Initial Binary Fraction Research Articles

Monte Carlo modeling of globular star clusters: many primordial binaries and IMBH formation

AbstractWe will discuss the evolution of star clusters with a large initial binary fraction, up to 95%. The initial binary population is chosen to follow the invariant orbital-parameter distributions suggested by Kroupa (1995). The Monte Carlo MOCCA simulations of star cluster evolution are compared to the observations of Milone et al. (2012) for photometric binaries. It is demonstrated that the observed dependence on cluster mass of both the binary fraction and the ratio of the binary fractions inside and outside of the half mass radius are well recovered by the MOCCA simulations. This is due to a rapid decrease in the initial binary fraction due to the strong density-dependent destruction of wide binaries described by Marks, Kroupa & Oh (2011). We also discuss a new scenario for the formation of intermediate mass black holes in dense star clusters. In this scenario, intermediate mass black holes are formed as a result of dynamical interactions of hard binaries containing a stellar mass black hole, with other stars and binaries. We will discuss the necessary conditions to initiate the process of intermediate mass black hole formation and the dependence of its mass accretion rate on the global cluster properties.

Binaries in the field: fossils of the star formation process?

Recent observations of binary stars in the Galactic field show that the binary fraction and the mean orbital separation both decrease as a function of decreasing primary mass. We present N-body simulations of the effects of dynamical evolution in star-forming regions on primordial binary stars to determine whether these observed trends can be explained by the dynamical processing of a common binary population. We find that dynamical processing of a binary population with an initial binary fraction of unity and an initial excess of intermediate/wide separation (100–104 au) binaries does not reproduce the observed properties in the field, even in initially dense (∼103 M⊙ pc−3) star-forming regions. If instead we adopt a field-like population as the initial conditions, most brown dwarf and M-dwarf binaries are dynamically hard and their overall fractions and separation distributions are unaffected by dynamical evolution. G-dwarf and A-star binaries in the field are dynamically intermediate in our simulated dense regions and dynamical processing does destroy some systems with separations >100 au. However, the formation of wide binaries through the dissolution of supervirial regions is a strong function of primary mass, and the wide G-dwarf and A-star binaries that are destroyed by dynamical evolution in subvirial regions are replenished by the formation of binaries in supervirial regions. We therefore suggest that the binary population in the field is indicative of the primordial binary population in star-forming regions, at least for systems with primary masses in the range 0.02–3.0 M⊙.

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 {\alpha} 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-{\alpha} 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.

MOCK OBSERVATIONS OF BLUE STRAGGLERS IN GLOBULAR CLUSTER MODELS

We created artificial color-magnitude diagrams of Monte Carlo dynamical models of globular clusters, and then used observational methods to determine the number of blue stragglers in those clusters. We compared these blue stragglers to various cluster properties, mimicking work that has been done for blue stragglers in Milky Way globular clusters to determine the dominant formation mechanism(s) of this unusual stellar population. We find that a mass-based prescription for selecting blue stragglers will choose approximately twice as many blue stragglers than a selection criterion that was developed for observations of real clusters. However, the two numbers of blue stragglers are well-correlated, so either selection criterion can be used to characterize the blue straggler population of a cluster. We confirm previous results that the simplified prescription for the evolution of a collision or merger product in the BSE code overestimates their lifetimes. We show that our model blue stragglers follow similar trends with cluster properties (core mass, binary fraction, total mass, collision rate) as the true Milky Way blue stragglers, as long as we restrict ourselves to model clusters with an initial binary fraction higher than 5%. We also show that, in contrast to earlier work, the number of blue stragglers in the cluster core does have a weak dependence on the collisional parameter Gamma in both our models and in Milky Way globular clusters.

The influence of stellar dynamical ejections and collisions on the relation between the maximum stellar and star cluster mass

We perform the largest currently available set of direct N-body calculations of young star cluster models to study the dynamical influence, especially through the ejections of the most massive star in the cluster, on the current relation between the maximum stellar mass and the star cluster mass. We vary several initial parameters such as the initial half-mass radius of the cluster, the initial binary fraction and the degree of initial mass segregation. Two different pairing methods are used to construct massive binaries for more realistic initial conditions of massive binaries. We find that lower mass clusters (⁠⁠) do not shoot out their heaviest star. In the case of massive clusters (⁠⁠), no most massive star escapes the cluster within 3 Myr regardless of the initial conditions if clusters have initial half-mass radii, r0.5, ≥0.8 pc. However, a few of the initially smaller sized clusters (r0.5= 0.3 pc), which have a higher density, eject their most massive star within 3 Myr. If clusters form with a compact size and their massive stars are born in a binary system with a mass ratio biased towards unity, the probability that the mass of the most massive star in the cluster changes due to the ejection of the initially most massive star can be as large as 20 per cent. Stellar collisions increase the maximum stellar mass in a large number of clusters when clusters are relatively dense (⁠ and r0.5= 0.3 pc) and binary rich. Overall, we conclude that dynamical effects hardly influence the observational maximum stellar mass–cluster mass relation.

