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Motivated by measurements of the rotation speed of accretor stars in post-mass-transfer (post-MT) systems, we investigate how magnetic braking affects the spin-down of individual stars during binary evolution with the MESAbinary module. Unlike the conventional assumption of tidal synchronization coupled with magnetic braking in binaries, we first calculate whether tides are strong enough to synchronize the orbit. Subsequently, this influences the spin-down of stars and the orbital separation. In this study, we apply four magnetic braking prescriptions to reduce the spin angular momentum of the two stars throughout the entire binary evolution simulation. Our findings reveal that despite magnetic braking causing continuous spin-down of the accretor, when the donor begins to transfer material onto the accretor, the accretor can rapidly spin up to its critical rotation rate. After MT, magnetic braking becomes more important in affecting the angular momentum evolution of the stars. Post-MT accretor stars thus serve as a valuable testbed for observing how the magnetic braking prescriptions operate in spinning down stars from their critical rotation, including the saturation regimes of the magnetic braking. The rotation rate of the accretor star, combined with its mass, could provide age information since the cessation of MT. By comparing the models against observation, the magnetic braking prescription by Garraffo et al. (2018b) is found to better align with the rotation data of post-MT accretors., Comment: 16 pages, 10 figures, 3 tables, accepted to ApJ

We study the effects of general relativity (GR) on the evolution and alignment of circumbinary disks around binaries on all scales. We implement relativistic apsidal precession of the binary into the hydrodynamics code {\sc phantom}. We find that the effects of GR can suppress the stable polar alignment of a circumbinary disk, depending on how the relativistic binary apsidal precession timescale compares to the disk nodal precession timescale. Studies of circumbinary disk evolution typically ignore the effects of GR which is an appropriate simplification for low mass or widely separated binary systems. In this case, polar alignment occurs providing that the disks initial misalignment is sufficiently large. However, systems with a very short relativistic precession timescale cannot polar align and instead move toward coplanar alignment. In the intermediate regime where the timescales are similar, the outcome depends upon the properties of the disk. Polar alignment is more likely in the wavelike disk regime (where the disk viscosity parameter is less than the aspect ratio, $\alpha

Wind Roche-Lobe Overflow (WRLOF) is a mass-transfer mechanism proposed by Mohamed and Podsiadlowski (2007) for stellar binaries wherein the wind acceleration zone of the donor star exceeds its Roche lobe radius, allowing stellar wind material to be transferred to the accretor at enhanced rates. WRLOF may explain characteristics observed in blue lurkers and blue stragglers. While WRLOF has been implemented in rapid population synthesis codes, it has yet to be explored thoroughly in detailed binary models such as MESA (a 1D stellar evolution code), and over a wide range of initial binary configurations. We incorporate WRLOF accretion in MESA to investigate wide low-mass binaries at solar metallicity. We perform a parameter study over the initial orbital period and stellar mass. In most of the models where we consider angular momentum transfer during accretion, the accretor is spun up to the critical (or break-up) rotation rate. Then we assume the star develops a boosted wind to efficiently reduce the angular momentum so that it could maintain a sub-critical rotation. Balanced by boosted wind loss, the accretor only gains $\sim 2\%$ of its total mass, but can maintain a near-critical rotation rate during WRLOF. Notably, the mass-transfer efficiency is significantly smaller than in previous studies in which the rotation of the accretor is ignored. We compare our results to observational data of blue lurkers in M67 and find that the WRLOF mechanism can qualitatively explain the origin of their rapid rotation, their location on the HR diagram and their orbital periods., Comment: 19 pages, 12 figures, 3 tables, accepted for publication in ApJ

We present a robust methodology for identifying photometric binaries in star clusters. Using Gaia DR3, Pan-STARRS and 2MASS data, we self-consistently define the cluster parameters and binary demographics for the open clusters (OCs) NGC 2168 (M35), NGC 7789, NGC 6819, NGC 2682 (M67), NGC 188, and NGC 6791. These clusters span in age from ~200 Myr (NGC 2168) to more than ~8 Gyr (NGC 6791) and have all been extensively studied in the literature. We use the Bayesian Analysis of Stellar Evolution software suite (BASE-9) to derive the age, distance, reddening, metallicity, binary fraction, and binary mass-ratio posterior distributions for each cluster. We perform a careful analysis of our completeness and also compare our results to previous spectroscopic surveys. For our sample of main-sequence stars with masses between 0.6 - 1 M_Sun, we find that these OCs have similar binary fractions that are also broadly consistent with the field multiplicity fraction. Within the clusters, the binary fraction increases dramatically toward the cluster centers, likely a result of mass segregation. Furthermore nearly all clusters show evidence of mass segregation within the single and binary populations, respectively. The OC binary fraction increases significantly with cluster age in our sample, possibly due to a combination of mass-segregation and cluster dissolution processes. We also find a hint of an anti-correlation between binary fraction and cluster central density as well as total cluster mass, possibly due to an increasing frequency of higher energy close stellar encounters that inhibit long-period binary survival and/or formation., Comment: 20 pages, 11 figures, and 5 tables. Accepted for publication in ApJ

We search for mass segregation in the intermediate-aged open cluster NGC 6819 within a carefully identified sample of probable cluster members. Using photometry from the Gaia, 2MASS, and Pan-STARRS surveys as inputs for a Bayesian statistics software suite, BASE-9, we identify a rich population of (photometric) binaries and derive posterior distributions for the cluster age, distance, metallicity and reddening as well as star-by-star photometric membership probabilities, masses and mass ratios (for binaries). Within our entire sample, we find 2632 cluster members and 777 binaries. We then select a main-sequence 'primary sample' with 14.85 < G < 19.5 containing 1342 cluster members and 250 binaries with mass ratios q > 0.5, to investigate for mass segregation. Within this primary sample, we find the binary radial distribution is significantly shifted toward the cluster center as compared to the single stars, resulting in a binary fraction that increases significantly toward the cluster core. Furthermore, we find that within the binary sample, more massive binaries have more centrally concentrated radial distributions than less massive binaries. The same is true for the single stars. We verify the expectation of mass segregation for this stellar sample in NGC 6819 through both relaxation time arguments and by investigating a sophisticated N-body model of the cluster. Importantly, this is the first study to investigate mass segregation of the binaries in the open cluster NGC 6819., Comment: 10 pages, 8 figures, Published in ApJ

M35 is a young open cluster and home to an extensive binary population. Using Gaia DR3, Pan-STARRS, and 2MASS photometry with the Bayesian statistical software, BASE-9, we derive precise cluster parameters, identify single and binary cluster members, and extract their masses. We identify 571 binaries down to Gaia G = 20.3 and a lower-limit on the binary frequency of f_b = 0.41 +/- 0.02. We extend the binary demographics by many magnitudes faint-ward of previous (radial-velocity) studies of this cluster and further away from the cluster center (1.78-degrees, roughly 10 core radii). We find the binary stars to be more centrally concentrated than the single stars in the cluster. Furthermore, we find strong evidence for mass segregation within the binary population itself, with progressively more massive binary samples becoming more and more centrally concentrated. For the single stars, we find weaker evidence for mass segregation; only the most massive single stars (> 2.5MSun) appear more centrally concentrated. Given the cluster age of ~200 Myr, and our derived half-mass relaxation time for the cluster of 230 +/- 84 Myr, we estimate ~47% of the binary stars and ~12% of single stars in the cluster have had time to become dynamically mass segregated. Importantly, when we investigate only stars with mass segregation timescales greater than the cluster age, we still find the binaries to be more centrally concentrated than the singles, suggesting the binaries may have formed with a primordially different spatial distribution than the single stars., Comment: 8 pages, 5 figures, published in ApJL

