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UC Berkeley UC Berkeley Electronic Theses and Dissertations UC Berkeley UC Berkeley Electronic Theses and Dissertations Title The Initial Conditions and Evolution of Open Clusters Permalink https://escholarship.org/uc/item/48f1d45h Author Converse, Joseph Mitchell Publication Date 2010 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California The Initial Conditions and Evolution of Open Clusters by Joseph Mitchell Converse A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Astrophysics in the Graduate Division of the University of California, Berkeley Committee in charge: Doctor Steven Stahler, Co-chair Professor Chris McKee, Co-chair Professor James Graham Professor Michael Manga Fall 2010 The Initial Conditions and Evolution of Open Clusters Copyright 2010 by Joseph Mitchell Converse 1 Abstract The Initial Conditions and Evolution of Open Clusters by Joseph Mitchell Converse Doctor of Philosophy in Astrophysics University of California, Berkeley Doctor Steven Stahler, Co-chair Professor Chris McKee, Co-chair Despite being some of the most familiar objects observed in the sky, much remains unknown about open clusters. The theory of their formation admits many unanswered questions, and the complex dynamics of their evolution remains an extremely difficult problem to address. In this thesis, I present results that both help to constrain formation theories, as well as to shed new understanding on the many physical processes that drive their evolution. Starting with a photometric catalog of a cluster, I employ a maximum likelihood tech- nique to determine the mass distribution of its members, including single stars and both components of binary systems. This method allows me to determine not just the fraction of systems which are binary, but also the typical degree of correlation between the masses of their components. I also examine the spatial distribution of the cluster members. The issue of mass segregation is also addressed, introducing a new method for quantifying it. After quantifying many different properties of the cluster, N-body simulations are used to find the initial state that evolves to most closely match the current cluster. Although a few similar studies have been done in the past, I use a far larger breadth of parameters to compare with the actual data than any previous work. This results in a fairly confident determination of the properties of very young clusters, which any theory of cluster formation will be required to explain. How the cluster evolves from that initial state to the current day and beyond is also examined in detail. These techniques are used to examine two relatively close and well-known examples of open clusters: the Pleiades and the Alpha Persei cluster. In the case of the former, I find in particular that the overall binary fraction is as high as 76%, significantly higher than the accepted field-star result. The primary and secondary masses within binaries are found to be correlated, in the sense that their ratios are closer to unity than under the hypothesis of random pairing. I also find unambiguous evidence of mass segregation within the cluster. Building on these results, I find the original cluster, newly stripped of gas, to have already had a virial radius of 4 pc. This configuration was larger than most observed, embedded clusters. Over time, the cluster expanded further and the central surface density fell by about a factor of two. I attribute both effects to the liberation of energy from 2 tightening binaries of short period. Indeed, the original binary fraction was close to unity. The ancient Pleiades also had significant mass segregation, which persists in the cluster today. In the future, the central density of the Pleiades will continue to fall. For the first few hundred Myr, the cluster as a whole will expand because of dynamical heating by binaries. The expansion process is aided by mass loss through stellar evolution, which weakens the system’s gravitational binding. At later times, the Galactic tidal field begins to heavily deplete the cluster mass. Barring destruction by close passage of a giant molecular cloud, the density falloff will continue for as long as 1 Gyr, by which time most of the cluster mass will have been tidally stripped away by the Galactic field. This same analysis is also applied to Alpha Persei. Here I fist compile the most complete photometric catalog of the system to date. The stellar mass function is found to be weighted more heavily toward higher-mass stars than in the Pleiades. Also in contrast with the Pleiades, I find there to be essentially no mass segregation in the cluster, either today or in its initial state. The binary fraction, however, is found to be quite similar between the two clusters, as high as 70% in Alpha Persei. Once more the initial state is found to be quite large compared to embedded systems. The results of these two clusters together argue strongly the young clusters experience a period of significant expansion associated with the loss of their natal gas. Over time, Alpha Persei will globally expanded as a result of the Galactic tidal field. Dynamical heating by binaries, along with mass loss through stellar evolution, will also inflate the cluster into the future. I predict that Alpha Persei will completely dissolve within the next 300 Myr. Utilizing a series of N-body simulations, I go on to argue that gravitationally bound stellar clusters of modest population evolve very differently from the picture presented by classical dynamical relaxation theory. The system’s most massive stars rapidly sink towards the center and form binary systems. These binaries efficiently heat the cluster, reversing any incipient core contraction and driving a subsequent phase of global expansion. Most previous theoretical studies demonstrating deep and persistent dynamical relaxation have either conflated the process with mass segregation, ignored three-body interactions, or else adopted the artificial assumption that all cluster members are single stars of identical mass. In such a uniform-mass cluster, binary formation is greatly delayed, as we confirm here both numerically and analytically. The relative duration of core contraction and global expansion is effected by stellar evolution, which causes the most massive stars to die out before they form binaries. In clusters of higher N, the epoch of dynamical relaxation lasts for progressively longer periods. By extrapolating our results to much larger populations we can understand, at least qualitatively, why some globular clusters reach the point of true core collapse. i TO MY MOTHER ii Contents List of Figures v List of Tables vii Acknowledgments viii 1 Introduction and Outline 1 1.1 Clusters of Stars . 1 1.2 Present Understanding . 2 1.2.1 The Formation of Open Clusters . 2 1.2.2 Stellar Dynamical Evolution . 4 1.2.3 Open Cluster Examples . 5 1.3 Outline of Thesis . 7 2 Methodology 9 2.1 Characterizing the Current State of a Cluster . 9 2.1.1 Stellar Mass Probability Function . 9 2.1.2 Maximum Likelihood Analysis . 13 2.1.3 Mass Segregation: The Gini Coefficient . 20 2.1.4 Procedure and Synthetic Data Tests . 23 2.2 Initial Cluster Parameters . 28 2.2.1 Density and Velocity Distribution . 28 2.2.2 Stellar Masses: Single and Binary . 36 2.3 N-Body Simulations . 41 2.3.1 Characterizing the Evolved Cluster . 41 2.3.2 Distribution of Binary Component Masses . 43 2.3.3 Optimization Procedure . 51 3 The Pleiades 54 3.1 Observational Data . 54 3.2 The Pleiades Today . 56 3.2.1 Empirical Mass Distributions . 56 Contents iii 3.2.2 Binarity . 62 3.2.3 Number and Mass Profiles . 63 3.2.4 Mass Segregation . 66 3.2.5 Potential Systematic Uncertainties . 69 3.3 Simulating the Seven Sisters . 73 3.3.1 The Initial State . 73 3.3.2 Past Evolution . 81 3.3.3 Future Evolution . 87 3.3.4 Conclusions from Simulations . 94 4 Alpha Persei 97 4.1 Constructing the Catalog . 97 4.1.1 Membership . 97 4.1.2 Photometry . 98 4.2 Alpha Persei Today: Computational Method . 100 4.2.1 Finding the Mass Function . 100 4.2.2 Cluster Shape . 101 4.3 Alpha Persei Today: Results . 105 4.3.1 Empirical Mass Distribution . 105 4.3.2 Binarity . 107 4.3.3 Surface Density . 110 4.4 Evolutionary Simulations . 114 4.4.1 Numerical Procedure . 114 4.4.2 Initial State . 115 4.4.3 Past Evolution . 118 4.4.4 Future Evolution . 123 4.5 Summary and Discussion of Alpha Persei . 127 4.5.1 Alpha Persei and the Pleiades . 127 4.5.2 Sources of Uncertainty . 129 4.A Alpha Persei Membership Catalog . 130 5 Dynamical Evolution of Clusters 148 5.1 Cluster Energetics . 148 5.1.1 Single-Mass Models . 148 5.1.2 Models with a Realistic Mass Function . 152 5.1.3 The Example of the Pleiades . 155 5.2 The Role of Binaries . 161 5.2.1 First Appearance . 161 5.2.2 Energy Input . 164 5.2.3 Very Massive Stars . 167 5.3 The Role of Stellar Evolution . 169 5.4 Discussion of Real Clusters . 172 Contents iv 5.4.1 Open vs. Globular Clusters . 172 5.4.2 Cluster Death . 174 5.4.3 Summary of Cluster Evolution . 175 Bibliography 176 v List of Figures 2.1 Fraction of systems observed with primary mass mp which are binary. 12 2.2 Sample synthetic data results for the single star mass function φ(m) . 25 2.3 Weighted sum of the biases as a function of the regularization parameter λ. 27 2.4 Comparison of our fitted correlation coefficient c with γ. 29 2.5 Systematic errors in parameters of the lognormal fit to φ(m).
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