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 three- and four-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 such as 47 Tuc, assuming an initial binary fraction of 100 per cent, is only ∼ 5–10 per cent. We show that this is in good agreement with recent Hubble Space Telescope 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 modelling of globular clusters, suggesting that 'realistic models' should incorporate much larger initial binary fractions than has usually been the case in the past.     

The formation of a bound star cluster: from the Orion nebula cluster to the Pleiades

Direct N -body calculations are presented of the formation of Galactic clusters using GasEx , which is a variant of the code Nbody6 . The calculations focus on the possible evolution of the Orion nebula cluster (ONC) by assuming that the embedded OB stars explosively drove out 2/3 of its mass in the form of gas about 0.4 Myr ago. A bound cluster forms readily and survives for 150 Myr despite additional mass loss from the large number of massive stars, and the Galactic tidal field. This is the very first time that cluster formation is obtained under such realistic conditions. The cluster contains about 1/3 of the initial 10⁴ stars, and resembles the Pleiades cluster to a remarkable degree, implying that an ONC-like cluster may have been a precursor of the Pleiades. This scenario predicts the present expansion velocity of the ONC, which will be measurable by upcoming astrometric space missions. These missions should also detect the original Pleiades members as an associated expanding young Galactic-field subpopulation. The results arrived at here suggest that Galactic clusters form as the nuclei of expanding OB associations.
The results have wide implications, also for the formation of globular clusters and the Galactic-field and halo stellar populations. In view of this, the distribution of binary orbital periods and the mass function within and outside the model ONC and Pleiades is quantified, finding consistency with observational constraints. Advanced mass segregation is evident in one of the ONC models. The calculations show that the primordial binary population of both clusters could have been much the same as is observed in the Taurus–Auriga star-forming region. The computations also demonstrate that the binary proportion of brown dwarfs is depleted significantly for all periods, whereas massive stars attain a high binary fraction.     

Direct N-body modelling of stellar populations: blue stragglers in M67

We present a state-of-the-art N -body code which includes a detailed treatment of stellar and binary evolution as well as the cluster dynamics. This code is ideal for investigating all aspects relating to the evolution of star clusters and their stellar populations. It is applicable to open and globular clusters of any age. We use the N -body code to model the blue straggler population of the old open cluster M67. Preliminary calculations with our binary population synthesis code show that binary evolution alone cannot explain the observed numbers or properties of the blue stragglers. On the other hand, our N -body model of M67 generates the required number of blue stragglers and provides formation paths for all the various types found in M67. This demonstrates the effectiveness of the cluster environment in modifying the nature of the stars it contains, and highlights the importance of combining dynamics with stellar evolution. We also perform a series of N =10 000 simulations in order to quantify the rate of escape of stars from a cluster subject to the Galactic tidal field.     

Effects of external tidal field on the evolution of the outer regions of multi-mass star clusters

We present N -body simulations (including an initial mass function) of globular clusters in the Galaxy in order to study effects of the tidal field systematically on the properties of the outer parts of globular clusters. Using nbody6 , which correctly takes into account the two-body relaxation, we investigate the development of tidal tails of globular clusters in the Galactic tidal field. For simplicity, we have employed only the spherical components (bulge and halo) of the Galaxy, and ignored the effects of stellar evolution which could have been important in the very early phase of the cluster evolution. The total number of stars in our simulations is about 20 000, which is much smaller than the realistic number of stars. All simulations had been done for several orbital periods in order to understand the development of the tidal tails. In our scaled-down models, the relaxation time is sufficiently short to show the mass segregation effect, but we did not go far enough to see the core collapse, and the fraction of stars lost from the cluster at the end of the simulations is only ∼10 per cent. The radial distribution of extra-tidal stars can be described by a power law with a slope around −3 in surface density. The directions of tidal tails are determined by the orbits and locations of the clusters. We find that the length of tidal tails increases towards the apogalacticon and decreases towards the perigalacticon. This is an anti-correlation with the strength of the tidal field, caused by the fact that the time-scale for the stars to respond to the potential is similar to the orbital time-scale of the cluster. The escape of stars in the tidal tails towards the pericentre could be another reason for the decrease of the length of tidal tails. We find that the rotational angular velocity of tidally induced clusters shows quite different behaviour from that of initially rotating clusters.     

