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Stars and stellar remnants orbiting a supermassive black hole (SMBH) can interact with an active galactic nucleus (AGN) disc. Over time, prograde orbiters (inclination $ii_{\rm ret}$ sBH decay towards embedded retrograde orbits $(i \to 180^{\circ})$. sBH near polar orbits $(i \sim 90^{\circ})$ and stars on nearly embedded retrograde orbits $(i \sim 180^{\circ})$ show the greatest decreases in $a$. Whether a star is captured by the disc within an AGN lifetime depends primarily on disc density, and secondarily on stellar type and initial $a$. For sBH, disc capture-time is longest for polar orbits, low mass sBH and lower density discs. Larger mass sBH should typically spend more time in AGN discs, with implications for the embedded sBH spin distribution., 9 pages, 7 figures, 1 table

Three-body interactions can eject stars from the core of a globular cluster, causing them to enter the Galactic halo as extra-tidal stars. While finding extra-tidal stars is imperative for understanding cluster evolution, connecting isolated extra-tidal field stars back to their birth cluster is extremely difficult. In this work, we present a new methodology consisting of high-dimensional data analysis and a particle spray code to identify extra-tidal stars of any Galactic globular cluster using M3 as a case study. Using the t-Stochastic Neighbour Embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP) machine learning dimensionality reduction algorithms, we first identify a set of 103 extra-tidal candidates in the APOGEE DR17 data catalogue with chemical abundances similar to M3 stars. To confirm each candidate's extra-tidal nature, we introduce corespray - a new Python-based three-body particle spray code that simulates extra-tidal stars for any Galactic globular cluster. Using Gaia EDR3 proper motions and APOGEE DR17 radial velocities, we apply multivariate Gaussian modelling and an extreme deconvolution to identify the extra-tidal candidates that are more likely to be associated with a distribution of corespray-simulated M3 extra-tidal stars than the field. Through these methods, we identify 10 new high-probability extra-tidal stars produced via three-body interactions in M3. We also explore whether any of our extra-tidal candidates are consistent with being ejected from M3 through different dynamical processes. Future applications of corespray will yield better understandings of core dynamics, star formation histories and binary fractions in globular clusters., Comment: 16 pages, 8 figures, 3 tables. Accepted for publication in Monthly Notices of the Royal Astronomical Society

Direct collisions between finite-sized particles occur commonly in many areas of astrophysics. Such collisions are typically mediated by chaotic, bound gravitational interactions involving small numbers of particles. An important application is stellar collisions, which occur commonly in dense star clusters, and their relevance for the formation of various types of stellar exotica. In this paper, we return to our study of the collision rates and probabilities during small-number chaotic gravitational interactions ($N\, \lesssim$ 10), moving beyond the small-number particle limit and into the realm of larger particle numbers ($N\, \gtrsim$ 103) to test the extent of validity of our analytic model as a function of the particle properties and the number of interacting particles. This is done using direct N-body simulations of stellar collisions in dense star clusters, by varying the relative numbers of particles with different particle masses and radii. We compute the predicted rate of collisions using the mean free path approximation, adopting the point-particle limit and using the sticky-star approximation as our collision criterion. We evaluate its efficacy in the regime where gravitational focusing is important by comparing the theoretical rates to numerical simulations. Using the tools developed in previous papers in this series, in particular Collision Rate Diagrams, we illustrate that our predicted and simulated rates are in excellent agreement, typically consistent with each other to within 1 standard deviation.

In this paper, we consider triple systems composed of main-sequence (MS) stars, and their internal evolution due to stellar and binary evolution. Our focus is on triples that produce white dwarfs (WDs), where Roche lobe overflow of an evolving tertiary triggers accretion onto the inner binary via a circumbinary disk (CBD) driving it toward a mass ratio of unity. We present a combination of analytic- and population synthesis-based calculations performed using the \texttt{SeBa} code to constrain the expected frequency of such systems, given a realistic initial population of MS triples, and provide the predicted distributions of orbital periods. We identify the parameter space for triples that can accommodate a CBD, to inform future numerical simulations of suitable initial conditions. We find that $\lesssim$ 10\% of all MS triples should be able to accommodate a CBD around the inner binary, and compute lower limits for the production rates. This scenario broadly predicts mergers of near equal-mass binaries, producing blue stragglers (BSs), Type Ia supernovae, gamma ray bursts and gravitational wave-induced mergers, along with the presence of an outer WD tertiary companion. We compare our predicted distributions to a sample of field BS binaries, and argue that our proposed mechanism explains the observed range of orbital periods. Finally, the mechanism considered here could produce hypervelocity MS stars, WDs and even millisecond pulsars with masses close to the Chandrasekhar mass limit, and be used to constrain the maximum remnant masses at the time of any supernova explosion., Comment: 15 pages, 7 figures; accepted for publication in MNRAS

