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Title: BATC 15 Band Photometry of the Open Cluster NGC 188
Author: Jiaxin Wang (1,2), Jun Ma (1), Zhenyu Wu (1), Song Wang (1), Xu Zhou (1) ((1) Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, (2) University of Chinese Academy of Sciences)

This paper presents CCD multicolour photometry for the old open cluster NGC 188. The observations were carried out as a part of the Beijing--Arizona--Taiwan--Connecticut Multicolour Sky Survey from 1995 February to 2008 March, using 15 intermediate-band filters covering 3000--10000 \AA. By fitting the Padova theoretical isochrones to our data, the fundamental parameters of this cluster are derived: an age of t=7.50.5 Gyr, a distant modulus of (m-M)0=11.170.08, and a reddening of E(B-V)=0.0360.010. The radial surface density profile of NGC 188 is obtained by star count. By fitting the King model, the structural parameters of NGC 188 are derived: a core radius of Rc=3.80', a tidal radius of Rt=44.78', and a concentration parameter of C0=log(Rt/Rc)=1.07. Fitting the mass function to a power-law function phi(m) \propto m, the slopes of mass functions for different spatial regions are derived. We find that NGC 188 presents a slope break in the mass function. The break mass is mbreak=0.885 solar masses. In the mass range above mbreak, the slope of the overall region is alpha=-0.76. The slope of the core region is alpha=1.09, and the slopes of the external regions are alpha=-0.86 and alpha=-2.15, respectively. In the mass range below mbreak, these slopes are alpha=0.12, alpha=4.91, alpha=1.33, and alpha=-1.09, respectively. The mass segregation in NGC 188 is reflected in the obvious variation of the slopes in different spatial regions of this cluster.

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Title: Direct N-Body Modelling of the Old Open Cluster NGC 188: A Detailed Comparison of Theoretical and Observed Binary Star and Blue Straggler Populations
Authors: Aaron M. Geller, Jarrod R. Hurley, Robert D. Mathieu

Following on from a recently completed radial-velocity survey of the old (7 Gyr) open cluster NGC 188 in which we study in detail the solar-type hard binaries and blue stragglers of the cluster, here we investigate the dynamical evolution of NGC 188 through a sophisticated N-body model. We employ the observed binary properties of the young (150 Myr) open cluster M35, where possible, to guide our choices for parameters of the initial binary population. At 7 Gyr the main-sequence solar-type hard-binary population in the model matches that of NGC 188 in both binary frequency and distributions of orbital parameters. This agreement between the model and observations is in a large part due to the similarities between the NGC 188 and M35 solar-type binaries. Indeed, among the 7 Gyr main-sequence binaries in the model, only those with P>1000 days show potentially observable evidence for modifications by dynamical encounters. This emphasizes the importance of defining accurate initial conditions for star cluster models, which we propose is best accomplished through comparisons with observations of young open clusters like M35. Furthermore, this suggests that observations of the present-day binaries in even old open clusters can provide valuable information on their primordial binary populations. However, despite the model's successes at matching the true cluster, the model underproduces blue stragglers and produces an abundance of long-period circular main-sequence--white-dwarf binaries as compared to NGC 188. We conclude that improvements in the physics of mass transfer and common envelope may in fact solve both discrepancies with the observations. This project highlights the unique accessibility of open clusters to both comprehensive observational surveys and full-scale N-body simulations, and underscores the importance of open clusters to the study of star cluster dynamics.

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Title: WIYN Open Cluster Study. XLVIII. The Hard-Binary Population of NGC 188
Authors: Aaron M. Geller, Robert D. Mathieu

We present an in-depth study of the hard-binary population of the old (7 Gyr) open cluster NGC 188. The main-sequence solar-type hard binaries in NGC 188 are nearly indistinguishable from similar binaries in the Galactic field. We find a global solar-type main-sequence hard-binary frequency in NGC 188 of 29 3 % for binaries with periods less than 10^4 days. For main-sequence hard binaries in the cluster we observe a log-period distribution that rises towards our detection limit, a roughly Gaussian eccentricity distribution centred on e = 0.35 (for binaries with periods longer than the circularisation period), and a secondary-mass distribution that rises towards lower-mass companions. Importantly, the NGC 188 blue straggler binaries show significantly different characteristics than the solar-type main sequence binaries in NGC 188. We observe a blue straggler hard-binary frequency of 76 19 %, three times that of the main sequence. The blue straggler binary eccentricity - log period distribution is distinct from that of the main sequence at the 99% confidence level, with the majority of the blue straggler binaries having periods of order 1000 days and lower eccentricities. The secondary-mass distribution for these long-period blue straggler binaries is narrow and peaked with a mean value of about 0.5 solar masses. Predictions for mass-transfer products are most closely consistent with the binary properties of these NGC 188 blue stragglers, which comprise two-thirds of the blue straggler population. Additionally we compare the NGC 188 binaries to those evolved within the sophisticated Hurley et al. (2005) N-body open cluster simulation. We find that additional simulations with initial conditions that are better motivated by observations are necessary to properly investigate the dynamical evolution of a rich binary population in open clusters like NGC 188.

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NGC 188 is an open cluster in the constellation Cepheus. It was discovered by John Herschel in 1825. Unlike most open clusters that drift apart after a few million years because of the gravitational interaction of our galaxy, NGC 188 lies far above the plane of the galaxy and is one of the most ancient of open clusters.
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