed color and 72:28 for the fixed magnitude ranges, which number ratios deviate largely from the input values of 38:62 and 65:35, respectively.

Finally, the SGB number ratios determined from the hk versus V CMD appear to be the most reliable. Because of the combined effect of the mean heavy metal and  CNO abundances on the location of the SGB sequence on the hk versus V CMD, the separation in the hk index between the two SGB groups is the most conspicuous. The EM estimator securely retrieves the input values within an uncertainty of $\leqslant \ \pm$ 0.2. Because our simulations suggest that the total number of stars available in our simulations for the hk versus V CMD is about three times larger for the case with the fixed magnitude range, we estimate the observed SGB number ratio from our HST observations of the cluster using the method with a fixed magnitude range, that is, using the distribution of individual stars against ${\rm{\Delta }}{hk}$, as for the RGB stars. Also, importantly, using the method with a fixed magnitude range has an advantage in correcting the evolutionary effect. The SGB number ratio of n(bSGB):n(fSGB) = 58:42 is, in fact, the evolutionary effect correction factor shown in Figure 8 (the yellow shaded area), and applying the correction factor of the differential evolutionary effect based on the V magnitude is more direct.

In Figure 12(a), we show the ${{hk}}_{\mathrm{STMAG}}$ versus ${m}_{{\rm{F}}547{\rm{M}}}$ CMD around the SGB region of M22. Also shown is the fiducial sequence for the bSGB group. Following a procedure similar to what we used for the RGB stars, we obtain the number ratio of n(bSGB):n(fSGB) = 69:31 (±6). If we apply the correction factor for the differential evolutionary effect between the two groups, the intrinsic number density becomes n(bSGB):n(fSGB) = 62:38 (±6). This SGB number ratio is in agreement with the RGB number ratio, n(Ca-w):n(Ca-s) = 70:30 ( ±3.3), within the measurement errors.

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As mentioned above, Marino et al. (2009, see references therein) already discovered the SGB split in their HST Advanced Camera for Surveys Wide Field Channel (ACS/WFC) observations of M22 using the F606W and F814W passbands, although the separation between the fSGB and the bSGB populations in the ${m}_{{\rm{F}}606{\rm{W}}}-{m}_{{\rm{F}}814{\rm{W}}}$ versus ${m}_{{\rm{F}}814{\rm{W}}}$ CMD is not as clear as that in the ${{hk}}_{\mathrm{STMAG}}$ versus ${m}_{{\rm{F}}547{\rm{M}}}$ CMD, as shown here. Their SGB number ratio is n(bSGB):n(fSGB) = 62:38 (±5), which is in excellent agreement with our true SGB number ratio of n(bSGB):n(fSGB) = 62:38 (±6).

Finally, it should be worth mentioning that the hk separation between the two SGB groups in the observed CMD (Figure 10) is more ambiguous than that of the simulated CMD with a proper treatment of the photometric measurement errors (Figure 11). This may indicate that not only the differential reddening but also the metallicity spreads in the double SGB populations are necessary to perform more realistic simulations. In fact, Marino et al. (2011) reported rather large metallicity spreads for the two groups of RGB stars: 0.10 dex for the s-process-poor group and 0.05 dex for the s-process-rich group. As shown in Figure 9, the $(b-y)$ width of M22 is compatible with that of the composite GC (i.e., NGC 6752 + M55), where the $(b-y)$ locus of the RGB sequence is less sensitive to the variation in the heavy metal abundance, and the hk width of M22 is broader than that of the composite GC. Given the current interstellar reddening law (see below for more details), the reasonable explanation for the broader RGB sequence of M22 in the hk index is likely the spread in the heavy metal abundances of both stellar groups in M22.

Hesser et al. (1977) and Hesser & Harris (1979) first noticed that M22 has RGB stars with heterogeneous light elemental abundances using DDO photometry and low-resolution spectroscopy, respectively, leading them to suggest that M22 may share similar elemental abundance anomalies with ω Cen. Later, Norris & Freeman (1983) performed a spectroscopic survey study of about 100 RGB stars in the cluster, and they showed that the calcium abundance is correlated with the CN-band and the G-band strengths in the RGB stars in M22.

In Figure 13, we show a plot of the calcium index A(Ca) as a function of V magnitude (see Equation (2) of Norris & Freeman for the definition of the A(Ca) index). In the figure, we also show the least squares fit to the Ca-w RGB stars, which can provide a baseline, and we calculate the deviations of individual stars from the fitted line. As discussed by Norris & Freeman (1983), the residuals of individual stars from this fitted line against the V magnitude may correct the temperature and the surface-gravity effects on the absorption strengths to the first order. The figure shows that the A(Ca) index of Norris & Freeman (1983) is correlated well with our hk index, which should not be a surprise because both quantities measure the same Ca ii H and K line strength of RGB stars photometrically and spectroscopically.

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Da Costa et al. (2009) studied M22 RGB stars using intermediate-resolution spectra, and they obtained infrared Ca ii triplet strengths Σ(CaT) (=${W}_{8542}+{W}_{8662}$) for membership RGB stars, finding a substantial intrinsic metallicity spread in M22 RGB stars. The advantage of using the infrared Ca ii triplet is that these lines arise from a lower energy level of 1.70 eV, whereas the lower energy level of Ca ii H and K lines is 0 eV. Therefore, the infrared Ca ii triplet lines do not suffer from interstellar reddening contamination.⁵ Also, because the absorption lines from other elements around the infrared Ca ii triplet lines are sparsely populated, contamination from absorption lines of other elements would be less severe.

In the upper panel of Figure 14, we show the plot of Σ(CaT) against $V-{V}_{\mathrm{HB}}$, the V magnitude difference from the HB. In the figure, we also show the least squares fit to the data with a dotted line. The residuals around this fitted line will correct the temperature and the surface-gravity effects on Σ(CaT) to the first order. As can be seen, the RGB stars in the Ca-s group have larger Σ(CaT) values at a given $V-{V}_{\mathrm{HB}}$ magnitude than those in the Ca-w group, consistent with our results that the Ca-s RGB stars are more calcium rich than the Ca-w RGB stars in M22.

