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 eccentricities of the barium stars

We investigate the eccentricities of barium (Ba  ii ) stars formed via a stellar wind accretion model. We carry out a series of Monte Carlo simulations using a rapid binary evolution algorithm, which incorporates full tidal evolution, mass loss and accretion, and nucleosynthesis and dredge-up on the thermally pulsing asymptotic giant branch. We follow the enhancement of barium in the envelope of the accreting main-sequence companion and dilution into its convective envelope once the star ascends the giant branch.
The observed eccentricities of Ba  ii stars are significantly smaller than those of an equivalent set of normal red giants but are nevertheless non-zero. We show that such a distribution of eccentricities is consistent with a wind accretion model for Ba  ii star production with weak viscous tidal dissipation in the convective envelopes of giant stars. We successfully model the distribution of orbital periods and the number of observed Ba  ii stars. The actual distribution of eccentricities is quite sensitive to the strength of the tides, so that we are able to confirm that this strength is close to, but less than, what is expected theoretically and found with alternative observational tests. Two systems – one very short-period but eccentric, and one long-period and highly eccentric – still lie outside the envelope of our models, and so require a more exotic formation mechanism. All our models, even those which were a good fit to the observed distributions, overproduced the number of high-period barium stars, a problem that could not be solved by some combination of the three parameters: tidal strength, tidal enhancement and wind accretion efficiency.     

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.     

The role of tidal interactions in star formation

Nearly all of the initial angular momentum of the matter that goes into each forming star must somehow be removed or redistributed during the formation process. The possible transport mechanisms and the possible fates of the excess angular momentum are discussed, and it is argued that transport processes in discs are probably not sufficient by themselves to solve the angular momentum problem, while tidal interactions with other stars in forming binary or multiple systems are likely to be of very general importance in redistributing angular momentum during the star formation process. Most, if not all, stars probably form in binary or multiple systems, and tidal torques in these systems can transfer much of the angular momentum from the gas around each forming star to the orbital motions of the companion stars. Tidally generated waves in circumstellar discs may contribute to the overall redistribution of angular momentum. Stars may gain much of their mass by tidally triggered bursts of rapid accretion, and these bursts could account for some of the most energetic phenomena of the earliest stages of stellar evolution, such as jet-like outflows. If tidal interactions are indeed of general importance, planet-forming discs may often have a more chaotic and violent early evolution than in standard models, and shock heating events may be common. Interactions in a hierarchy of subgroups may play a role in building up massive stars in clusters and in determining the form of the upper initial mass function (IMF) . Many of the processes discussed here have analogues on galactic scales, and there may be similarities between the formation of massive stars by interaction-driven accretion processes in clusters and the buildup of massive black holes in galactic nuclei.     

Populating the Galaxy with pulsars – I. Stellar and binary evolution

The computation of theoretical pulsar populations has been a major component of pulsar studies since the 1970s. However, the majority of pulsar population synthesis has only regarded isolated pulsar evolution. Those that have examined pulsar evolution within binary systems tend to either treat binary evolution poorly or evolve the pulsar population in an ad hoc manner. Thus, no complete and direct comparison with observations of the pulsar population within the Galactic disc has been possible to date. Described here is the first component of what will be a complete synthetic pulsar population survey code. This component is used to evolve both isolated and binary pulsars. Synthetic observational surveys can then be performed on this population for a variety of radio telescopes. The final tool used for completing this work will be a code comprised of three components: stellar/binary evolution, Galactic kinematics and survey selection effects. Results provided here support the need for further (apparent) pulsar magnetic field decay during accretion, while they conversely suggest the need for a re-evaluation of the assumed typical millisecond pulsar formation process. Results also focus on reproducing the observed     diagram for Galactic pulsars and how this precludes short time-scales for standard pulsar exponential magnetic field decay. Finally, comparisons of bulk pulsar population characteristics are made to observations displaying the predictive power of this code, while we also show that under standard binary evolutionary assumption binary pulsars may accrete much mass.     

The evolution of the binary population in globular clusters: a full analytical computation

I present a simplified analytical model that simulates the evolution of the binary population in a dynamically evolving globular cluster. A number of simulations have been run spanning a wide range in initial cluster and environmental conditions by taking into account the main mechanisms of formation and destruction of binary systems. Following this approach, I investigate the evolution of the fraction, the radial distribution, the distribution of mass ratios and periods of the binary population. According to these simulations, the fraction of surviving binaries appears to be dominated by the processes of binary ionization and evaporation. In particular, the frequency of binary systems changes by a factor of 1–5 depending on the initial conditions and on the assumed initial distribution of periods. The comparison with the existing estimates of binary fractions in Galactic globular clusters suggests that significant variations in the initial binary content could exist among the analysed globular cluster. This model has been also used to explain the observed discrepancy found between the most recent N -body and Monte Carlo simulations in the literature.     

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.     

