The Hubble Space Telescope UV Legacy Survey of Galactic Globular Clusters. XXII. Relative ages of multiple populations in five Globular Clusters
AAstronomy & Astrophysics manuscript no. raGCs_v9 ©ESO 2020December 15, 2020
The
Hubble Space Telescope
UV Legacy Surveyof Galactic Globular Clusters
XXII. Relative ages of multiple populations in five Globular Clusters.
F. Lucertini , D. Nardiello , , G. Piotto , Departamento de Física, Faculdad de Ciencia Exactas, Universidad Andrés Bello, Fernández Concha 700, Santiago,Chile Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France Istituto Nazionale di Astrofisica - Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, Padova, IT-35122 Dipartimento di Fisica e Astronomia "Galileo Galilei", Universitá di Padova, Vicolo dell’Osservatorio 3, PadovaIT-35122Received XXX ; accepted YYY
ABSTRACT
Aims.
We present a new technique to estimate the relative ages of multiple stellar populations hosted by five globularclusters: NGC 104 (47 Tuc), NGC 6121 (M4), NGC 6352, NGC 6362 and NGC 6723.
Methods.
We used the catalogs of the database “HST UV Globular cluster Survey (HUGS)” to create color-magnitudeand two-color diagrams of the Globular Clusters. We identified the multiple populations within each globular cluster,and we divided them into two main stellar populations: POPa or first generation (1G) and POPb, composed of all thesuccessive generations of stars. The new technique allows us to obtain an accurate estimate of the relative ages betweenPOPa and POPb.
Results.
The multiple populations of NGC 104 and NGC 6121 are coeval within 220 Myr and 214 Myr, while those ofNGC 6352, NGC 6362 and NGC 6723 are coeval within 336 Myr, 474 Myr and 634 Myr, respectively. These results wereobtained combining all the sources of uncertainties.
Key words.
Techniques: photometric – Stars: Population II – (Galaxy:) globular clusters: general
1. INTRODUCTION
The concept that Galactic Globular Clusters (GCs) hostmultiple stellar populations is supported by an overwhelm-ing amount of observational facts, and accepted by the as-tronomical community. However, the origin and the time-scales for the formation and the evolution of multiple pop-ulations (MPs) are still under debate and study. The mostaccredited scenarios support that MPs phenomenon in GCsis due to multiple events of star formation. These formationscenarios consider the existence of a first generation (1G)characterized by stars having chemical properties similar tothat of the interstellar medium out of which they formed,and a second generation (2G), formed from the materialprocessed by 1G stars. Among the proposed alternatives toexplain 2G stars, the intermediate mass Asymptotic giantbranch (AGB) scenario (D’Antona et al. 2002) predicts that2G stars were born from the AGB ejecta within 100 Myr(D’Ercole et al. 2012). On the other hand, de Mink et al.(2009) proposed that 2G population was born from pro-cessed low-velocity material ejected by massive binaries ina time-scale of ∼ M ∼ M (cid:12) as 1G stars, Denissenkov & Hartwick (2014)demonstrated that 2G stars from in 10 yr. Therefore, therelative age of MPs can provide clues about formation andevolution of these populations and can also discriminateamong the different scenarios proposed. In the last years, the investigation of MPs was expandedto GCs outside the Milky Way (MW). The fact that notonly our Galaxy hosts MPs allows us to compare GCsformed in systems with different star formation histories,providing clues on MPs phenomenon. Moreover, it turnsout that the environment is not one primary requirementof MPs formation. Nardiello et al. (2019) analyzed the stel-lar populations within the GC Mayall II (G1), located inthe halo of the nearby Andromeda galaxy. Several worksfocused on the discovery that intermediate age (1-2 Gyr)clusters in the Magellanic Clouds show extended main se-quence turn off and splitted main sequence (MS) (Saracinoet al. 2019, Gilligan et al. 2019, Martocchia et al. 2019).Bastian & de Mink (2009) proposed the rotational veloc-ity of stars with masses between 1.2-1.7 M (cid:12) to explain thepresence of double MS. The age is another fundamentalfactor, since the lower age limit of a star cluster to showMPs is 2 Gyr (Martocchia et al. 2017). The MPs in theyoung star cluster NGC 1978 in the Magellanic Clouds arecoeval within 1 ±
