John M. Fregeau

Stellar collisions during binary-binary and binary-single star interactions

Physical collisions between stars occur frequently in dense star clusters, either via close encounters between two single stars, or during strong dynamical interactions involving binary stars. Here we study stellar collisions that occur during binary-single and binary-binary interactions, by performing numerical scattering experiments. Our results include cross-sections, branching ratios and sample distributions of parameters for various outcomes. For interactions of hard binaries containing main-sequence stars, we find that the normalized cross-section for at least one collision to occur (between any two of the four stars involved) is essentially unity, and that the probability of collisions involving more than two stars is significant. Hydrodynamic calculations have shown that the effective radius of a collision product can be 2-30 times larger than the normal main-sequence radius for a star of the same total mass. We study the effect of this expansion, and find that it increases the probability of further collisions considerably. We discuss these results in the context of recent observations of blue stragglers in globular clusters with masses exceeding twice the main-sequence turn-off mass. We also present FEWBODY, a new, freely available numerical toolkit for simulating small-N gravitational dynamics that is particularly suited to performing scattering experiments.

Formation and evolution of compact binaries in globular clusters – II. Binaries with neutron stars

In this paper, the second of a series, we study the stellar dynamical and evolutionary processes leading to the formation of compact binaries containing neutron stars (NSs) in dense globular clusters. For this study, 70 dense clusters were simulated independently, with a total stellar mass ∼2 × 10 7 M� , exceeding the total mass of all dense globular clusters in our Galaxy. We find that, in order to reproduce the empirically derived formation rate of low-mass X-ray binaries (LMXBs), we must assume that NSs can be formed via electron-capture supernovae with typical natal kicks smaller than in core-collapse supernovae. Our results explain the observed dependence of the number of LMXBs on ‘collision number’ as well as the large scatter observed between different globular clusters. We predict that the number of quiescent LMXBs in different clusters should not have a strong metallicity dependence. We compare the results obtained from our simulations with the observed population of millisecond pulsars (MSPs). We find that in our cluster model the following mass-gaining events create populations of MSPs that do not match the observations (either they are inconsistent with the observed LMXB production rates, or the inferred binary periods or companion masses are not observed among radio bMSPs): (i) accretion during a common-envelope event with a NS formed through electron-capture supernovae (ECSNe), and (ii) mass transfer (MT) from a white dwarf donor. Some processes lead only to a mild recycling ‐ physical collisions or MT in a post-accretion-induced collapse system. In addition, for MSPs, we distinguish low magnetic field (long-lived) and high magnetic field (short-lived) populations, where in the latter NSs are formed as a result of accretion-induced collapse or merger-induced collapse. With this distinction and by considering only those mass-gaining events that appear to lead to NS recycling, we obtain good agreement of our models with the numbers and characteristics of observed MSPs in 47 Tuc and Terzan 5, as well as with the cumulative statistics for MSPs detected in globular clusters of different dynamical properties. We find that significant production of merging double NSs potentially detectable as short γ -ray bursts occurs only in very dense, most likely core-collapsed clusters.

Binary Mergers and Growth of Black Holes in Dense Star Clusters

We model the dynamical evolution of primordial black holes (BHs) in dense star clusters using a simplified treatment of stellar dynamics in which the BHs are assumed to remain concentrated in an inner core, completely decoupled from the background stars. Dynamical interactions involving BH binaries are computed exactly and are generated according to a Monte Carlo prescription. Recoil and ejections lead to complete evaporation of the BH core on a timescale ~109 yr for typical globular cluster parameters. Orbital decay driven by gravitational radiation can make binaries merge, and, in some cases, successive mergers can lead to significant BH growth. Our highly simplified treatment of the cluster dynamics allows us to study a large number of models and to compute statistical distributions of outcomes, such as the probability of massive BH growth and retention in a cluster. We find that, in most models, there is a significant probability (~20%-80%) of BH growth with final masses 100 M☉. In one case, a BH formed with mass ≈620 M☉. However, if the typical merger recoil speed (due to asymmetric emission of gravitational radiation) significantly exceeds the cluster escape speed, no growth ever occurs. Independent of the recoil speed, we find that BH-BH mergers enhanced by dynamical interactions in cluster cores present an important source of gravitational waves for ground-based laser interferometers. Under optimistic conditions, the total rate of detections by Advanced LIGO could be as high as a few tens of events per year from inspiraling BHs from clusters.