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Finally, we make use of the results from high-resolution spectroscopy by Marino et al. (2011). In Figure 15, we show plots of the [Ca/H] versus [Fe/H] and the [Na/Fe] versus [O/Fe] for RGB stars in the Ca-w and the Ca-s groups. Similar to the results in Lee et al. (2009a, 2009b), the plot of [Ca/H] versus [Fe/H] shows that the RGB stars in the Ca-w group have lower calcium and iron abundances than those in the Ca-s group, confirming that our hk index measures the calcium abundances of RGB stars in M22. The plot of [Na/Fe] versus [O/Fe] shows that each group based on our hk index exhibits its own Na–O anticorrelation. This was also pointed out by Marino et al. (2011), who found two separate Na–O anticorrelations in M22 RGB stars with different s-process elemental abundances. Note that the separation in the hk index in our current work is equivalent to that in the s-process elemental abundances by Marino et al. (2011). These separate Na–O anticorrelations caused Marino et al. (2011) to suggest that M22 may be composed of the merger of two clusters. In fact, NGC 1851 shows similar behavior in the Na–O anticorrelations between the two distinct RGB populations. Carretta et al. (2010) suggested that the simple explanation for the observational evidence of NGC 1851 would be a merger scenario, preferentially in a dwarf galaxy environment.

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However, it is worth emphasizing the fact that the mean values of the Ca-w RGB stars appear to have higher oxygen and lower sodium abundances, representative of the primordial elemental abundance pattern, than do the Ca-s RGB stars, consistent with the result by Marino et al. (2011). Also, lighter elements C and N and heavy elements Ca and Fe abundances are different between the two groups (Marino et al. 2011). Therefore, the feedback on the overall chemical evolution between the two groups cannot be completely neglected.

From comparisons of our hk photometry with three independent works by others, we conclude that our hk index measurements for RGB stars in M22 are very consistent with the calcium abundance measurements by others from Ca ii H and K, infrared Ca ii triplet lines, and visual Ca i lines. Therefore, the hk index can be securely and efficiently used to distinguish the difference in the calcium abundances at a given luminosity and furthermore the multiple RGB populations in GCs.

Lim et al. (2015) presented low-resolution spectroscopy for M22 RGB stars and confirmed the CN–CH positive correlation discovered by Norris & Freeman (1983; see also Anthony-Twarog et al. 1995).⁶ Here, we discuss further the metallicity effect on the CN–CH positive correlation between the two RGB groups in M22.

The variations in lighter elements in GC stars have been known for more than three decades, pioneered by Cohen (1978), and the variation is now generally believed to be rooted in the primordial origin (Cottrell & Da Costa 1981; Kraft 1994). The CN–CH anticorrelation is one of the well-known characteristics in the Galactic GC system. One probable explanation for the origin of this CN–CH anticorrelation can be found in Grundahl et al. (2002). They nicely demonstrated that a CH-NH anticorrelation and a CN-NH positive correlation exist among RGB stars in NGC 6752, suggesting that the nitrogen abundance is inversely correlated with the carbon abundance.

The CN–CH positive correlation shown in Figure 13 of Lim et al. (2015) appears at first glance to show two separate CN–CH anticorrelations among stars in each group. It would have been very surprising if a single CN–CH anticorrelation existed between the Ca-w and Ca-s groups in M22. It is thought that a CN–CH positive correlation superposed on two separate CN–CH anticorrelations in M22 can be expected naturally if M22 is composed of two groups of stars with heterogeneous metallicities. It is because the positive correlation in the δCN versus δCH relation can occur when one compares the δCN and δCH of different groups of stars with heterogeneous metallicities (see Norris et al. 1981 for the definition of δCN and δCH).

In order to investigate the metallicity effect on the positive correlation between the CN and CH band strengths, we used the homogeneous measurements of the CN and CH band strengths for stars in eight GCs observed in the course of the Sloan Digital Sky Survey (SDSS) by Smolinski et al. (2011). Because they provided the magnitudes of stars in the SDSS photometric system, we converted their SDSS photometry to the Johnson system using the relation given by Jester et al. (2005):

$$\begin{eqnarray}&&V=g-0.59(g-r)-0.01,\end{eqnarray} \tag{ 2 }$$

and we calculated the $V-{V}_{\mathrm{HB}}$ using the ${V}_{\mathrm{HB}}$ values given by Harris (1996).

In Figure 16, we show distributions of the CN(3839) and CH(4300) indexes against $V-{V}_{\mathrm{HB}}$ for eight GCs. As shown, the CH(4300) strengths are well correlated with the metallicity of GCs at a given magnitude (for example, the RGB stars around the level of the HB magnitude shown with vertical dashed lines), whereas the CN(3839) strengths exhibit a rather weak correlation against metallicity, mainly due to the multimodal distributions of the CN(3839) strengths of individual GCs (for example, see Figure 4 of Smolinski et al. 2011). Also shown are M22 and NGC 288 from Lim et al. (2015), whose measurements do not agree with those of Smolinski et al. (2011) due to a heterogeneous definition of the band strengths between the two works. Note that Smolinski et al. (2011) used the definition of the CN(3839) band strength by Norris et al. (1981) for RGB and SGB stars, that by Harbeck et al. (2003) for MS stars, and the definition of the CH(4300) band strength by Lee (1999), whereas Lim et al. (2015) used the definitions by Harbeck et al. (2003) for both bands. Because of the heterogeneous definitions of the molecule band strengths, the extent of the CN(3839) band strengths for M22 and NGC 288 by Lim et al. (2015) is greater than for those by Smolinski et al. (2011). Also, the CH(4300) values for M22 and NGC 288 by Lim et al. (2015) are ≳1.0, and they are out of range in the figure. Therefore, a direct comparison between the two works is not feasible.