20 Myr (Martocchia et al. 2018). Similarly,Saracino et al. (2020) found that the star cluster NGC 2121hosts coeval MPs within 6 ±
12 Myr. These results revealthat young GCs put tighter constraints than older ones onthe MPs formation timescale.The Treasury program “The Hubble Space Telescope (HST)UV Legacy Survey of Galactic Globular Clusters” (GO-
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2. OBSERVATION AND DATA REDUCTION
In this work we used the catalogs obtained in the project“HST UV Globular cluster Survey" (HUGS , Nardielloet al. 2018a). For a detailed description of the data-reduction pipeline used to obtain these catalogs, we re-fer the reader to Bellini et al. (2017) and Nardiello et al.(2018b). The catalogs contain the positions of the stars, themagnitude in five filters (F275W, F336W, F438W, F606W,and F814W), and quality parameters such as the photo-metric errors in a filter X ( σ X ), the quality-of-fit (QFIT),and the shape of the source (SHARP).To analyze the MPs within GCs, we selected well measuredstars on the basis of these parameters, as done by Nardielloet al. (2018b). Briefly, we divided the sample of stars in agiven filter X into bins of 0.5 magnitudes, and we calcu-lated the 3 σ -clipping median values in each bin. We inter-polated these median values using a spline, and we rejectedall the stars that are 3 σ above (in the case of σ X ) or be-low (in the case of QFIT) the median parameters. Starswith -0.2 < SHARP < https://archive.stsci.edu/prepds/hugs/DOI: 10.17909/T9810F Fig. 1.
Procedure adopted to select MS (left-hand panels),SGB (middle panels) and RGB stars (right-hand panels) inthe m F814W versus m F606W − m F814W (top panels), m F814W versus m F336W − m F814W (middle panels) and m F814W versus m F275W − m F814W (bottom panels) CMDs of NGC 6362. Thehand drawn fiducial lines of each evolutionary phase are reportedin blue and red. Grey and black points represent rejected and se-lected stars, respectively. The m F814W magnitude ranges whereMS, SGB and RGB stars were selected are shown by horizontaldashed lines in the top panels. without taking into consideration the differential reddeningcorrection for these objects.
3. MULTIPLE STELLAR POPULATIONSWITHIN GLOBULAR CLUSTERS
Since optical filters are less sensitive to light elements vari-ations, such as C, N and O, they allow us to identify MPsin CMDs only when metallicity and/or C+N+O contentchanges among the cluster stars (NGC 1851, Milone et al.2012b; M22 Milone et al. 2012b and M2, Milone et al. 2015).Each cluster analyzed in this work hosts stars having allthe same metallicities and C+N+O content, and in thismanuscript we refer to multiple populations as the phe-nomenon due to the variation of light elements (C,N,O)among the cluster stars. In this context, the UV HST fil-ters F275W, F336W and F438W are efficient for the iden-tification of MPs in GCs, because they are sensitive to thevariations of the molecular bands of OH, NH, CH and CN.Taking advantage of this possibility, we selected stars on theMS, sub-giant branch (SGB) and red-giant branch (RGB)and rejected those that are not on these three evolution-ary phases, in three steps. The GC NGC 6362 is taken asan example in Fig. 1. First, we selected the stars in the m F814W versus m F606W − m F814W
CMD (top panels). Wedraw by hand two fiducial lines: one on the blue and oneon the red side of each evolutionary phase. We rejectedthe stars lying on the left-hand side and on the right-handside of the blue and red fiducial lines, respectively (greypoints). The stars lying between the two fiducial lines andin a specific m F814W range were selected (black points).
