We present results from 13776 radial-velocity (RV) measurements of 1278 candidate members of the old (4 Gyr) open cluster M67 (NGC 2682). The measurements are the results of a long-term survey that includes data from seven telescopes with observations for some stars spanning over 40 years. For narrow-lined stars, RVs are measured with precisions ranging from about 0.1 to 0.8 km s −1 . The combined stellar sample reaches from the brightest giants in the cluster down to about 4 mag below the main-sequence turnoff (V 16.5 = ), covering a mass range of about 1.34 M  to 0.76 M  . Spatially, the sample extends to a radus of 30 arcmin (7.4 pc in projection at a distance of 850 pc or 6-7 core radii). We find M67 to have a mean RV of 33.64 + km s −1 (with an internal precision of ±0.03 km s −1 ) well separated from the mean velocity of the field. For stars with 3  measurements, we derive RV membership probabilities and identify RV variables, finding 562 cluster members, 142 of which show significant RV variability. We use these cluster members to construct a color-magnitude diagram and identify a rich sample of stars that lie far from the standard single star isochrone, including the well-known blue stragglers, sub-subgiants and yellow giants. These exotic stars have a binary frequency of (at least) 80%, more than three times that detected for stars in the remainder of the sample. We confirm that the cluster is mass segregated, finding the binaries to be more centrally concentrated than the single stars in our sample at the 99.8% confidence level (and at the 98.7% confidence level when only considering main-sequence stars). The blue stragglers are centrally concentrated as compared to the solar-type main-sequence single stars in the cluster at the 99.7% confidence level. Accounting for measurement precision, we derive an RV dispersion in M67 of 0.80 ± 0.04 km s −1 for our sample of single main-sequence stars, subgiants and giants with V 15.5  . When corrected for undetected binaries, this sample yields a true RV dispersion of 0.59 0.06 0.07 -+ km s −1 . The radial distribution of the velocity dispersion is consistent with an isothermal distribution within our stellar sample. Using the cluster RV dispersion, we estimate a virial mass for the cluster of 2100 550 610 -+ M  .

We present the results of our ongoing radial-velocity (RV) survey of the old (7 Gyr) open cluster NGC 188. Our WIYN 3.5 m data set spans a time baseline of 11 years, a magnitude range of 12 V 16.5 (1.18-0.94 M ), and a 1• diameter region on the sky. With the addition of a Domain Astrophysical Observatory data set we extend our bright limit to V = 10.8 and, for some stars, extend our time baseline to 35 years. Our magnitude limits include solar-mass main-sequence stars, subgiants, giants, and blue stragglers (BSs), and our spatial coverage extends radially to 17 pc (∼13 core radii). For the WIYN data we present a detailed description of our data reduction process and a thorough analysis of our measurement precision of 0.4 km s −1 for narrow-lined stars. We have measured radial velocities for 1046 stars in the direction of NGC 188, and have calculated RV membership probabilities for stars with 3 measurements, finding 473 to be likely cluster members. We detect 124 velocityvariable cluster members, all of which are likely to be dynamically hard-binary stars. Using our single member stars, we find an average cluster radial velocity of −42.36 ± 0.04 km s −1 . We use our precise RV and proper-motion membership data to greatly reduce field-star contamination in our cleaned color-magnitude diagram, from which we identify six stars of note that lie far from a standard single-star isochrone. We present a detailed study of the spatial distribution of cluster-member populations, and find the binaries to be centrally concentrated, providing evidence for the presence of mass segregation in NGC 188. We observe the BSs to populate a bimodal spatial distribution that is not centrally concentrated, suggesting that we may be observing two populations of BSs in NGC 188, including a centrally concentrated distribution as well as a halo population. Finally, we find NGC 188 to have a global RV dispersion of 0.64 ± 0.04 km s −1 , which may be inflated by up to 0.23 km s −1 from unresolved binaries. When corrected for unresolved binaries, the NGC 188 RV dispersion has a nearly isothermal radial distribution. We use this mean-corrected velocity dispersion to derive a virial mass of 2300 ± 460 M .

