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Ages of Young Star Clusters, Massive Blue Stragglers, and the Upper Mass Limit of Stars: Analyzing Age-Dependent Stellar Mass Functions

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Ages of Young Star Clusters, Massive Blue Stragglers, and the Upper Mass Limit of Stars: Analyzing Age-Dependent Stellar Mass Functions The Astrophysical Journal, 780:117 (16pp), 2014 January 10 doi:10.1088/0004-637X/780/2/117 C 2014. The American Astronomical Society. All rights reserved. Printed in the U.S.A. AGES OF YOUNG STAR CLUSTERS, MASSIVE BLUE STRAGGLERS, AND THE UPPER MASS LIMIT OF STARS: ANALYZING AGE-DEPENDENT STELLAR MASS FUNCTIONS F. R. N. Schneider1, R. G. Izzard1,S.E.deMink2,3,11, N. Langer1, A. Stolte1, A. de Koter4,5, V. V. Gvaramadze6,7,B.Hußmann1, A. Liermann8,9, and H. Sana4,10 1 Argelander-Institut fur¨ Astronomie der Universitat¨ Bonn, Auf dem Hugel¨ 71, D-53121 Bonn, Germany; [email protected] 2 Observatories of the Carnegie Institution for Science, 813 Santa Barbara St, Pasadena, CA 91101, USA 3 Cahill Center for Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA 4 Astronomical Institute “Anton Pannekoek”, Amsterdam University, Science Park 904, 1098 XH, Amsterdam, The Netherlands 5 Instituut voor Sterrenkunde, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium 6 Sternberg Astronomical Institute, Lomonosov Moscow State University, Universitetskij Pr. 13, Moscow 119992, Russia 7 Isaac Newton Institute of Chile, Moscow Branch, Universitetskij Pr. 13, Moscow 119992, Russia 8 Max Planck Institut fur¨ Radioastronomie, Auf dem Hugel¨ 69, D-53121 Bonn, Germany 9 Leibniz Institute for Astrophysics Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam, Germany 10 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA Received 2013 September 15; accepted 2013 November 13; published 2013 December 16 ABSTRACT Massive stars rapidly change their masses through strong stellar winds and mass transfer in binary systems. The latter aspect is important for populations of massive stars as more than 70% of all O stars are expected to interact with a binary companion during their lifetime. We show that such mass changes leave characteristic signatures in stellar mass functions of young star clusters that can be used to infer their ages and to identify products of binary evolution. We model the observed present-day mass functions of the young Galactic Arches and Quintuplet star clusters using our rapid binary evolution code. We find that the shaping of the mass function by stellar wind mass loss allows us to determine the cluster ages as 3.5 ± 0.7 Myr and 4.8 ± 1.1 Myr, respectively. Exploiting the effects of binary mass exchange on the cluster mass function, we find that the most massive stars in both clusters are rejuvenated products of binary mass transfer, i.e., the massive counterpart of classical blue straggler stars. This resolves the problem of an apparent age spread among the most luminous stars exceeding the expected duration of star formation in these clusters. We perform Monte Carlo simulations to probe stochastic sampling, which support the idea of the most massive stars being rejuvenated binary products. We find that the most massive star is expected to be a binary product after 1.0 ± 0.7 Myr in Arches and after 1.7 ± 1.0 Myr in Quintuplet. Today, the most massive 9 ± 3 stars in Arches and 8 ± 3 in Quintuplet are expected to be such objects. Our findings have strong implications for the stellar upper mass limit and solve the discrepancy between the claimed 150 M limit and observations of four stars with initial masses of 165–320 M in R136 and of supernova 2007bi, which is thought to be a pair-instability supernova from an initial 250 M star. Using the stellar population of R136, we revise the upper mass limit to values in the range 200–500 M. Key words: binaries: general – blue stragglers – open clusters and associations: individual (Arches, Quintuplet) – stars: luminosity function, mass function – stars: mass-loss Online-only material: color figures 1. INTRODUCTION expected to form stars in a time span shorter than the lifetime of their most massive members (Elmegreen 2000; Kudryavtseva Massive stars play a key role in our universe. They drive et al. 2012). In contrast, the most luminous stars in two of the the chemical evolution of galaxies by synthesizing most of the richest young clusters in our Galaxy, the Arches and Quintuplet heavy elements. Their strong stellar winds, radiation feedback, clusters, show an apparently large age range. Their hydrogen- powerful supernova explosions, and long gamma-ray bursts and nitrogen-rich Wolf–Rayet (WNh) stars appear significantly shape the interstellar medium. They are thought to have played younger than most of their less luminous O stars (Martins et al. an essential role in reionizing the universe after the dark ages 2008; Liermann et al. 2012). Similar age discrepancies are ob- and are visible up to large distances. served in other young stellar systems (Massey 2003), such as Unfortunately, our understanding of the formation and evolu- the Cyg OB2 association (Herrero et al. 1999; Gvaramadze tion of the most