Monte Carlo simulations of star clusters – IV. Calibration of the Monte Carlo code and comparison with observations for the open cluster M67

We outline the steps needed in order to incorporate the evolution of single and binary stars into a particular Monte Carlo code for the dynamical evolution of a star cluster. We calibrate the results against N -body simulations, and present models for the evolution of the old open cluster M67 (which has been studied thoroughly in the literature with N -body techniques). The calibration is done by choosing appropriate free code parameters. We describe, in particular, the evolution of the binary, white dwarf and blue straggler populations, though not all channels for blue straggler formation are represented yet in our simulations. Calibrated Monte Carlo runs show good agreement with results of N -body simulations not only for global cluster parameters, but also for, for example, binary fraction, luminosity function and surface brightness. Comparison of Monte Carlo simulations with observational data for M67 shows that it is possible to get reasonably good agreement between them. Unfortunately, because of the large statistical fluctuations of the numerical data and uncertainties in the observational data the inferred conclusions about the cluster initial conditions are not firm.     

Evolution of globular cluster systems in three galaxies of the Fornax cluster

We studied and compared the radial profiles of globular clusters and of the stellar bulge component in three galaxies of the Fornax cluster observed with the WFPC2 of the Hubble Space Telescope ( HST ). The stars are more concentrated toward the galactic centres than globular clusters, in agreement with what has already been observed in many other galaxies: if the observed difference is the result of evolution of the globular cluster systems starting from initial profiles similar to those of the halo–bulge stellar components, a relevant fraction of their initial mass (74, 47 and 52 per cent for NGC 1379, 1399 and 1404, respectively) should have disappeared in the inner regions. This mass has probably contributed to the nuclear field population, local dynamics and high-energy phenomena in the primeval life of the galaxy. An indication in favour of the evolutionary interpretation of the difference between the globular cluster system and stellar bulge radial profiles is given by the positive correlation we found between the value of the mass lost from the globular cluster system and the central galactic black hole mass in the set of seven galaxies for which these data are available.     

Predictions for triple stars with and without a pulsar in star clusters

Though about 80 pulsar binaries have been detected in globular clusters so far, no pulsar has been found in a triple system in which all three objects are of comparable mass. Here, we present predictions for the abundance of such triple systems, and for the most likely characteristics of these systems. Our predictions are based on an extensive set of more than 500 direct simulations of star clusters with primordial binaries, and a number of additional runs containing primordial triples. Our simulations employ a number N _tot of equal-mass stars from   N _tot= 512  to  19 661  and a primordial binary fraction from 0 to 50 per cent. In addition, we validate our results against simulations with   N = 19 661  that include a mass spectrum with a turn-off mass at  0.8 M_⊙  , appropriate to describe the old stellar populations of Galactic globular clusters. Based on our simulations, we expect that typical triple abundances in the core of a dense cluster are two orders of magnitude lower than the binary abundances, which in itself already suggests that we do not have to wait too long for the first comparable-mass triple with a pulsar to be detected.     

Star clusters with primordial binaries – I. Dynamical evolution of isolated models

In order to interpret the results of complex realistic star cluster simulations, which rely on many simplifying approximations and assumptions, it is essential to study the behaviour of even more idealized models, which can highlight the essential physical effects and are amenable to more exact methods. With this aim, we present the results of N -body calculations of the evolution of equal-mass models, starting with primordial binary fractions of 0–100 per cent, with values of N ranging from 256 to 16 384. This allows us to extrapolate the main features of the evolution to systems comparable in particle number with globular clusters.
In this range, we find that the steady-state 'deuterium main sequence' is characterized by a ratio of the core radius to half-mass radius that follows qualitatively the analytical estimate by Vesperini & Chernoff, although the N dependence is steeper than expected. Interestingly, for an initial binary fraction f greater than 10 per cent, the binary heating in the core during the post-collapse phase almost saturates (becoming nearly independent of f ), and so little variation in the structural properties is observed. Thus, although we observe a significantly lower binary abundance in the core with respect to the Fokker–Planck simulations by Gao et al., this is of little dynamical consequence.
At variance with the study of Gao et al., we see no sign of gravothermal oscillations before 150 half-mass relaxation times. At later times, however, oscillations become prominent. We demonstrate the gravothermal nature of these oscillations.     

