Binary-driven stellar rotation evolution at the main-sequence turn-off in star clusters
MMNRAS , 1–9 (2020) Preprint 5 February 2021 Compiled using MNRAS L A TEX style file v3.0
Binary-driven stellar rotation evolution at the main-sequence turn-off instar clusters
Weijia Sun , , , ★ Richard de Grijs , , , Licai Deng , , and Michael D. Albrow Department of Astronomy, School of Physics, Peking University, Beijing 100871, China Key Laboratory for Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing 100012, China Department of Physics and Astronomy, Macquarie University, Balaclava Road, Sydney, NSW 2109, Australia Centre for Astronomy, Astrophysics and Astrophotonics, Macquarie University, Balaclava Road, Sydney, NSW 2109, Australia International Space Science Institute–Beijing, 1 Nanertiao, Zhongguancun, Hai Dian District, Beijing 100190, China School of Astronomy and Space Science, University of the Chinese Academy of Sciences, Huairou 101408, China Department of Astronomy, China West Normal University, Nanchong 637002, China School of Physical and Chemical Sciences, University of Canterbury, Private Bag 4800, Christchurch, New Zealand
Accepted. Received; in original form
ABSTRACT
The impact of stellar rotation on the morphology of star cluster colour–magnitude diagrams is widely acknowledged. However,the physics driving the distribution of the equatorial rotation velocities of main-sequence turn-off (MSTO) stars is as yet poorlyunderstood. Using
Gaia
Data Release 2 photometry and new Southern African Large Telescope medium-resolution spectroscopy,we analyse the intermediate-age ( ∼ Key words: galaxies: star clusters: general – techniques: spectroscopic
Extended main-sequence turn-offs (eMSTOs; e.g., Mackey & BrobyNielsen 2007; Goudfrooij et al. 2011) and split main sequences (MSs;e.g., D’Antona et al. 2015; Li et al. 2017a) pose a fundamental chal-lenge to our traditional understanding of star clusters as ‘simple stellarpopulations’. Both features are thought to be driven by differences instellar rotation rates (e.g., Niederhofer et al. 2015), supported by anincreasing body of spectroscopic evidence in both Magellanic Cloudclusters (Dupree et al. 2017; Kamann et al. 2020) and Galactic openclusters (OCs; Bastian et al. 2018; Sun et al. 2019a,b). Fast rotatorsappear redder than their slowly rotating counterparts because of thecompound effects of gravity darkening and rotational mixing (Yanget al. 2013).As the effects of stellar rotation in defining the morphology of clus-ter colour–magnitude diagrams (CMDs) are now well-understood,the rotation distributions of MSTO stars and their origin in star clus-ters represent the next key open question. A cluster mostly composedof initially rapidly rotating stars may reproduce the observed ‘con-verging’ subgiant branch in NGC 419 (Wu et al. 2016). D’Antona etal. (2015) argued that split MSs are composed of two coeval popula-tions with different rotation rates: a slowly rotating blue-MS (bMS)and a rapidly rotating red-MS (rMS) population. This bimodal ro- ★ Contact e-mail: this.is.weij[email protected] tational velocity distribution was confirmed for NGC 2287 (Sun etal. 2019b), where the well-separated double MS in this young OC istightly correlated with a dichotomous distribution of stellar rotationrates. Kamann et al. (2020) also discovered a bimodal distribution inthe rotation rates of MSTO stars in the 1.5 Gyr-old cluster NGC 1846.However, the peak rotational velocities in this cluster are slower thanthose in the younger cluster NGC 2287, thus offering a hint of stellarrotation evolution.This naturally raises the question as to the origin of such a bimodalrotation distribution. D’Antona et al. (2015, 2017) suggested thatbMS stars in young clusters might have resulted from tidal brakingof initially fast rotators on time-scales of a few × yr. Alterna-tively, the bimodal rotation distribution could have been establishedwithin the first few Myr, regulated by either the disc-locking time-scale (Bastian et al. 2020) or the accretion abundance of circumstellardiscs (Hoppe et al. 2020). In this paper, we discover a tight corre-lation between the stellar rotation rates and binary fractions in fiveintermediate-age Galactic OCs with similar dynamical ages, favour-ing a binary-driven model. This is further supported by the greatercentral concentration of the bMS stars relative to the rMS populationin at least two of our clusters. Intriguingly, our observational resultsare inconsistent with the prevailing theoretical models, which thusinvites more detailed future investigations.This paper is organised as follows. We present our photometric andspectroscopic data reduction in Section 2. Our analysis to unravel the © a r X i v : . [ a s t r o - ph . S R ] F e b W. Sun et al.
OCs’ rotation distributions and its validation are described in Sec-tion 3. A discussion about the formation mechanism determining thestellar rotation rates in clusters and our conclusions are summarisedin Section 4.