massive stars in the local universe is incomplete & Bomans 2008a; Negueruela et al. 2008) and the star (Langer 2012). Recently, it was established that most of the clusters Pismis 24 (Gvaramadze et al. 2011) and NGC 6611 massive stars in the Milky Way are actually part of a binary star (Hillenbrand et al. 1993; Gvaramadze & Bomans 2008b). system and that more than 70% of them will exchange mass The second controversy, the maximum stellar mass problem, with a companion during their life (Sana et al. 2012). Our un- concerns the stellar upper mass limit. Such an upper mass limit derstanding of these stars is further hampered by two major is theoretically motivated by the Eddington limit, which may controversies. The first one, the cluster age problem, concerns prevent stellar mass growth by accretion above a certain mass the ages of the youngest star clusters. Emerging star clusters are (Larson & Starrfield 1971). Observationally, an upper mass limit of about 150 M is derived from the individual stellar 11 Einstein Fellow. mass distributions of the Arches and the R136 clusters (Weidner 1 The Astrophysical Journal, 780:117 (16pp), 2014 January 10 Schneider et al. & Kroupa 2004; Figer 2005; Koen 2006) and from a broader of the stellar masses and of other stellar properties as a function analysis of young stellar clusters (Oey & Clarke 2005). This of time. Our code is based on a rapid binary evolution code result is questioned by a recent analysis of very massive stars (Hurley et al. 2002) that uses analytic functions (Hurley et al. in the core of R136, in which stars with initial masses of up to 2000) fitted to stellar evolutionary models with convective core about 320 M are found (Crowther et al. 2010). Furthermore, overshooting (Pols et al. 1998) to model the evolution of single recently detected ultraluminous supernovae in the local universe stars across the whole Hertzsprung–Russell diagram. We use a are interpreted as explosions of very massive stars (Langer et al. metallicity of Z = 0.02. 2007); for example, SN 2007bi is well explained by a pair- Stellar wind mass loss (Nieuwenhuijzen & de Jager 1990)is instability supernova from an initially 250 M star (Gal-Yam applied to all stars with luminosities larger than 4000 L (Hurley et al. 2009; Langer 2009). et al. 2000). The mass accretion rate during mass transfer is Here we show that both controversies can be resolved by limited to the thermal rate of the accreting star (Wellstein et al. considering a time-dependent stellar mass function in young 2001). Binaries enter a contact phase and merge if the mass ratio star clusters that accounts for stellar wind mass loss and binary of accretor to donor is smaller than a critical value at the onset mass exchange. We perform detailed population synthesis of Roche lobe overflow (RLOF; de Mink et al. 2013a). When calculations of massive single and binary stars that include two main-sequence (MS) stars merge, we assume that 10% of all relevant physical processes affecting the stellar masses and the total mass is lost and that 10% of the envelope mass is mixed compare them to the observed present-day mass functions with the convective core (de Mink et al. 2013a). of the Arches and Quintuplet clusters. Our methods and the Photometric observations of star clusters cannot resolve observations of the mass functions of the Arches and Quintuplet individual binary components. In order to compare our models clusters are described in Section 2. We analyze the Arches to observations we assume that binaries are unresolved in our and Quintuplet clusters in Section 3 to derive cluster ages models and determine masses from the combined luminosity of and identify possible binary products by fitting our models to both binary components utilizing our mass–luminosity relation. the observed mass functions. Stochastic sampling effects are Hence, unresolved, preinteraction binaries contribute to our investigated in Section 4, and the implications of our findings mass functions. for the upper mass limit are explored in Section 5. We discuss We concentrate on MS stars because stars typically spend our results in Section 6 and give final conclusions in Section 7. about 90% of their lifetime in this evolutionary phase; moreover, our sample stars used for comparison are observationally color 2. METHODS AND OBSERVATIONAL DATA selected to remove post-MS objects. If a binary is composed of a post-MS and an MS star, we take only the MS component into We analyze the Arches and Quintuplet clusters in two account. steps. First, we model their observed stellar mass functions to determine, e.g., the initial mass function (IMF) slopes and the 2.2. Initial Distribution Functions for cluster ages. We set up a dense grid of single and binary stars, Stellar Masses and Orbital Periods assign each stellar system in the grid a probability of existence We assume that primary stars in binaries and single stars given the initial distribution functions (see Section 2.2), and have masses M distributed according to a power-law IMF evolve the stars in time using our rapid binary evolution 1 with slope Γ, code (see Section 2.1).
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