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Measuring the Binary Fraction of Massive Stars Using Young Star Clusters: the Resolved Cluster RSGC1

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Measuring the Binary Fraction of Massive Stars Using Young Star Clusters: the Resolved Cluster RSGC1 MNRAS 000,1{9 (2017) Preprint 21 April 2017 Compiled using MNRAS LATEX style file v3.0 Measuring the binary fraction of massive stars using young star clusters: the resolved cluster RSGC1 Ben Davies1,? J.J. Eldridge2, Emma R. Beasor1, Nate Bastian1, Rolf-Peter Kudritzki3 1Astrophysics Research Institute, Liverpool John Moores University, Liverpool Science Park ic2, 146 Brownlow Hill, Liverpool L3 5RF, UK 2Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand 3Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA Accepted XXX. Received YYY; in original form ZZZ ABSTRACT We present a new method to measure the binary fraction of a star cluster by comparing its dynamical mass Mdyn to the photometric mass Mphot as determined from the near-infrared flux. The latter quantity is extremely dependent on the number of Red Supergiants (RSGs) per unit cluster mass, which itself is very sensitive to the binary fraction fbin of the stars in the cluster which had the same initial mass as those currently in the RSG phase. In this technique we employ two species of population synthesis models, one consisting of single stars and the other of binaries, to obtain two estimates of Mphot. We then combine the two populations, adjusting fbin to optimise the agreement between Mdyn and the total Mphot. In this paper we use the resolved Milky Way cluster RSGC1 as our first test object. Formally, the derived binary fraction +27 for the stars of the same mass as the RSGs, in this case ∼18M , is fbin=37−23. However, when considering all possible sources of systematic error on both Mdyn and Mphot, we find that this value can only decrease, implying that our measurement of fbin is an upper limit. This result is somewhat at odds with other recent estimates of binary fractions of massive stars as measured from radial velocity surveys in massive your clusters, which have yielded values of fbin in the region of 50-80%. After considering several possible causes for this discrepancy, we suggest that most likely explanations are that either fbin decreases for stars with masses ∼<20M , the period distribution of massive binaries is skewed towards longer periods for lower primary star masses, or stellar models underestimated the RSG lifetime by ∼30%. Key words: binaries: general { stars: massive { stars: evolution 1 INTRODUCTION tion for massive stars may be very high, 50 − 70% (Sana et al. 2012, 2013). These results imply that effects of bina- It has long since been known that a substantial fraction rity on the evolution of massive stars cannot be neglected, (>50%) of massive stars are in binaries, and that the com- ∼ and therefore call into question all predictions for massive panion mass distribution is skewed to higher masses than stellar evolution which have their foundation in single-star would be expected if it were randomly sampled from the models. initial mass function (IMF) (e.g. Abt & Levy 1978; Gar- many et al. 1980; Gies 1987; Mason et al. 1998; Garc´ıa & Though the details of binary interaction (e.g. mass Mermilliod 2001; Kobulnicky & Fryer 2007). In terms of the transfer, common envelope evolution) are complex and can impact of binarity on stellar evolution, the important quan- vary greatly from system to system, the augmentation of tity is not what fraction of massive stars are in binaries, but the star's evolution across the H-R diagram is driven largely what fraction will interact during their lifetime. The most re- by one effect: the stripping of all or part of the star's enve- cent measurements indicate that the interacting binary frac- lope by the companion at a rate far beyond that possible by the star's wind alone (e.g. Vanbeveren 1991; Podsiadlowski et al. 1992; Vanbeveren et al. 2007). This can prevent the ? E-mail: [email protected] star from evolving to the Red Supergiant (RSG) phase, and c 2017 The Authors 2 B. Davies et al. instead favour the formation of a Blue Supergiant (BSG) or RSGs in the region of the Scutum tangent region of the a Wolf-Rayet (WR). Averaged over a population of stars, Milky Way (Figer et al. 2006, hereafter F06). The radial ve- this results in (a) bluer integrated colours; (b) an increase locities of each of the RSGs, their luminosities, and the clus- in the integrated ionising flux; and (c) an increase in the ter's distance and half-light radius, were measured in Davies rate of stripped or partially-stripped (i.e. type Ibc, IIb) to et al.(2008, hereafter D08). These authors determined a dy- 4 unstripped (i.e. type II-P or II-L) core-collapse supernovae namical mass for this cluster of (5±1) ×10 M . (e.g. Belkus et al. 2003; Eldridge et al. 2008; Stanway et al. 2014, 2016). 