We study the stellar kinematic properties and spatial distribution of the association Cyg OB3 using precise astrometric data from Gaia DR2. All known O- and B-type stars in Cyg OB3 region with positions, parallaxes and proper motions available are included, comprising a total of 41 stars. The majority of stars are found to be concentrated at a heliocentric distance of 2.0 +/- 0.3 kpc. The mean peculiar velocity of the sample after removing Galactic rotation and solar motion is ~22 km/s, dominated by the velocity component towards the Galactic center. The relative position and velocity of the black hole X-ray binary Cyg X-1 with respect to the association suggest that Cyg OB3 is most likely its parent association. The peculiar kinematic properties of some of the stars are revealed and are suggestive of past stellar encounters. The sample includes a previously known runaway star HD 227018, and its high peculiar velocity of ~50 km/s is confirmed with Gaia. We estimated the velocities of stars relative to the association and the star HD 225577 exhibits peculiar velocity smaller than its velocity relative to the association. The star has lower value of proper motion than the rest of the sample. The results suggest a slowly expanding nature of the association, which is supported by the small relative speeds, Accepted for publication in MNRAS

We present a half-life formalism for describing the disruption of gravitationally-bound few-body systems, with a focus on binary-binary scattering. For negative total encounter energies, the four-body problem has three possible decay products in the point particle limit. For each decay product and a given set of initial conditions, we obtain directly from numerical scattering simulations the half-life for the distribution of disruption times. As in radioactive decay, the half-lives should provide a direct prediction for the relative fractions of each decay product. We test this prediction with simulated data and find good agreement with our hypothesis. We briefly discuss applications of this feature of the gravitational four-body problem to populations of black holes in globular clusters. This paper, the second in the series, builds on extending the remarkable similarity between gravitational chaos at the macroscopic scale and radioactive decay at the microscopic scale to larger-N systems., 17 pages, 18 figures, 2 tables; accepted for publication in MNRAS

We use N-body simulations to model the 12 Gyr evolution of a suite of star clusters with identical initial stellar mass functions over a range of initial cluster masses, sizes, and orbits. Our models reproduce the distribution of present-day global stellar mass functions that is observed in the Milky Way globular cluster population. We find that the slope of a star cluster's stellar mass function is strongly correlated with the fraction of mass that the cluster has lost, independent of the cluster's initial mass, and nearly independent of its orbit and initial size. Thus, the mass function - initial mass relation can be used to determine a Galactic cluster's initial total stellar mass, if the initial stellar mass function is known. We apply the mass function - initial mass relation presented here to determine the initial stellar masses of 33 Galactic globular clusters, assuming an universal Kroupa initial mass function. Our study suggests that globular clusters had initial masses that were on average a factor of 4.5 times larger than their present day mass, with three clusters showing evidence for being 10 times more massive at birth., Comment: Revised Version: 11 pages, 4 figures, Accepted for publication in MNRAS

In a virialized stellar system, the mean-square velocity is a direct tracer of the energy per unit mass of the system. Here, we exploit this to estimate and compare root-mean-square velocities for a large sample of nuclear star clusters and their host (late- or early-type) galaxies. Traditional observables, such as the radial surface brightness and second-order velocity moment profiles, are subject to short-term variations due to individual episodes of matter infall and/or star formation. The total mass, energy and angular momentum, on the other hand, are approximately conserved. Thus, the total energy and angular momentum more directly probe the formation of galaxies and their nuclear star clusters, by offering access to more fundamental properties of the nuclear cluster-galaxy system than traditional observables. We find that there is a strong correlation, in fact a near equality, between the root-mean-square velocity of a nuclear star cluster and that of its host. Thus, the energy per unit mass of a nuclear star cluster is always comparable to that of its host galaxy. We interpret this as evidence that nuclear star clusters do not form independently of their host galaxies, but rather that their formation and subsequent evolution are coupled. We discuss how our results can potentially be used to offer a clear and observationally testable prediction to distinguish between the different nuclear star cluster formation scenarios, and/or quantify their relative contributions., 12 pages, 3 figures, 4 tables; accepted for publication in MNRAS