We obtained photometry and astrometry of cluster stars from
Gaia
Data Release (DR) 2 (Gaia Collaboration et al. 2016, 2018b) anddetermined their cluster membership probabilities based on proper-motion and parallax analysis, as follows.First, we downloaded the
Gaia
DR2 astrometry, proper mo-tions, photometry and parallaxes for all stars located within1 degree of a cluster’s centre. We selected all sources with parallax_over_error > ,RUWE < .
4. We also used the flux excess factor, 𝐸 = ( 𝐼 BP + 𝐼 RP )/ 𝐼 G ( phot_bp_rp_excess_factor )—where 𝐼 X is the photometric fluxin band 𝑋 (Evans et al. 2018)—to exclude possible issues with the Gaia
BP and RP photometry (Gaia Collaboration et al. 2018a):1 . + . ( 𝐺 BP − 𝐺 RP ) < 𝐸 < . + . ( 𝐺 BP − 𝐺 RP ) . (1)The final step before member selection involved correcting the Gaia magnitudes for the effects of saturation at bright magnitudes. Thiswas done by employing the equations of Evans et al. (2018). Weadopted the corrected magnitudes for subsequent analysis.Next, to derive a clean sample of member stars, we analysed thevector-point diagram (VPD) of the stellar proper motions and lo-cated the distribution’s centre based on 2D kernel density estimation(KDE). A cut in 𝜇 R = √︁ ( 𝜇 𝛼 cos 𝜃 − (cid:104) 𝜇 𝛼 cos 𝜃 (cid:105)) + ( 𝜇 𝛿 − (cid:104) 𝜇 𝛿 (cid:105)) was applied to perform the primary membership selection. We thenfurther selected the remaining stars based on their parallaxes, 𝜛 ,rejecting all stars whose parallaxes deviated from the mean value bymore than four times the corresponding r.m.s. (see Fig. 1). By com-paring the CMDs composed of our selection of cluster member starswith their literature counterparts (Bastian et al. 2018; Cordoni et al.2018; Cantat-Gaudin et al. 2018; Sun et al. 2019a), we concludedthat our selection approach is indeed robust and reliable.The clusters’ ages, distances and extinction values were estimatedbased on visual comparison with the MIST isochrones (Choi et al.2016). The parameters of the best-fitting isochrone to the blue edgeof the bulk stellar population of each cluster (Fig. 1, right) are in-cluded in Table 1. Our independently derived cluster parameters areconsistent with literature values (e.g., Bossini et al. 2019); minordifferences relate to the choice of stellar models adopted. For three ∼ same as that adopted by Sun et al. (2019a). The PG2300 gratingwas used at a grating angle of 34.25 degrees and a camera stationangle of 68.5 degrees. This configuration, combined with a slit widthof 1 arcsec, yields a central wavelength of 4884.4 Å and a spectralcoverage of ∼ 𝑅 ∼ 𝛽 and the Mg i triplet with the syn-thetic stellar spectra from the Pollux database (Palacios et al. 2010),convolved with the rotational profile for a given rotational velocityand implemented by adopting instrumental broadening. The errorwas estimated through a comparison of the rotational velocities ofthe mock data with those derived through profile fitting (Sun et al.2019a, their figure 4). For IC 4756 we also included stellar rota-tion measurements from Schmidt & Forbes (1984) and Strassmeieret al. (2015). For stars with multi-epoch observations, a variabilitytest indicated no significant variation of either the radial or the rota-tional velocities in our data set (except for one star in NGC 6134; seeSection 4). As such, we adopted the average rotational velocity. Wethus obtained rotation measurements of 29, 25 and 49 stars in NGC3960, NGC 6134 and IC 4756, respectively. In Fig. 2, we presentthe CMDs of NGC 3960, NGC 6134 and IC 4756, with the memberstars colour-coded by their rotational velocities. Combined with 24stars in NGC 5822 and 57 in NGC 2818, we achieved 20–30 per centcompleteness across the eMSTO for all five clusters. This is sufficientto reliably derive their rotation distributions (see Section 3.1.2). All sample clusters have similar chronological and dynamical ages(see Appendix A), thus enabling direct comparison upon correctionof the clusters’ photometry for extinction and distance differences: seeFig. 3 (left). Whereas the clusters’ MSTOs exhibit different patterns,their lower MSs converge at approximately the same position in CMDspace. We selected samples of MSTO and MS stars to better illustratetheir morphologies using Δ ( 𝐺 BP − 𝐺 RP ) pseudo-colour distributions.The selection boundaries applied to the MSTO stars are shown inFig. 3 (grey enclosure): stars bluer than 𝐺 BP − 𝐺 RP = Δ ( 𝐺 BP − 𝐺 RP ) pseudo-colour is defined asthe difference in colour with respect to a cluster’s ridge line. Weexcluded a number of possible blue straggler stars at colours bluerthan the best-fitting isochrone to the cluster’s bulk stellar populationminus 3 𝜎 (see Section 3). Next, we defined a straight line parallelto the MS, at 2 . (cid:54) 𝑀 𝐺 (cid:54) . ∼ . MNRAS , 1–9 (2020) inary-driven stellar rotation evolution − − − − − − µ α cos θ (mas yr − )01234 µ δ ( m a s y r − ) . . . . . $ (mas) G ( m ag ) .