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In the figure, the thick solid lines are the common lower envelopes for eight GCs. Because of the difference in the mean metallicity among GCs, these common lower envelopes may not correct both the temperature and the surface-gravity effects simultaneously on the CN(3839) and the CH(4300) band strengths for eight GCs. This is exactly what is expected to happen when one compares two groups of RGB stars in M22 with different mean metallicities using a single fitted line because the two groups of RGB stars in M22 have very different metallicities. In Figure 17, we show the distributions of δCN and δCH against metallicity, where δCN and δCH are defined to be the differences in the CN and CH between individual stars and the common lower envelopes. As expected from Figure 16, δCN and δCH have substantial gradients against metallicity, 0.169 ± 0.031 and 0.077 ± 0.010 mag dex⁻¹, respectively. It is believed that these positive slopes are the source of the CN–CH positive correlation when one compares the δCN and the δCH of stars with heterogeneous metallicities.

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In Figure 18, we show the CN(3839) and CH(4300) band strengths by Lim et al. (2015) against the V magnitude. Also shown are the lower envelopes for the Ca-w (blue dotted line) and Ca-s (red dotted line) groups. Stars with $-1.0\;\leqslant V-{V}_{\mathrm{HB}}\leqslant 0.5$ mag are shown with plus signs (Ca-w) and crosses (Ca-s). Note that the lower envelope for the Ca-w group can serve as the common lower envelope for both groups.

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Figure 19(a) shows a distribution of δCN versus δCH of the M22 RGB stars, where δCN and δCH are calculated with respect to the common lower envelope (i.e., the blue dotted lines in Figure 18). This plot is similar to Figure 13 of Lim et al. (2015), where the CN–CH positive correlation can be seen. Note that Lim et al. (2015) used the mean fitted line, not the lower envelope used in this analysis or those of others (for example, Norris et al. 1981; Kayser et al. 2008; Smolinski et al. 2011), and the detailed distributions of individual stars are slightly different from those presented here.

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In Figures 19(b) and (c), we show distributions of δCN versus δCH for the Ca-w and Ca-s groups using their own lower envelopes. Each plot appears to show its own CN–CH anticorrelation, a well-known characteristic of normal GCs. This is also consistent with the presence of the separate C–N anticorrelations in each of the two s-process groups (Marino et al. 2011). Because its own lower envelope for each group can correct the metallicity effects, the δCN and δCH values calculated from its own lower envelope reflect the relative CN and CH band strengths at a given metallicity and surface gravity. As a consequence, the CN–CH positive correlation with an apparently ambiguous origin disappears. In this regard, the simplest explanation would be a merger of two GCs with different metallicities. Each group of stars could have been chemically enriched independently and exhibits its own CN–CH anticorrelation, as observed in normal GCs in our Galaxy.

Finally, it is worth pointing out again that the ranges in the δCN and δCH of M22 using the data by Lim et al. (2015) are greater than those that can be expected from the slopes in the metallicity gradients as shown in Figure 17. This is partially due to the different definitions in the CN and CH band strengths. It would be highly desirable to reanalyze the spectra in a homogeneous manner in the future.

Yong et al. (2008) investigated the nitrogen abundances of RGB stars in NGC 6752 using NH molecule lines. They noted that the Strömgren u passband contains the NH molecule band at λ 3360 Å, and they showed that the c₁ index is correlated with the nitrogen abundances of individual stars. They devised an arbitrary empirical index ${cy}\ [={c}_{1}-(b-y)]$ and derived a well-correlated relation between the nitrogen abundance and the cy index of RGB stars at about ${V}_{\mathrm{HB}}$ of NGC 6752, [N/Fe] $\propto 16.11\times {cy}$.

In Figure 20, we show the cy versus V CMDs of M22 RGB stars, showing broad spreads in the cy index in both groups. Assuming Gaussian distributions, we calculated the standard deviation around the mean cy values and obtained $\sigma ({cy})\ \approx 0.03$ mag at ${V}_{\mathrm{HB}}$ for both groups of stars in M22. Because the metallicity of M22 is comparable to that of NGC 6752, and if the spread in the NH absorption strengths in individual RGB stars is solely responsible for the spreads in the cy index, $\sigma ({cy})\ \approx$ 0.03 mag corresponds to σ[N/Fe] ≈ 0.5 dex in each group of stars.

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Note that our photometric estimates of the spread in nitrogen abundances in M22 RGB stars appear to be slightly larger than those of Marino et al. (2011), who obtained σ[N/Fe] ≈ 0.2 dex for their s-poor and s-rich groups based on observations of 14 stars.

One of the remarkable features that can be seen in Figure 20 is that the RGB bump magnitudes of both populations appear to be different. In the right panel of Figure 20, we show the cumulative LFs for the Ca-w and Ca-s populations. We show by arrows the V magnitude levels of the RGB bump, ${V}_{\mathrm{bump}}$, where the slope of the LF changes abruptly, for each population. We obtained ${V}_{\mathrm{bump}}$ = 13.91 mag for the Ca-w population and 14.06 mag for the Ca-s population.

Here, we explore more details of the RGB bump in M22. As already shown in the left panel of Figure 7, it can be seen that the V magnitude level of the RGB bump appears to be positively correlated with the ${\rm{\Delta }}{hk}$ values of RGB stars at around V ≈ 14.0 mag. Especially because of its high stellar number density, the tilted ${V}_{\mathrm{bump}}$ magnitude level against ${\rm{\Delta }}{hk}$ for the Ca-w group is conspicuous, but the tilted HB structure in the Ca-w group cannot be seen in the cy versus V CMD shown in Figure 20. It is worth noting that neither this tilted V magnitude against ${\rm{\Delta }}{hk}$ in the Ca-w group nor the difference in the bump magnitude between the two groups can be explained by the differential reddening effect (see also Lee et al. 2009a).