Populating the Galaxy with low-mass X-ray binaries

We perform binary population-synthesis calculations to investigate the incidence of low-mass X-ray binaries (LMXBs) and their birth rate in the Galaxy. We use a binary-evolution algorithm that models all the relevant processes including tidal circularization and synchronization. Parameters in the evolution algorithm that are uncertain and may affect X-ray binary formation are allowed to vary during the investigation. We agree with previous studies that under standard assumptions of binary evolution the formation rate and number of black hole (BH) LMXBs predicted by the model are more than an order of magnitude less than what is indicated by observations. We find that the common-envelope process cannot be manipulated to produce significant numbers of BH LMXBs. However, by simply reducing the mass-loss rate from helium stars adopted in the standard model, to a rate that agrees with the latest data, we produce a good match to the observations. Including LMXBs that evolve from intermediate-mass systems also leads to favourable results. We stress that constraints on the X-ray binary population provided by observations are used here merely as a guide as surveys suffer from incompleteness and much uncertainty is involved in the interpretation of results.     

On rejuvenation in massive binary systems

We introduce a set of stellar models for massive stars whose evolution has been affected by mass transfer in a binary system, at a range of metallicities. As noted by other authors, the effect of such mass transfer is frequently more than just rejuvenation. We find that, whilst stars with convective cores which have accreted only H-rich matter rejuvenate as expected, those stars which have accreted He-rich matter (e.g. at the end stages of conservative mass transfer) evolve in a way that is qualitatively similar to rejuvenated stars of much higher metallicity. Thus, the effects of non-conservative evolution depend strongly on whether He-rich matter is amongst the portion accreted or ejected. This may lead to a significant divergence in binary evolution paths with only a small difference in initial assumptions. We compare our models to observed systems and find approximate formulae for the effect of mass accretion on the effective age and metallicity of the resulting star.     

The influence of binary interactions on infrared passbands of populations

In our evolutionary population synthesis models, samples of binaries are reproduced by a ' patched ' Monte Carlo simulation and the stellar masses, integrated   J ,  H ,  K ,  L ,  L 2  and M magnitudes, mass-to-light ratios and broad colours involving infrared bands are presented for an extensive set of instantaneous-burst binary stellar populations. In addition, the fluctuations in the integrated colours, which have been given by Zhang et al., are reduced.
By comparing the results for binary stellar populations with (Model A) and without (Model B) binary interactions, we show that the inclusion of binary interactions makes the stellar mass of a binary stellar population smaller (  ∼3.6–4.5  per cent during the past 15 Gyr), magnitudes greater (except   U , ∼ 0.18 mag  at the most), colours bluer (∼0.15 mag for   V − K   at the most) and mass-to-light ratios greater (∼0.06 for K band) except those in the U and B passbands at higher metallicities. Binary interactions make the V magnitude less sensitive to age, and R and I magnitudes more sensitive to metallicity.
Given an age, the absolute values of the differences in the stellar mass, magnitudes and mass-to-light ratios (except those in the U and B bands) between Models A and B reach a maximum at   Z = 0.0001  , i.e. the effects of binary interactions on these parameters reach a maximum, while the differences in some colours reach a maximum at   Z ∼ 0.01–0.0004  . In contrast, the absolute value of the difference in the stellar mass is minimal at   Z = 0.03  ; those in the   U ,  B ,  V   magnitudes and the mass-to-light ratios in the U and B bands reach a minimum at   Z ∼ 0.01–0.004  .     

Very low mass stars in binaries: a theoretical look

We have undertaken a series of hydrodynamic + N ‐body simulations in order to explore the binary properties of young stars. We find that multiple stars are a natural outcome of collapsing turbulent flows, with a high incidence of N > 2 multiples, specially among the higher mass objects. We find a positive correlation of multiplicity with primary mass and a companion frequency that decreases with age, during the first few Myr after formation. Binary brown dwarfs are rarely formed, in conflict with observations. Brown dwarfs as companions are predominantly found orbiting binaries or triples at large separations. The paucity of ultra low mass and low mass ratio binaries has been investigated further, and we tentatively conclude that their formation is intricately related to an appropriate selection of initial conditions and an accurate modelling of disc accretion and evolution. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of Binary Interactions on the Early-type Galaxy Chemical Evolution and Gas Cooling Functiontwo

In the galaxy parameter fitting by means of stellar population synthesis, it is found that compared with the evolutionary population synthesis (EPS) model without binary interactions, the stellar age and metallicity of a galaxy derived from the EPS model with binary interactions are larger. But, we are still unclear how the binary interactions affect the galaxy evolution. For the early-type galaxies with the UV-excess phenomenon, there are two main-stream explanations: recent star formation (RSF) and binary interactions. In this study, we obtain the mass return rate and chemical yield for the stellar populations with and without binary interactions. In combination with the galaxy chemical evolution and photoionization models, we study the effects of binary interactions on the chemical evolution and metallicity evolution for the early-type galaxies with the UV-excess phenomenon under the two formation mechanisms. We find that the inclusion of binary interactions can raise the ejected mass, metallicity, alpha element, and accelerate the gas cooling. These can reasonably explain the conclusions made by the EPS models. Moreover, we find that the gas cooling is more efficient under the UV-excess formation mechanism by the binary interactions rather than the RSF, and the ratio of element abundance is different for the two mechanisms, which can be further used to distinguish these two mechanisms.     

