Structure of our Galactic Bulge from CN Measurements
aa r X i v : . [ a s t r o - ph . GA ] A p r D RAFT VERSION A PRIL
22, 2019Typeset using L A TEX twocolumn style in AASTeX62
Structure of our Galactic Bulge from CN Measurements J AE -W OO L EE Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro, Gwangjin-Gu, Seoul, 05006, Republic of Korea; [email protected],[email protected]
ABSTRACTThe double red clumps (DRCs) are now dominantly believed to be the strong observational line of evidenceof the so-called X-shaped Galactic bar structures. Recently, Y.-W. Lee et al. (2018) reported a subtle mean δ CN(3839) difference between the DRCs and suggested a dichotomic picture that can be seen in globular clus-ters: the faint red clump is the first generation, while the bright red clump corresponds to the second generation(SG). They argued that the magnitude difference between the DRCs is due to different stellar populations, andis not due to the geometric difference between the DRCs. Our reanalysis shows that their data do not appear tosupport the idea of the multiple population-induced DRCs in our Galactic bulge. We perform fully empiricalMonte Carlo simulations and find that the shape of the δ CN(3839) distributions is the most stringent evidenceto pursue. Our results strongly suggest that the CN distributions toward the Galactic bulge are qualitativelyconsistent with the X-shaped Galactic bulge with a minor fraction of the SG of about 2 – 3%.
Keywords:
Galaxy: bulge – Galaxy: structure – Galaxy: formation – stars: abundances – stars: evolution –globular clusters: general INTRODUCTIONThe CN molecules have played some important rolesin stellar astrophysics for more than one hundred years(Lindblad 1922), because usually very strong CN absorp-tion strengths can easily be detectable with great accuracynot only in low-resolution spectroscopy but also in photom-etry (see, e.g., McClure & van den Bergh 1968; Lee 2017,2018, 2019a). In recent years, the study of CN molecu-lar bands, especially in the blue where the distinctive bandfeatures exist, regained its popularity since the CN measure-ments appear to provide promptly pivotal information on themultiple populations (MPs) in globular clusters (GCs).However, the understanding of the line formation ofmolecular bands may not be as simple as it might seem.For example, the rate of CN molecule formation depends onvarious factors: (1) The available carbon and nitrogen atomsthat will be involved in the CN molecule formation dependon abundances of other molecules, such as, NH, CH, C , andCO (see, e.g., Tsuji 1973). These diatomic molecules havedifferent dissociation energies and therefore they experiencedifferent degrees of the luminosity effect and temperature ef-fect. Similar to other molecules, CN also suffers from lumi-nosity and temperature effects to a rather serious degree (see,e.g., Gray & Corbally 2009). (2) The CN band strengths canalso be affected by the metallicity effect, in particular throughthe degree of the formation rate of the negative hydrogen ion,which is the dominant continuum opacity source in cool stars(see, e.g., Suntzeff 1981; Lee 2015). (3) The C/ C ratio can affect the CN band strengths, in particular the CN bandat λ δ CN(3839), to delineatethe relative CN contents in a GC. Basically, they defineda lower envelope in a plot of the CN(3839) versus V mag-nitude and then they derived the relative CN(3839) offsetvalues from the baseline at a given magnitude to estimatethe relative CN contents. This approach can overcome theluminosity and temperature effects to some degree withoutdifficulty. Through this procedure, they constructed a con-crete picture of the bimodal CN distributions in GC red giantbranch (RGB) stars. The CN(3839) index used in this Letter is not exactly the same as thatdefined by Norris et al. (1981), S (3839). The CN(3839) index is definedby Harbeck et al. (2003) in their study of the main-sequence stars to avoidthe contamination from the hydrogen Balmer lines, which become strongerin dwarf stars as with the Stark effect. Therefore the bandwidth and thecontinuum sideband of the CN(3839) are different from those of S (3839),and it is very unfortunate that any direct comparisons between these twoindices should