The evolution of binary fractions in globular clusters

We study the evolution of binary stars in globular clusters using a new Monte Carlo approach combining a population synthesis code (StarTrack), and a simple treatment of dynamical interactions in the dense cluster core using a new tool for computing 3-body and 4-body interactions (Fewbody). We find that the combination of stellar evolution and dynamical interactions (binary–single and binary–binary) leads to a rapid depletion of the binary population in the cluster core. The maximum binary fraction today in the core of a typical dense cluster like 47 Tuc, assuming an initial binary fraction of 100%, is only about 5–10%. We show that this is in good agreement with recent HST observations of close binaries in the core of 47 Tuc, provided that a realistic distribution of binary periods is used to interpret the results. Our findings also have important consequences for the dynamical modeling of globular clusters, suggesting that “realistic models” should incorporate much larger initial binary fractions than has usually been done in the past.

Accretion onto Fast X-Ray Pulsars

The recent emergence of a new class of accretion-powered, transient, millisecond X-ray pulsars presents some difficulties for the conventional picture of accretion onto rapidly rotating magnetized neutron stars and their spin behavior during outbursts. In particular, it is not clear that the standard paradigm can accommodate the wide range in (i.e., a factor of 50) over which these systems manage to accrete and the high rate of spin-down that the neutron stars exhibit in at least a number of cases. When the accretion rate drops sufficiently, the X-ray pulsar is said to become a fast rotator, and in the conventional view, this is accompanied by a transition from accretion to propellering, in which accretion ceases and the matter is ejected from the system. On the theoretical side, we note that this scenario for the onset of propellering cannot be entirely correct because it is not energetically self-consistent. We show that, instead, the transition is likely to take place through disks that combine accretion with spin-down and terminate at the corotation radius. We demonstrate the existence of such disk solutions by modifying the Shakura-Sunyaev equations with a simple magnetic torque prescription. The solutions are completely analytic and have the same dependence on and α (the viscosity parameter) as the original Shakura-Sunyaev solutions, but the radial profiles can be considerably modified, depending on the degree of fastness. We apply these results to compute the torques expected during the outbursts of the transient millisecond pulsars and find that we can explain the large spin-down rates that are observed for quite plausible surface magnetic fields of ~109 G.

Formation and evolution of compact binaries in globular clusters ¿ I. Binaries with white dwarfs

In this paper, the first of a series, we study the stellar dynamical and evolutionary processes leading to the formation of compact binaries containing white dwarfs (WDs) in dense globular clusters (GCs). We examine the processes leading to the creation of X-ray binaries such as cataclysmic variables (CVs) and AM CVn systems. Using numerical simulations, we identify the dominant formation channels and we predict the expected numbers and characteristics of detectable systems, emphasizing how the cluster sources differ from the field population. We explore the dependence of formation rates on cluster properties and we explain in particular why the distribution of CVs has only a weak dependence on cluster density. We also discuss the frequency of dwarf nova outbursts in GCs and their connection with moderately strong WD magnetic fields. We examine the rates of Type Ia supernovae (SNe Ia) via both single and double degenerate channels in clusters and we argue that those rates may contribute to the total SN Ia rate in elliptical galaxies. Considering coalescing WD binaries, we discuss possible constraints on the common envelope evolution of their progenitors and we derive theoretical expectations for gravitational wave detection by Laser Interferometer Space Antenna (LISA).

Monte carlo simulations of globular cluster evolution. IV. Direct integration of strong interactions

We study the dynamical evolution of globular clusters containing populations of primordial binaries, using our newly updated Monte Carlo cluster evolution code with the inclusion of direct integration of binary scattering interactions. We describe the modifications we have made to the code, as well as improvements we have made to the core Monte Carlo method. We present several test calculations to verify the validity of the new code and perform many comparisons with previous analytical and numerical work in the literature. We simulate the evolution of a large grid of models, with a wide range of initial cluster profiles and with binary fractions ranging from 0 to 1, and compare with observations of Galactic globular clusters. We find that our code yields very good agreement with direct N-body simulations of clusters with primordial binaries, but yields some results that differ significantly from other approximate methods. Notably, the direct integration of binary interactions reduces their energy generation rate relative to the simple recipes used in Paper III and yields smaller core radii. Our results for the structural parameters of clusters during the binary-burning phase are now in the tail of the range of parameters for observed clusters, implying that either clusters are born significantly more or less centrally concentrated than has been previously considered or there are additional physical processes beyond two-body relaxation and binary interactions that affect the structural characteristics of clusters.

FORMATION OF BLACK HOLE X-RAY BINARIES IN GLOBULAR CLUSTERS

Inspired by the recent identification in extragalactic globular clusters of the first candidate black hole-white dwarf (BH-WD) X-ray binaries, where the compact accretors may be stellar-mass black holes (BHs), we explore how such binaries could be formed in a dynamical environment. We provide analyses of the formation rates via well-known formation channels like binary exchange and physical collisions and propose that the only possibility of forming BH-WD binaries is via coupling these usual formation channels with subsequent hardening and/or triple formation. In particular, we find that the most important mechanism for the creation of a BH-WD X-ray binary from an initially dynamically formed BH-WD binary is mass transfer induced in a triple system via the Kozai mechanism. Furthermore, we find that BH-WD binaries that evolve into X-ray sources can be formed by exchanges of a BH into a WD-WD binary or possibly by collisions of a BH and a giant star. If BHs undergo significant evaporation from the cluster or form a completely detached subcluster of BHs, then we cannot match the observationally inferred production rates even using the most optimistic estimates of formation rates. To explain the observations with stellar-mass BH-WD binaries, at least 1% of all formed BHs, or presumably 10% of the BHs present in the core now, must be involved in interactions with the rest of the core stellar population.

Dynamical Interactions of Planetary Systems in Dense Stellar Environments

We study dynamical interactions of star-planet binaries with other single stars. We derive analytical cross sections for all possible outcomes and confirm them with numerical scattering experiments. We find that a wide mass ratio in thebinaryintroducesaregioninparameterspacethatisinaccessibletocomparable-masssystems,inwhichthenature of the dynamical interaction is fundamentally different from what has traditionally been considered in the literature on binary scattering. We study the properties of the planetary systems that result from the scattering interactions for all regions of parameter space, paying particular attention to the location of the ‘‘hard-soft’’ boundary. The structure of the parameter space turns out to be significantly richer than a simple statement of the location of the hard-soft boundarywouldimply.Weconsidertheimplicationsofourfindings, calculatingcharacteristic lifetimesforplanetary systemsindensestellarenvironmentsandapplyingtheresultstopreviousanalyticalstudies,aswellaspastandfuture observations. Since we recognized that the system PSR B1620� 26 in the globular cluster M4 lies in the ‘‘new’’ region of parameter space, we performed a detailed analysis quantifying the likelihood of different scenarios in forming the system we see today. Subject headings: celestial mechanics — globular clusters: general — methods: n-body simulations — planetary systems — pulsars: individual (PSR B1620� 26)

EVOLUTION OF THE BINARY FRACTION IN DENSE STELLAR SYSTEMS

Using our recently improved Monte Carlo evolution code, we study the evolution of the binary fraction in globular clusters. In agreement with previous N-body simulations, we find generally that the hard binary fraction in the core tends to increase with time over a range of initial cluster central densities for initial binary fractions 90%. The dominant processes driving the evolution of the core binary fraction are mass segregation of binaries into the cluster core and preferential destruction of binaries there. On a global scale, these effects and the preferential tidal stripping of single stars tend to roughly balance, leading to overall cluster binary fractions that are roughly constant with time. Our findings suggest that the current hard binary fraction near the half-mass radius is a good indicator of the hard primordial binary fraction. However, the relationship between the true binary fraction and the fraction of main-sequence stars in binaries (which is typically what observers measure) is nonlinear and rather complicated. We also consider the importance of soft binaries, which not only modify the evolution of the binary fraction, but can also drastically change the evolution of the cluster as a whole. Finally, we briefly describe the recent addition of single and binary stellar evolution to our cluster evolution code.