The difference in the mean ${\rm{\Delta }}{hk}$ values between the Ca-w stars with ${\rm{\Delta }}{hk}$ < 0 mag and those with ${\rm{\Delta }}{hk}$ $\geqslant$ 0 mag at V = 13.95 mag is ${\rm{\Delta }}{hk}$ = 0.04 mag. Again, assuming that the conventional interstellar reddening law by Anthony-Twarog et al. (1991) is applicable, E(hk) = −0.16 × $E(b-y)$ ≈ −0.12 × $E(B-V)$, and that the differential reddening effect across the cluster is the main reason for showing a broad RGB sequence in the hk index, this 0.04 mag difference in the ${\rm{\Delta }}{hk}$ index can be translated into A_V = −1.05 mag, in the sense that the Ca-w RGB stars with ${\rm{\Delta }}{hk}$ $\geqslant$ 0 mag should be about 1 mag brighter than those with ${\rm{\Delta }}{hk}$ < 0 mag. This is the opposite of what is observed in M22. As shown in Figure 21, the V magnitude for the RGB bump of the Ca-w stars with ${\rm{\Delta }}{hk}$ $\geqslant$ 0 mag is about 0.06 mag fainter than that of the Ca-w stars with ${\rm{\Delta }}{hk}$ < 0 mag (see also Figure 20). Also, if this 0.04 mag difference in ${\rm{\Delta }}{hk}$ originates solely in the differential reddening across the cluster, not from the difference in chemical compositions, the $(b-y)$ color of the Ca-w group should have been broadened by ≈0.25 mag. However, the RGB sequence in M22 is not as broad as 0.25 mag, as shown in Figure 4. Therefore, the difference in the RGB bump magnitude is not mainly due to the differential reddening effect but is due to the difference in chemical compositions.

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It is well known that at a given age the RGB bump becomes fainter with increasing metallicity and with decreasing helium abundance because of changes in the envelope radiative opacity (see, for example, Cassisi & Salaris 2013). The fainter ${V}_{\mathrm{bump}}$ magnitude with increasing ${\rm{\Delta }}{hk}$ can be interpreted as ${\rm{\Delta }}{hk}$ increasing with either increasing metallicity or decreasing helium abundance. One can quantitatively estimate the effect of metallicity and the helium abundance on the RGB bump luminosity (Bjork & Chaboyer 2006; Valcarce et al. 2012).

In their Table 2, Bjork & Chaboyer (2006) presented the absolute V magnitude of the RGB bump with metallicity, and we obtained ${\rm{\Delta }}{M}_{V,\mathrm{bump}}/{\rm{\Delta }}$[Fe/H] ≈ 0.93 mag dex⁻¹ for 13 Gyr. The effect of helium abundances on the RGB bump can be found in Valcarce et al. (2012). From their Figure 9, we obtained ${\rm{\Delta }}{m}_{\mathrm{bol}}\approx 2.5\times {\rm{\Delta }}Y$ for the isochrones with $Z=1.6\times {10}^{-3}$ and 12.5 Gyr. If the 0.06 mag spread in the RGB bump magnitude in the Ca-w group is solely due to metallicity, one expects to see a spread in metallicity by Δ[Fe/H] ≈ 0.06 dex. Similarly, the 0.15 mag difference between the Ca-w and the Ca-s groups can translate into Δ[Fe/H] ≈ 0.16 dex, which agrees well with what Marino et al. (2011) obtained for the s-poor and the s-rich groups, Δ[Fe/H] ≈ 0.15 ± 0.02 dex. However, if we take into account the enhanced helium abundance for the Ca-s group by ${\rm{\Delta }}Y$ ≈ 0.09 (Joo & Lee 2013), the RGB bump magnitude for the Ca-s group should be $\approx \;0.08$ ($=\;0.23-0.15$) mag brighter than that for the Ca-w group, which is not the case for our observations. The formation of the EBHB stars, as progenies of the Ca-s RGB stars, may require the enhanced helium abundance, but the difference in the RGB bump magnitude is difficult to explain in this scenario. Might this suggest that only a fraction of the Ca-s RGB stars have evolved into EBHB?

In Figure 23, we show the number ratios of RGB stars in the Ca-s group to those in the Ca-w group against the radial distance from the center using the coordinates of the center by Goldsbury et al. (2010). It is worth noting that a weak gradient appears to exist in the number ratio between the two populations against the radial distance from the center, indicating that the distribution of the Ca-w group is slightly more centrally concentrated. However, the differences in the mean number ratio are in agreement within the measurement errors from the central part of the cluster up to ≈800 arcsec from the center, about four times the half-light radius of M22, similar to that seen in NGC 1851. Milone et al. (2008) showed that the number ratio between the two distinctive populations in NGC 1851 does not appear to vary up to 1.7 arcmin from the center, which is about two times the half-light radius of the cluster.⁷ The flat number ratio between the multiple populations in M22 and NGC 1851 is in sharp contrast with that in ω Cen. Bellini et al. (2009) found that both the intermediate-metallicity and metal-rich RGB populations are more centrally concentrated than is the metal-poor RGB population in ω Cen (see also Sollima et al. 2007).

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The relaxation time at the half-mass radius for ω Cen is about 10 Gyr (Harris 1996), and it is large enough that the later generation of stars in ω Cen may not have had sufficient time to be homogenized completely. As a consequence, the later generation of stars fails to achieve a radial distribution similar to the early generation of stars in the cluster. On the other hand, the relaxation times at the half-mass radius for M22 and NGC 1851 are about 1.7 and 0.7 Gyr, respectively, significantly smaller than that of ω Cen. If the SG of stars in M22 and NGC 1851 formed from gaseous ejecta expelled from the FG of stars, they might have enough time to become relaxed systems. In this regard, Decressin et al. (2008) claimed that stars initially centrally concentrated toward the center need about two relaxation times to achieve a complete homogenization throughout the cluster, and any radial difference among multiple stellar populations would be erased over the dynamical history of old GCs.⁸ However, it is also possible that the merger of two GCs can maintain a flat RGB number ratio in M22.