be avoided. L EE It should be emphasized that this approach must be appliedto a simple population with similar surface gravity and ef-fective temperature. In heterogeneous systems, the magic of δ CN(3839) is no longer effective (see, e.g., Lee 2015). Atthe same time, using the baseline, not the linear fit to thedata, can be very critical when comparing relative CN con-tents with different luminosities or effective temperatures. Inspite of its objectiveness, the results from the linear fit canbe vulnerable to the incompleteness of the sample, which wewill discuss later. Therefore, the δ CN(3839) index can be aversatile but deceptive tool.In our work, we reanalyze the CN measurements towardthe Galactic bulge field by Y.-W. Lee et al. (2018, hereafterYWL18), and find that their results are peculiarly biased. Inour work, we will focus on the CN(3839) and δ CN(3839).The CN(4142) and CH(4300) indices tend to not show clearbifurcation as the CN(3839) and δ CN(3839) do between MPsin GCs, and the former two indices may have potential prob-lems with the continuum sideband assignments (Lee 2019b). NOTES ON Y.-W. LEE ET AL. (2018)Before we proceed further, we would like to discuss fourpoints on the results presented by YWL18.First, in Figure 4 of YWL18, it is clear that the range ofthe CN(3839) dispersion of the bright RGB (bRGB) starswith K S . σ [CN(3839)]= 0.15, while σ [CN(3839)] = 0.21, 0.24, and 0.25 for thebright red clump (bRC), faint red clump (fRC), and faintRGB (fRGB), respectively. We performed randomizationtests to see if the CN distribution of the bRGB is the sameas other groups, and we found very low probabilities of thebRGB being drawn from the empirical distributions of bRC,fRC, and fRGB, 5.74 ± ± ± From a statistical perspective, it can besaid that the bRGB is a totally alien population.
In addition,what is more difficult to understand is that the locations of thebRGB stars tend to occupy the CN-weak side of the plot. Aswe will show later, the standard deviations from each mag-nitude bin should be similar, if they were drawn from unbi-ased parent distributions. Furthermore, if these bRGB starswere selected from an unbiased sample and they were reallybright RGB stars with a mixture of the first generation (FG)and the second generation (SG) of stars as can be found inGCs, bf the σ [CN(3839)] of the bRGB group is expected tobe slightly larger than those of other groups due to the well-known luminosity effect (see, e.g., Figure 16 of Lee 2015). Our randomization tests for the HK ′ , whose science band lies right nextto the CN band at λ ± ± ± ′ domain. Second, YWL18 adopted a linear fit to remove the lumi-nosity effect assuming that all their sample stars are homo-geneous and are located at the same distance from us. Aswe already mentioned, using the lower envelope baseline isa more fail-free approach. By doing that, the CN differencebetween the bRC and fRC found by YWL18 can be natu-rally reduced or even erased and, as a consequence, a null δ CN(3839) gradient between the bRC and fRC can be estab-lished.Third, due to the presence of the RGB bump (RGBB)and the increasing stellar number density with magnitude(e.g., see Figure 1), the fRC can contain a considerableamount of the SG in a picture of the MP-induced double redclumps (DRCs). As we will show later, the DRCs in a sin-gle bar structure with the empirical luminosity function (LF)of 47 Tuc, the number ratios between the FG and SG, areabout 16:84 and 70:30 for bRC and fRC, respectively, whichweaken the argument raised by YWL18.Finally, as we will show later, the presence of the mirror-image asymmetric δ CN(3839) distributions is a more strin-gent observational line of evidence of the MPs as the originof the DRCs. A subtle change in the mean δ CN(3839) caneasily be sneaked depending on the adopted slope of the fit-ted line, especially in heterogeneous stellar systems. In sharpcontrast, the shape of the δ CN(3839) distribution is less vul-nerable to such artifacts. It is fair to mention that the asym-metric distributions were also hinted at YWL18 in a weakform in their Figure 3, but their results failed to show it. MONTE CARLO SIMULATIONS FOR THE DRCS:SYMMETRIC, SKEWED, AND ASYMMETRICMIRROR-IMAGE DISTRIBUTIONS ARE INVOLVED3.1.