Article number, page 2 of 11. Lucertini, D. Nardiello, G. Piotto: Relative ages of multiple populations in five Globular Clusters.
Fig. 2.
Statistic separation of MS stars of the GC NGC 6362. Inthe m F814W vs C F275W , F336W , F438W pseudo-CMD are reportedwell measured (grey) and MS selected (black) stars. The blueand red fiducial line represent the 4 th and 96 th percentiles of thedistribution in color. The left bottom panel shows the vertical-ized MS region. The histogram represents the stars distributionof the verticalized pseudo-CMD. The vertical cyan line is usedto discriminate between MS of POPa (left hand-side) and Ms ofPOPb (right hand-side). Then, we followed the same procedure in the m F814W versus m F336W − m F814W
CMD, considering the previously selectedstars (middle panels). In the final step, we selected in thesame way the stars in the m F814W versus m F275W − m F814W
CMD (bottom panels).For the final goal of this work, it is not necessary to per-fectly separate all the MPs hosted by the GCs. Indeed, weare interested to identify a statistic amount of each popu-lation stars. For this reason, we will divide the MPs of eachGC into two main stellar populations. In particular, fromnow on, we will refer to population-a (POPa) as the firstgeneration stars (Na- and N- poor, and O- and C-rich) andto population-b (POPb) as successive generations.Since our technique is based on the use of the MSTO color,we need to identify the bulk of POPa and POPb stars on theMS of each cluster. We applied a statistical identificationbased on the use of the pseudo-color C F275W , F336W , F438W =( m F275W − m F336W ) − ( m F336W − m F438W ), that allows usto maximize the separation between the different popula-tions (see Milone et al. 2013). Figure 2 shows the proce-dure adopted. Well measured stars are reported in gray,while black points are the selected MS stars. The blue andred fiducial lines are the 4 th and 96 th percentiles of thecolor distribution of MS stars. In order to obtain the fidu-cial lines, we divided the MS into a set of F814W mag-nitude bins of size δm , subdivided into sub-bins of δm/ th , 96 th percentiles of the color distribution and the mean F814Wmagnitude within each bin. The points were smoothed with a boxcar averaging filter and interpolated with splines. Inorder to verticalize the pseudo-CMD, we transformed the C F275W , F336W , F438W color using the following equation:∆
CF275W , F336W , F438W = Y fiducialR − YY fiducialR − Y fiducialB (1)where Y = C F275W , F336W , F438W , "fiducialR" and "fiducialB"are the red and blue fiducial lines. The distribution of starsin the m F814W vs ∆
CF275W , F336W , F438W diagram is repre-sented by the histogram. Fitting a bimodal gaussian profile,we identified the ∆
CF275W , F336W , F438W value useful to sepa-rate the stars into the MPs which they belong to. The starson the left and right hand-side of the cyan vertical line wereclassified as MSa and MSb, respectively. The two-color di-agram m F336W − m F438W versus m F275W − m F336W of MSstars of each GC are shown in Figures 3 and4. We built thesame diagrams for SGB and RGB stars of each GC. Sincein the two-color diagrams of SGB and RGB stars two se-quences are always clearly visible, in this case we dividedthe MPs drawing by hand a continuous line. We identi-fied stars below and above the line as stars belonging toPOPa (green) and stars belonging to POPb (magenta), re-spectively. The samples of stars that belong to POPa andPOPb of each GC analyzed in this work are formed by thecombination of MS, SGB and RGB selected stars.