We show a comparison of cumulative distributions of RGB stars in both groups in the lower panel of Figure 23. As can be seen, the radial distribution of RGB stars in the Ca-w group is slightly more centrally concentrated. We performed a Kolmogorov–Smirnov (K–S) test, and we found that the probability of being drawn from identical populations is 0.1%, with a K–S discrepancy of 0.10, indicating that they have different parent populations. As we have demonstrated earlier, the difference in the radial distribution is not likely due to the field star contamination.

Although small, the difference in the distributions of RGB stars is difficult to understand within the current theoretical framework of the GC formation. If the SG of stars is formed from gas expelled from the FG of stars in the central part of the cluster (see Bekki 2010, for example), the SG of stars should have a more centrally concentrated distribution in the early history of the cluster. Also, importantly, if the complete homogenization had been achieved within a couple of relaxation times, the two different populations in M22 would be expected to have indistinguishable radial distributions.

We speculate that the difference in the radial distributions of RGB stars may suggest that either (or perhaps both) of the following is correct: (1) the Ca-s population did not form from the gaseous ejecta of the FG of stars, or (2) complete homogenization may require a much longer timescale than that proposed by Decressin et al. (2008). In this regard, the merger of two GCs can naturally explain the observed radial distributions of RGB stars.

We turn our attention to the spatial distributions of RGB stars in both groups. In the top panel of Figure 24, we show the projected spatial distributions of RGB stars in the Ca-w and Ca-s groups in M22. In the figure, the offset values of the projected right ascension and the declination in units of arcseconds were calculated using the transformation relations in van de Ven et al. (2006):

$$\begin{eqnarray}{\rm{\Delta }}{\rm{R.A.}} & = & \displaystyle \frac{648000}{\pi }\mathrm{cos}\delta \mathrm{sin}{\rm{\Delta }}\alpha ,\\ {\rm{\Delta }}\mathrm{decl}. & = & \displaystyle \frac{648000}{\pi }(\mathrm{cos}\delta \mathrm{cos}{\delta }_{0}-\mathrm{cos}\delta \mathrm{sin}{\delta }_{0}\mathrm{cos}{\rm{\Delta }}\alpha ),\end{eqnarray} \tag{ 3 }$$

where ${\rm{\Delta }}\alpha =\alpha -{\alpha }_{0}$ and ${\rm{\Delta }}\delta =\delta -{\delta }_{0}$, and ${\alpha }_{0}$ and ${\delta }_{0}$ are the coordinates of the center. For our calculations, we adopted the coordinates for the cluster center measured by Goldsbury et al. (2010).

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In the lower panel of the figure, we show smoothed density distributions of RGB stars along with isodensity contours for each population. For the smoothed density distribution of each population, we applied a fixed Gaussian kernel estimator algorithm with a FWHM of 70 arcsec (Silverman 1986). We show the FWHM of our Gaussian kernel in the lower left panel of the figure. To derive the isodensity contour for each population, we applied the second moment analysis (Dodd & MacGillivary 1986; Stone 1989). In the figure, we show the isodensity contour lines for 90%, 70%, 50%, and 30% of the peak values for both populations.

In a glance of the figure, the distribution of the Ca-s group appears to be spatially more elongated than that of the Ca-w group. In Table 6, we show the axial ratio, $b/a$, and the ellipticity, e $(=1-b/a)$, and we show radial distributions of the axial ratio and the ellipticity of the Ca-w and Ca-s groups in Figure 25. As shown, the radial distributions for both groups agree rather well up to ≈130 arcsec (≈1.5 core radii of the cluster) from the center, but the two distributions bifurcate at the larger radial distance, in the sense that the Ca-s group is more elongated.

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Table 6.  Ellipse Fitting Parameters

Pop.	Grid	Ellipse center		θ	$b/a$	e
		ΔX('')	ΔY('')
Ca-w	0.9	10.5 ± 0.4	4.2 ± 0.4	1.6 ± 1.4	0.929 ± 0.016	0.071
	0.8	10.1 ± 0.6	4.6 ± 0.6	3.2 ± 1.3	0.931 ± 0.015	0.069
	0.7	9.2 ± 0.7	5.2 ± 0.7	4.9 ± 1.2	0.937 ± 0.014	0.063
	0.6	7.9 ± 0.7	5.0 ± 0.8	7.3 ± 1.1	0.940 ± 0.013	0.060
	0.5	6.2 ± 0.8	4.3 ± 0.8	11.2 ± 1.0	0.943 ± 0.011	0.057
	0.4	3.5 ± 0.8	2.7 ± 0.8	17.4 ± 0.8	0.942 ± 0.010	0.058
	0.3	0.2 ± 0.7	−0.6 ± 0.8	24.3 ± 0.7	0.934 ± 0.008	0.066
	0.2	−2.3 ± 0.7	−5.2 ± 0.7	31.4 ± 0.5	0.912 ± 0.006	0.088
Ca-s	0.9	−6.6 ± 0.4	6.2 ± 0.4	15.3 ± 1.3	0.943 ± 0.015	0.057
	0.8	−3.3 ± 0.6	5.4 ± 0.6	18.9 ± 1.2	0.943 ± 0.014	0.057
	0.7	0.1 ± 0.7	3.6 ± 0.7	24.1 ± 1.1	0.944 ± 0.013	0.056
	0.6	3.8 ± 0.8	0.8 ± 0.7	29.2 ± 1.0	0.941 ± 0.011	0.059
	0.5	6.8 ± 0.8	−3.2 ± 0.8	35.4 ± 0.8	0.934 ± 0.010	0.066
	0.4	8.1 ± 0.8	−8.0 ± 0.8	42.7 ± 0.7	0.912 ± 0.008	0.088
	0.3	6.6 ± 0.7	−13.2 ± 0.8	41.8 ± 0.6	0.872 ± 0.006	0.128
	0.2	2.4 ± 0.7	−13.5 ± 0.7	37.6 ± 0.4	0.837 ± 0.005	0.163