Mutually misaligned circumbinary planets may form in a warped or broken gas disc or from later planet-planet interactions. With numerical simulations and analytic estimates we explore the dynamics of two circumbinary planets with a large mutual inclination. A coplanar inner planet causes prograde apsidal precession of the binary and the stationary inclination for the outer planet is higher for larger outer planet orbital radius. In this case a coplanar outer planet always remains coplanar. On the other hand, a polar inner planet causes retrograde apsidal precession of the binary orbit and the stationary inclination is smaller for larger outer planet orbital radius. For a range of outer planet semi-major axes, an initially coplanar orbit is librating meaning that the outer planet undergoes large tilt oscillations. Circumbinary planets that are highly inclined to the binary are difficult to detect -- it is unlikely for a planet to have an inclination below the transit detection limit in the presence of a polar inner planet. These results suggest that there could be a population of circumbinary planets that are undergoing large tilt oscillations., Comment: Accepted for publication in ApJL. 7 pages and 4 figures

We present the first comprehensive study of the most massive globular cluster Omega Centauri in the far-ultraviolet (FUV) extending from the center to ~ 28% of the tidal radius using the Ultraviolet Imaging Telescope aboard AstroSat. A comparison of the FUV-optical color-magnitude diagrams with available canonical models reveals that the horizontal branch (HB) stars bluer than the knee (hHBs) and the white dwarfs (WDs) are fainter in the FUV by ~ 0.5 mag than model predictions. They are also fainter than their counterparts in M13, another massive cluster. We simulated HB with at least five subpopulations, including three He-rich populations with a substantial He enrichment of Y up to 0.43 dex, to reproduce the observed FUV distribution. We find the He-rich younger subpopulations to be radially more segregated than the He-normal older ones, suggesting an in-situ enrichment from older generations. The Omega Cen hHBs span the same effective temperature range as their M13 counterparts, but some have smaller radii and lower luminosities. This may suggest that a fraction of Omega Cen hHBs are less massive than those of M13, similar to the result derived from earlier spectroscopic studies of outer extreme HB stars. The WDs in Omega Cen and M13 have similar luminosity-radius-effective temperature parameters, and 0.44 - 0.46 M$_\odot$ He-core WD model tracks evolving from progenitors with Y = 0.4 dex are found to fit the majority of these. This study provides constraints on the formation models of Omega Cen based on the estimated range in age, [Fe/H] and Y (in particular), for the HB stars., Comment: Accepted for publication in ApJL; 13 pages, 5 figures, 1 table

We present Firefly, a new browser-based interactive tool for visualizing 3D particle data sets. On a typical personal computer, Firefly can simultaneously render and enable real-time interactions with > ~10 million particles, and can interactively explore datasets with billions of particles using the included custom-built octree render engine. Once created, viewing a Firefly visualization requires no installation and is immediately usable in most modern internet browsers simply by visiting a URL. As a result, a Firefly visualization works out-of-the-box on most devices including smartphones and tablets. Firefly is primarily developed for researchers to explore their own data, but can also be useful to communicate results to researchers/collaborators and as an effective public outreach tool. Every element of the user interface can be customized and disabled, enabling easy adaptation of the same visualization for different audiences with little additional effort. Creating a new Firefly visualization is simple with the provided Python data pre-processor (PDPP) that translates input data to a Firefly-compatible format and provides helpful methods for hosting instances of Firefly both locally and on the internet. In addition to visualizing the positions of particles, users can visualize vector fields (e.g., velocities) and also filter and color points by scalar fields. We share three examples of Firefly applied to astronomical datasets: 1) the FIRE cosmological zoom-in simulations, 2) the SDSS galaxy catalog, and 3) Gaia DR3. A gallery of additional interactive demos is available at https://alexbgurvi.ch/Firefly., Comment: 26 pages, 9 figures

We present the first results of eight Globular Clusters (GCs) from the AstroSat/UVIT Legacy Survey program GlobULeS based on the observations carried out in two FUV filters (F148W and F169M). The FUV-optical and FUV-FUV color-magnitude diagrams (CMDs) of GCs with the proper motion membership were constructed by combining the UVIT data with HST UV Globular Cluster Survey (HUGS) data for inner regions and Gaia Early Data Release (EDR3) for regions outside the HST's field. We detect sources as faint as F148W $\sim$ 23.5~mag which are classified based on their locations in CMDs by overlaying stellar evolutionary models. The CMDs of 8 GCs are combined with the previous UVIT studies of 3 GCs to create stacked FUV-optical CMDs to highlight the features/peculiarities found in the different evolutionary sequences. The FUV (F148W) detected stellar populations of 11 GCs comprises 2,816 Horizontal Branch (HB) stars (190 Extreme HB candidates), 46 post-HB (pHB), 221 Blue Straggler Stars (BSS), and 107 White Dwarf (WD) candidates. We note that the blue HB color extension obtained from F148W$-$G color and the number of FUV detected EHB candidates are strongly correlated with the maximum internal Helium (He) variation within each GC, suggesting that the FUV-optical plane is the most sensitive to He abundance variations in the HB. We discuss the potential science cases that will be addressed using these catalogues including HB morphologies, BSSs, pHB, and, WD stars., Comment: Accepted for publication in MNRAS; 24 pages, 20 Figures, 6 Tables

Sub-subgiant stars (SSGs) fall below the subgiant branch and/or red of the giant branch in open and globular clusters, an area of the color-magnitude diagram (CMD) not populated by standard stellar evolution tracks. One hypothesis is that SSGs result from rapid rotation in subgiants or giants due to tidal synchronization in a close binary. The strong magnetic fields generated inhibit convection, which in turn produces large starspots, radius inflation, and lower-than-expected average surface temperatures and luminosities. Here we cross-reference a catalog of active giant binaries (RS CVns) in the field with Gaia EDR3. Using the Gaia photometry and parallaxes we precisely position the RS CVns in a CMD. We identify stars that fall below a 14 Gyr, metal-rich isochrone as candidate field SSGs. Out of a sample of 1723 RS CVn, we find 448 SSG candidates, a dramatic expansion from the 65 SSGs previously known. Most SSGs have rotation periods of 2-20 days, with the highest SSG fraction found among RS CVn with the shortest periods. The ubiquity of SSGs among this population indicates SSGs are a normal phase in evolution for RS CVn-type systems, not rare by-products of dynamical encounters found only in dense star clusters as some have suggested. We present our catalog of 1723 active giants, including Gaia photometry and astrometry, and rotation periods from TESS and VSX. This catalog can serve as an important sample to study the impacts of magnetic fields in evolved stars., Comment: 16 pages, 7 Figures, 1 Table. Accepted for publication in ApJ