2.1 Estimating the photometric mass Since there are a broad range of possible outcomes from close binary interaction, to test the predictions of binary star The first step is to determine RSGC1's photometric mass evolution we need to average over a population of stars. To Mphot from both assumptions of single star and binary evo- do this, we need to know the binary fraction, the mass ratio lution. We do this with a comparison to BPASS v2.0 evo- and period distribution functions, and how these quantities lutionary models (Eldridge et al. 2008; Eldridge & Stanway depend on e.g. the mass of the primary, metallicity, and clus- 2009; Stanway et al. 2016), which provide predicted photom- tered versus unclustered environment. Measurements thus etry from population synthesis using both single star and bi- far have concentrated on multi-epoch studies of resolved nary evolutionary calculations. The latter include the effects star-forming regions, looking for periodic radial velocity vari- of Roche-lobe overflow and common-envelope evolution on ables, and determining the binary fraction after first cor- the integrated spectral appearance of a stellar population, recting for observational biases (e.g. Sana et al. 2012). Since at the expense of two extra free functions { the distribution the mass ratio and period distribution functions can also be functions of the mass-ratios (q ≡ M2=M1) and the orbital modelled, the fraction of stars that will undergo binary in- separations a (or periods, P ). In BPASS these two distribu- teraction can also be estimated. These studies have yielded tions are assumed to be flat between 0 ≤ log(P=days) ≤ 4 bias-corrected binary fractions for massive stars of fbin of and 0:1 ≤ q ≤ 0:9 (Eldridge et al. 2008). 50-70% (Sana et al. 2012, 2013). Further, it has been argued Our methodology can be summarised as follows: we as- that these numbers may be systematically underestimated, sume an instantaneous starburst event, and use BPASS to since radial velocity surveys are insensitive to primordial predict the integrated K-band flux of the stellar population binary systems that have already merged (de Mink et al. as a function of age and total cluster mass for the cases of 2014). 100% single stars and 100% binaries. We then compare to In this paper, we provide a totally independent method the sum of the K-band fluxes of the RSGs in RSGC1, as- of inferring a star cluster's binary fraction. It is based on suming that the rest of the cluster's stellar population con- using population synthesis to estimate the number of RSGs tribute negligible flux at this wavelength (following Gazak present in a cluster as a function of its mass and age. If we et al. 2012, 2014), to derive the cluster mass for each case. have an independent measurement of a cluster's mass, such In practice, there are several steps involved in convert- as the dynamical mass Mdyn estimated from the cluster's ve- ing the cluster flux into a mass, each with its own uncer- locity dispersion vdisp, we can then compare this to mass es- tainty, which can be non-linear and asymmetric. To fully timated by fitting the number of RSGs (or equivalently, the take account of these errors, we employ a Monte-Carlo (MC) cluster's integrated near-infrared brightness) using both sin- approach to determine the probability density function of gle star and binary population synthesis (hereafter Mphot;sin the cluster's photometric mass. Below we describe each step and Mphot;bin respectively). In the absence of any system- in detail. atic errors1, a binary fraction of zero should result in perfect agreement between Mphot;sin and Mdyn. Conversely, a bi- 2.1.1 Cluster distance, D nary fraction of unity would be implied by Mphot;bin=Mdyn. In practice, we expect the values of Mphot;sin and Mphot;bin In D08, RSGC1's kinematic distance was determined from should bracket Mdyn, which then tells us the binary fraction the average radial velocity of its RSGs. When compared to fbin. the Galactic rotation curve, this placed the cluster close to We begin in Sect.2 where we apply this technique to the tangent point, at a distance of 6.6kpc. When considering the resolved star cluster, RSGC1, and measure its binary local random deviations from the rotation curve, errors in fraction. We will discuss at length the possible sources of the distance to the Galactic centre and the rotation speed of systematic error on the three mass estimates, and the impli- the Sun, as well as uncertainties in cluster's radial velocity, cations for our conclusions. Our results are discussed in the D08 determined the upper and lower limits to the distance context of other binary fraction estimates in Sect.3, and we to RSGC1 to be ±0.8kpc.
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