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 In recent years, the nature of the multiple stellar populations of HB stars in GCs has emerged through detailed spectroscopic studies (e.g., Marino et al. 2013; Gratton et al. 2014; Marino et al. 2014a). Marino et al. (2013) studied seven HB stars in M22, and they found that all of their HB stars are Ba-poor and Na-poor, equivalent to the s-poor RGB population, leading them to suggest that the position of an HB star is strictly related to chemical composition. More recently, Gratton et al. (2014) investigated the chemical compositions of more than 90 HB stars in M22 using the multiobject spectroscopy facility. Their results showed that three different groups of HB stars appear to exist in M22. However, they did not find any severely O-depleted HB stars. They claimed that the progeny of the severely O-depleted RGB stars may evolve into the hotter part of the HB, where the surface temperature of these HB stars are beyond the temperature range of their sample.

In addition to metallicity and age, it is generally believed that the HB morphology of GCs can be governed by helium abundances (e.g., D'Antona et al. 2002; Joo & Lee 2013; Milone et al. 2014), and there also exists direct spectroscopic observational evidence of helium enhancement in GC HB stars (Gratton et al. 2014; Marino et al. 2014a).

In their recent work, Joo & Lee (2013) investigated M22 HB populations using synthetic population models. Although simplistic, they divided the M22 HB populations into two groups, the BHB and the EBHB, and they delineated a connection between the RGB and the HB of M22 (see their Figure 13). Here, we explore more details of the number ratio and the spatial distribution of the HB populations in M22 using our wide-field data. Note that the hk index is not a useful tool to study the BHB or the EBHB stars because the Ca ii H and K lines become suppressed, and the absorption strength of ${{\rm{H}}}_{\epsilon }$ at λ 3970 Å reaches its maximum at A0 and can contaminate the adjacent Ca ii H line at the high effective surface temperature of BHB or EBHB stars.

In Figure 26, we show CMDs of the HB region of M22. As for the RGB populations, we used all available multicolor information in order to remove the contamination from the off-cluster field-star population in our study. Also shown in the figure is the cumulative LF of the HB stars, where the slope in the cumulative LF of HB stars becomes briefly zero at the location of the HB gap at V = 15.97 mag. This magnitude is about the same magnitude level at which Joo & Lee (2013) separated the BHB and the EBHB populations in M22. Furthermore, Joo & Lee (2013) claimed that the BHB stars are the FG of stars (corresponding to the progeny of the Ca-w RGB population in our notation), and the EBHB stars are the SG of stars (the Ca-s population) of the cluster.

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In our photometric data, the observed number ratio between the BHB and the EBHB stars becomes n(BHB):n(EBHB) = 80:20 (±9), marginally in agreement with those of the RGB populations, n(Ca-w):n(Ca-s) = 69:31 (±3), and the SGB populations, n(bSGB):n(fSGB) = 69:31 (±6), without the correction for the evolutionary effect. With the correction for the evolutionary effect, the HB number ratio does not agree with that of SGB, n(bSGB):n(fSGB) = 62:38 (±6). Note that our HB number ratio includes the completeness correction that is shown in Figure 3. We calculated the average completeness fraction as a function of V magnitude using those from the central and outer part of the cluster, as shown in Figure 3, and we applied the correction factor to individual HB stars by interpolating the average completeness fraction against the V magnitude. As discussed above, our photometry is complete down to ≈18.5 mag. Therefore, only the the EBHB population is insignificantly affected $(\approx 0.6\%)$ by the completeness correction.

In the upper panel of Figure 27, we show the number ratios of the EBHB to the BHB populations against the radial distance from the center. Although the HB number ratios against the radial distance are in agreement within measurement errors up to about three times the half-light radius of the cluster, the mean HB number ratio appears to have a weak gradient against the radial distance, in the sense that the BHB stars are slightly more centrally concentrated than are the EBHB stars, similar to that seen in the RGB stars in Figure 23. In the bottom panel of the figure, we show the cumulative distributions of the BHB and EBHB populations against the distance from the center. The BHB population is more centrally concentrated than is the EBHB population, qualitatively consistent with that seen in the RGB populations. The K–S test indicates a probability of 1.8% that two HB populations are drawn from the same parent population, suggesting that they have different parent populations, as can be seen in the RGB stars.

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As done for the RGB and SGB populations, because of different masses and chemical compositions, the different lifetimes of individual HB stars should be taken into account. We compared the lifetimes between the BHB and the EBHB populations using the HB tracks by Joo & Lee (2013) and obtained the correction factor in terms of the number of HB stars, n(BHB):n(EBHB) = 56.5:43.5 (±4.0). Because the EBHB stars live longer, one naturally expects to observe a larger number of EBHB stars if initially even numbers of stars are distributed on both the BHB and EBHB locations.

In addition, the number of HB stars evolved from the Ca-w and Ca-s RGB populations will be slightly different because the RGB-tip masses between the two groups will be different. If the Ca-s population has a higher helium abundance by ${\rm{\Delta }}Y=0.09$ (Joo & Lee 2013), the evolution of stars in the Ca-s population would be faster than those in the Ca-w population due to increasing mean molecular weight, resulting in smaller RGB-tip masses in the Ca-s population. With the HB mass dispersion adopted by Joo & Lee (2013), ${\sigma }_{M}$ = $0.023{M}_{\odot }$ for both populations, we calculated the number of stars within $4\times {\sigma }_{M}$ from the RGB-tip masses⁹ of both isochrones using the same evolutionary population synthesis model that we constructed previously. For this purpose, we populated 10⁷ artificial stars in each group using Salpeter's IMF, and we generated 50 different sets for both groups. We obtained the correction factor, n(BHB):n(EBHB) = 58.9:41.1 (±0.1), in the sense that the observed number of HB stars that evolved from the Ca-s population gets larger because the RGB-tip mass of the Ca-s is smaller owing to its faster evolution from the MS through the RGB phases. If we take these effects into consideration, the number ratio between the BHB and EBHB stars becomes n(BHB):n(EBHB) = 88.2:11.8 (±9.8), significantly different from those of the RGB and the SGB populations. It should be noted that this result is based on the assumption that the BHB stars are the progeny of the Ca-w RGB stars and the EBHB stars are the progeny of the Ca-s RGB stars, as proposed by Joo & Lee (2013).