4. RELATIVE AGE OF MPs WITHIN THESELECTED GCs.
The analysis of relative ages of MPs allows us to improveour knowledge about the formation and evolution of thedifferent populations hosted by GCs.In this work we propose a new technique to estimate the rel-ative age of the two main populations, POPa and POPb,hosted by five GCs: NGC 104 (47 Tuc), NGC 6121 (M4),NGC 6352, NGC 6362, NGC 6723.In the previous section, we have taken advantage of theUV filters to identify the two main populations hosted byour sample of GCs. In order to obtain the relative age be-tween POPa and POPb we considered them as simple stel-lar populations, and we used the optical m F814W versus m F606W − m F814W
CMD because (in first approximation)these filters are not affected by light element variations.We estimated the relative age of the two populations com-paring the observed MSTO color with theoretical models.Our technique is inspired by the horizontal method intro-duced by Rosenberg et al. (1999). This method considersa point on the RGB and, the shape of this evolutionaryphase mainly depends on the metallicity of the population.In “normal” GCs the different MPs have the same metalcontent within the errors, consequently, the point definedon the RGB will be almost the same. In order to avoid theintroduction of more photometric errors associated with theRGB color in the computation of relative ages, we used amethod that does not take into account this point. Theinnovation of our method resides on the MSTO colors dif-ference, imposing strong constraints on metallicity and He-lium content. In this way, we achieve a differential measureof age that is independent from distance and reddening.
The procedure adopted to obtain the theoretical models isshown in Figure 5, where NGC 6362 is taken as an example.
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Fig. 3.
The m F336W − m F438W versus m F275W − m F336W two-color diagram of MS (bottom panels), SGB (middle panels) and RGB(top panels) stars of POPa (green) and POPb (magenta) belonging to NGC 104 (left-hand panels), NGC 6121 (center panels),NGC 6352 (right-hand panels).
Table 1. [Fe/H] (Carretta et al. 2009 for NGC 104, NGC 2808, NGC 6121, NGC 6723; Nardiello et al. 2015 for NGC 6352; Massariet al. 2017 for NGC 6362), [ α /Fe], mean difference in helium ∆ Y between POPa and POPb (Milone et al. 2018) and absolute ageof POPa, Age(POPa), (Dotter et al. 2010), considered to obtain the theoretical model of each GC. Cluster [Fe/H] [ α /Fe] ∆ Y Age(POPa) [Gyr]NGC 104 -0.76 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Table 2.
Value of color and magnitude of MSTO and observed δ c TO obtained for POPa and POPb within GCs Cluster MSTO(POPa) MSTO(POPb) δ c T O m F606W − m F814W m F814W m F606W − m F814W m F814W
NGC 104 0.5368 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Article number, page 4 of 11. Lucertini, D. Nardiello, G. Piotto: Relative ages of multiple populations in five Globular Clusters.
Fig. 4.
As in Fig.3 for the GCs NGC 6362 (lef-hand panels) and NGC 6723 (right-hand panels).
For POPa, we considered a set of isochrones from the Dart-mouth Stellar Evolution Database (DSED, Dotter et al.2008) characterized by [Fe/H]= − .
07 (Massari et al. 2017),[ α /Fe]= 0 .
4, primordial helium Y p = 0 . Y = 0 . α /Fe] and range inage, but with Y = 0 .
33. Panel (a) of Figure 5 shows threeisochrones calculated for an age of 12.5 Gyr, [Fe/H]= − . α /Fe]= 0 .
4, but different helium content: the green model(POPa) has primordial helium Y p = 0 . Y = 0 . Y = 0 . ≤ M F814W ≤
6, whosepoints are evenly spaced by 0.001 mag. For each isochrone http://stellar.dartmouth.edu/models/ of each population, we identify the MS turn-off (MSTO)as the bluer point of the MS. In order to obtain a theo-retical model appropriate for NGC 6362, we considered forPOPa the isochrone having [Fe/H]= − .
07, [ α /Fe]= 0 . Y p = 0 . α /Fe], but Y = 0 . δ c T O , as the dif-ference between the MSTO color of POPa and POPb. Inpanel (b) of Fig. 5 we show two cases to clarify this passage.The green isochrone represents POPa and corresponds to[Fe/H]= − .
