An Introduction - The Simulation & How We Used It
For this study the N-Body portion of the code, that is the component of the code that allows Blue Straggler Stars (BSs) to be created through three and four body encounters, was omitted. This omission was with the intent of recreating the number and nature of the BSs observed in open clusters through binary evolution, alone.
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Initializing a Binary Population
Before a simulation can take place a binary population must be initialized. Initialization is the process of assigning mass, orbital period, and eccentricity to every binary in the parent population. To do this, the algorithm uses various distributions to assign these parameters to all the initial binary systems at once. The BSE also allows the choice of distributions taken from both observation and theory in order to compare how these initial conditions affect the number and nature of produced BSs.
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Choosing the Distribution that Maximizes BSs Production |
In the Model of M67 by Hurley et al. (2001) a study was carried out to determine which combination of distribution functions for the orbital parameters of the initial binaries would maximize the number of BSs produced. They found that choosing the orbital separation from a flat distribution of log a (where a is the separation distance between the stars in the binary) or equivalently log p (where p is the period), (Abt 1983) in combination with a thermal eccentricity distribution (Heggie 1975) could in fact reproduce the number of BSs in M67 given that all of the binaries that would eventually produce BSs are retained by the cluster over its lifetime.
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The Histograms at right represent Hurley's Parent distributions of period (top) and eccentricity (bottom). The term 'Parent' is used since all of the binary orbital parameters are assigned from these distributions, and from thence evolve; a select few of the binaries from the parent populations will form BSs.
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While the number of BSs may be duplicable through binary evolution only, the nature of the BSs in M67, along with those of other simulated clusters such as NGC 188 in our case, do not match observation (see the histograms below for the observed parent distribution). For example, only 25% of the BSs are in binaries and all of these have circular orbits with most having an orbital period of less than a year. The fact that no BSs were found in wide circular binaries at any time during the simulation presents a problem for the M67 model.
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Implementing the Observed Distributions
Instead of modeling M67, our study chose NGC 188. Geller et al. (2008) provided the observational results that the theoretical simulation should be capable of predicting if binary evolution alone could indeed produce the number and nature of BSs in the old open cluster.
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When one speaks of the “nature” of BSs, there are a variety of characteristics that “nature” might infer such as, chemical abundances, orbital velocities (if the BSs is in a binary), and spin or rotational velocities. Our study considered only the period (time of one complete revolution) and eccentricity (orbit shape) for those BSs found in binary systems. More precisely, the distributions of the period and eccentricities of all observed and simulated BSs in binaries were compared.
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As part of our study, we not only chose to use the observed period distribution given by Duquennoy & Mayor (1990), but also appended the Binary Star Evolution (BSE) algorithm with an observed eccentricity distribution also found by D&M (1990). Duquennoy & Mayor (1990) made observations of binary field stars and then compared their distribution of orbit eccentricity and period to those of binaries in young open clusters. Interestingly, the parameters of the field binaries matched those of young open clusters. This correlation indicates the eccentricities and period of binaries in young open clusters represents the distributions of the “parent” binary populations.
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As can be seen in the above histograms, the observed parent period distribution (left) can be remarkably approximated by a Gaussian relation with a peak at 4.8 log days (about 63,000 days) and a standard deviation of 2.3. Likewise, the observed parent eccentricity distribution (right) is also approximated by a Gaussian with a mean eccentricity of 0.33 and a standard deviation of 0.156.
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