25 0 .
50 0 .
75 1 .
00 1 .
25 1 .
50 1 . G BP − G RP (mag) G ( m ag ) Figure 1.
Illustration of the procedure adopted to select probable members of NGC 3960. (left) VPD of the proper motions of bright field stars (grey) and brightcluster members (red) in the cluster’s field. The primary selection boundary, based on proper motion constraints, is indicated by the blue circle (1 mas yr − ).(middle) 𝐺 -band photometry versus stellar parallaxes. Candidates from the primary selection step are shown as blue dots, whereas those selected based on theirparallaxes are shown as red dots. The vertical dashed lines represent the parallax selection boundaries. (right) CMD of all stars in the field (grey) and the NGC3960 member stars (red). The best-fitting isochrone to the bulk stellar population is also shown. Table 1.
Derived properties of our intermediate-age OCsCluster log ( 𝑡 yr − ) ( 𝑚 − 𝑀 ) [Fe/H] 𝐴 𝑉 𝑓 b 𝜎 𝑁 slow / 𝑁 tot Λ MSR , b Λ MSR , r (mag) (dex) (mag) (mag)(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)NGC 3960 8.98 11.35 − . + . − . . + . − . . + . − . . ± .
25 1 . ± . . + . − . . + . − . . + . − . . ± .
08 – 𝑎 IC 4756 8.94 8.16 0.00 0.50 0 . + . − . . + . − . . + . − . . ± .
12 – 𝑎 NGC 5822 8.90 9.46 0.00 0.50 0 . + . − . . + . − . . + . − . . ± .
20 1 . ± . . + . − . . + . − . . + . − . . ± .
11 0 . ± . 𝑎 Insufficient sample size.(1) Cluster name; (2) Age; (3) Distance modulus; (4) Metallicity; (5) Extinction; (6) Total binary fraction; (7) Scatter in pseudo-colour; (8)Slow-rotator number fraction among synthetic MSTO stars; (9, 10) Mass segregation ratios (MSRs) of (9) bMS and (10) rMS stars. . . . G BP − G RP (mag) . . . . . . . . . G ( m ag ) NGC 3960 v s i n i ( k m s − ) . . . G BP − G RP (mag) . . . . . . . . . G ( m ag ) NGC 6134 v s i n i ( k m s − ) . . . . . . G BP − G RP (mag) G ( m ag ) IC 4756 v s i n i ( k m s − ) Figure 2.
CMDs of (left) NGC 3960, (middle) NGC 6134 and (right) IC 4756 with their member stars colour-coded by their projected rotational velocities.Slow rotators (blue) are preferentially found on the blue side of the MSTO, whereas fast rotators (yellow) tend to be located on the red side.MNRAS000
CMDs of (left) NGC 3960, (middle) NGC 6134 and (right) IC 4756 with their member stars colour-coded by their projected rotational velocities.Slow rotators (blue) are preferentially found on the blue side of the MSTO, whereas fast rotators (yellow) tend to be located on the red side.MNRAS000 , 1–9 (2020)
W. Sun et al. − .
25 0 .
00 0 .
25 0 .
50 0 .
75 1 .
00 1 . G BP − G RP (mag) M G ( m ag ) NGC 3960NGC 6134IC 4756NGC 5822NGC 2818 . . . . ∆( G BP − G RP ) (mag) D e n s i t y MSTO
NGC 3960NGC 6134IC 4756NGC 5822NGC 2818 − . − . . . . . ∆( G BP − G RP ) (mag) D e n s i t y MS NGC 3960NGC 6134IC 4756NGC 5822NGC 2818
Figure 3. (left) CMD of our cluster member stars in
Gaia passbands. The MSTO and MS samples are highlighted as solid dots. Grey dashed line: MSTO stars.Dark grey lines: Ridge lines used to calculate the populations’ pseudo-colours. (right) KDEs of the (top) MSTO and (bottom) MS samples. The peaks of the MSdistributions have been aligned and shifted for clarity and comparison. Any misalignment is owing to minor differences in the clusters’ ages and metallicities.