Our result may suggest that the connection between the RGB and HB populations may not be as clear as what Joo & Lee (2013) claimed. Note that Joo & Lee (2013) adopted the number ratio between the BHB and EBHB of 70:30 in their synthetic HB model construction, and they claimed that their HB number ratio does not disagree with the previous estimates by others of RGB or SGB number ratios between the two populations. It is thought that Joo & Lee (2013) overestimated the EBHB fraction in their calculation compared to our observation. As Joo & Lee (2013) suggested, if the EBHB population is the only progeny of the SG of the RGB population (i.e., the Ca-s population), the discrepancy in the number ratios between the two populations in the HB and SGB/RGB is difficult to explain. For instance, it is evident that the R value, the number ratio of the HB to the RGB stars (Caputo et al. 1987), of each population is against the theoretical expectation. The observed R value of a simple stellar population is the measure of the helium abundance in the sense that the R value increases with the helium abundance. We define the modified R value, which includes RGB stars from ${V}_{\mathrm{HB}}$ (=14.15 mag for M22) to 12.0 mag (not the tip of the RGB sequence), because we already selected bright RGB stars with 12 mag $\leqslant \ V\ \leqslant$ 16.5 mag in both populations, as discussed above. Then we have the modified R values of 1.73 ± 0.14 for the BHB versus the Ca-w RGB populations and 1.21 ± 0.17 for the EBHB versus the Ca-s RGB populations. If the EBHB and the Ca-s RGB populations are the SG of the stars in the cluster and they formed out of interstellar gas enriched in helium by the FG of stars, one would naturally expect to have a larger R value for the EBHB and the Ca-s RGB populations. However, the observed R value for the EBHB and the Ca-s RGB populations is smaller than that for BHB and the Ca-w RGB populations, and the observed R values are the opposite of the theoretical expectation. Our result may suggest that, like other lighter elemental abundances, there may exist a spread in the helium abundance of the SG of stars, and at least about half of the Ca-s RGB stars must have evolved into the BHB sequence (which requires no or little helium enrichment), and a significant fraction of the Ca-s RGB stars failed to become EBHB stars (which requires a helium enrichment of ${\rm{\Delta }}Y\ \approx$ 0.09; see Joo & Lee 2013) in M22.

It would be very interesting to point out the recent result by Gratton et al. (2014). They carried out a spectroscopic survey of the BHB stars in M22 and found a significant fraction (≈18%) of metal-rich helium-enhanced BHB stars in their sample (Group 3 designated by Gratton et al.). If we consider that the Group 3 BHB stars by Gratton et al. (2014) are the progeny of the Ca-s RGB stars, the number ratio between the SG and the FG of HB stars becomes 34:66, and this number ratio is in good agreement with those from the RGB and the SGB stars. Perhaps this is also hinted at by the separate Na–O distribution of M22 RGB stars, indicative of internal He spread in both the Ca-w and the Ca-s groups. If so, the Ca-s population of M22 may be exactly what we observe in NGC 6752, which contains both the BHB and the EBHB populations maintaining a rather monotonous metallicity distribution.

First, we estimated the mean rotation of the cluster by using the radial velocity distribution against the position angle of individual stars (Peterson & Cudworth 1994). In Figure 29, we show the radial velocities of individual stars in each group against their position angles measured from North. We chose the RGB stars¹⁰ with a proper motion membership probability larger than 90% from Peterson & Cudworth (1994), and we merge their radial velocity measurements with our photometric data. We show the radial velocities from Peterson & Cudworth (1994) against the position angle for individual RGB stars in Figure 29(a). We performed a sinusoidal fit to the data, and we obtained an amplitude of the mean rotation of all RGB stars of about 4.2 km s⁻¹, which is comparable to that from Peterson & Cudworth (1994), 3.8 km s⁻¹ (Meylan & Heggie 1999).

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Next, we investigate the mean rotational velocity of the Ca-w and Ca-s groups. We divided the RGB stars from Peterson & Cudworth (1994) into two groups based on the hk index of individual stars in Figure 7, and we show plots of radial velocities against the position angle of RGB stars in the Ca-w and Ca-s groups in Figures 29(b) and (c). The amplitude of the sinusoidal fit to the Ca-w group is about 3.6 km s⁻¹, whereas that to the Ca-s group is about 5.6 km s⁻¹. The amplitude of the projected rotation of the Ca-s group is larger than that of the Ca-w group.

We carried out the same procedure using the radial velocities by Lane et al. (2009). As shown in the bottom panels of Figure 29, similar results can be found from the radial velocity data by Lane et al. (2009), although the mean radial velocities and the amplitudes of the mean rotation are different from those from Peterson & Cudworth (1994). We obtained the amplitude of mean rotation for the Ca-w group at about 1.5 km s⁻¹, while that for the Ca-s group is about 3.6 km s⁻¹. Again, the amplitude of the mean rotation for the Ca-s group is larger than that for the Ca-s group.