We present a study of the detection and recovery efficiency of the Rubin Observatory for detached eclipsing binaries (EBs) in the galactic field, globular clusters (GCs) and open clusters (OCs), with a focus on comparing two proposed observing strategies: a standard cadence ("baseline"), and a cadence which samples the galactic plane more evenly ("colossus"). We generate realistic input binary populations in all observing fields of the Rubin Observatory, simulate the expected observations in each filter, and attempt to characterize the EBs using these simulated observations. In our models, we predict the baseline cadence will enable the Rubin Observatory to observe about three million EBs; our technique could recover and characterize nearly one million of these in the field and thousands within star clusters. If the colossus cadence is used, the number of recovered EBs would increase by an overall factor of about 1.7 in the field and in globular clusters, and a factor of about three in open clusters. Including semi-detached and contact systems could increase the number of recovered EBs by an additional factor of about 2.5 to 3. Regardless of the cadence, observations from the Rubin Observatory could reveal statistically significant physical distinctions between the distributions of EB orbital elements between the field, GCs and OCs. Simulations such as these can be used to bias correct the sample of Rubin Observatory EBs to study the intrinsic properties of the full binary populations in the field and star clusters., Comment: 15 pages, 8 figures, accepted for publication in ApJ

We present and analyse 120 spectroscopic binary and triple cluster members of the old (4 Gyr) open cluster M67 (NGC 2682). As a cornerstone of stellar astrophysics, M67 is a key cluster in the WIYN Open Cluster Study (WOCS); radial-velocity (RV) observations of M67 are ongoing and extend back over 45 years, incorporating data from seven different telescopes, and allowing us to detect binaries with orbital periods <~10^4 days. Our sample contains 1296 stars (604 cluster members) with magnitudes of 10 <= V <= 16.5 (about 1.3 to 0.7 Msolar), from the giants down to ~4 mag below the main-sequence turnoff, and extends in radius to 30 arcminutes (7.4 pc at a distance of 850 pc, or ~7 core radii). This paper focuses primarily on the main-sequence binaries, but orbital solutions are also presented for red giants, yellow giants and sub-subgiants. Out to our period detection limit and within our magnitude and spatial domain, we find a global main-sequence incompleteness-corrected binary fraction of 34% +/- 3%, which rises to 70% +/- 17% in the cluster center. We derive a tidal circularization period of P_circ = 11.0 +1.1 -1.0 days. We also analyze the incompleteness-corrected distributions of binary orbital elements and masses. The period distribution rises toward longer periods. The eccentricity distribution, beyond P_circ, is consistent with a uniform distribution. The mass-ratio distribution is also consistent with a uniform distribution. Overall, these M67 binaries are closely consistent with similar binaries in the galactic field, as well as the old (7 Gyr) open cluster NGC 188. WIYN Open Cluster Study. 83., Comment: Accepted for publication in AJ; 13 figures, 7 tables

We introduce the stellar sample of the WIYN Open Cluster Study radial-velocity survey for the rich open cluster NGC 7789 (1.6 Gyr, [Fe/H] = +0.02). This sample lies within an 18$'$ circular radius from the cluster center (10 pc in projection, or about 2 core radii), and includes giants, red-clump stars, blue stragglers, red stragglers, sub-subgiants, and main-sequence stars down to one mag below the turnoff. Our survey began in 2005 and comprises more than 9,000 radial-velocity measurements from the Hydra Multi-Object Spectrograph on the WIYN 3.5m telescope. We identify 564 likely cluster members and present the orbital solutions for 83 cluster binary stars with periods between 1.45$\,$d and 4200$\,$d. From the main-sequence binary solutions we fit a circularization period of 8.22$^{+3.51}_{-1.35}\,$d. We calculate an incompleteness-corrected main-sequence binary frequency of 31% $\pm$ 3% for binaries with periods less than 10$^{4}$ days, similar to other WOCS open clusters of all ages. We detect a blue straggler binary frequency of 31% $\pm$ 15%, consistent with the similarly aged cluster NGC 6819., Comment: 47 pages, 16 figures. Submitted to AJ

To fully understand the diverse population of exoplanets, we must study their early lives within open clusters, the birthplace of most stars with masses $>0.5M_\odot$ (including those currently in the field). Indeed, when we observe planets within clustered environments, we notice highly eccentric and odd systems that suggest the importance of dynamical pathways created by interactions with additional bodies (as in the case of HD 285507b). However, it has proven difficult to investigate these effects, as many current numerical solvers for the multi-scale $N$-body problem are simplified and limited in scope. To remedy this, we aim to create a physically complete computational solution to explore the role of stellar close encounters and interplanetary interactions in producing the observed exoplanet populations for both open cluster stars and field stars. We present a new code, TYCHO, which employs a variety of different computational techniques, including multiple $N$-body integration methods, close encounter handling, modified Monte Carlo scattering experiments, and a variety of empirically informed initial conditions. We discuss the methodology in detail, and its implementation within the AMUSE software framework. Approximately 1$\%$ of our systems are promptly disrupted by star-star encounters contributing to the rogue planets occurrence rate. Additionally, we find that close encounters which perturb long-period planets lead to 38.3$\%$ of solar-system-like planetary systems becoming long-term unstable., Comment: 16 Pages, 9 Figures, 4 Tables; Submitted to ApJ

The binary fractions of open and globular clusters yield powerful constraints on their dynamical state and evolutionary history. We apply publicly available Bayesian analysis code to a $UBVRIJHK_{S}$ photometric catalog of the old open cluster NGC 188 to detect and characterize photometric binaries along the cluster main sequence. This technique has the advantage that it self-consistently handles photometric errors, missing data in various bandpasses, and star-by-star prior constraints on cluster membership. Simulations are used to verify uncertainties and quantify selection biases in our analysis, illustrating that among binaries with mass ratios >0.5, we recover the binary fraction to better than 7% in the mean, with no significant dependence on binary fraction and a mild dependence on assumed mass ratio distribution. Using our photometric catalog, we recover the majority (65%$\pm$11%) of spectroscopically identified main sequence binaries, including 8 of the 9 with spectroscopically measured mass ratios. Accounting for incompleteness and systematics, we derive a mass ratio distribution that rises toward lower mass ratios (within our $q >$0.5 analysis domain). We observe a raw binary fraction for solar-type main sequence stars with mass ratios $q >$0.5 of 42%$\pm$4%, independent of the assumed mass ratio distribution to within its uncertainties, consistent with literature values for old open clusters but significantly higher than the field solar-type binary fraction. We confirm that the binaries identified by our method are more concentrated than single stars, in agreement with previous studies, and we demonstrate that the binary nature of those candidates which remain unidentified spectroscopically is strongly supported by photometry from Gaia DR2., Comment: AJ accepted