(abridged) In this paper, we constrain the properties of primordial binary populations in Galactic globular clusters using the MOCCA Monte Carlo code for cluster evolution. Our results are compared to the observations of Milone et al. (2012) using the photometric binary populations as proxies for the true underlying distributions, in order to test the hypothesis that the data are consistent with an universal initial binary fraction near unity and the binary orbital parameter distributions of Kroupa (1995). With the exception of a few possible outliers, we find that the data are to first-order consistent with the universality hypothesis. Specifically, the present-day binary fractions inside the half-mass radius r$_{\rm h}$ can be reproduced assuming either high initial binary fractions near unity with a dominant soft binary component as in the Kroupa distribution combined with high initial densities (10$^4$-10$^6$ M$_{\odot}$ pc$^{-3}$), or low initial binary fractions ($\sim$ 5-10%) with a dominant hard binary component combined with moderate initial densities near their present-day values (10$^2$-10$^3$ M$_{\odot}$ pc$^{-3}$). This apparent degeneracy can be broken using the binary fractions outside r$_{\rm h}$- only high initial binary fractions with a significant soft component combined with high initial densities can contribute to reproducing the observed anti-correlation between the binary fractions outside r$_{\rm h}$ and the total cluster mass. We further illustrate using the simulated present-day binary orbital parameter distributions and the technique introduced in Leigh et al. (2012) that the relative fractions of hard and soft binaries can be used to further constrain the initial cluster density and mass-density relation. Our results favour an initial mass-density relation of the form r$_{\rm h} \propto$ M$_{\rm clus}^{\alpha}$ with $\alpha, Comment: 17 pages; 5 figures; 1 table; accepted for publication in MNRAS

In this paper, we consider how gas damping affects the dynamical evolution of gas-embedded star clusters. Using a simple three-component (i.e. one gas and two stellar components) model, we compare the rates of mass segregation due to two-body relaxation, accretion from the interstellar medium, and gas dynamical friction in both the supersonic and subsonic regimes. Using observational data in the literature, we apply our analytic predictions to two different astrophysical environments, namely galactic nuclei and young open star clusters. Our analytic results are then tested using numerical simulations performed with the NBSymple code, modified by an additional deceleration term to model the damping effects of the gas. The results of our simulations are in reasonable agreement with our analytic predictions, and demonstrate that gas damping can significantly accelerate the rate of mass segregation. A stable state of approximate energy equilibrium cannot be achieved in our model if gas damping is present, even if Spitzer's Criterion is satisfied. This instability drives the continued dynamical decoupling and subsequent ejection (and/or collisions) of the more massive population. Unlike two-body relaxation, gas damping causes overall cluster contraction, reducing both the core and half-mass radii. If the cluster is mass segregated (and/or the gas density is highest at the cluster centre), the latter contracts faster than the former, accelerating the rate of core collapse., Comment: 17 pages, 8 figures, 1 table; accepted for publication in MNRAS

Over the last few decades, observational surveys have revealed that high-order multiple-star systems (e.g. triples, quadruples, etc.), and triples in particular, are common in our Galaxy. In this paper, we consider the dynamical significance of this transformation in our understanding of stellar multiplicity. Using empirically constrained binary and triple fractions in those star clusters for which these values are available in the literature, we compare analytic rates for encounters involving single, binary, and triple stars. Our results show that, \textit{even for relatively low triple fractions, dynamical interactions involving triples occur roughly as often as encounters involving either single or binary stars alone, particularly in low-mass star clusters}. More generally, using empirically-derived multiple star catalogues for the young star-forming association Taurus-Auriga and the Galactic field, we show that the data are consistent with the gravitationally-focused cross section for encounters increasing with increasing multiplicity. Consequently, triple stars, and even higher-order multiples, could be more important than previously realized for a number of astrophysical phenomena, including the formation and destruction of compact binaries and various types of stellar exotica, and the dynamical evolution of star clusters., Comment: 7 pages, 3 figures, 1 table; accepted for publication in MNRAS