Several recent attempts have been made to unravel cluster rotationdistributions (Gossage et al. 2019; de Juan Ovelar et al. 2020). How-ever, most of these estimates were based solely on their CMD mor-phologies (see also Kamann et al. 2020), i.e., based on the probabilityof models matching the observations using Hess diagrams. Whereasthis may be suitable for MC clusters, where the numbers of memberstars are sufficiently large and where it is difficult or impossible toobtain direct velocity information, such analyses of OCs inevitablysuffer from stochastic sampling effects (see Section 3.1.2). Spectro-scopic observations can ameliorate these effects.We used the SYCLIST stellar rotation models (Georgy et al. 2013,2014) to generate synthetic clusters, assuming solar metallicity ( 𝑍 = . ( 𝑡 yr − ) = .
95 and a 50 per cent binary fraction.The model also considers limb darkening (Claret 2000). We adoptedthe gravity-darkening law of Espinosa Lara & Rieutord (2011). Theinclination angles follow a random distribution. The model suite islimited to a minimum stellar mass of 1 . (cid:12) and it does not accountfor the evolution of interacting binary systems.Since the SYCLIST models are limited to high masses ( (cid:62) . (cid:12) ; suitable for covering the MSTO) and it is difficult to constraina cluster’s binary fraction based on the morphology of its MSTO,we exploited the less massive MS stars (see Fig. 3) to derive totalbinary fractions, 𝑓 b , at masses where the effects of stellar rotation arenegligible. Binary models were generated from the MIST isochronesby adding unresolved binaries with different mass ratios, assuminga flat mass-ratio distribution. Next, we compared the pseudo-colour distributions of stars in our synthetic clusters with those in the ob-served clusters, using the same MS selection criteria. The goodnessof the comparison is given by the Anderson–Darling 𝑝 value. Weadded a second parameter, 𝜎 , to characterise the observational scat-ter in the pseudo-colour, combining the effects of a possible internalage spread, photometric uncertainties and differential extinction. Aminor colour shift among the clusters was also taken into considera-tion. We employed the Markov-chain Monte Carlo method ( emcee ;Foreman-Mackey et al. 2013) to determine the best model and esti-mate the uncertainties in the resulting parameters.We adopted this binary fraction as our input parameter and ap-plied a similar method to the MSTO stars to derive their rotationdistribution. In the SYCLIST models, on the zero-age MS (ZAMS)this distribution is controlled by the ratio of the equatorial angularvelocity, Ω , to the critical velocity Ω crit . The latter is the rotationalangular velocity where the surface gravity can no longer maintainequilibrium with the centrifugal motion. We binned the resulting ro-tation rates into 10 bins, from Ω / Ω crit , ZAMS = . 𝐹 Ω 𝑖 . Each weight corresponded to thefraction of stars with a given rotation rate.We first generated a model cluster of 200,000 stars with a flatrotation distribution. For each set of input parameters ( 𝑓 b , 𝐹 Ω 𝑖 ), werandomly selected the 𝑁 most appropriate stars from the total poolto generate a new synthetic cluster which satisfied the rotation distri-bution required. Subsequently, we added scatter ( 𝜎 ) to the syntheticcluster and selected the remaining MSTO stars for comparison withthe observed cluster. In practice, when selecting MSTO stars andcalculating their pseudo-colours, we shifted the ridge line towards MNRAS , 1–9 (2020) inary-driven stellar rotation evolution bluer colours by 0.3 mag to include MSTO stars which have scatteredaway from the MSTO region.As for the MS region, a comparison of the pseudo-colour distribu-tions of MSTO stars in the synthetic and observed clusters yields thecorresponding 𝑝 phot values. We also used the rotational velocitiesto address the degeneracy between the pseudo-colour and rotation-velocity distributions (see Section 3.1.2). For each MSTO star withspectroscopic measurements, we selected the closest 100 stars in thesynthetic cluster’s CMD. We then computed the probability of de-riving the same 𝑣 sin 𝑖 distribution as observed. We first resampledthe measured projected rotational velocities according to the errordistribution and estimated the probabilities for this alternative reali-sation. We iterated each run 100 times and adopted the median valueto minimise stochastic sampling effects. Finally, we combined thecorresponding 𝑝 spec values from the spectroscopic data with 𝑝 phot and used emcee to find the rotation model which best reproducesboth the pseudo-colour and the 𝑣 sin 𝑖 distributions. The uncertain-ties were derived from the samples’ 16th and 84th percentiles in themarginalised distributions. In this section, we examine the accuracy of our parameter recovery,specifically for two crucial parameters, i.e., the binary fraction ( 𝑓 b )and the rotation rate ( 𝐹 Ω 𝑖 ). We discuss the importance of knowing therotational velocity for the determination of the rotation distribution. We applied our method to a few additional clusters to verify ourcalculation of the binary fraction. We selected 12 OCs with binaryfraction measurements available in the literature (Bica & Bonatto2005; Cordoni et al. 2018; de Juan Ovelar et al. 2020) as our compar-ison sample. Given that these clusters are younger than or of similarage as our sample OCs, our selection of MS stars is not affected byany MSTO broadening and is thus suitable for validation purposes.In Fig. 4, we show our results (vertical axis) versus the correspondingliterature mean values (horizontal axis). Considering possible differ-ences in the sample selection and the estimation method used, ourestimates for these OCs are consistent with the literature valuesOne possible flaw inherent to the derivation of binary fractionsbased on
Gaia data is that some binaries could be (partially) resolved,which is not taken into account in the application of this method. If so,this would lead to an underestimation of the binary fraction and thiscould be important for clusters which are sufficiently close. However,this effect should not have a major impact on our sample clusters.Even for the nearest cluster analysed in this paper, IC 4756, only widebinaries with separations larger than ∼
800 AU (2 arcsec, adoptedfrom Arenou et al. 2018) can be resolved by
Gaia , which applies toless than 2 per cent of binaries in OCs (Deacon & Kraus 2020).