A stochastic Monte Carlo approach to model real star cluster evolution – II. Self-consistent models and primordial binaries

The new approach outlined in Paper I to follow the individual formation and evolution of binaries in an evolving, equal point-mass star cluster is extended for the self-consistent treatment of relaxation and close three- and four-body encounters for many binaries (typically a few per cent of the initial number of stars in the cluster mass). The distribution of single stars is treated as a conducting gas sphere with a standard anisotropic gaseous model. A Monte Carlo technique is used to model the motion of binaries, their formation and subsequent hardening by close encounters, and their relaxation (dynamical friction) with single stars and other binaries. The results are a further approach towards a realistic model of globular clusters with primordial binaries without using special hardware. We present, as our main result, the self-consistent evolution of a cluster consisting of 300 000 equal point-mass stars, plus 30 000 equal-mass binaries over several hundred half-mass relaxation times, well into the phase where most of the binaries have been dissolved and evacuated from the core. The cluster evolution is about three times slower than found by Gao et al. Other features are rather comparable. At every moment we are able to show the individual distribution of binaries in the cluster.     

Evolution of the mass function of the Galactic globular cluster system

In this work we investigate the evolution of the mass function of the Galactic globular cluster system (GCMF) taking into account the effects of stellar evolution, two-body relaxation, disc shocking and dynamical friction on the evolution of individual globular clusters. We have adopted a lognormal initial GCMF and considered a wide range of initial values for the dispersion, σ, and the mean value, 〈log  M 〉. We have studied in detail the dependence on the initial conditions of the final values of σ, 〈log  M 〉, the fraction of the initial number of clusters surviving after one Hubble time and the difference between the properties of the GCMF of clusters closer to the Galactic Centre and those of clusters located in the outer regions of the Galaxy. In most of the cases considered, evolutionary processes alter significantly the initial population of globular clusters and the disruption of a significant number of globular clusters leads to a flattening in the spatial distribution of clusters in the central regions of the Galaxy. The initial lognormal shape of the GCMF is preserved in most cases and if a power-law in M is adopted for the initial GCMF, evolutionary processes tend to modify it into a lognormal GCMF. The difference between initial and final values of σ and 〈log  M 〉 as well as the difference between the final values of these parameters for inner and outer clusters can be positive or negative depending on initial conditions. A significant effect of evolutionary processes does not necessarily give rise to a strong trend of 〈log  M 〉 with the galactocentric distance. The existence of a particular initial GCMF able to keep its initial shape and parameters unaltered during the entire evolution through a subtle balance between disruption of clusters and evolution of the masses of those which survive, suggested by Vesperini, is confirmed.     

Extragalactic novae

Novae are expected to form in all stellar systems with a binary population. Detection of extragalactic novae provides direct evidence of close binary populations and possible spatial variations in those populations. Comparison of extragalactic novae with their local counterparts can yield valuable tests of close binary evolution theory. I report early results from surveys of globular clusters, the Large Magellanic Cloud and M81 for classical novae in eruption and in quiescence. T Sco, the nova of 1860 A.D. in the globular cluster M80, has now been recovered. It is three magnitudes fainter than canonical old novae, though this might be an inclination effect. Seven quiescent old novae in the Large Magellanic Cloud have been recovered (at brightnesses comparable to their Galactic counterparts). Their orbital periods are now within reach. Twenty-three novae have been detected on archival 5 meter Palomar plates of M81. The spatial distribution of these novae strongly suggests that most come from the spiral arm population.     

Evolution of binary stars and the effect of tides on binary populations

We present a rapid binary-evolution algorithm that enables modelling of even the most complex binary systems. In addition to all aspects of single-star evolution, features such as mass transfer, mass accretion, common-envelope evolution, collisions, supernova kicks and angular momentum loss mechanisms are included. In particular, circularization and synchronization of the orbit by tidal interactions are calculated for convective, radiative and degenerate damping mechanisms. We use this algorithm to study the formation and evolution of various binary systems. We also investigate the effect that tidal friction has on the outcome of binary evolution. Using the rapid binary code, we generate a series of large binary populations and evaluate the formation rate of interesting individual species and events. By comparing the results for populations with and without tidal friction, we quantify the hitherto ignored systematic effect of tides and show that modelling of tidal evolution in binary systems is necessary in order to draw accurate conclusions from population synthesis work. Tidal synchronism is important but, because orbits generally circularize before Roche lobe overflow, the outcome of the interactions of systems with the same semilatus rectum is almost independent of eccentricity. It is not necessary to include a distribution of eccentricities in population synthesis of interacting binaries; however, the initial separations should be distributed according to the observed distribution of semilatera recta rather than periods or semimajor axes.     