We investigate the old open cluster M67 using ultraviolet photometric data of Ultra-Violet Imaging Telescope in multi-filter far-UV bands. M67, well known for the presence of several blue straggler stars (BSS), has been put to detailed tests to understand their formation pathways. Currently, there are three accepted formation channels: mass transfer due to Roche-lobe overflow in binary systems, stellar mergers either due to dynamical collisions or through coalescence of close binaries. So far, there had not been any confirmed detection of a white dwarf (WD) companion to any of the BSSs in this cluster. Here, we present the detection of WD companions to 5 bright BSSs in M67. The multiwavelength spectral energy distributions covering 0.12 -11.5 $\mu$m range, were found to require binary spectral fits for 5 BSSs, consisting of a cool (BSS) and a hot companion. The parameters (Luminosity, Temperature, Radius and Mass) of the hot companions suggest them to be WDs with mass in the range 0.2 - 0.35 M$_{\odot}$ with T$_{eff}$ $\sim$ 11000 - 24000 K., Comment: 4 pages, 2 figures, to appear in IAU Symposium No. 351 proceedings - Star Clusters: From the Milky Way to the Early Universe, 2019

The old open cluster M67, populated with blue straggler stars (BSSs), is a well known test bed to study the BSS formation pathways. Here, we report the first direct detection of a white dwarf (WD) companion to a BSS in M67, using far-UV images from the \textit{Ultra Violet Imaging telescope} ({\it UVIT}) on {\it ASTROSAT}. Near-simultaneous observations in three far-UV bands combined with {\it GALEX}, {\it IUE}, ground and space based photometric data covering 0.14 -11.5 $\mu$m range for WOCS1007 were found to require a binary fit to its spectral energy distribution (SED), consisting of a BSS and a hot companion. On the other hand, a single spectral fit was found to be satisfactory for the SEDs of two other BSSs, WOCS1006 and WOCS2011, with the latter showing a deficient far-UV flux. The hot companion of WOCS1007 is found to have a T$_{eff}$ $\sim$ 13250-13750K and a radius of 0.09$\pm$0.01 R$_\odot$. A comparison with WD models suggests it to be a low mass WD ($\sim$ 0.18$M_\odot$), in agreement with the kinematic mass from the literature. As a low mass WD ($<$ 0.4$M_\odot$) necessitates formation through mass transfer (MT) in close binaries, WOCS1007 with a known period of 4.2 days along with its fast rotation, is likely to be formed by a case A or case B binary evolution., Comment: 11 pages, 4 figures, Accepted for publication in Astrophysical Journal

Recent studies show that the majority of blue straggler stars (BSSs) in old open clusters are formed through mass transfer from an evolved star onto a main-sequence companion, resulting in a BSS and white dwarf (WD) in a binary system. We present constraints on the mass transfer histories of two BSS-WD binaries in the open cluster NGC 188, using WD temperatures and surface gravities measured with HST COS far-ultraviolet spectroscopy. Adopting a Gaia-based cluster distance of $1847\pm107$ pc, we determine that one system, WOCS 4540, formed through Case C mass transfer resulting in a CO-core white dwarf with $T_{\text{eff}}=17000^{+140}_{-200}$ K and a $\log g=7.80^{+0.06}_{-0.06}$, corresponding to a mass of $0.53^{+0.03}_{-0.03}$ $M_{\odot}$ and a cooling age of $105^{+6}_{-5}$ Myr. The other system, WOCS 5379, formed through Case B mass transfer resulting in a He-core white dwarf with $T_{\text{eff}}=15500^{+170}_{-150}$ K and a $\log g=7.50^{+0.06}_{-0.05}$, corresponding to a mass of $0.42^{+0.02}_{-0.02}$ $M_{\odot}$ and an age of $250^{+20}_{-20}$ Myr. The WD parameters are consistent across four different cluster distance assumptions. We determine possible progenitor binary systems with a grid of accretion models using MESA, and investigate whether these systems would lead to stable or unstable mass transfer. WOCS 4540 likely resulted from stable mass transfer during periastron passage in an eccentric binary system, while WOCS 5379 challenges our current understanding of the expected outcomes for mass transfer from red giant branch stars. Both systems are examples of the value in using detailed analyses to fine-tune our physical understanding of binary evolutionary processes., Comment: 16 pages, 10 figures, 2 tables, submitted to Astrophysical Journal

At least $70\%$ of massive OBA-type stars reside in binary or higher-order systems. The dynamical evolution of these systems can lend insight into the origins of extreme phenomena such as X-ray binaries and gravitational wave sources. In one such dynamical process, the Eccentric Kozai-Lidov (EKL) Mechanism, a third companion star alters the secular evolution of a binary system. For dynamical stability, these triple systems must have a hierarchical configuration. We explore the effects of a distant third companion's gravitational perturbations on a massive binary's orbital configuration before significant stellar evolution has taken place ($\leq 10$ Myr). We include tidal dissipation and general relativistic precession. With large ($38,000$ total) Monte-Carlo realizations of massive hierarchical triples, we characterize imprints of the birth conditions on the final orbital distributions. Specifically, we find that the final eccentricity distribution over the range $0.1-0.7$ is an excellent indicator of its birth distribution. Furthermore, we find that the period distributions have a similar mapping for wide orbits. Finally, we demonstrate that the observed period distribution for approximately $10$ Myr-old massive stars is consistent with EKL evolution., Comment: Submitted

We report the discovery of a hot white dwarf (WD) companion to a blue straggler star (BSS) in the globular cluster (GC) NGC 5466, based on observations from the Ultra-Violet Imaging Telescope (UVIT) on board AstroSat. The Spectral Energy Distribution (SED) of the Far-UV detected BSS NH 84 was constructed by combining the flux measurements from 4 filters of UVIT, with GALEX, GAIA and other ground-based observations. The SED of NH 84 reveals the presence of a hot companion to the BSS. The temperature and radius of the BSS (T$_{\mathrm{eff}} = 8000^{+1000}_{-250}$ K, R/R$_\odot = 1.44 \pm 0.05$) derived from Gemini spectra and SED fitting using Kurucz atmospheric models are consistent with each other. The temperature and radius of the hotter companion of NH 84 (T$_{\mathrm{eff}} = 32,000 \pm 2000$ K, R/R$_\odot = 0.021 \pm 0.007$) derived by fitting Koester WD models to the SED suggest that it is likely to be a hot WD. The radial velocity derived from the spectra along with the proper motion from GAIA DR2 confirms NH 84 to be a kinematic member of the cluster. This is the second detection of a BSS-WD candidate in a GC, and the first in the outskirts of a low density GC. The location of this BSS in NGC 5466 along with its dynamical age supports the mass-transfer pathway for BSS formation in low density environments., Comment: 12 pages, 20 figures. accepted for publication in ApJ