Verification of the rotation rates was done based on mock tests. Wegenerated mock data for various rotation distributions and applied ourmethod to verify whether the rotation rates were robustly recovered.In particular, we generated a synthetic cluster with 200 MSTO stars(similar to the observed number) and a spectroscopic completenesslevel of 25 per cent. The binary fraction and 𝜎 were set at 20 per centand 0.02 mag, respectively.Fig. 5 shows two representations of our mock tests. One is based on . . . . . . . f b , lit . . . . . . . f b NGC 1245NGC 1817NGC 2099NGC 2287NGC 2360NGC 2818NGC 3114NGC 3532NGC 5822NGC 6705IC 2714MELOTTE 71
Figure 4.
Comparison of our newly derived binary fractions, 𝑓 b , with themean value of previously published results. The grey dashed line representsthe linear, one-to-one relation. a skewed normal distribution (first row) and the other is characterisedby a bimodal distribution (second row). The input and recovered ro-tation rates are shown in the left-hand column as the orange and bluehistograms, respectively. Our derived rotation rates are consistentwith the mock data’s true values (most fall within 1 𝜎 ).We also checked the performance of our approach in the presenceof less or no spectroscopic information. The results for syntheticclusters with 10 and 0 per cent of 𝑣 sin 𝑖 information are shown in themiddle and right-hand columns, respectively. The recovered rotationrates exhibit strong deviations from the input distribution. Althougha general trend can tentatively still be produced, the correspondingaccuracy is far from satisfactory. Although analyses of massive MCclusters solely based on photometric data are practical (e.g., Gossageet al. 2019), one should be careful when applying this approach toGalactic OCs. This final test highlights the degeneracy resulting fromfitting models to poorly sampled data and underscores the need foradditional information (such as 𝑣 sin 𝑖 measurements). The best-fitting rotation rates’ weights are shown in Fig. 6 (smallpanels), whereas the rotation rate probability distributions of theMSTO stars for all clusters are shown in the top left-hand panel. Allfive clusters contain a significant fraction of fast rotators. However,the locations and fractions of fast rotators vary among the clusters.Whereas some clusters, like NGC 6134 and NGC 2818, appear tohost three rotational populations (including two slowly rotating pop-ulations), it is difficult to reliably separate between populations ofslow rotators because of their minor colour differences. Therefore,we exercise caution and suggest that these clusters may only con-tain two distinct populations (i.e., a bimodal distribution) in stellarrotation space.The number fraction of slow rotators, 𝑁 slow / 𝑁 tot , among syn-thetic MSTO stars shows a positive correlation with the clusters’ MNRAS000
Comparison of our newly derived binary fractions, 𝑓 b , with themean value of previously published results. The grey dashed line representsthe linear, one-to-one relation. a skewed normal distribution (first row) and the other is characterisedby a bimodal distribution (second row). The input and recovered ro-tation rates are shown in the left-hand column as the orange and bluehistograms, respectively. Our derived rotation rates are consistentwith the mock data’s true values (most fall within 1 𝜎 ).We also checked the performance of our approach in the presenceof less or no spectroscopic information. The results for syntheticclusters with 10 and 0 per cent of 𝑣 sin 𝑖 information are shown in themiddle and right-hand columns, respectively. The recovered rotationrates exhibit strong deviations from the input distribution. Althougha general trend can tentatively still be produced, the correspondingaccuracy is far from satisfactory. Although analyses of massive MCclusters solely based on photometric data are practical (e.g., Gossageet al. 2019), one should be careful when applying this approach toGalactic OCs. This final test highlights the degeneracy resulting fromfitting models to poorly sampled data and underscores the need foradditional information (such as 𝑣 sin 𝑖 measurements). The best-fitting rotation rates’ weights are shown in Fig. 6 (smallpanels), whereas the rotation rate probability distributions of theMSTO stars for all clusters are shown in the top left-hand panel. Allfive clusters contain a significant fraction of fast rotators. However,the locations and fractions of fast rotators vary among the clusters.Whereas some clusters, like NGC 6134 and NGC 2818, appear tohost three rotational populations (including two slowly rotating pop-ulations), it is difficult to reliably separate between populations ofslow rotators because of their minor colour differences. Therefore,we exercise caution and suggest that these clusters may only con-tain two distinct populations (i.e., a bimodal distribution) in stellarrotation space.The number fraction of slow rotators, 𝑁 slow / 𝑁 tot , among syn-thetic MSTO stars shows a positive correlation with the clusters’ MNRAS000 , 1–9 (2020)