Testing the universality of star formation - I. Multiplicity in nearby star-forming regions

We have collated multiplicity data for five clusters (Taurus, Chamaeleon I, Ophiuchus, IC348, and the Orion Nebula Cluster). We have applied the same mass ratio (flux ratios of delta K <= 2.5) and primary mass cuts (~0.1-3.0 Msun) to each cluster and therefore have directly comparable binary statistics for all five clusters in the separation range 62-620 au, and for Taurus, Chamaeleon I, and Ophiuchus in the range 18-830 au. We find that the trend of decreasing binary fraction with cluster density is solely due to the high binary fraction of Taurus, the other clusters show no obvious trend over a factor of nearly 20 in density. With N-body simulations we attempt to find a set of initial conditions that are able to reproduce the density, morphology and binary fractions of all five clusters. Only an initially clumpy (fractal) distribution with an initial total binary fraction of 73 per cent (17 per cent in the range 62-620 au) is able to reproduce all of the observations (albeit not very satisfactorily). Therefore, if star formation is universal the initial conditions must be clumpy and with a high (but not 100 per cent) binary fraction. This could suggest that most stars, including M-dwarfs, form in binaries.

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 non-linear and rather complicated. We also consider the importance of soft binaries, which not only modify the evolution of the binary fraction, but can drastically change the evolution of the cluster as a whole. Finally, we describe in some detail the recent addition of single and binary stellar evolution to our cluster evolution code.

COMPARING GC AND FIELD LMXBs IN ELLIPTICAL GALAXIES WITH DEEPCHANDRAANDHUBBLEDATA

We present a statistical study of the low-mass X-ray binary (LMXB) populations of three nearby, old elliptical galaxies: NGC 3379, NGC 4278, and NGC 4697. With a cumulative ~1 Ms Chandra ACIS observing time, we detect 90-170 LMXBs within the D25 ellipse of each galaxy. Cross-correlating Chandra X-ray sources and HST optical sources, we identify 75 globular cluster (GC) LMXBs and 112 field LMXBs with LX > 1036 erg s–1 (detections of these populations are 90% complete down to luminosities in the range of 6 × 1036 to 1.5 × 1037 erg s–1). At the higher luminosities explored in previous studies, the statistics of this sample are consistent with the properties of GC-LMXBs reported in the literature. In the low-luminosity range allowed by our deeper data (LX < 5 × 1037 erg s–1), we find a significant relative lack of GC-LMXBs, when compared with field sources. Using the co-added sample from the three galaxies, we find that the incompleteness-corrected X-ray luminosity functions (XLFs) of GC and field LMXBs differ at ~4σ significance at LX < 5 × 1037 erg s–1. As previously reported, these XLFs are consistent at higher luminosities. The presently available theoretical models for LMXB formation and evolution in clusters are not sophisticated enough to provide a definite explanation for the shape of the observed GC-LMXB XLF. Our observations may indicate a potential predominance of GC-LMXBs with donors evolved beyond the main sequence, when compared to current models, but their efficient formation requires relatively high initial binary fractions in clusters. The field LMXB XLF can be fitted with either a single power-law model plus a localized excess at a luminosity of (5-6) × 1037 erg s–1, or a broken power law with a similar low-luminosity break. This XLF may be explained with NS-red-giant LMXBs, contributing to ~15% of total LMXBs population at ~5 × 1037 erg s–1. The difference in the GC and field XLFs is consistent with different origins and/or evolutionary paths between the two LMXB populations, although a fraction of the field sources are likely to have originated in GCs.

Young massive star clusters: achievements and challenges

AbstractIn spite of significant recent and ongoing research efforts, most of the early evolution and long-term fate of young massive star clusters remain clouded in uncertainties. Here, I discuss our understanding of the initial conditions of star cluster formation and the importance of initial substructure for the subsequent dynamical-evolution and mass-segregation timescales. I also assess our current understanding of the (initial) binary fraction in star clusters and the shape of the stellar initial mass function at the low-mass end in the low-metallicity environment of the Large Magellanic Cloud. Finally, I question the validity of our assumptions leading to dynamical cluster mass estimates. I conclude that it seems imperative that observers, modellers and theorists combine efforts and exchange ideas and data freely for the field to make a major leap forward.