The Red Clump Frequencies of 47 Tuc and theIntermediate-age Large Magellanic Cloud clusters: ASanity Check
In order to understand the behavior of the CN distributionbetween the DRCs with different groups of stars, we con-structed fully empirical models to perform Monte Carlo sim-ulations using our high-precision multicolor photometry of47 Tuc.In Figure 1, we show our CMD and LF of the bright starsin the metal-rich ([Fe/H] = − ◦ × ◦ photometric study, aimedat revealing the MPs of the cluster, and will be published ina forthcoming paper. Our LF of the cluster shows the pro-nounced RHB bump (RHBB) and RGBB as well.47 Tuc is slightly more metal poor than the mean metal-licity of the RGB stars in the high galactic latitude bulgeN T OWARD G ALACTIC B ULGE F IELD Figure 1.
Left top panels: the CMD and the LF for 47 Tuc. The cn JWL versus V CMD for RHB (red dots) and RGB (gray dots) stars in 47 Tucis shown in the inset. Right panels: CMDs and LFs for 14 LMC star clusters. r cls and r HM denote the cluster and the half-mass radii, while f ( g − i ≥ .
65) denotes the normalized number of stars with ( g − i ) ≥ .
65 mag.
Table 1.
The observed RHB and RC frequencies per unit magni-tude Obj n (RC)/ n (bRGB) n (RC)/ n (fRGB)47 Tuc (RHB) 6.37 2.40LMC (All | g − i ≥ r cls | g − i ≥ r HM | g − i ≥ field, ( l , b ) ≈ (1 ◦ , − . ◦ − < [Fe/H] < +0.3, with a median of about − ≈ − Ingredients for Models
The detailed underlying basic schemes are already givenin our previous work (see Lee 2015), and here we briefly dis-cussed observational ingredients of our models. We adoptedour 47 Tuc’s LF as shown in Figure 1, where our cn JWL ofthe RHB stars are superposed onto the RGB. In our previ-ous study, we showed that our cn JWL index is a very accuratephotometric measure of CN(3839) and therefore our resultssuggest that the CN(3839) of the RHB should be very similarto that of the RGB stars with a similar magnitude (Lee 2017,2018, 2019a). We extracted the CN-weak (the first gener-ation, FG) and CN-strong (the second generation, SG) se-quences of NGC 362 from Lim et al. (2016), who employedthe same CN(3839) index that YWL18 adopted, and we de-rived the fiducial sequences for both populations. Then wecalculated the scatters of individual stars around the fiducialsequences, finding σ [CN(3839)] ≈ σ [CN(3839)] ≈ Single RC Population in an X-shaped Bulge+Minor SGPopulation
First, we developed a model for the single RC popu-lation in an X-shaped Galactic bulge, which is a domi- L EE Figure 2.
Plots of the synthetic CN(3839) versus M V , LFs, and the CN(3839) distributions of the bRGB (green), bRC (red), fRC (blue), andfRGB (dark gray). nantly accepted picture for our Galactic bulge (see, e.g.McWilliam & Zoccali 2010; Wegg & Gerhard 2013). In ourmodel, we allocated the even number of stars to the individ-ual bar branches and we assumed that they are all composedof the FG population. In addition to the DRCs, we also addeda minor SG population (an additional 10% of the total num-ber of stars).Figure 2 shows plots of the CN(3839) versus M V , LFs,and δ CN(3839) distributions for two sets of models with σ [CN(3839)] = 0.06 and 0.20. To calculate δ CN(3839), weadopted the scheme that Norris et al. (1981) devised. The in-fluence of the RGBBs is noticeable in LFs: the RGBB of thefRC population is clearly visible at M V ≈ δ CN(3839) value at the peak of the bRC distribution isslightly smaller than that of the fRC, but we strongly believethat this small difference should not be considered as con-clusive evidence. Instead, the shape of the δ CN(3839) distri-bution, which is almost independent of the adopted baselineduring the δ CN(3839) calculations, provides a more informa-tive and, perhaps, the most practical probe to explore the ex- istence of the SG population in our Galactic bulge. Withoutthe minor SG population, the shapes of all δ CN(3839) distri-butions are almost symmetric: not only the bRC and fRC butalso the bRGB and fRGB. When some fractions of the minorSG population are included, the shapes of the δ CN(3839) dis-tribution show a weak secondary peak at larger δ CN(3839)regimes.In the case of σ [CN(3839)] = 0.20, which is for the hetero-geneous stellar populations with a metallicity spread, the in-clusion of the minor SG population makes all the δ CN(3839)distributions skewed to larger δ CN(3839), not to smaller δ CN(3839).3.4.