About a century ago, Jeans (1919) discovered that if binary stars reach a state approximating energy equipartition, for example through many dynamical encounters that exchange energy, their eccentricity distribution can be described by : dN/de = 2e. This is referred to as the thermal eccentricity distribution, and has been widely used for initial conditions in theoretical investigations of binary stars. However, observations suggest that the eccentricity distributions of most observed binaries, and particularly those with masses < 5 Msun, are flatter than thermal and follow more closely to a uniform distribution. Nonetheless, it is often argued that dynamical interactions in a star cluster would quickly thermalize the binaries, which could justify imposing a thermal eccentricity distribution at birth for all binaries. In this paper we investigate the validity of this assumption. We develop our own rapid semi-analytic model for binary evolution in star clusters, and also compare with detailed N-body and Monte Carlo star cluster models. We show that, for nearly all binaries, dynamical encounters fail to convert an initially uniform eccentricity distribution to thermal within a star cluster's lifetime. Thus, if a thermal eccentricity distribution is observed, it is likely imprinted upon formation rather than through subsequent long-term dynamical processing. Theoretical investigations that initialize all binaries with a thermal distribution will make incorrect predictions for the evolution of the binary population. Such models may overpredict the merger rate for binaries with modest orbital separations by a factor of about two., Comment: 14 pages, 7 figures, accepted for publication in The Astrophysical Journal

In this paper, the fourth in the series, we continue our study of combinatorics in chaotic Newtonian dynamics. We focus once again on the chaotic four-body problem in Newtonian gravity assuming finite-sized particles, and interactions that produce direct collisions between any two particles. Our long-term goal is to predict the probability of a given collision event occurring over the course of an interaction, as a function of the numbers and properties of the particles. In previous papers, we varied the number of interacting particles, as well as the distributions of particle radii and masses. Here, we refine the methods developed in these preceding studies, and arrive at a final and robust methodology that can be used to study collisional dynamics in a variety of astrophysical contexts, ranging from stars in star clusters, galaxies in galaxy groups and clusters and even the collisional growth of planetesimals in protoplanetary disks. We further present and refine the concept of a Collision Rate Diagram (CRD), the primary tool we use to quantify the relative rates for different collision scenarios to occur. The agreement between our final theoretical model and the results of numerical scattering simulations is excellent., Comment: 10 pages, 5 figures, 1 table; accepted for publication in MNRAS

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 $N_{\rm GW}$ 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 $N_{\rm GW}$ to include gravitational wave emission between scattering events. For astrophysically plausible models we find that typically $N_{\rm GW} \lesssim$ 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., Comment: 13 pages, 9 figures, accepted for publication in MNRAS

In this paper, the third in the series, we continue our study of combinatorics in chaotic Newtonian dynamics. We study the chaotic four-body problem in Newtonian gravity assuming finite-sized particles, and we focus on interactions that produce direct collisions between any two stars. Our long-term goal is to construct an equation that gives the probability of a given collision event occurring over the course of the interaction, as a function of the total encounter energy and angular momentum as well as the numbers and properties of the particles. In previous papers, we varied the number of interacting particles and the distribution of particle radii, for all equal mass particles. Here, we focus on the effects of different combinations of particle masses. We develop an analytic formalism for calculating the time-scales for different collision scenarios to occur. Our analytic time-scales reproduce the simulated time-scales when gravitational focusing is included. We present a method for calculating the relative rates for different types of collisions to occur, assuming two different limits for the particle orbits; radial and tangential. These limits yield relative collision probabilities that bracket the probabilities we obtain directly from numerical scattering experiments, and are designed to reveal important information about the (time-averaged) trajectories of the particles as a function of the interaction parameters. Finally, we present a Collision Rate Diagram (CRD), which directly compares the predictions of our analytic rates to the simulations and quantifies the quality of the agreement. The CRD will facilitate refining our analytic collision rates in future work, as we expand in to the remaining parameter space., Comment: 13 pages, 6 figures, 2 tables; accepted for publication in MNRAS

Sub-subgiants are a new class of stars that are optically redder than normal main-sequence stars and fainter than normal subgiant stars. Sub-subgiants, and the possibly related red stragglers (which fall to the red of the giant branch), occupy a region of the color-magnitude diagram that is predicted to be devoid of stars by standard stellar evolution theory. In previous papers we presented the observed demographics of these sources and defined possible theoretical formation channels through isolated binary evolution, the rapid stripping of a subgiant's envelope, and stellar collisions. Sub-subgiants offer key tests for single- and binary-star evolution and stellar collision models. In this paper, we synthesize these findings to discuss the formation frequencies through each of these channels. The empirical data, our analytic formation rate calculations, and analyses of sub-subgiants in a large grid of Monte Carlo globular cluster models suggest that the binary evolution channels may be the most prevalent, though all channels appear to be viable routes to sub-subgiant creation (especially in higher-mass globular clusters). Multiple formation channels may operate simultaneously to produce the observed sub-subgiant population. Finally, many of these formation pathways can produce stars in both the sub-subgiant and red straggler (and blue straggler) regions of the color-magnitude diagram, in some cases as different stages along the same evolutionary sequence., Comment: 14 pages, 6 figures, 1 table, accepted for publication in ApJ

Sub-subgiant stars (SSGs) lie to the red of the main-sequence and fainter than the red giant branch in cluster color-magnitude diagrams (CMDs), a region not easily populated by standard stellar evolution pathways. While there has been speculation on what mechanisms may create these unusual stars, no well-developed theory exists to explain their origins. Here we discuss three hypotheses of SSG formation: (1) mass transfer in a binary system, (2) stripping of a subgiant's envelope, perhaps during a dynamical encounter, and (3) reduced luminosity due to magnetic fields that lower convective efficiency and produce large star spots. Using the stellar evolution code MESA, we develop evolutionary tracks for each of these hypotheses, and compare the expected stellar and orbital properties of these models with six known SSGs in the two open clusters M67 and NGC 6791. All three of these mechanisms can create stars or binary systems in the SSG CMD domain. We also calculate the frequency with which each of these mechanisms may create SSG systems, and find that the magnetic field hypothesis is expected to create SSGs with the highest frequency in open clusters. Mass transfer and envelope stripping have lower expected formation frequencies, but may nevertheless create occasional SSGs in open clusters. They may also be important mechanisms to create SSGs in higher mass globular clusters., Comment: 17 pages, 8 Figure, accepted to ApJ

Sub-subgiants are stars observed to be redder than normal main-sequence stars and fainter than normal subgiant (and giant) stars in an optical color-magnitude diagram. The red straggler stars, which lie redward of the red giant branch, may be related and are often grouped together with the sub-subgiants in the literature. These stars defy our standard theory of single-star evolution, and are important tests for binary evolution and stellar collision models. In total, we identify 65 sub-subgiants and red stragglers in 16 open and globular star clusters from the literature; 50 of these, including 43 sub-subgiants, pass our strict membership selection criteria (though the remaining sources may also be cluster members). In addition to their unique location on the color-magnitude diagram, we find that at least 58% (25/43) of sub-subgiants in this sample are X-ray sources with typical 0.5-2.5 keV luminosities of order 10^30 - 10^31 erg/s. Their X-ray luminosities and optical-to-X-ray flux ratios are similar to those of RS CVn active binaries. At least 65% (28/43) of the sub-subgiants in our sample are variables, 21 of which are known to be radial-velocity binaries. Typical variability periods are <15 days. At least 33% (14/43) of the sub-subgiants are H-alpha emitters. These observational demographics provide strong evidence that binarity is important for sub-subgiant formation. Finally, we find that the number of sub-subgiants per unit mass increases toward lower-mass clusters, such that the open clusters in our sample have the highest specific frequencies of sub-subgiants., Comment: 21 pages, 7 figures, 4 tables, accepted for publication in ApJ

In this paper, we study the chaotic four-body problem in Newtonian gravity. Assuming point particles and total encounter energies $\le$ 0, the problem has three possible outcomes. We describe each outcome as a series of discrete transformations in energy space, using the diagrams first presented in Leigh \& Geller (2012; see the Appendix). Furthermore, we develop a formalism for calculating probabilities for these outcomes to occur, expressed using the density of escape configurations per unit energy, and based on the Monaghan description originally developed for the three-body problem. We compare this analytic formalism to results from a series of binary-binary encounters with identical point particles, simulated using the \texttt{FEWBODY} code. Each of our three encounter outcomes produces a unique velocity distribution for the escaping star(s). Thus, these distributions can potentially be used to constrain the origins of dynamically-formed populations, via a direct comparison between the predicted and observed velocity distributions. Finally, we show that, for encounters that form stable triples, the simulated single star escape velocity distributions are the same as for the three-body problem. This is also the case for the other two encounter outcomes, but only at low virial ratios. This suggests that single and binary stars processed via single-binary and binary-binary encounters in dense star clusters should have a unique velocity distribution relative to the underlying Maxwellian distribution (provided the relaxation time is sufficiently long), which can be calculated analytically., Comment: 18 pages, 12 figures; accepted for publication in MNRAS

What is the difference between a long-lived unstable (or quasi-stable) multiple star system and a bona fide star cluster? In this paper, we present a possible framework to address this question, by studying the distributions of disruption times for chaotic gravitational encounters as a function of the number of interacting particles. To this end, we perform a series of numerical scattering experiments with the \texttt{FEWBODY} code, to calculate the distributions of disruption times as a function of both the particle number N and the virial coefficient k. The subsequent distributions are fit with a physically-motivated function, consisting of an initial exponential decay followed by a very slowly decreasing tail at long encounter times due to long-lived quasi-stable encounters. We find three primary features characteristic of the calculated distributions of disruption times. These are: (1) the system half-life increases with increasing particle number, (2) the fraction of long-lived quasi-stable encounters increases with increasing particle number and (3) both the system half-life and the fraction of quasi-stable encounters increase with decreasing virial coefficient. We discuss the significance of our results for collisional dynamics, and consider the extrapolation of our results to larger-N systems. We suggest that this could potentially offer a clear and unambiguous distinction between star clusters and (unstable or quasi-stable) multiple star systems. Although we are limited by very small-number statistics, our results tentatively suggest that (for our assumptions) this transition occurs at a critical particle number of order 100., Comment: 7 pages, 4 figures, 2 tables; accepted for publication in MNRAS

Stars in star clusters are thought to form in a single burst from a common progenitor cloud of molecular gas. However, massive, old globular clusters -- with ages greater than 10 billion years and masses of several hundred thousand solar masses -- often harbour multiple stellar populations, indicating that more than one star-forming event occurred during their lifetimes. Colliding stellar winds from late-stage, asymptotic-giant-branch stars are often invoked as second-generation star-formation trigger. The initial cluster masses should be at least 10 times more massive than they are today for this to work. However, large populations of clusters with masses greater than a few million solar masses are not found in the local Universe. Here we report on three 1-2 billion-year-old, massive star clusters in the Magellanic Clouds, which show clear evidence of burst-like star formation that occurred a few hundred million years after their initial formation era. We show that such clusters could accrete sufficient gas reservoirs to form new stars if the clusters orbited in their host galaxies' gaseous discs throughout the period between their initial formation and the more recent bursts of star formation. This may eventually give rise to the ubiquitous multiple stellar populations in globular clusters., Comment: 10 pages, 11 figures, Authors' version of a letter published in Nature (27 January 2016), including Methods and Extended Data

As part of our study of the old (~2.5 Gyr) open cluster NGC 6819 in the Kepler field, we present photometric (Kepler and ground-based BVRcIc) and spectroscopic observations of the detached eclipsing binary WOCS 24009 (Auner 665; KIC 5023948) with a short orbital period of 3.6 days. WOCS 24009 is a triple-lined system, and we verify that the brightest star is physically orbiting the eclipsing binary using radial velocities and eclipse timing variations. The eclipsing binary components have masses M_B =1.090+/-0.010 Msun and M_C =1.075+/-0.013 Msun, and radii R_B =1.095+/-0.007 Rsun and R_C =1.057+/-0.008 Rsun. The bright non-eclipsing star resides at the cluster turnoff, and ultimately its mass will directly constrain the turnoff mass: our preliminary determination is M_A =1.251+/-0.057 Msun. A careful examination of the light curves indicates that the fainter star in the eclipsing binary undergoes a very brief period of total eclipse, which enables us to precisely decompose the light of the three stars and place them in the color-magnitude diagram. We also present improved analysis of two previously discussed detached eclipsing stars in NGC 6819 (WOCS 40007 and WOCS 23009) en route to a combined determination of the cluster's distance modulus (m-M)_V=12.38+/-0.04. Because this paper significantly increases the number of measured stars in the cluster, we can better constrain the age of the color-magnitude diagram to be 2.21+/-0.10+/-0.20 Gyr. Additionally, using all measured eclipsing binary star masses and radii, we constrain the age to 2.38+/-0.05+/-0.22 Gyr. The quoted uncertainties are estimates of measurement and systematic uncertainties (due to model physics differences and metal content), respectively., Comment: accepted to AJ, 13 figures, eclipse timings and radial velocity data will be available with the journal article

Binary mass transfer is at the forefront of some of the most exciting puzzles of modern astrophysics, including Type Ia supernovae, gamma-ray bursts, and the formation of most observed exotic stellar populations. Typically, the evolution is assumed to proceed in isolation, even in dense stellar environments such as star clusters. In this paper, we test the validity of this assumption via the analysis of a large grid of binary evolution models simulated with the SeBa code. For every binary, we calculate analytically the mean time until another single or binary star comes within the mean separation of the mass-transferring binary, and compare this time-scale to the mean time for stable mass transfer to occur. We then derive the probability for each respective binary to experience a direct dynamical interruption. The resulting probability distribution can be integrated to give an estimate for the fraction of binaries undergoing mass transfer that are expected to be disrupted as a function of the host cluster properties. We find that for lower-mass clusters ($\lesssim 10^4$ M$_{\odot}$), on the order of a few to a few tens of percent of binaries undergoing mass-transfer are expected to be interrupted by an interloping single, or more often binary, star, over the course of the cluster lifetime, whereas in more massive globular clusters we expect $\ll$ 1% to be interrupted. Furthermore, using numerical scattering experiments performed with the FEWBODY code, we show that the probability of interruption increases if perturbative fly-bys are considered as well, by a factor $\sim 2$., Comment: 6 pages, 4 figures, 1 table; accepted for publication in ApJ