07, [ α /Fe]= 0 . Y p = 0 . α /Fe] of POPa, Y = 0 . δ c T O , are shown as purple and cyan lines. We calculated∆Age subtracting from the MSTO age of POPa, i.e the ab-solute age of 12.5 Gyr, the MSTO age of all the isochronesof POPb. The theoretical model δ c T O vs ∆Age is reportedin panel (c) of Fig. 5. The purple and cyan points representthe cases explained in panel (b). In order to obtain a morerobust model we interpolated these points with a second-
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Fig. 5.
Procedure adopted to obtain the reference theoretical models for NGC 6362. Panel (a) shows three isochrones of 12.5 Gyr,for [Fe/H]=-1.07, [ α /Fe]=0.4 and different helium content. The red isochrone with Y=0.2526 (helium-enriched by ∆Y=0.003) isobtained interpolating the isochrone with primordial helium, Y p =0.2496 (green), with the Y=0.33 helium-enriched one (blue).Panel (b) shows how the difference in color among the MSTOs, from which the δc TO is calculated. The green isochrone is the sameas in panel (a) and represents POPa. The purple and cyan isochrones have the same chemical content as the red isochrone of panel(a), but with age of 11 Gyr and 10 Gyr, respectively. The corresponding δc TO of each case is a horizontal line. The theoreticalmodel δ c TO vs ∆Age for NGC 6362 is shown in panel (c). The purple and cyan points are the theoretical model values as obtainedfrom the cases of panel (b). order polynomial, where the order was chosen to minimizethe χ between the polynomial and the observed profile. Inthis way, we obtained the black theoretical model.Performing the same procedure and considering the valuesof [Fe/H] (Carretta et al. 2009 for NGC 104, NGC 6121,NGC 6723; Nardiello et al. 2015 for NGC 6352; Massariet al. 2017 for NGC 6362), [ α/ Fe], ∆ Y (Milone et al. 2018)and absolute age (Dotter et al. 2010) reported in Table 1,we achieved the theoretical models of the other GCs. A dif-ferent choice of α -enrichment strongly influence the modelstrend on the RGB, while the position of the MSTO changesinsignificantly. Since the sum of light elements is constant,we can assume the same [ α /Fe] value for POPa and POPb,making the relative MSTO position even more invariant.It is worth noting that the theoretical models are built as-suming a fixed absolute age for POPa based on the Dotter et al. (2010) estimation, which uncertainties are of 0.5 Gyr.In Appendix A, we evaluate how the theoretical model is af-fected by this error, and we prove that it does not influencethe final relative age result. To obtain the relative age between POPa and POPb withinthe five GCs we compared the theoretical models and theobserved δ c T O values, as shown in Figures 6 and 7.The GC NGC 6362 in the middle panel of Figure 7 istaken as an example to explain this step. We measuredthe color and the magnitude of the MSTOs of POPa andPOPb in the m F814W versus m F606W − m F814W
CMD.The MSTO of each population were obtained using fidu-
Article number, page 6 of 11. Lucertini, D. Nardiello, G. Piotto: Relative ages of multiple populations in five Globular Clusters.
Fig. 6.
Application of our technique to estimate the relative ages of MPs in NGC 104 and NGC 6121. In the observed m F814W versus m F606W − m F814W
CMDs POPa (green), POPb (magenta) and their respective MSTOs are plotted. The inserts (a) show azoomed of the MSTO region. The blue and red fiducial lines are representative of POPa and POPb, respectively. The theoreticalmodels in the insert (b) were obtained assuming the parameters list on the top of the figure. cial lines: we divided the MS F814W magnitudes regime17 . ≤ m F814W ≤ . σ -clipping procedure. The median points weresmoothed with boxcar averaging filter having a window of3 points and then were interpolated with a spline to obtainthe fiducial line. The MSTO of each population is the bluerpoint of the corresponding fiducial line. We found that thecolor and F814W magnitude of the MSTOs of POPa andPOPb of NGC 6362 are (0 . ± . , . ± . . ± . , . ± . δ c T O =0.001 ± m F814W versus m F606W − m F814W
CMD of NGC 6362 (Figure 7), POPa and POPb are shown in green and magenta and theirrespective MSTOs are reported as filled circles colored asthe population they belong to.The MSTO colors and F814W magnitudes and the observed δ c T O obtained for the five GCs considered in this work arereported in Table 2.In order to estimate the relative age between POPa andPOPb in NGC 6362, in the insert of Figure 7, we show theobserved δ c T O on the theoretical model. We concluded thatthe two main populations of NGC 6362 have a difference inage ∆Age=73 ±
92 Myr. The uncertainty associated to thisestimation of relative age was obtained interpolating the δ c T O errors with the theoretical model, and it is only dueto internal errors.In addition to these internal errors, we analyzed how the
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Fig. 7.
