Draft version November 13, 2018 Typeset using LATEX twocolumn style in AASTeX62 Kinematics in Young Star Clusters and Associations with Gaia DR2 Michael A. Kuhn,1 Lynne A. Hillenbrand,1 Alison Sills,2 Eric D. Feigelson,3 and Konstantin V. Getman3 1Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA 2Department of Physics & Astronomy, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4M1, Canada 3Department of Astronomy & Astrophysics, 525 Davey Laboratory, Pennsylvania State University, University Park, PA 16802, USA (Received July 5, 2018; Revised October 31, 2018; Accepted November 5, 2018) Submitted to ApJ ABSTRACT The Gaia mission has opened a new window into the internal kinematics of young star clusters at the sub-km s−1 level, with implications for our understanding of how star clusters form and evolve. We use a sample of 28 clusters and associations with ages from ∼1{5 Myr, where lists of members are available from previous X-ray, optical, and infrared studies. Proper motions from Gaia DR2 reveals that at least 75% of these systems are expanding; however, rotation is only detected in one system. Typical expansion velocities are on the order of ∼0.5 km s−1, and, in several systems, there is a positive radial gradient in expansion velocity. Systems that are still embedded in molecular clouds are less likely to be expanding than those that are partially or fully revealed. One-dimensional velocity −1 dispersions, which range from σ1D = 1 to 3 km s , imply that most of the stellar systems in our sample are supervirial and that some are unbound. In star-forming regions that contain multiple clusters or subclusters, we find no evidence that these groups are coalescing, implying that hierarchical cluster assembly, if it occurs, must happen rapidly during the embedded stage. Keywords: astrometry; stars: formation; stars: kinematics and dynamics; open clusters and associa- tions: general 1. INTRODUCTION (Feigelson 2018), while the Gaia mission (Gaia Collabo- While star formation in the Galaxy occurs in large ration et al. 2016) is expected to revolutionize the study star-forming complexes, most of the stars formed in of their internal kinematics (Allison 2012; Clarke et al. these complexes quickly disperse into the field without 2015; Moraux 2016). remaining bound to one another as members of open The kinematics of young stars should reflect the pro- clusters (Adams 2010; Gouliermis 2018). Star formation cesses of star cluster formation. Two principal paths takes place in turbulent, clumpy giant molecular clouds, from theoretical studies are: \monolithic" cluster for- and yet the star clusters that do remain bound tend to mation, in which a young star cluster is born in a single have smooth stellar density distributions. The processes molecular cloud core, and \hierarchical" cluster forma- of cluster assembly, equilibration, and dissolution have tion, in which larger clusters are built via the accumu- remained poorly constrained by observation for two rea- lation of smaller subclusters (Elmegreen 2000; Bonnell sons: the difficulty of obtaining reliable samples of clus- et al. 2003; Banerjee & Kroupa 2015). Young stellar objects (YSOs) that are embedded or partially embed- arXiv:1807.02115v3 [astro-ph.GA] 11 Nov 2018 ter members in nebulous regions with many field star contaminants and the absence of kinematic information ded in star-forming clouds typically have clumpy distri- for faint stars. The nearby Orion Nebula Cluster (ONC) butions, where groups are known as subclusters (e.g., has been extensively characterized, but these difficul- Aarseth & Hills 1972; Lada & Lada 1995; Kuhn et al. ties have been overcome only more recently for other 2014; Megeath et al. 2016; Sills et al. 2018). It has been massive star-forming complexes. In these regions, sam- unclear, however, whether the subclusters will disperse ples of members emerge from multi-wavelength surveys once the molecular gas disperses, or if they will merge into larger, possibly bound clusters that survive gas ex- pulsion. Examination of the motions of these subclus- Corresponding author: Michael A. Kuhn ters can help constrain cluster formation scenarios. [email protected] The evolution of a young cluster depends on its dy- namical state (e.g., Parker et al. 2014; Sills et al. 2018), 2 Kuhn et al. as well as changes in the gravitational potential due Section7 relates internal cluster kinematics to other to the dispersal of the molecular cloud (e.g., Tutukov physical properties. A discussion of the observational 1978; Hills 1980) and tidal interactions with clouds results, along with a comparison to a cluster formation and clusters (e.g., Kruijssen 2012). Much attention simulation, are provided in Section8. Section9 is the has been focused on the role of gas expulsion, which conclusion. will cause a cluster to expand and can cause bound embedded clusters to become unbound (Mathieu 