In this paper, we study small-N gravitational dynamics involving up to six objects. We perform a large suite of numerical scattering experiments involving single, binary, and triple stars. This is done using the FEWBODY numerical scattering code, which we have upgraded to treat encounters involving triple stars. We focus on outcomes that result in direct physical collisions between stars, within the low angular momentum and high absolute orbital energy regime. The dependence of the collision probability on the number of objects involved in the interaction, N, is found for fixed total energy and angular momentum. Our results are consistent with a collision probability that increases approximately as N 2 . Interestingly, this is also what is expected from the mean free path approximation in the limit of very large N. A more thorough exploration of parameter space will be required in future studies to fully explore this potentially intriguing connection. This study is meant as a first step in an on-going effort to extend our understanding of small-N collisional dynamics beyond the threeand four-body problems and into the realm of larger-N.

We combine published photometry for the nuclear star clusters and stellar spheroids of 51 low-mass, early-type galaxies in the Virgo cluster with empirical mass-to-light ratios, in order to complement previous studies that explore the dependence of nuclear star cluster (NSC) masses on various properties of their host galaxies. We confirm a roughly linear relationship between NSC mass and luminous host spheroid mass, albeit with considerable scatter (0.57 dex). In order to translate this to an MNSC σ relation, we estimate velocity dispersions from the virial theorem, assuming all galaxies in our sample share a common dark matter fraction and are dynamically relaxed. We then find that MNSC � σ 2.73±0.29 , with a slightly reduced scatter of 0.54 dex. This confirms recent results that the shape of the MCMO σ relation is different for NSCs and super-massive black holes (SMBHs). We discuss this result in the context of the generalized idea of "central massive objects" (CMOs). In order to assess which physical parameters drive the observed nuclear cluster masses, we also carry out a joint multi-variate power-law fit to the data. In this, we allow the nuclear cluster mass to depend on spheroid mass and radius (and hence implicitly on velocity dispersion), as well as on the size of the globular cluster reservoir. When considered together, the dependences on MSph and RSph are roughly consistent with the virial theorem, and therefore MNSC / σ 2 . However, the only statistically significant correlation appears to be a simple linear scaling between NSC mass and luminous spheroid mass. We proceed to directly compare the derived NSC masses with predictions for two popular models for NSC formation, namely i) globular cluster infall due to dynamical friction, and ii) in-situ formation during the early phases of galaxy formation that is regulated via momentum feedback from stellar winds and/or supernovae. Neither model can directly predict the observations, and we discuss possible interpretations of our findings.

We present a new technique to quantify cluster-to-cluster variations in the observed present-day stellar mass functions of a large sample of star clusters. Our method quantifies these differences as a function of both the stellar mass and the total cluster mass, and offers the advantage that it is insensitive to the precise functional form of the mass function. We applied our technique to data taken from the ACS Survey for Globular Clusters, from which we obtained completeness-corrected stellar mass functions in the mass range 0.25-0.75 M$_{\odot}$ for a sample of 27 clusters. The results of our observational analysis were then compared to Monte Carlo simulations for globular cluster evolution spanning a range of initial mass functions, total numbers of stars, concentrations, and virial radii. We show that the present-day mass functions of the clusters in our sample can be reproduced by assuming an universal initial mass function for all clusters, and that the cluster-to-cluster differences are consistent with what is expected from two-body relaxation. A more complete exploration of the initial cluster conditions will be needed in future studies to better constrain the precise functional form of the initial mass function. This study is a first step toward using our technique to constrain the dynamical histories of a large sample of old Galactic star clusters and, by extension, star formation in the early Universe.

We present an analytic model for blue straggler formation in globular clusters. We assume that blue stragglers are formed only through stellar collisions and binary star evolution, and compare our predictions to observed blue straggler numbers. We can summarize our key results as follows. (1) Binary star evolution consistently dominates blue straggler production in all our best-fitting models. (2) In order to account for the observed sublinear dependence of blue straggler numbers on the core masses, the core binary fraction must be inversely proportional to the total cluster luminosity and should always exceed at least a few per cent. (3) In at least some clusters, blue straggler formation must be enhanced by dynamical encounters (either via direct collisions or by stimulating mass transfer to occur by altering the distribution of binary orbital parameters) relative to what is expected by assuming a simple population of binaries evolving in isolation. (4) The agreement between the predictions of our model and the observations can be improved by including blue stragglers that form outside the core but later migrate in due to dynamical friction. (5) Longer blue straggler lifetimes are preferred in models that include blue stragglers formed outside the core since this increases the fraction that will have sufficient time to migrate in via dynamical friction.