It should be noted that the difference in the mean radial velocities of the cluster using the data from Peterson & Cudworth (1994), −149.1 km s⁻¹, and Lane et al. (2009), −144.6 km s⁻¹, may suggest that the two sets of radial velocity data are heterogeneous. Therefore, we did not attempt to merge the two sets of data to investigate the rotation of the cluster. The amplitude of the mean rotation using the data by Lane et al. (2009) is smaller than that by Peterson & Cudworth (1994). Because the number of RGB stars being used is smaller for the case using data by Peterson & Cudworth (1994), it is suspected that a few stars with large deviations from the mean velocity can affect the results. In the upper panel of Figure 29, the radial velocities of three RGB stars deviate more than 3 σ levels from the mean value: IV-20 (−166.78 km s⁻¹), 2–73 (−127.65 km s⁻¹), and I-27 (−127.51 km s⁻¹). If we exclude these three stars in our calculations, the amplitudes of the mean rotations become 2.7, 2.5, and 3.3 km s⁻¹ for all RGB stars, the Ca-w groups, and the Ca-s groups, respectively. These values become comparable to those using data from Lane et al. (2009).

Next, we estimated the amplitude of the mean rotation of the cluster using the method described by Lane et al. (2009). Assuming an isothermal rotation, the mean rotation can be measured by dividing the cluster in half at a given position angle and calculating the differences between the average velocities in the two halves. We repeated this calculation by increasing the position angle of the boundary of the two halves by ${10}^{\circ }$. Then the net rotation velocity is half of the amplitude of the sinusoidal function in the differences between the average velocities in the two halves.

We show the differences in the mean radial velocities as a function of position angle (east = ${0}^{\circ }$ and north = ${90}^{\circ }$) along with the best-fitting sine function in Figure 30. Our result for all RGB stars in the cluster is shown in the top panel of the figure. We obtained the mean rotation velocity of 1.4 ± 0.3 km s⁻¹ and the position angle of the equator (i.e., the axis perpendicular to the rotation axis) of the rotation of ${76}^{\circ }$ (i.e., ≈north), which are very consistent with those of previous studies by Lane et al. (2009, 2010), 1.5 ± 0.4 km s⁻¹ and approximately north-south, respectively.

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In the middle and bottom panels of Figure 30, we show plots of differences in the mean radial velocities for the Ca-w and Ca-s groups. We obtained the mean rotation of 1.0 ± 0.4 km s⁻¹ with the position angle of ${89}^{\circ }$ for the Ca-w group and 2.5 ± 0.8 km s⁻¹ with the position angle of ${64}^{\circ }$ for the Ca-s group. Again, the amplitude of the mean rotation of the Ca-s group is slightly larger than that of the Ca-w group.

Note that the mean rotations of this method are smaller than those of the sinusoidal fit to individual stars on the radial velocity versus position angle. As we have demonstrated above, the sinusoidal fit to the individual stars is suspected to be vulnerable to stars with large velocity deviations from the mean value. This may explain the difference in the amplitudes of the mean rotation between the two methods.

Finally, we examine the rotation of the cluster by using the radial velocity profile along the axis perpendicular to the mean rotation. In the top panel of Figure 31, we show the distributions of RGB stars in the Ca-w and Ca-s groups with the radial velocity measurements. In the figure, the blue and red colors denote blueshift and redshift from the mean radial velocity of the cluster, respectively, and the size of each circle represents the velocity deviation from the mean value of the cluster. We also show grids for calculating the group velocity and the velocity dispersion with rectangles with a width of 800 arcsec and a height of 100 arcsec. We adopt the tilted angle of the grid rectangles that we obtained in Section 4.6.2, 89${}^{\circ }$ for the Ca-w group and ${64}^{\circ }$ for the Ca-s group.

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We calculated the mean radial velocity and the velocity dispersion in each grid rectangle. Our results are shown in the bottom panels of Figure 31. Inside the half radius of the cluster, the velocity dispersion of the Ca-s population appears to be slightly larger, consistent with our previous result presented in Section 4.5. Also, the radial velocity profile against the projected distance perpendicular to the rotation axis is different.

We performed a least squares fit to the line-of-sight velocity versus the projected distance perpendicular to the rotation axis. We found a maximum velocity of 1.0 km s⁻¹ for the Ca-w group and 4.3 km s⁻¹ for the Ca-s group at the half-light radius of the cluster. Again, the RGB stars in the Ca-s group appear to rotate faster than do those in the Ca-w group,consistent with our previous results.

We examined the anisotropy parameter of the cluster (see, for example, Bender et al. 1991):

$$\begin{eqnarray}&&{\left(\displaystyle \frac{{V}_{\mathrm{rot}}^{\mathrm{max}}}{{\sigma }_{{\rm{m}}}}\right)}^{*}=\left(\displaystyle \frac{{V}_{\mathrm{rot}}^{\mathrm{max}}}{{\sigma }_{{\rm{m}}}}\right)\sqrt{(1-e)/e}\end{eqnarray} \tag{ 5 }$$

where ${\sigma }_{{\rm{m}}}$ is the mean velocity dispersion and e is the ellipticity of the cluster. Note that ${\left({V}_{\mathrm{rot}}^{\mathrm{max}}/{\sigma }_{{\rm{m}}}\right)}^{*}$ $\ll$ 1 indicates strong anisotropy. Using the relation above, we obtained the anisotropy parameter ${\left({V}_{\mathrm{rot}}^{\mathrm{max}}/{\sigma }_{{\rm{m}}}\right)}^{*}$ = 0.707 for the Ca-w group and 1.62 for the Ca-s group, where we adopted e = 0.074, ${V}_{\mathrm{rot}}^{\mathrm{max}}$ = 1.0 km s⁻¹, and ${\sigma }_{{\rm{m}}}$= 5.0 km s⁻¹ for the Ca-w group and e = 0.106, ${V}_{\mathrm{rot}}^{\mathrm{max}}$ = 4.3 km s⁻¹, and ${\sigma }_{{\rm{m}}}$ = 7.7 km s⁻¹ for the Ca-s group. For ellipticity, we used the simple mean of those given in Table 6 within about 210 arcsec from the center (i.e., about the half-light radius of the cluster). The large values of anisotropy parameters for both populations suggest that the flattening observed in M22 most likely originates from the presence of internal rotation.