Double RC Populations in a Single Bar
To examine the idea proposed by YLW18, we constructedmodels for a single Galactic bar with MPs, where the fRCcorresponds to the FG population, while the bRC corre-sponds to the SG population. Our results are shown in Fig-ure 2.In the model with a GC-like dispersion, i.e., σ [CN(3839)]= 0.06, the discrete double sequences are eminent for allmagnitude regimes. Moreover, the shape of the δ CN(3839)distributions of the bRC and fRC show a mirror-image char-acteristic, leaving a distinctive and the most profound observ-N T
OWARD G ALACTIC B ULGE F IELD Figure 3. (Left panels) Plots of the CN(3839) and δ CN(3839)against K S . The solid line denotes the fitted line by YWL18, whilethe dashed line denotes our baseline. In the bottom panel, a groupof stars shown with star marks is most likely the SG in our Galacticbulge. (Middle panels) Histograms for the CN(3839) distributions.The gray, blue, red, and green solid lines denote the CN(3839) and δ CN(3839) distributions of the fRGB, fRC, bRC, and bRGB, re-spectively. Note that the bRGB does not agree with those fromother groups, a strong evidence that the bRGB sample by YWL18is heavily biased. (Right panels) Stars classified as main-sequencesor sub-giants from the second
Gaia date release. able footprint, which has not been observed so far. For bothRGB regimes, the relative frequencies of the peaks with alarge δ CN(3839) are slightly larger than those of the peakswith a small δ CN(3839), due to slight differences in the evo-lutionary speed with luminosity.In the case of σ [CN(3839)] = 0.20, the δ CN(3839) dis-tributions of the bRC and fRC are asymmetric and show amirror-image characteristic, while those of the RGB regimesshow near-symmetric distributions, which show very differ-ent characteristics from those from a single RC population inan X-shaped bulge.3.5.
Comparisons with YWL18
In Figure 3, we show plots of CN(3839) and δ CN(3839)against K S and histograms for each group of stars thatYWL18 studied. As we mentioned earlier, the slope fromthe fitted line adopted by YWL18 is slightly different fromthe slope of the baseline that is conventionally used. In thefigure, it is very clear that the histograms for the bRGB arein total disagreement with those of other groups, suggestingthat the bRGB sample must have been heavily biased. Noneof our simulations can explain this strange behavior of thebRGB stars. This is very critical in comparing δ CN(3839) values from different magnitudes as the way YWL18 did, asit is most likely that they relied on the biased reference fittedline to derive their δ CN(3839). It is strongly believed that theCN gradient between the bRC and fRC reported by YWL18is not real but is mainly due to the incorrect assignment ofthe reference line.We emphasize that the observed δ CN(3839) distributionsother than the bRGB are qualitatively very consistent withour results from the single RC population in an X-shapedGalactic bulge with a minor SG population. If this is thecase, about 11 stars ( ≈ δ CN(3839) & Gaia data release canprovide a wonderful opportunity to assure the evolutionarystage of YWL18’s sample. We cross-matched the coordi-nates of the YWL18’s sample and we were able to identify25 stars. Unfortunately, all of them were turned out to be ei-ther the dwarf or subgiant based on the radius and luminosityestimates (Andrae et al. 2018).In Figure 3, we also show plots of the CN(3839) and δ CN(3839) versus K S for the known dwarfs and subgiantsin YWL18’s sample. We calculated the δ CN(3839) differ-ence for the dwarfs and subgiants, finding that ∆ δ CN(3839)= 0.155 ± δ CN(3839) value of the dwarfs and subgiants included inthe bRC group is larger than that in the fRC. Furthermore, ∆ δ CN(3839) from the dwarfs and subgiants is consistentwith that between the bRC and fRC found by YWL18, ∆ δ CN(3839) = 0.125 ± δ CN(3839) gradient argued by YWL18 is most likely an ar-tifact. In sharp contrast, from our analysis the ∆ δ CN(3839)between the two groups of dwarfs and subgiants is 0.100 ± δ CN(3839) becomes almostnull, which is very natural to expect.Our exercises presented here strongly suggest that the δ CN(3839) gradient between the two RCs reported byYWL18 is mainly due to two reasons: (1) the use of an incor-rect assignment of the reference line in deriving δ CN(3839),and (2) the inclusion of the nonnegligible fraction of the mis-representative