W. Sun et al. .
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Figure 5.
Recovered rotation distributions from our mock tests. Two synthetic models of different rotation distributions are shown in the top and bottom rows.Histograms of the input mock data are compared with the best-fitting models (blue). The fits were done for different levels of 𝑣 sin 𝑖 completeness, including(left) 25 per cent, (middle) 10 per cent, and (right) 0. total binary fraction 𝑓 b : see Fig. 7. We verified that our approachto selecting slowly and rapidly rotating subsamples, within reason-able ranges, minimally affects this correlation by changing the ve-locity adopted for our subsample selection to fixed values. In alltests, the correlation between the number fraction of slow rotatorsand the binary fractions of the clusters remains almost the same, modulo minor shifts in the absolute value of 𝑁 slow / 𝑁 tot In fact,one slow rotator ( 𝑣 sin 𝑖 = . − ) in NGC 6134 ( Gaia
DR2ID 5941409684301615360) exhibited variation in its radial velocityduring two observation epochs, spanning three days. The observedvariation is around 80 km s − , which is four times larger than the un-certainty associated with the velocity measurements. The estimatedrotational velocities remained unchanged, with differences of lessthan the 𝑣 sin 𝑖 error (7 km s − ). If this radial-velocity variation wereinduced by binaries, the star is likely a member of a close binarysystem with a separation of a few tens of solar radii. To arrive at thisestimate, we assumed that its luminosity is not severely affected bythe companion and we adopted the observed variation as the ampli-tude of radial velocity curve. Follow-up time-series observations arerequired to confirm this star’s nature.The approximately constant number ratios of bMS stars found inmassive MC clusters (Milone et al. 2018) may result from the similarbinary fractions ( ∼ .
3) which are prevalent in MC clusters (Miloneet al. 2009) if the correlation of Fig. 7 also pertains to more massiveclusters. For instance, Milone et al. (2017) estimated that the numberratio of bMS stars in NGC 1866 is 35 per cent; the cluster’s overallbinary fraction is 0.28. These properties will place it comfortably on the apparent correlation. However, some younger clusters, e.g.,NGC 1818 ( ∼
40 Myr) and NGC 330 ( ∼
40 Myr), do not follow thecorrelation if we adopt their binary fractions from Li et al. (2017a)and their number ratios from Milone et al. (2018). This may suggestthat these young clusters are still in the early stages of their stellarrotation evolution, which may last for several tens of Myr. In NGC1846 ( ∼ . ∼
45 per cent ofMSTO stars are slow rotators. They derived a binary fraction of ∼ MNRAS , 1–9 (2020) inary-driven stellar rotation evolution . . . . . . / Ω crit P r o b a b ili t y d i s t r i bu t i o n NGC 3960NGC 6134IC 4756NGC 5822NGC 2818 . . . . . . Ω / Ω crit . . . . . N u m b e r f r a c t i o n NGC 3960 . . . . . . Ω / Ω crit . . . . . N u m b e r f r a c t i o n NGC 6134 . . . . . . Ω / Ω crit . . . . . . . . . N u m b e r f r a c t i o n NGC 2818 . . . . . . Ω / Ω crit . . . . . N u m b e r f r a c t i o n NGC 5822 . . . . . . Ω / Ω crit . . . . . . . . N u m b e r f r a c t i o n IC 4756
Figure 6. (top left) Rotation rate ( Ω 𝑖 / Ω crit , ZAMS ) probability distribution of the MSTO stars according to the best-fitting models. The arrows indicate thevelocities adopted for selection of the slowly and rapidly rotating subsamples in each of our clusters, corresponding to the local minima of the (mostly) bimodaldistributions. (small panels) Rotation-rate distributions (bottom, top axes) for (clockwise from top right) NGC 3960, NGC 6134, IC 4756, NGC 5822 and NGC2818. a larger fraction of slow rotators for a higher binary fraction, every-thing else being equal, the fraction of slow rotators can never exceedthe binary fraction. Since only close binaries may become tidallylocked, only a small subset of binaries could contribute. However,as shown in Fig. 7, the slow rotators’ number ratios are comparableto or even higher than the binary fractions. Moreover, the slope be-tween 𝑁 slow / 𝑁 tot and 𝑓 b is close to unity regardless of the subsampleselection, thus suggesting an alternative binary-driven mechanism.However, we cannot rule out a possible origin associated with theinitial phase. The slow rotators we observe at the present time orig- inate from both the initial population of slow rotators and may alsohave evolved from the fast rotators. Huang et al. (2010, their figure 7)selected a young subpopulation of B-type stars that just evolved fromthe zero-age main sequence and showed that a large fraction of themwere formed as slow rotators. So far, it is unclear which physicalproperty of (close and wide) binaries determines the rotation distri-butions. This may explain why Kamann et al. (2020) did not find anysignificant differences among the binary fractions of slow and fastrotators. If we consider the possibility of missing binaries from their MNRAS000