We present the current state of the WOCS radial-velocity (RV) survey for the rich open cluster NGC 6819 (2.5 Gyr) including 93 spectroscopic binary orbits with periods ranging from 1.5 to 8,000 days. These results are the product of our ongoing RV survey of NGC 6819 using the Hydra Multi-Object Spectrograph on the WIYN 3.5 m telescope. We also include a detailed analysis of multiple prior sets of optical photometry for NGC 6819. Within a 1 • field of view, our stellar sample includes the giant branch, the red clump, and blue straggler candidates, and extends to almost 2 mag below the main-sequence (MS) turnoff. For each star observed in our survey we present all RV measurements, the average RV and velocity variability information. Additionally, we discuss notable binaries from our sample, including eclipsing binaries (WOCS 23009, WOCS 24009, and WOCS 40007), stars noted in Kepler asteroseismology studies (WOCS 4008, WOCS 7009, and WOCS 8007), and potential descendants of past blue stragglers (WOCS 1006 and WOCS 6002). We find the incompletenesscorrected binary fraction for all MS binaries with periods less than 10 4 days to be 22% ± 3% and a tidal circularization period of 6.2 +1.1 −1.1 days for NGC 6819.

We assess the contribution of dynamical hardening by direct three-body scattering interactions to the rate of stellar-mass black hole binary (BHB) mergers in galactic nuclei. We derive an analytic model for the single-binary encounter rate in a nucleus with spherical and disk components hosting a super-massive black hole (SMBH). We determine the total number of encounters N GW needed to harden a BHB to the point that inspiral due to gravitational wave emission occurs before the next three-body scattering event. This is done independently for both the spherical and disk components. Using a Monte Carlo approach, we refine our calculations for N GW to include gravitational wave emission between scattering events. For astrophysically plausible models we find that typically N GW 10.We find two separate regimes for the efficient dynamical hardening of BHBs: (1) spherical star clusters with high central densities, low velocity dispersions and no significant Keplerian component; and (2) migration traps in disks around SMBHs lacking any significant spherical stellar component in the vicinity of the migration trap, which is expected due to effective orbital inclination reduction of any spherical population by the disk. We also find a weak correlation between the ratio of the second-order velocity moment to velocity dispersion in galactic nuclei and the rate of BHB mergers, where this ratio is a proxy for the ratio between the rotation-and dispersion-supported components. Because disks enforce planar interactions that are efficient in hardening BHBs, particularly in migration traps, they have high merger rates that can contribute significantly to the rate of BHB mergers detected by the advanced Laser Interferometer Gravitational-Wave Observatory.

Blue straggler stars lie on or near the main sequences of star clusters (all members of which formed around the same time), but typically are more luminous than the turn-off stars and therefore long ago should have evolved off the main sequence to become giants and white dwarfs. They are thought to derive from normal main-sequence stars that have undergone a recent increase in mass. Statistical evidence indicates that in globular star clusters the blue stragglers probably form from binary stars. The specific formation processes, such as mass transfer, mergers or stellar collisions during dynamical encounters of binary stars, remain unresolved. Here we report that 16 of the 21 blue stragglers (76 per cent) in the old (7-Gyr; ref. 2) open cluster NGC 188 are currently in binary systems, a frequency three times that found among normal solar-type main-sequence stars. These blue straggler binaries have a remarkable period-eccentricity distribution, with all but three having orbital periods of approximately 1,000 days. Moreover, these stars are rotating faster than normal main-sequence stars of the same surface temperatures. These data show that most, and possibly all, blue stragglers derive from multiple-star systems, and indicate that the several formation processes operate simultaneously. We suggest that rapid rotation of blue stragglers may place upper limits on their ages.