As in Figure 6 for the GCs NGC 6352, NGC 6362 and NGC 6723. helium uncertainty σ ∆Y = ± .
011 (Milone et al. 2018)and the metallicity one σ [Fe / H] = ± .
05 (Massari et al.2017) affect the measure of ∆Age. We produced two ad-ditional sets of isochrones for POPb characterized by thesame [Fe/H]=-1.07 and [ α /Fe]=0.4 of POPa, but with twodifferent helium enhancements: ∆Y=0.003+0.011=0.014and ∆Y=0.003-0.011=-0.008. We extracted the theoreti-cal models, adopting these two helium enhanced isochronesfor POPb and the same isochrone as used above for POPa.Following the procedure previously outlined and compar-ing the observed δ c T O with these models we found that anuncertainty of ± .
011 dex in ∆Y leads to an uncertaintyon ∆Age of σ ∆ Age (∆ Y ) = ±
126 Myr. Similarly, we cal-culated the impact of [Fe/H] variations on the estimate of∆Age. In this case, we used for POPb two sets of isochroneswith [ α /Fe]=0.4, enhanced in helium by ∆Y=0.003 butdifferent metallicity: [Fe/H]= − .
07 + 0 .
05 = − .
02 and[Fe/H]= − . − .
05 = − .
12. We found that an errorof σ [Fe / H] = ± σ ∆ Age ([Fe/H]) =448 Myr.Combining all the sources of uncertainties we can estab-lish an upper limit for the uncertainty of the relative agebetween the two main populations within the cluster. We found that POPa and POPb of NGC 6362 are coeval within ∼
474 Myr.We performed the same procedure for the others GCs us-ing the values reported in Table 1. The final results aresummarized in Table 3.
5. DISCUSSION
The mechanisms that have brought to the formation of MPsin GCs are still subject of debate. Despite the increasing in-terest in this topic in the last couple of decades, further anddeeper analyses are needed. This work aims to introduce anew technique that can contribute to put light on this as-tronomical issue. Indeed, a good relative age estimate ofMPs leads to clues regarding the formation and the evolu-tion of these last.In literature, most of the works on the relative age of MPsconcern GCs with a large variation of metallicity betweendifferent populations. According to Marino et al. (2012),M 22 hosts MPs coeval within ∼
300 Myr. Studying the glob-ular cluster NGC 2419, Lee et al. (2013) showed that thisobject hosts two stellar populations characterized by a largedifference in metallicity and helium abundance. They found
Article number, page 8 of 11. Lucertini, D. Nardiello, G. Piotto: Relative ages of multiple populations in five Globular Clusters.
Table 3.
MPs relative ages and their uncertainties.