Figure 6. (top left) Rotation rate ( Ω 𝑖 / Ω crit , ZAMS ) probability distribution of the MSTO stars according to the best-fitting models. The arrows indicate thevelocities adopted for selection of the slowly and rapidly rotating subsamples in each of our clusters, corresponding to the local minima of the (mostly) bimodaldistributions. (small panels) Rotation-rate distributions (bottom, top axes) for (clockwise from top right) NGC 3960, NGC 6134, IC 4756, NGC 5822 and NGC2818. a larger fraction of slow rotators for a higher binary fraction, every-thing else being equal, the fraction of slow rotators can never exceedthe binary fraction. Since only close binaries may become tidallylocked, only a small subset of binaries could contribute. However,as shown in Fig. 7, the slow rotators’ number ratios are comparableto or even higher than the binary fractions. Moreover, the slope be-tween 𝑁 slow / 𝑁 tot and 𝑓 b is close to unity regardless of the subsampleselection, thus suggesting an alternative binary-driven mechanism.However, we cannot rule out a possible origin associated with theinitial phase. The slow rotators we observe at the present time orig- inate from both the initial population of slow rotators and may alsohave evolved from the fast rotators. Huang et al. (2010, their figure 7)selected a young subpopulation of B-type stars that just evolved fromthe zero-age main sequence and showed that a large fraction of themwere formed as slow rotators. So far, it is unclear which physicalproperty of (close and wide) binaries determines the rotation distri-butions. This may explain why Kamann et al. (2020) did not find anysignificant differences among the binary fractions of slow and fastrotators. If we consider the possibility of missing binaries from their MNRAS000 , 1–9 (2020)
W. Sun et al. . . . . f b . . . . . . . . N s l o w / N t o t NGC 3960NGC 6134IC 4756NGC 5822NGC 2818NGC 1866 (200 Myr)NGC 1818 (40 Myr)NGC 330 (40 Myr)
Figure 7.
Number fraction of slow rotators to the total number of MSTOstars in the best-fitting synthetic cluster versus their binary fractions. Theuncertainties in 𝑁 slow / 𝑁 tot were estimated by resampling the best-fittingmodel parameters. The correlation between 𝑁 slow / 𝑁 tot and 𝑓 b suggests abinary-driven mechanism behind the rotation rates. The majority of MCclusters reside in the dashed rectangle. Three young MC clusters—NGC1866, NGC 1818 and NGC 330—are shown using grey symbols (their agesare included in the legend). The deviations of these younger clusters from thecorrelation suggest that they may be at an earlier stage of tidal braking. sample, combined with the disruption of wide binaries, there couldbe distinct differences between slow and fast rotating populations.If binaries are the dominant drivers of slow rotators, one wouldexpect slow rotators to be more centrally concentrated in a clusterbecause they are generally more massive than their rapidly rotatingcounterparts, and they would thus sink more easily to the clustercentre owing to two-body relaxation (dynamical mass segregation;Binney & Tremaine 1987). However, this scenario appears at oddswith recent observations in young MC clusters. Dupree et al. (2017)and Milone et al. (2017) found that in NGC 1866 ( ∼
400 Myr), bMSstars (slow rotators) are less centrally concentrated than rMS stars(fast rotators). Meanwhile, in NGC 1856 ( ∼
300 Myr-old), the num-ber ratios of bMS and rMS stars remain unchanged at different radii,thus suggesting that they are spatially homogeneously distributed (Liet al. 2017b).We used the best-fitting synthetic cluster to infer the rotationalvelocities for all member stars (Sun et al. 2019a) and employed thespatial locations of the observed stars to estimate their degree ofmass segregation. Because of their low number densities, it is hardto robustly determine the centres of OCs. Therefore, we adoptedminimum spanning trees (MSTs) to quantify a cluster’s degree ofmass segregation (Allison et al. 2009). The mass segregation ratio, Λ MSR , of a given population is defined as the ratio of the averagerandom path length, 𝑙 random , to that of the entire population, 𝑙 pop , Λ MSR = (cid:104) 𝑙 random (cid:105) 𝑙 pop ± 𝜎 random 𝑙 pop , (2)where 𝑙 represents the length of the shortest path connecting alldata points and (cid:104) 𝑙 random (cid:105) ± 𝜎 random quantifies the length distribution. We determined the OCs’ MSTs using MiSTree (Naidoo 2019), incelestial coordinates. Given our OCs’ close proximity and the lowstellar densities, the impact of sampling incompleteness of the low-mass stars in estimating Λ MSR is negligible.To link our results with the observations of blue and red MSs, weadopted bMS stars as those stars with 𝑣 sin 𝑖 <