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. Fifteen of these member binaries are double lined. Our stellar sample spans a magnitude range of 10.8 <=V<= 16.5 (1.14-0.92 Msun) 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)., Comment: 31 pages, 5 (multi-panel) figures, published in AJ

(Abridged) We present the results of our ongoing radial-velocity (RV) survey of the old (7 Gyr) open cluster NGC 188. Our WIYN 3.5m data set spans a time baseline of 11 years, a magnitude range of 12<=V<=16.5 (1.18-0.94 MSun), and a 1 deg. diameter region on the sky. With the addition of a Dominion Astrophysical Observatory (DAO) 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 find a measurement precision of 0.4 km/s for narrow-lined stars. We have measured RVs for 1046 stars in the direction of NGC 188, finding 473 to be likely cluster members. We detect 124 velocity-variable cluster members, all of which are likely to be dynamically hard-binary stars. Using our single member stars, we find an average cluster RV of -42.36 +/- 0.04 km/s. 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 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. 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 MSun., Comment: 16 pages, 9 figures, published in AJ

We present results of a Hubble Space Telescope far-ultraviolet (FUV) survey searching for white dwarf (WD) companions to blue straggler stars (BSSs) in open cluster NGC 188. The majority of NGC 188 BSSs (15 of 21) are single-lined binaries with properties suggestive of mass-transfer formation via Roche lobe overflow, specifically through an asymptotic giant branch star transferring mass to a main sequence secondary, yielding a BSS binary with a WD companion. In NGC 188, a BSS formed by this mechanism within the past 400 Myr will have a WD companion hot and luminous enough to be directly detected as a FUV photometric excess with HST. Comparing expected BSS FUV emission to observed photometry reveals four BSSs with WD companions above 12,000 K (younger than 250 Myr) and three WD companions with temperatures between 11,000-12,000 K. These BSS+WD binaries all formed through recent mass transfer. The location of the young BSSs in an optical color-magnitude diagram (CMD) indicates that distance from the zero-age main sequence does not necessarily correlate with BSS age. There is no clear CMD separation between mass transfer-formed BSSs and those likely formed through other mechanisms, such as collisions. The seven detected WD companions place a lower limit on the mass-transfer formation frequency of 33%. We consider other possible formation mechanisms by comparing properties of the BSS population to theoretical predictions. We conclude that 14 BSS binaries likely formed from mass transfer, resulting in an inferred mass-transfer formation frequency of approximately 67%., Comment: 13 pages, 6 figures, accepted to the Astrophysical Journal

Characterization of the binary fractions in star clusters is of fundamental importance for many fields in astrophysics. Observations indicate that the majority of stars are found in binary systems, while most stars with masses greater than $0.5 M_\odot$ are formed in star clusters. In addition, since binaries are on average more massive than single stars, in resolved star clusters these systems are thought to be good tracers of (dynamical) mass segregation. Over time, dynamical evolution through two-body relaxation will cause the most massive objects to migrate to the cluster center, while the relatively lower-mass objects remain in or migrate to orbits at greater radii. This process will globally dominate a cluster's stellar distribution. However, close encounters involving binary systems may disrupt `soft' binaries. This process will occur more frequently in a cluster's central, dense region than in its periphery, which may mask the effects of mass segregation. Using high resolution Hubble Space Telescope observations, combined with sophisticated $N$-body simulations, we investigate the radial distributions of the main-sequence binary fractions in massive young Large Magellanic Cloud star clusters. We show that binary disruption may play an important role on very short timescales, depending on the environmental conditions in the cluster cores. This may lead to radial binary fractions that initially decline in the cluster centers, which is contrary to the effects expected from dynamical mass segregation., Comment: To appear in Proc. IAU Symp. 316, XXIXth IAU General Assembly, August 2015, Honolulu (HI, USA); eds. C. Charbonnel & A. Nota (6 pages, LaTeX, using iau.cls); invited review

(Abridged) 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. The combined stellar sample reaches from the brightest giants in the cluster down to about 4 magnitudes below the main-sequence turnoff (V = 16.5), covering a mass range of about 1.34 MSun to 0.76 MSun. Spatially, the sample extends to a radius of 30 arcmin (7.4 pc in projection at a distant of 850 pc or 6-7 core radii). We find M67 to have a mean RV of +33.64 km/s (with an internal precision of +/- 0.03 km/s). 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. 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 both measurement precision and undetected binaries, we derive a RV dispersion in M67 of 0.59 +0.07 -0.06 km/s, which yields a virial mass for the cluster of 2100 +610 -550 MSun. WIYN Open Cluster Study. LXVII., Comment: 19 pages, 10 figures, 4 tables, accepted for publication in The Astronomical Journal

Strong encounters between single stars and binaries play a pivotal role in the evolution of star clusters. Such encounters can also dramatically modify the orbital parameters of binaries, exchange partners in and out of binaries, and are a primary contributor to the rate of physical stellar collisions in star clusters. Often, these encounters are studied under the approximation that they happen quickly enough and within a small enough volume to be considered isolated from the rest of the cluster. In this paper, we study the validity of this assumption through the analysis of a large grid of single - binary and binary - binary scattering experiments. For each encounter we evaluate the encounter duration, and compare this with the expected time until another single or binary star will join the encounter. We find that for lower-mass clusters, similar to typical open clusters in our Galaxy, the percent of encounters that will be "interrupted" by an interloping star or binary may be 20-40% (or higher) in the core, though for typical globular clusters we expect <1% of encounters to be interrupted. Thus, the assumption that strong encounters occur in relative isolation breaks down for certain clusters. Instead, many strong encounters develop into more complex "mini-clusters", which must be accounted for in studying, for example, the internal dynamics of star clusters, and the physical stellar collision rate., Comment: 5 pages, 4 figures, accepted for publication in The Astrophysical Journal Letters

We present the Robert C. Byrd Green Bank Telescope discovery of the highly eccentric binary millisecond pulsar PSR J1835$-$3259A in the Fermi Large Area Telescope-detected globular cluster NGC 6652. Timing over one orbit yields the pulse period 3.89 ms, orbital period 9.25 d, eccentricity $\sim 0.95$, and an unusually high companion mass of $0.74\,M_{\odot}$ assuming a $1.4\,M_{\odot}$ pulsar. We caution that the lack of data near periastron prevents a precise measurement of the eccentricity, and that further timing is necessary to constrain this and the other orbital parameters. From tidal considerations, we find that the companion must be a compact object. This system likely formed through an exchange encounter in the dense cluster environment. Our initial timing results predict the measurements of at least two post-Keplerian parameters with long-term phase-connected timing: the rate of periastron advance $\dot{\omega} \sim 0.1^{\circ}\,$yr$^{-1}$, requiring 1 yr of phase connection; and the Einstein delay $\gamma_{\mathrm{GR}} \sim 10\,$ms, requiring 2-3 yr of timing. For an orbital inclination $i > 50^{\circ}$, a measurement of $\sin{i}$ is also likely. PSR J1835$-$3259A thus provides an opportunity to measure the neutron star mass with high precision; to probe the cluster environment; and, depending on the nature of the companion, to investigate the limits of general relativity., Comment: Accepted by ApJ Letters; 7 pages, 3 tables, 2 figures

We develop a formalism for calculating probabilities for the outcomes of stellar dynamical interactions, based on results from $N$-body scattering experiments. We focus here on encounters involving up to six particles and calculate probabilities for direct stellar collisions; however our method is in principle valid for larger particle numbers. Our method relies on the binomial theorem, and is applicable to encounters involving any combination of particle radii. We further demonstrate that our base model is valid to within a few percent for any combination of particle masses, provided the minimum mass ratio is within a factor of a few from unity. This method is particularly suitable for models of collisional systems involving large numbers of stars, such as globular clusters, old open clusters and galactic nuclei, where small subsets of stars may regularly have very close encounters, and the direct integration of all such encounters is computationally expensive. Variations of our method may also be used to treat other encounter outcomes, such as ejections and exchanges., Comment: 10 pages, 4 figures, 3 tables; accepted for publication in MNRAS

The two Large Magellanic Cloud star clusters NGC 1805 and NGC 1818 are approximately the same chronological age (~30 Myr), but show different radial trends in binary frequency. The F-type stars (1.3 - 2.2 MSun) in NGC 1818 have a binary frequency that decreases towards the core, while the binary frequency for stars of similar mass in NGC 1805 is flat with radius, or perhaps bimodal (with a peak in the core). We show here, through detailed N-body modeling, that both clusters could have formed with the same primordial binary frequency and with binary orbital elements and masses drawn from the same distributions (defined from observations of open clusters and the field of our Galaxy). The observed radial trends in binary frequency for both clusters are best matched with models that have initial substructure. Furthermore, both clusters may be evolving along a very similar dynamical sequence, with the key difference that NGC 1805 is dynamically older than NGC 1818. The F-type binaries in NGC 1818 still show evidence of an initial period of rapid dynamical disruptions (which occur preferentially in the core), while NGC 1805 has already begun to recover a higher core binary frequency, owing to mass segregation (which will eventually produce a distribution in binary frequency that rises only towards the core, as is observed in old Milky Way star clusters). This recovery rate increases for higher-mass binaries, and therefore even at one age in one cluster, we predict a similar dynamical sequence in the radial distribution of the binary frequency as a function of binary primary mass., Comment: 11 pages, 7 figures, accepted for publication in ApJ

This paper provides a detailed comparison of the differences in parameters derived for a star cluster from its color-magnitude diagrams depending on the filters and models used. We examine the consistency and reliability of fitting three widely-used stellar evolution models to fifteen combinations of optical and near-IR photometry for the old open cluster NGC 188. The optical filter response curves match those of the theoretical systems and are thus not the source of fit inconsistencies. NGC 188 is ideally suited to the present study thanks to a wide variety of high-quality photometry and available proper motions and radial velocities which enable us to remove non-cluster members and many binaries. Our Bayesian fitting technique yields inferred values of age, metallicity, distance modulus, and absorption as a function of the photometric band combinations and stellar models. We show that the historically-favored three band combinations of UBV and VRI can be meaningfully inconsistent with each other and with longer baseline datasets such as UBVRIJHKs. Differences among model sets can also be substantial. For instance, fitting Yi et al. (2001) and Dotter et al. (2008) models to UBVRIJHKs photometry for NGC 188 yields the following cluster parameters: age={5.78+ 0.03, 6.45+-0.04} Gyr, [Fe/H]={+0.125+-0.003, -0.077+-0.003} dex, m-M={11.441+-0.007, 11.525+-0.005} mag, and Av={0.162+-0.003, 0.236+-0.003} mag, respectively. Within the formal fitting errors, these two fits are substantially and statistically different. Such differences amongst fits using different filters and models are a cautionary tale regarding our current ability to fit star cluster color-magnitude diagrams. Additional modeling of this kind, with more models and star clusters, and future GAIA parallaxes are critical for isolating and quantifying the most relevant uncertainties in stellar evolutionary models., Comment: 19 pages, 6 figures, AJ accepted

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-degree 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 incompleteness-corrected binary fraction for all MS binaries with periods less than 10,000 days to be 22% +/- 3% and a tidal circularization period of 6.2 +/- 1.1 days for NGC 6819., Comment: 22 pages, 12 figures

In this paper, we address the question: What is the probability of stellar-mass black hole (BH) binaries co-existing in a globular cluster with an intermediate-mass black hole (IMBH)? Our results suggest that the detection of one or more BH binaries can strongly constrain the presence of an IMBH in most Galactic globular clusters. More specifically, the detection of one or more BH binaries could strongly indicate against the presence of an IMBH more massive than $\gtrsim 10^3$ M$_{\rm \odot}$ in roughly 80\% of the clusters in our sample. To illustrate this, we use a combination of N-body simulations and analytic methods to weigh the rate of formation of BH binaries against their ejection and/or disruption rate via strong gravitational interactions with the central (most) massive BH. The eventual fate of a sub-population of stellar-mass BHs (with or without binary companions) is for all BHs to be ejected from the cluster by the central IMBH, leaving only the most massive stellar-mass BH behind to form a close binary with the IMBH. During each phase of evolution, we discuss the rate of inspiral of the central BH-BH pair as a function of both the properties of the binary and its host cluster., Comment: 16 pages, 8 figures, 1 table, accepted for publication in MNRAS

The old (7 Gyr) open cluster NGC 188 has yielded a wealth of astrophysical insight into its rich blue straggler population. Specifically, the NGC 188 blue stragglers are characterized by: A binary frequency of 80% for orbital periods less than $10^4$ days;Typical orbital periods around 1000 days;Typical secondary star masses of 0.5 M$_{\odot}$; At least some white dwarf companion stars; Modestly rapid rotation; A bimodal radial spatial distribution; Dynamical masses greater than standard stellar evolution masses (based on short-period binaries); Under-luminosity for dynamical masses (short-period binaries). Extensive $N$-body modeling of NGC 188 with empirical initial conditions reproduces the properties of the cluster, and in particular the main-sequence solar-type binary population. The current models also reproduce well the binary orbital properties of the blue stragglers, but fall well short of producing the observed number of blue stragglers. This deficit could be resolved by reducing the frequency of common-envelope evolution during Roche lobe overflow. Both the observations and the $N$-body models strongly indicate that the long-period blue-straggler binaries - which dominate the NGC 188 blue straggler population - are formed by asymptotic-giant (primarily) and red-giant mass transfer onto main sequence stars. The models suggest that the few non-velocity-variable blue stragglers formed from mergers or collisions. Several remarkable short-period double-lined binaries point to the importance of subsequent dynamical exchange encounters, and provide at least one example of a likely collisional origin for a blue straggler., Comment: Chapter 3, in Ecology of Blue Straggler Stars, H.M.J. Boffin, G. Carraro & G. Beccari (Eds), Astrophysics and Space Science Library, Springer