1983; 2. DATA SETS Elmegreen 1983; Adams 2000; Kroupa et al. 2001; Good- 2.1. YSOs in Clusters and Associations win & Bastian 2006; Pelupessy & Portegies Zwart 2012; Brinkmann et al. 2017). However, recent simulations This Gaia study is based on samples of YSOs, with have suggested that gas expulsion may play a less im- typical ages of 1{5 Myr, from the Massive Young Star- portant role in cluster disruption if there is spatial de- Forming Complex Study in Infrared and X-ray survey coupling between stars and gas (Dale et al. 2015). (MYStIX; Broos et al. 2013; Feigelson et al. 2013), the The empirical relationship between size and density of Star-Formation in Nearby Clouds study (SFiNCs; Get- young star clusters and associations provides indirect ev- man et al. 2017), and a similar study of NGC 6231 idence for their expansion (Pfalzner 2009, 2011; Pfalzner (Kuhn et al. 2017b). In each of these studies, X-ray et al. 2014). For subclusters, size has been found to be emission was used to classify probable cluster members negatively correlated with density, and positively corre- based on the higher expected X-ray luminosities of pre{ lated with age, as would be expected if they were ex- main-sequence stars compared to main-sequence field panding (Kuhn et al. 2015a; Getman et al. 2018a). Fur- stars. MYStIX and SFiNCs also include sources selected thermore, Marks & Kroupa(2012) argue that the low by infrared excess, which indicates YSOs with disks and binary fractions observed in young star clusters imply envelopes that may or may not be X-ray emitters. The these clusters were more compact upon formation. infrared-selected samples come from Povich et al.(2013) Direct evidence of cluster expansion via proper-motion and Getman et al.(2017), with careful attention to re- measurements has been difficult to obtain. Recent stud- duce contamination by post{main-sequence dusty red ies of OB associations have yielded either no evidence giants. Reducing field star contamination is particularly of expansion (Ward & Kruijssen 2018) or no evidence of important for these massive star forming regions that lie expansion from a single compact system (Wright et al. in the Galactic Plane. 2016; Wright & Mamajek 2018). For the ONC, there In this study, we include only the regions that contain has long been debate about whether the system is ex- rich clusters visible in the optical. We omit the regions panding or contracting (Muench et al. 2008). In recent with few stars, and those for which Gaia is limited by work, Dzib et al.(2017) find no evidence of expansion high optical extinction (e.g., Serpens South or DR 21). or contraction of the ONC using proper motions from For inclusion in our study, a region must contain at least radio observations, while Da Rio et al.(2017) report a 20 cluster members with reliable Gaia proper motions. correlation between radial velocity (RV) and extinction These criteria yield a sample of 28 star clusters and as- that can be explained by expansion, and Kounkel et al. sociations which reside in 21 star-forming regions (Ta- (2018) report a preference for expansion among stars ble1). around the outer edges of Orion A. In this paper, we use the term \stellar system" to indi- In this paper, we use the superb astrometry of Gaia's cate a major group of spatially associated stars, which Second Data Release (DR2; Gaia Collaboration et al. includes embedded clusters, bound open clusters, and compact associations of unbound stars (Kuhn et al. 2018a) to elucidate the formation (evidence for or 1 against hierarchical assembly) and dynamical state 2014). Some of the regions contain multiple stellar (expansion, contraction, or equilibrium) of young star systems that are analyzed individually. Notable exam- clusters. We use a sample of young star clusters and ples include NGC 2264 (containing a loose association associations, ranging from 0.3{3.7 kpc, that were the around S Mon and embedded clusters around IRS 1 and focus of a series of studies combining NASA's Chandra IRS 2 adjacent to the Cone Nebula), NGC 6357 (con- X-ray, Spitzer mid-infrared, and ground-based optical taining Pismis 24, G353.1+0.6, and G353.2+0.7), the and near-infrared images to provided reliable samples Carina Nebula (including Tr 14, Tr 15, and Tr 16), and of tens-of-thousands of YSOs (Feigelson et al. 2013; the Cep OB3b association (containing a group to the Getman et al. 2017; Kuhn et al. 2017b). Section2 describes the data, and Section3 derives 1 Historically, it has been difficult to distinguish between bound basic cluster properties that are used in the analysis. and unbound young stellar systems from observations. Studies Section4 addresses the question of whether clusters are of cluster density have shown that there is no density threshold in equilibrium, expanding, or contracting, and whether that divides \clustered" and \distributed" star formation (e.g., Bressert et al.