samples. Therefore, one can naturally arguethat the results presented by YWL18 do not support the ideaof the MP-induced DRCs in our Galactic bulge. SUMMARY AND DISCUSSIONIn order to understand what stellar populations constitutethe X-shaped Galactic bulge, we performed fully empiri-cal Monte Carlo simulations. In sharp contrast to YWL18,who argued a small δ CN(3839) difference between the DRCsas conclusive observational evidence, our study highlightedthe importance of examining the shape of the δ CN(3839)distributions to understand underlying stellar populations.Our results strongly suggested that the CN measurements by L EE YWL18 are qualitatively more consistent with the X-shapeGalactic bulge with a minor SG fraction of about 2 – 3 %(see, e.g., Martell et al. 2011). We also showed the inclu-sion of a nonnegligible fraction of dwarfs and subgiants inthe sample by YWL18. Furthermore, their bRGB sample ap-peared to be severely and quizzically biased, insufficient forbeing a reference in deriving the δ CN(3839) index.If about an half of the Galactic bulge stars are formerly GCSG stars that are now dissolved, as YWL18 suggested, thenone can anticipate the clear and present difficulty of the ab-sence of the reservoir of the dissolved FG population, whichsupplied an enormous amount of lighter elements to make theSG population that is now observed as the bRC, as YWL18claimed. The total mass of our Galactic bulge is about 2 × M ⊙ , which is about 1000 time more massive than the to-tal mass of the Galactic GCs (see, e.g., Valenti et al. 2016).One of the unsolved problems in the formation of GCs withMPs is the so-called mass-budget problem. To explain thechemical evolution of GCs, at least about 10 to 100 timesmore FG stars were required in the past to form the SG pop-ulation than can be found in GCs, and most of the FG pop-ulations in Galactic GC systems must have been lost duringthe early phases of the GC evolution. The main body of ourGalaxy must have been the reservoir of the GC FG stars that are now dissolved. Then where did the FG of the bRC go?If about the half of the Galactic bulge is the SG, then morethan about 10 – 10 M ⊙ of the formerly GC FG stars nowdissolved in our Galaxy, including the Galactic bulge, whichwill make the populational number ratio of 10 – 100:1 be-tween the FG and SG. In our Galactic bulge, however, thepopulational number ratio should be about 1:1 between theFG and SG based on the observed number ratio between thefRC and bRC, and the number simply does not add up in thedichotomic population picture by YWL18.We strongly believe that, for example, sodium abundancemeasurements from high-resolution spectroscopy with goodestimates of the stellar parameters will shed more light on theMPs in our Galactic bulge in the future.J.-W.L. sincerely thanks the Lord for having extremely badweather conditions and fatal instrument failures during hisobserving run in 2019 February, which enabled him to con-ceive the idea and complete this work in a very short periodof time. The anonymous referee is thanked for useful com-ments. Financial support from the Basic Science ResearchProgram (grant No. 2016-R1A2B4014741) through the Na-tional Research Foundation of Korea (NRF) funded by theKorea government (MSIP) is acknowledged.REFERENCESof the formerly GC FG stars nowdissolved in our Galaxy, including the Galactic bulge, whichwill make the populational number ratio of 10 – 100:1 be-tween the FG and SG. In our Galactic bulge, however, thepopulational number ratio should be about 1:1 between theFG and SG based on the observed number ratio between thefRC and bRC, and the number simply does not add up in thedichotomic population picture by YWL18.We strongly believe that, for example, sodium abundancemeasurements from high-resolution spectroscopy with goodestimates of the stellar parameters will shed more light on theMPs in our Galactic bulge in the future.J.-W.L. sincerely thanks the Lord for having extremely badweather conditions and fatal instrument failures during hisobserving run in 2019 February, which enabled him to con-ceive the idea and complete this work in a very short periodof time. The anonymous referee is thanked for useful com-ments. Financial support from the Basic Science ResearchProgram (grant No. 2016-R1A2B4014741) through the Na-tional Research Foundation of Korea (NRF) funded by theKorea government (MSIP) is acknowledged.REFERENCES