Brown dwarf populations in open clusters

We present the results of multiple simulations of open clusters, modelling the dynamics of a population of brown dwarf members. We consider the effects of a large range of primordial binary populations, including the possibilities of having brown dwarf members contained within a binary system. We also examine the effects of various cluster diameters and masses. Our examination of a population of wide binary systems containing brown dwarfs, reveals evidence for exchange reactions whereby the brown dwarf is ejected from the system and replaced by a heavier main-sequence star. We find that there exists the possibility of hiding a large fraction of the brown dwarfs contained within the primordial binary population. We conclude that it is probable that the majority of brown dwarfs are contained within primordial binary systems which then hides a large proportion of them from detection.     

Close encounters in young stellar clusters: implications for planetary systems in the solar neighbourhood

The stars that populate the solar neighbourhood were formed in stellar clusters. Through N -body simulations of these clusters, we measure the rate of close encounters between stars. By monitoring the interaction histories of each star, we investigate the singleton fraction in the solar neighbourhood. A singleton is a star which formed as a single star, has never experienced any close encounters with other stars or binaries, or undergone an exchange encounter with a binary. We find that, of the stars which formed as single stars, a significant fraction is not singletons once the clusters have dispersed. If some of these stars had planetary systems, with properties similar to those of the Solar System, the planets' orbits may have been perturbed by the effects of close encounters with other stars or the effects of a companion star within a binary. Such perturbations can lead to strong planet–planet interactions which eject several planets, leaving the remaining planets on eccentric orbits. Some of the single stars exchange into binaries. Most of these binaries are broken up via subsequent interactions within the cluster, but some remain intact beyond the lifetime of the cluster. The properties of these binaries are similar to those of the observed binary systems containing extrasolar planets. Thus, dynamical processes in young stellar clusters will alter significantly any population of Solar System-like planetary systems. In addition, beginning with a population of planetary systems exactly resembling the Solar System around single stars, dynamical encounters in young stellar clusters may produce at least some of the extrasolar planetary systems observed in the solar neighbourhood.     

Constraints on the initial conditions of globular clusters

N -body simulations are made with a variety of initial conditions, in particular clumpy and flattened distributions, to attempt to constrain the possible initial conditions of globular clusters, using the observations that young LMC globular clusters appear relaxed after only 20 to 40 Myr. It is found that violent relaxation is able to erase most of the initial substructure in only ≈ 6 crossing times. However, initially very clumpy distributions (≲ 100 clumps) form clusters that are too concentrated to resemble real globular clusters. Such clusters also often have large clumps in long-lasting (≳ 30 crossing times) orbits which do not appear in observed cluster profiles. It is also found that even modest amounts of initial flattening produce clusters that are too elliptical to resemble real globular clusters. In such a scenario, cloud–cloud collisions and similar energetic processes would be unlikely to produce sufficiently spherical globular clusters. It is suggested that globular clusters form from roughly spherical initial conditions with star formation occurring either smoothly or in many small clumps.     

Neutron star retention and millisecond pulsar production in globular clusters

We investigate the conditions by which neutron star retention in globular clusters is favoured. We find that neutron stars formed in massive binaries are far more likely to be retained. Such binaries are likely to then evolve into contact before encountering other stars, possibly producing a single neutron star after a common envelope phase. A large fraction of the single neutron stars in globular clusters are then likely to exchange into binaries containing moderate-mass main-sequence stars, replacing the lower-mass components of the original systems. These binaries will become intermediate-mass X-ray binaries (IMXBs), once the moderate-mass star evolves off the main sequence, as mass is transferred on to the neutron star, possibly spinning it up in the process. Such systems may be responsible for the population of millisecond pulsars (MSPs) that has been observed in globular clusters. Additionally, the period of mass-transfer (and thus X-ray visibility) in the vast majority of such systems will have occurred 5–10 Gyr ago, thus explaining the observed relative paucity of X-ray binaries today, given the MSP population.     

Inclusion of binaries in evolutionary population synthesis

Using evolutionary population synthesis we present integrated colours, integrated spectral energy distributions and absorption-line indices defined by the Lick Observatory image dissector scanner (referred to as the Lick/IDS) system, for an extensive set of instantaneous-burst binary stellar populations with and without binary interactions. The ages of the populations are in the range 1–15 Gyr and the metallicities are in the range 0.0001–0.03. By comparing the results for populations with and without binary interactions we show that the inclusion of binary interactions makes the integrated U – B , B – V , V – R and R – I colours and all Lick/IDS spectral absorption indices (except for H_β) substantially smaller. In other words, binary evolution makes a population appear bluer. This effect raises the derived age and metallicity of the population.
We calculate several sets of additional solar-metallicity binary stellar populations to explore the influence of the binary evolution algorithm input parameters (the common-envelope ejection efficiency and the stellar wind mass-loss rate) on the resulting integrated colours. We also look at the dependence on the choice of distribution functions used to generate the initial binary population. The results show that variations in the choice of input model parameters and distributions can significantly affect the results. However, comparing the discrepancies that exist between the colours of various models, we find that the differences are less than those produced between the models with and those without binary interactions. Therefore it is very necessary to consider binary interactions in order to draw accurate conclusions from evolutionary population synthesis work.     

Neutron stars in globular clusters: Formation and observational manifestations

Population synthesis is used to model the number of neutron stars in globular clusters that are observed as low-mass X-ray sources and millisecond radio pulsars. The dynamical interactions between binary and single stars in a cluster are assumed to take place only with a continuously replenished “background” of single stars whose properties keep track of the variations in parameters of the cluster as a whole and the evolution of single stars. We use the hypothesis that the neutron stars forming in binary systems from components with initial masses of ～8–12 M _⊙ during the collapse of degenerate O-Ne-Mg cores through electron captures do not acquire a high space velocity. The remaining neutron stars (from single stars with masses >8 M _⊙ or from binary components with masses >12 M _⊙) are assumed to be born with high space velocities. According to this hypothesis, a sizeable fraction of the forming neutron stars remain in globular clusters (about 1000 stars in a cluster with a mass of 5 × 10⁵ M _⊙). The number of millisecond radio pulsars forming in such a cluster in the case of accretion-driven spinup in binary systems is found to be ～10, in agreement with observations. Our modeling also reproduces the observed shape of the X-ray luminosity function for accreting neutron stars in binary systems with normal and degenerate components and the distribution of spin periods for millisecond pulsars.     

The massive star binary fraction in young open clusters – I. NGC 6231 revisited

We present the results of a long-term high-resolution spectroscopy campaign on the O-type stars in NGC 6231. We revise the spectral classification and multiplicity of these objects and we constrain the fundamental properties of the O-star population. Almost three quarters of the O-type stars in the cluster are members of a binary system. The minimum binary fraction is 0.63, with half the O-type binaries having an orbital period of the order of a few days. The eccentricities of all the short-period binaries are revised downward, and henceforth match a normal period–eccentricity distribution. The mass ratio distribution shows a large preference for O + OB binaries, ruling out the possibility that, in NGC 6231, the companion of an O-type star is randomly drawn from a standard initial mass function. Obtained from a complete and homogeneous population of O-type stars, our conclusions provide interesting observational constraints to be confronted with the formation and early evolution theories of O-stars.     

Warped discs and the directional stability of jets in active galactic nuclei

The radial distribution of globular clusters in galaxies is always less peaked to the centre than that of the halo stars. Extending previous work to a sample of Hubble Space Telescope globular cluster systems in ellipticals, we evaluate the number of clusters potentially lost to the galactic centre as the integrals of the difference between the observed globular cluster system distribution and the underlying halo light profile. In the sample of galaxies examined it is found that the initial populations of globular clusters may have been ∼30 per cent to 50 per cent richer than now. If these 'missing' globular clusters have decayed and have been partly destroyed in the very central galactic zones, they have carried there a significant quantity of mass that, plausibly, contributed to the formation and feeding of a massive object therein. It is relevant to note that the observed correlation between the core radius of the globular cluster system and the parent galaxy luminosity can be interpreted as a result of evolution.