150 km s − , whereasrMS stars have 𝑣 sin 𝑖 >
150 km s − . This velocity threshold wasselected based on the velocity dip at 𝑣 sin 𝑖 ≈
100 km s − observedin NGC 1846 (Kamann et al. 2020). Given the mass differencesof MSTO stars in clusters with different ages, this corresponds to 𝑣 sin 𝑖 ≈
150 km s − for our sample. We assumed that the rotationrate ( Ω / Ω crit ) of the dip does not change for clusters of either 1 Gyr or1.5 Gyr (NGC 1846). The critical rotation velocity only marginallydecreases as a star evolves, whereas the rotation velocity stronglydepends on stellar mass (Bastian et al. 2020, their figure 1). Thetypical MSTO stellar mass is around 1 . − . (cid:12) and 1 . (cid:12) forNGC 1846 and our cluster sample, respectively. Based on Georgy etal. (2014), the velocity dip for bMS and rMS should be ∼ Λ MSR values are listed in Table 1. In all clus-ters, except for NGC 2818, the bMS stars exhibit significant spatialsegregation, Λ MSR >
1. Moreover, Λ MSR , b > Λ MSR , r in NGC 3860and NGC 5822, with differences > 𝜎 . This suggests that the bMSstars in these clusters are more centrally concentrated than their rMScounterparts. This, hence, offers promising supporting evidence ofa more massive origin of the bMS stars in these OCs. However, thisis at odds with MC cluster results (e.g., Milone et al. 2017; Kamannet al. 2020). The difference could be attributed to binary disruptionin the cluster centre. Milone et al. (2017) found the binary fractionto increase towards the cluster outskirts, following the same radialdistribution as the bMS stars in NGC 1866, whereas this effect is notobvious in OCs.In summary, we have discovered a strong observational correlationbetween the number ratios of the slow rotators and the binary frac-tions in five Galactic OCs and shown support for a marked concen-tration of bMS stars. Future work will extend the survey to youngerclusters, cover a larger parameter space (e.g., in 𝑓 b , stellar and clus-ter mass, metallicity, etc.) and study the detailed history of stellarrotation in cluster environments to gain additional important insightsinto the star cluster formation processes. ACKNOWLEDGEMENTS
W.S. thanks Xiao-Wei Duan for insightful discussions. He is grate-ful for financial support from the China Scholarship Council. L.D.acknowledges research support from the National Natural ScienceFoundation of China through grants 11633005, 11473037 andU1631102. This work has made use of data from the EuropeanSpace Agency (ESA) mission
Gaia ( ), processed by the Gaia
Data Processing and AnalysisConsortium (DPAC, ). DATA AVAILABILITY
The data analysed in this paper will be shared upon request.
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APPENDIX A: DYNAMICAL TIMESCALE
Dynamical modelling of OCs is rendered uncertain by the smallnumbers of their member stars. To derive approximate dynamicalages for our sample OCs, we calculated their half-mass relaxationtime-scales (Meylan 1987), 𝑡 rh = . × 𝑀 / ¯ 𝑚 𝑟 / ln ( . 𝑀 tot / ¯ 𝑚 ) yr , (A1)where 𝑟 is the half-mass radius derived from number counts, 𝑀 tot is the total mass derived following Sun et al. (2019a) and ¯ 𝑚 is thetypical mass of stars in the cluster. This estimate yields relativelysimilar half-mass relaxation time-scales for all of our sample OCs,ranging from ∼
60 Myr to ∼
120 Myr. We double checked this resultby comparison with Binney & Tremaine (1987) 𝑡 relax = 𝑁 𝑁 𝑡 cross , (A2)where 𝑡 cross = 𝑟 / 𝜎 𝑣 is the crossing time, 𝑁 is the total number ofstars and 𝜎 𝑣 is the velocity dispersion. We adopted the latter fromSoubiran et al. (2018). Both estimates are in reasonable mutual agree-ment, in the sense that the clusters’ dynamical time-scales are around100 Myr, varying by a factor of up to 2. This means that our clus-ters have evolved through approximately 9–16 half-mass relaxationtime-scales and share similar dynamical ages. This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS000