MNRAS 000,1–9 (2020) Preprint 5 February 2021 Compiled using MNRAS LATEX style file v3.0 Binary-driven stellar rotation evolution at the main-sequence turn-off in star clusters Weijia Sun1,2,3,4¢ Richard de Grijs3,4,5, Licai Deng2,6,7 and Michael D. Albrow8 1Department of Astronomy, School of Physics, Peking University, Beijing 100871, China 2Key Laboratory for Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing 100012, China 3Department of Physics and Astronomy, Macquarie University, Balaclava Road, Sydney, NSW 2109, Australia 4Centre for Astronomy, Astrophysics and Astrophotonics, Macquarie University, Balaclava Road, Sydney, NSW 2109, Australia 5International Space Science Institute–Beijing, 1 Nanertiao, Zhongguancun, Hai Dian District, Beijing 100190, China 6School of Astronomy and Space Science, University of the Chinese Academy of Sciences, Huairou 101408, China 7Department of Astronomy, China West Normal University, Nanchong 637002, China 8School 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 poorly understood. Using Gaia Data Release 2 photometry and new Southern African Large Telescope medium-resolution spectroscopy, we analyse the intermediate-age (∼ 1 Gyr-old) Galactic open clusters NGC 3960, NGC 6134 and IC 4756 and develop a novel method to derive their stellar rotation distributions based on SYCLIST stellar rotation models. Combined with literature data for the open clusters NGC 5822 and NGC 2818, we find a tight correlation between the number ratio of slow rotators and the clusters’ binary fractions. The blue-main-sequence stars in at least two of our clusters are more centrally concentrated than their red-main-sequence counterparts. The origin of the equatorial stellar rotation distribution and its evolution remains as yet unidentified. However, the observed correlation in our open cluster sample suggests a binary-driven formation mechanism. Key words: galaxies: star clusters: general – techniques: spectroscopic 1 INTRODUCTION tational velocity distribution was confirmed for NGC 2287 (Sun et al. 2019b), where the well-separated double MS in this young OC is Extended main-sequence turn-offs (eMSTOs; e.g., Mackey & Broby tightly correlated with a dichotomous distribution of stellar rotation Nielsen 2007; Goudfrooij et al. 2011) and split main sequences (MSs; rates. Kamann et al.(2020) also discovered a bimodal distribution in e.g., D’Antona et al. 2015; Li et al. 2017a) pose a fundamental chal- the rotation rates of MSTO stars in the 1.5 Gyr-old cluster NGC 1846. lenge to our traditional understanding of star clusters as ‘simple stellar However, the peak rotational velocities in this cluster are slower than populations’. Both features are thought to be driven by differences in those in the younger cluster NGC 2287, thus offering a hint of stellar stellar rotation rates (e.g., Niederhofer et al. 2015), supported by an rotation evolution. increasing body of spectroscopic evidence in both Magellanic Cloud clusters (Dupree et al. 2017; Kamann et al. 2020) and Galactic open This naturally raises the question as to the origin of such a bimodal clusters (OCs; Bastian et al. 2018; Sun et al. 2019a,b). Fast rotators rotation distribution. D’Antona et al.(2015, 2017) suggested that arXiv:2102.02352v1 [astro-ph.SR] 4 Feb 2021 appear redder than their slowly rotating counterparts because of the bMS stars in young clusters might have resulted from tidal braking compound effects of gravity darkening and rotational mixing (Yang of initially fast rotators on time-scales of a few ×107 yr. Alterna- et al. 2013). tively, the bimodal rotation distribution could have been established As the effects of stellar rotation in defining the morphology of clus- within the first few Myr, regulated by either the disc-locking time- ter colour–magnitude diagrams (CMDs) are now well-understood, scale (Bastian et al. 2020) or the accretion abundance of circumstellar the rotation distributions of MSTO stars and their origin in star clus- discs (Hoppe et al. 2020). In this paper, we discover a tight corre- ters represent the next key open question. A cluster mostly composed lation between the stellar rotation rates and binary fractions in five of initially rapidly rotating stars may reproduce the observed ‘con- intermediate-age Galactic OCs with similar dynamical ages, favour- verging’ subgiant branch in NGC 419 (Wu et al. 2016). D’Antona et ing a binary-driven model. This is further supported by the greater al.(2015) argued that split MSs are composed of two coeval popula- central concentration of the bMS stars relative to the rMS population tions with different rotation rates: a slowly rotating blue-MS (bMS) in at least two of our clusters. Intriguingly, our observational results and a rapidly rotating red-MS (rMS) population. This bimodal ro- are inconsistent with the prevailing theoretical models, which thus invites more detailed future investigations. This paper is organised as follows. We present our photometric and ¢ Contact e-mail: this.is.weij[email protected] spectroscopic data reduction in Section2. Our analysis to unravel the © 2020 The Authors 2 W. Sun et al. OCs’ rotation distributions and its validation are described in Sec- same as that adopted by Sun et al.(2019a). The PG2300 grating tion3. A discussion about the formation mechanism determining the was used at a grating angle of 34.25 degrees and a camera station stellar rotation rates in clusters and our conclusions are summarised angle of 68.5 degrees. This configuration, combined with a slit width in Section4. of 1 arcsec, yields a central wavelength of 4884.4 Å and a spectral coverage of ∼4345–5373 Å at a resolving power of ' ∼ 4000 (the detector’s wavelength coverage also depends on the location of the 2 OBSERVATIONS AND DATA REDUCTION slits). Argon lamp exposures and flat-field calibration frames were taken at the end of each observation for wavelength calibration and 2.1 Photometric data flat-field correction, respectively. We did not observe standard-star spectra, since flux calibration does not affect the line profiles of the We obtained photometry and astrometry of cluster stars from Gaia Mg i triplets used for the rotational velocity estimation. Overscan Data Release (DR) 2 (Gaia Collaboration et al. 2016, 2018b) and correction, bias subtraction, gain correction and wavelength calibra- determined their cluster membership probabilities based on proper- tion were done using the PySALT package (Crawford et al. 2010). motion and parallax analysis, as follows. The exposure time was adjusted based on the average brightness of Gaia First, we downloaded the DR2 astrometry, proper mo- the stars in the mask to ensure a typical minimum signal-to-noise tions, photometry and parallaxes for all stars located within ratio (S/N) per pixel exceeding 200. 1 degree of a cluster’s centre. We selected all sources with We determined the stars’ projected rotational velocities following parallax_over_error ¡ 1 1 and a renormalised unit weight error , Sun et al.(2019a) by fitting H V and the Mg i triplet with the syn- < . 퐸 = ¹퐼 ¸퐼 º/퐼 RUWE 1 4. We also used the flux excess factor, BP RP G thetic stellar spectra from the Pollux database (Palacios et al. 2010), phot_bp_rp_excess_factor 퐼 ( )—where X is the photometric flux convolved with the rotational profile for a given rotational velocity - in band (Evans et al. 2018)—to exclude possible issues with the and implemented by adopting instrumental broadening. The error Gaia BP and RP photometry (Gaia Collaboration et al. 2018a): was estimated through a comparison of the rotational velocities of 2 2 1.0 ¸ 0.015¹퐺BP − 퐺RPº < 퐸 < 1.3 ¸ 0.06¹퐺BP − 퐺RPº . (1) the mock data with those derived through profile fitting (Sun et al. 2019a, their figure 4). For IC 4756 we also included stellar rota- The final step before member selection involved correcting the Gaia tion measurements from Schmidt & Forbes(1984) and Strassmeier magnitudes for the effects of saturation at bright magnitudes. This et al.(2015). For stars with multi-epoch observations, a variability was done by employing the equations of Evans et al.(2018). We test indicated no significant variation of either the radial or the rota- adopted the corrected magnitudes for subsequent analysis. tional velocities in our data set (except for one star in NGC 6134; see Next, to derive a clean sample of member stars, we analysed the Section4). As such, we adopted the average rotational velocity. We vector-point diagram (VPD) of the stellar proper motions and lo- thus obtained rotation measurements of 29, 25 and 49 stars in NGC cated the distribution’s centre based on 2D kernel density estimation 3960, NGC 6134 and IC 4756, respectively. In Fig.2, we present p 2 2 (KDE). A cut in `R = ¹`U cos \ − h`U cos \iº ¸ ¹` X − h` Xiº the CMDs of NGC 3960, NGC 6134 and IC 4756, with the member was applied to perform the primary membership selection. We then stars colour-coded by their rotational velocities. Combined with 24 further selected the remaining stars based on their parallaxes, s, stars in NGC 5822 and 57 in NGC 2818, we achieved 20–30 per cent rejecting all stars whose parallaxes deviated from the mean value by completeness across the eMSTO for all five clusters. This is sufficient more than four times the corresponding r.m.s. (see Fig.1). By com- to reliably derive their rotation distributions (see Section 3.1.2). paring the CMDs composed of our selection of cluster member stars with their literature counterparts (Bastian et al.