CLUSTER ∆ Age σ ∆ Age (Internal) σ ∆ Age (∆Y) σ ∆ Age ([Fe/H]) σ ∆ Age [Myr] [Myr] [Myr] [Myr] [Myr]NGC 104 -70 49 74 202 +220NGC 6121 -77 130 68 157 +214NGC 6352 273 150 206 220 +336NGC 6362 73 92 126 448 +474NGC 6723 25 65 72 627 +634that the most metal-rich population is younger than 2 Gyr.The relative ages of the MPs in NGC 2808 were analyzed byRoh et al. (2011); they found that, if 2G stars are heliumand metal enhanced by ∆Y=0.03 and ∆Y=0.16, respec-tively, compared to 1G stars, then the 2G population is ∼ . HST data, Souza et al. (2020) estimated an age dif-ference of 550 ±
410 Myr between the first and the thirdgenerations in NGC 6752. The uncertainty of their resultdecreases to 400 Myr when the helium enhancement is con-sidered.We compare the results in literature with what we obtainedin this work, in cases where the same source of uncertaintieswere taken into account.Nardiello et al. (2015) applied isochrone fitting over syn-thetic CMDs with χ calculations to evaluate the rela-tive age of MPs within NGC 6352. Assuming [Fe/H]=-0.67, [ α /Fe]=+0.4 and ∆Y=0.029, they derived an agedifference of 10 ±
110 Myr. Considering the same value ofmetallicity and α -enhancement and ∆Y=0.019, we esti-mate ∆Age=273 ±
150 Myr for NGC 6352. Adopting a dif-ference in [Fe/H] and [ α /Fe] of 0.02 dex, Nardiello et al.(2015) found that the two populations are coeval within ∼
300 Myr. This result is perfectly in agreement with ourvalue of σ ∆ Age =336 Myr, when all the uncertainties areconsidered.Recently, Oliveira et al. (2020) used statistical isochrone fit-ting to estimate the relative age of MPs within eight GCs:NGC 6304, NGC 6352, NGC 6362, NGC 6624, NGC 6637,NGC 6652, NGC 6717 and NGC 6723. They found thatthe individual MPs are coeval within 500 Myr. Moreover,they derived a weighted mean age difference of 41 ± ±
170 when He-enhancement is taken into account.Considering [Fe/H]=-0.59, [ α /Fe]=+0.2 and ∆Y=0.027,they derived an age difference of 500 ±
480 Myr forNGC 6352. This estimation is comparable to our of 273 ± ±
410 Myr. Using ∆Y=0.003, we estimated∆Age=73 ±
92 Myr. Despite our mean differential age esti-mation is slightly higher, it agrees within 1 σ with the valueobtained by Oliveira et al. (2020).Finally, we found ∆Age=25 ±
65 Myr for the MPs inNGC 6723, which is in agreement with the difference in age-100 ±
510 Myr obtained by Oliveira et al. (2020).In Figure 8, this work and literature results for GCs in com-mon are compared. We conclude that our new techniqueleads to consistent result with those in literature and with,on average, smaller error bars.
Fig. 8.
Comparison between this work results (blue) with thoseobtained by Nardiello et al. (2015) (green) and Oliveira et al.(2020) (red) for NGC 6352, NGC 6362 and NGC 6723. The errorsbars of NGC 6352 ∗ include all the uncertainties, while those ofthe other results consider only the uncertainty on ∆Y.
6. CONCLUSIONS
We developed a new technique to estimate the relative agesof the MPs hosted by GCs. In this work, we applied themethod to five clusters: NGC 104, NGC 6121, NGC 6352,NGC 6362, NGC 6723.We used the astro-photometric catalogs released byNardiello et al. (2018a) and we selected the well measuredstars on the basis of their photometric parameters.A statistical test was used to divide the MPs along theMS of the GCs. We built the m F336W − m F438W versus m F275W − m F336W two-color diagram of SGB and RGBstars in order to divide the stars in the different evolution-ary phases into the populations which they belong to. Wedefined POPa as the 1G stars and POPb as all the succes-sive generations of stars, and we considered them as simplestellar populations to estimate their relative age.Considering the values of [Fe/H], [ α /Fe], Y reported inTab.1, we built the δ c T O versus ∆Age theoretical modelfor each GCs. We defined δ c T O as the difference in color
Article number, page 9 of 11 &A proofs: manuscript no. raGCs_v9 between the MSTO color of a fixed isochrone age for POPaand the MSTO of all ages isochrones for POPb and the∆Age as the difference between a fixed age of POPa andall the ages of POPb. The observed δ c T O was calculatedin the m F814W versus m F606W − m F814W
CMD, and we ob-tained the relative age between the two main populations.The conclusions drawn from our new technique are: – An uncertainty of ± – Combining all the sources of uncertainties (photome-try, metallicity and He-enrichment) we estimated an up-per limit on the relative ages. We found that the MPsof NGC 104 and NGC 6121 are coeval within 220 Myrand 214 Myr, while those of NGC 6352 , NGC 6362 andNGC 6723 are coeval within 336 Myr, 474 Myr and 634Myr. – Within the limits of the errors on relative ages aboveindicated, the different populations in the single clustersare coeval.The results obtained with our technique are consistent withthose in literature. We can affirm that the new method isa good tool to estimate relative ages of MPs within GCs.Finally, our results turn out new observational evidence toput constrains on the formation of MPs in GCs. Severaltheoretical scenarios were proposed to explain this astro-nomical topic, even if none of them is able to explain all theobservational facts obtained in the last years (Renzini et al.2015). The most accredited scenarios involve IntermediateMassive AGB stars (D’Antona et al. 2002, D’Ercole et al.2012), Fast Rotating Massive Stars (Decressin et al. 2007a,2007b), Massive Interacting Binaries (de Mink et al. 2009,Bastian et al. 2013), or Supermassive stars (Denissenkov &Hartwick 2014, Denissenkov et al. 2015). According to thesescenarios the time scales for the formation of the other pop-ulations run from few million years to some hundred Myr.Unfortunately, with the results obtained in this work we cannot discriminate which scenario is the most appropriate todescribe the formation of MPs. Anyway joining our resultswith the relative ages measured in previous works, we canput a strong constraint: the formation of MPs happens onthe same time scale for all the normal GCs.
Acknowledgements.
DNa acknowledges the support from the FrenchCentre National d’Etudes Spatiales (CNES).
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Article number, page 10 of 11. Lucertini, D. Nardiello, G. Piotto: Relative ages of multiple populations in five Globular Clusters.
Appendix A: Theoretical model
The relative age values are given comparing the observed δc T O and the theoretical models. The theoretical modelsare based on an assumption on the absolute age of POPa.In this work, we adopted the ages obtained by Dotter et al.(2010), with on average an uncertainty of ± α /Fe]=+0.4,primordial helium Y=0.2496 and age 12.5 Gyr (Dotter et al.2010). On the other hand, the set of isochrones for POPbhas same [Fe/H] and [ α /Fe], He-enrichment ∆Y=0.003(Milone et al. 2018) and ages that run from 10 000 Myrto 15 000 Myr, in step of 100 Myr. As described in sec-tion 4.1 and Figure 5, we derived the theoretical model forthis GC, as shown in Figure A.1 with the color magenta.Reporting the observed δc T O on this profile, we obtaineda relative age of 73 ±
92 Myr. The same Figure displaysthe theoretical models obtained considering an age of 12Gyr (cyan) and 13 Gyr (green) for POPa. As shown in theinsert, there is a negligible difference among the three mod-els in the region where the observed δc T O lies. Indeed, therelative ages found considering the cyan and green modelsare 84 ±
87 Myr and 78 ±
97 Myr, respectively. We con-clude that an uncertainty of ± ±
75 Myr and 107 ±
118 Myr, respectively. Despitethe inclination variation of the theoretical model, the finalresults are consistent within error bars. We can affirm thata different choice of POPa age within ± Fig. A.1.
Application of the new technique to estimate therelative age of MPs within NGC 6362. The theoretical modelswere obtained considering POPa ages of 12 Gyr (cyan), 12.5 Gyr(magenta) and 13 Gyr (green). A better comparison between thethree models is shown in the insert.