The main sequence of star clusters

ABSTRACT A novel way of looking at the evolution of star clusters is presented. With a dynamicaltemperature, given by the mean kinetic energy of the cluster stars, and a dynamicalluminosity, which is defined as the kinetic energy of the stars leaving the cluster inanalogy to the energy of photons emitted by a star, the dissolution of star clusters isstudied using a new dynamical temperature-luminosity diagram for star clusters. Theinvestigation contains a parameter-space study of open clusters of up to N = 32768single-mass stars with different initial density distributions, half-mass radii, tidal con-ditions and binary fractions. The clusters show a strong correlation between dynamicaltemperature and dynamical luminosity and most of the investigated cluster familiesshare a common sequence in such a dynamical temperature-luminosity diagram. Devi-ations from this sequence are analyzed and discussed. After core collapse, the positionof a cluster within this diagram can be defined by three parameters: the mass, thetidal conditions and the binary fraction. Due to core collapse all initial conditions arelost and the remaining stars adjust to the given tidal conditions. Binaries as internalenergy sourcesinfluence this adjustment. A further finding concerns the Lagrangeradiiof star clusters: Throughout the investigated parameter space nearly all clusters showa constant half-mass radius for the time after core collapse until dissolution. Further-more, the ratio of half-mass radius to tidal radius evolves onto a common sequencewhich only depends on the mass left in the cluster.Keywords: stellar dynamics – galaxies: star clusters – methods: N-body simulations– Hertzsprung–Russel (HR) diagram – open clusters and assoziations: general

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 behavior 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 %, with values of N ranging from 256 to 16384. 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 (1994), although the N dependence is steeper than expected. Interestingly, for an initial binary fraction f greater than 10%, 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. (1991), this is of little dynamical consequence. At variance with the study of Gao et al. (1991), we see no sign of gravothermal oscillations before 150 halfmass relaxation times. At later times, however, oscillations become prominent. We demonstrate the gravothermal nature of these oscillations.

Wolf--Rayet and O star runaway populations from supernovae

We present numerical simulations of the runaway fractions expected amongst O and Wolf-Rayet star populations resulting from stars ejected from binaries by the supernova of the companion. Observationally the runaway fraction for both types of star is similar, prompting the explanation that close dynamical interactions are the main cause of these high-velocity stars. We show that, provided that the initial binary fraction is high, a scenario in which two-thirds of massive runaways are from supernovae is consistent with these observations. Our models also predict a low frequency of runaways with neutron star companions and a very low fraction of observable Wolf-Rayet--compact companion systems.

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.

Hubble Space TelescopeNICMOS Observations of the Embedded Cluster in NGC 2024: Constraints on the Initial Mass Function and Binary Fraction

We present an analysis of NICMOS observations of the embedded cluster associated with NGC 2024. An analysis of the cluster color-magnitude diagram (CMD) using the models of D'Antona & Mazzitelli and Baraffe et al. (published in 1997 and 1998, respectively) indicates that the ratio of intermediate-mass (1.0–10.0 M⊙) to low-mass (0.1–1.0 M⊙) stars is consistent with the stellar initial mass function (IMF) for the field. In addition to the CMD analysis, we present results on the multiplicity of stars in the region. Three companions (in a sample of 95 potential primaries) were found, with angular separations between 04 and 10, translating to a projected linear separation of 184–460 AU for an estimated distance of 460 pc. The completeness of binary detections is assessed using recovery fractions calculated by a series of tests using artificially generated companions to potential primaries in the data frames. We find that the binary fraction in NGC 2024 is consistent with that of Duquennoy & Mayor (published in 1991) for solar neighborhood stars over the range of separations and companion masses appropriate for our survey.

A Method for Determining the Star Formation History of a Mixed Stellar Population

We present a method to determine the star formation history of a mixed stellar population from its photometry. We perform a chi-squared minimization between the observed photometric distribution and a model photometric distribution, based on theoretical isochrones. The initial mass function, distance modulus, interstellar reddening, binary fraction and photometric errors are incorporated into the model, making it directly comparable to the data. The model is a linear combination of individual synthetic color-magnitude diagrams (CMDs), each of which represents the predicted photometric distribution of a stellar population of a given age and metallicity. We present extensive tests of the algorithm, using both simulated and actual photometric data. From a preliminary application of the algorithm to a subregion of the Large Magellanic Cloud (LMC), we find that the that the lull in star formation observed among the LMC's cluster population between 3 and 8 Gyr ago is also present in the field population. The method was designed with flexibility and generality in mind, and we make the code available for use by the astronomical community.

Population synthesis for double white dwarfs

We model the population of double white dwarfs in the Galaxy and find a better agreement with observations compared to earlier studies, due to two modifications. The first is the treatment of the first phase of unstable mass transfer and the second the modelling of the cooling of the white dwarfs. A satisfactory agreement with observations of the local sample of white dwarfs is achieved if we assume that the initial binary fraction is ~ 50% and that the lowest mass white dwarfs (M < 0.3 Msun) cool faster than the most recently published cooling models predict. With this model we find a Galactic birth rate of close double white dwarfs of 0.05 yr^{-1}, a birth rate of AM CVn systems of 0.005 yr^{-1}, a merger rate of pairs with a combined mass exceeding the Chandrasekhar limit (which may be progenitors of SNe Ia) of 0.003 yr^{-1} and a formation rate of planetary nebulae of 1 yr^{-1}. We estimate the total number of double white dwarfs in the Galaxy as 2.5 10^8. In an observable sample with a limiting magnitude V_lim = 15 we predict the presence of ~855 white dwarfs of which ~220 are close pairs. Of these 10 are double CO white dwarfs of which one has a combined mass exceeding the Chandrasekhar limit and will merge within a Hubble time.