We present a homogeneous catalogue for blue straggler, red giant branch, horizontal branch and main-sequence turn-off stars in a sample of 35 clusters taken from the ACS Survey for Globular Clusters. As a result of the superior photometry and relatively large field of view offered by the ACS data, this new catalogue is a significant improvement upon the one presented in Leigh, Sills & knigge (2007). Using our catalogue, we study and compare the radial distributions of the different stellar populations. We have confirmed our previous result (Knigge, Leigh & Sills 2009) that there is a clear, but sub-linear, correlation between the number of blue stragglers found in the cluster core and the total stellar mass contained within it. By considering a larger spatial extent than just the core, our results suggest that mass segregation is not the dominant effect contributing to the observed sub-linearity. We also investigate the radial distributions of the different stellar populations in our sample of clusters. Our results are consistent with a linear relationship between the number of stars in these populations and the total mass enclosed within the same radius. Therefore, we conclude that the cluster dynamics does not significantly affect the relative distributions of these populations in our sample.

We present a technique to identify the most probable dynamical formation scenario for an observed binary or triple system containing one or more merger products or, alternatively, to rule out the possibility of a dynamical origin. Our method relies on an analytic prescription for energy conservation during stellar encounters. With this, observations of the multiple star system containing the merger product(s) can be used to work backwards in order to constrain the initial orbital energies of any single, binary or triple systems that went into the encounter. The initial semi-major axes of the orbits provide an estimate for the collisional cross section and therefore the time-scale for the encounter to occur in its host cluster. We have applied our analytic prescription to observed binary and triple systems containing blue stragglers, in particular the triple system S1082 in M67 and the period distribution of the blue straggler binaries in NGC 188. We have shown that both S1082 and most of the blue straggler binaries in NGC 188 could have a dynamical origin, and that encounters involving triples could be a significant contributor to BS populations in old open clusters. In general, our results suggest that encounters involving triples could make up a significant fraction of those dynamical interactions that result in stellar mergers, in particular encounters that produce multiple star systems containing one or more blue stragglers.

It has become clear in recent years that globular clusters are not simple stellar populations, but may host chemically distinct sub-populations, typically with an enhanced helium abundance. These helium-rich populations can make up a substantial fraction of all cluster stars. One of the proposed formation channels for blue straggler stars is the physical collision and merger of two stars. In the context of multiple populations, collisions between stars with different helium abundances should occur and contribute to the observed blue straggler population. This will affect the predicted blue straggler colour and luminosity function. We quantify this effect by calculating models of mergers resulting from collisions between stars with different helium abundances and using these models to model a merger population. We then compare these results to four observed clusters, NGC 1851, NGC 2808, NGC 5634 and NGC 6093. As in previous studies our models deviate from the observations, particularly in the colour distributions. However, our results are consistent with observations of multiple populations in these clusters. In NGC 2808, our best fitting models include normal and helium enhanced populations, in agreement with helium enhancement inferred in this cluster. The other three clusters show better agreement with models that do not include helium enhancement. We discuss future prospects to improve the modelling of blue straggler populations and the role that the models we present here can play in such a study.

We investigate the relationship between the mass of a globular cluster core and the sizes of its various stellar populations in a sample of 56 globular clusters. The number of core red giant branch stars is found to scale sub-linearly with core mass at the 3-$\sigma$ confidence level, whereas the relation is linear to within one standard deviation for main-sequence turn-off and sub-giant branch stars. We interpret our results as evidence for a surplus of red giant branch stars in the least massive cluster cores which is not seen for main-sequence turn-off and sub-giant branch stars. We explore various possibilities for the source of this discrepancy, discussing our results primarily in terms of the interplay between the cluster dynamics and stellar evolution., Comment: 5 pages, 2 figures, accepted by MNRAS Letters