arXiv subjects

Nathan W. C. Leigh

Publications and source records attributed to Nathan W. C. Leigh.

66 records · Page 4Linked to original sources

arXiv2016

When does a star cluster become a multiple star system? I. Lifetimes of equal-mass small-N systems

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.

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arXiv2016

Interrupted Binary Mass Transfer in Star Clusters

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 $\sim 2$.

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arXiv2015

Back to the Future: Estimating Initial Globular Cluster Masses from their Present Day Stellar Mass Functions

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.

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arXiv2015

Interrupted Stellar Encounters in Star Clusters

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.

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arXiv2015

Small-N collisional dynamics II: Roaming the realm of not-so-small-N

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.

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arXiv2014

The state of globular clusters at birth: emergence from the gas-embedded phase

In this paper, we discuss the origin of the observed correlation between cluster concentration c and present-day mass function (PDMF) slope α reported by De Marchi, Paresce & Pulone. This relation can either be reproduced from universal initial conditions combined with some dynamical mechanism(s) that alter(s) the cluster structure and mass function over time, or it must arise early on in the cluster lifetime, such as during the gas-embedded phase of cluster formation. Using a combination of Monte Carlo and N-body models for globular cluster evolution performed with the MOCCA and NBODY6 codes, respectively, we explore a number of dynamical mechanisms that could affect the observed relation. For the range of initial conditions considered here, our results are consistent with an universal initial binary fraction \approx 10% (which does not, however, preclude 100%) and an universal initial stellar mass function resembling the standard Kroupa distribution. Most of the dispersion observed in the c-α relation can be attributed to two-body relaxation and Galactic tides. However, dynamical processes alone could not have reproduced the dispersion in concentration, and we require at least some correlation between the initial concentration and the total cluster mass. We argue that the origin of this trend could be connected to the gas-embedded phase of cluster evolution.

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arXiv2014

Modifying two-body relaxation in N-body systems by gas accretion

We consider the effects that accretion from the interstellar medium onto the particles of an N-body system has on the rate of two-body relaxation. To this end, we derive an accretion-modified relaxation time by adapting Spitzer's two-component model to include the damping effects of accretion. We consider several different mass-dependencies and efficiency factors for the accretion rate, as well as different mass ratios for the two components of the model. The net effect of accretion is to accelerate mass segregation by increasing the average mass $\bar{m}$, since the relaxation time is inversely proportional to $\bar{m}$. Under the assumption that the accretion rate increases with the accretor mass, there are two additional effects that accelerate mass segregation. First, accretion acts to increase the range of any initial mass spectrum, quickly driving the heaviest members to even higher masses. Second, accretion acts to reduce the velocities of the accretors due to conservation of momentum, and it is the heaviest members that are affected the most. Using our two-component model, we quantify these effects as a function of the accretion rate, the total cluster mass, and the component masses. We conclude by discussing the implications of our results for the dynamical evolution of primordial globular clusters, primarily in the context of black holes formed from the most massive stellar progenitors.

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arXiv2014

The state of globular clusters at birth II: primordial binaries

(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$_{\rm clus}^α$ with $α<$ 1/3.

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arXiv2014

On the coexistence of stellar-mass and intermediate-mass black holes in globular clusters

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.

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arXiv2014

Stellar dynamics in gas: The role of gas damping

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.

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arXiv2013

The Dynamical Significance of Triple Star Systems in Star Clusters

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.

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arXiv2012

Gas depletion in primordial globular clusters due to accretion onto stellar-mass black holes

(abridged) We consider the effect of stellar remnants on the interstellar medium of a massive star cluster following the initial burst of star formation. We argue that accretion onto stellar-mass black holes (BHs) is an effective mechanism for rapid gas depletion in clusters of all masses, as long as they contain progenitor stars more massive than \gtrsim 50\msun. This scenario is attractive for the progenitor systems of present-day massive globular clusters (GCs) which likely had masses M \gtrsim 10^7\msun. In such clusters, supernovae and stellar winds cannot provide a plausible explanation for the sudden removal of the primordial gas reservoir that is required to explain their complex chemical enrichment history. In order to consider different regimes in the gas accretion rate onto stellar-mass BHs, we consider both the Bondi-Hoyle and Eddington approximations. For either model, our results show that the gas can be significantly depleted within only a few tens of Myrs. This process will affect the distribution of BH masses, and may accelerate the dynamical decoupling of the BH population and, ultimately, their dynamical ejection. Moreover, the timescales for gas depletion are sufficiently short that the accreting BHs could significantly affect the chemistry of subsequent star formation episodes. The gas depletion times and final mass in BHs are sensitive to the assumed model for the accretion rate, and to the initial mass of the most massive BH which, in turn, is determined by the upper mass cut-off of the stellar IMF. Our results imply that the remnant accretion history can have an important bearing on the observed present-day cluster mass-to-light ratio. In particular, we show that an increase of the upper mass cut-off with decreasing metallicity could contribute to the observed anti-correlation between the mass-to-light ratio and the metallicity of GCs.

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