In open star clusters, where all members formed at about the same time, blue straggler stars are typically observed to be brighter and bluer than hydrogen-burning main-sequence stars, and therefore should already have evolved into giant stars and stellar remnants. Correlations between blue straggler frequency and cluster binary fraction 1 , core mass 2 , and radial position 3 suggest that mass transfer or mergers in binary stars dominates the production of blue stragglers in open clusters. Analytic models 4, 5 , detailed observations 6 , and sophisticated N-body simulations 7 , however, argue in favor of stellar collisions. Here we report that the blue stragglers in long-period binaries in the old 8 (7 Gyr) open cluster NGC 188 have companions with masses of about half a solar mass, with a surprisingly narrow mass distribution. This conclusively rules out a collisional origin, as the collision hypothesis predicts a companion-mass distribution with significantly higher masses. Mergers in hierarchical triple stars 9 are marginally permitted by the data, but the observations do not favor this hypothesis. The data are closely consistent with a mass transfer origin for the long-period blue straggler binaries in NGC 188, in which the companions would be white dwarfs of about half a solar mass.The NGC 188 blue stragglers have a very high binary frequency of 76 ± 19% (for periods < 10 4 days). 10 The orbital period distribution is remarkable; 12 of the 16 blue straggler binaries have periods of order 1000 days, and all but two of the blue straggler binaries have periods longer than 100 days. The two short-period blue straggler binaries show evidence for binary encounters were involved in their formation. 10 We focus here on the "long-period" blue straggler binaries, whose orbital solutions yield periods longer than 100 days.In Figure 1 we show the companion-mass distribution for the twelve NGC 188 blue straggler binaries with periods of order 1000 days. The orbital solutions are derived from spectroscopic data 11, 12 obtained in the WIYN Open Cluster Study (WOCS). Because we do not detect the flux from the companions to these blue stragglers, the orbital solutions provide mass functions rather than mass ratios. We therefore use a statistical algorithm 13 to convert the mass functions to the companion-mass distribution shown here (see Supplementary Information). The distribution is narrow and peaked with a mean of 0.53 M ⊙ and a mode of 0.5 M ⊙ .Predictions for the companions to blue stragglers resulting from mass transfer in solar-type stars are well established by theory. Case C mass transfer (from an asymptotic-giant to a mainsequence star) leaves a Carbon-Oxygen white dwarf companion in an orbit of order 1000 days with a mass of about 0.5 M ⊙ to 0.6 M ⊙ , dictated by the core mass of the asymptotic-giant donor at the end of the mass-transfer phase. [14][15][16][17] This prediction is qualitatively reproduced by the NGC 188 blue straggler companion-mass distribution shown in Figure 1. To check quantitatively for 1 con...

We present 98 spectroscopic binary orbits resulting from our ongoing radial-velocity survey of the old (7 Gyr) open cluster NGC 188. All but 13 are high-probability cluster members based on both radial-velocity and proper-motion membership analyses. 15 of these member binaries are double lined. Our stellar sample spans a magnitude range of 10.8≤V≤16.5 (1.14-0.92 M ⊙ ) and extends spatially to 17 pc (∼13 core radii). All of our binary orbits have periods ranging from a few days to on the order of 10 3 days, and thus are hard binaries that dynamically power the cluster. For each binary, we present the orbital solutions and place constraints on the component masses. Additionally, we discuss a few binaries of note from our sample, identifying a likely blue straggler -blue straggler binary system (7782), a double-lined binary with a secondary star which is under-luminous for its mass (5080), two potential eclipsing binaries (4705 and 5762), and two binaries which are likely members of a quadruple system (5015a and 5015b).

We present an in-depth study of the hard-binary population of the old (7 Gyr) open cluster NGC 188. Utilizing 85 spectroscopic binary orbits out of a complete sample of 129 detected binary members, we study the cluster binary frequency and the distributions of binary orbital elements amongst the main-sequence, giant and blue straggler populations. The results are derived from our ongoing radialvelocity survey of the cluster, which spans in magnitude from the brightest stars in the cluster to V = 16.5 (about 1.1 -0.9 M ⊙ ), and extends to a projected radius of 17 pc (∼13 core radii). Our detectable binaries have periods ranging from a few days to of order 10 4 days, and thus are hard binaries that dynamically power the cluster. The main-sequence solar-type hard binaries in NGC 188 are nearly indistinguishable from similar binaries in the Galactic field. We observe a global solar-type main-sequence hard-binary frequency in NGC 188 of 23 ± 2 %, which when corrected for incompleteness results in a frequency 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 centered on e = 0.35 (for binaries with periods longer than the circularization 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 excess of this binary frequency over the normal main-sequence binary frequency is valid at the >99% confidence level. Furthermore, 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 longperiod blue straggler binaries is narrow and peaked with a mean value of about 0.5 M ⊙ . 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. The main-sequence hard-binary population predicted by the simulation is significantly different from the main-sequence hard-binary population observed in NGC 188, in frequency and distributions of period and eccentricity. Many of these differences result from the adopted initial binary population, while others reflect on the physics used in the simulation (e.g., tidal circularization). Additional simulations with initial conditions that are better motivated by observations are necessary to properly investigate the dynamical evolution of a rich binary pop...