A Binary Evolution Model with Non-synchronous Rotations

By calculating the angular momentum transport during the evolution of a binary system, the variations of the rotational and revolution periods of the binary system under the tidal action, as well as the tidal effect on the evolution of the system are investigated. The calculated results indicate that when a close binary system evolves in the main sequence, the tidal friction will make the rotation and revolution approach to a closed state in a short time, but it takes a long time to attain a complete synchronization. After mass exchange started, the synchronous rotation can be changed more easily into the non-synchronous rotation for the semi-detached binaries. But for the contact binaries, the mass exchange is not strong enough to break the synchronization. The evolutionary tracks of the synchronization and non-synchronization models in the HR diagram are also compared with each other, and the result shows that for the non-synchronization model, the evolutionary curve of the primary star moves toward the direction of high luminosity and high effective temperature on the HR diagram at the mass exchange stage. Finally, by analyzing the statistical data of observations, it is found that the observed fact that the non-synchronous rotation exists in a period even longer than the tide-locking timescale can be explained by this model.     

How abundant is the population of binary radio pulsars with black holes?

Using a 'scenario machine' we have carried out a population synthesis of radio pulsars with black hole binaries (BH+Psr) in the context of the most widespread assumptions concerning star mass loss during evolution, the mass ratio distribution of binary stars, the kick velocity and the envelope mass loss during collapse. Our purpose is to show that under any plausible parameters for the evolution scenario, the BH+Psr population should be abundant in the Galaxy. It is shown that in all models (including those evolved by Heger et al. and Woosley, Heger & Weaver), the expected number of black holes paired with radio pulsars is sufficient for such systems to be discovered within the next few years.     

Stability of magnetic flux tubes in close binary stars

Photometric and Doppler imaging observations of active binaries indicate the existence of starspots at preferred longitudes (position angles with respect to the companion star). We investigate the stability of magnetic flux tubes in the convection zone of close, fast‐rotating binary stars and explore whether the observed preferred longitudes could be caused by tidal forces and the deformation of the active star. We assume a synchronized binary system with spin axes perpendicular to the orbital plane and a rotation period of a few days. The tidal force and the deviation from spherical structure are considered in lowest‐order perturbation theory. The magnetic field is in the form of toroidal magnetic flux rings, which are stored in mechanical equilibrium within the stably stratified overshoot region beneath the convection zone until the field has grown sufficiently strong for the undulatory instability to initiate the formation of rising loops. Frequencies and geometry of stable as well as growth rates of unstable eigenmodes are determined by linear stability analysis. Particular consideration is given to the question whether the effects of tidal forces and perturbations of the stellar structure can force a rising flux loop to enter the convection zone at specific longitudes.     

Modelling the binary progenitor of Supernova 1993J

We have developed a detailed stellar evolution code capable of following the simultaneous evolution of both stars in a binary system, together with their orbital properties. To demonstrate the capabilities of the code, we investigate potential progenitors for the Type IIb Supernova 1993J, which is believed to have been an interacting binary system prior to its primary exploding. We use our detailed binary stellar evolution code to model this system to determine the possible range of primary and secondary masses that could have produced the observed characteristics of this system, with particular reference to the secondary. Using the luminosities and temperatures for both stars (as determined by Maund et al.) and the remaining mass of the hydrogen envelope of the primary at the time of explosion, we find that if mass transfer is 100 per cent efficient, the observations can be reproduced by a system consisting of a  15 M_⊙  primary and a  14 M_⊙  secondary in an orbit with an initial period of 2100 days. With a mass transfer efficiency of 50 per cent, a more massive system consisting of a  17 M_⊙  primary and a  16 M_⊙  secondary in an initial orbit of 2360 days is needed. We also investigate some of the uncertainties in the evolution, including the effects of tidal interaction, convective overshooting and thermohaline mixing.     

Close binary systems among very low‐mass stars and brown dwarfs

Using Monte Carlo simulations and published radial velocity surveys we have constrained the frequency and separation (a ) distribution of very low‐mass star (VLM) and brown dwarf (BD) binary systems.We find that simple Gaussian extensions of the observed wide binary distribution, with a peak at 4AU and 0.6 < σ _{log(a /AU)} < 1.0, correctly reproduce the observed number of close binary systems, implying a close (a < 2.6 AU) binary frequency of 17–30% and overall frequency of 32–45%. N‐body models of the dynamical decay of unstable protostellar multiple systems are excluded with high confidence because they do not produce enough close binary VLMs/BDs. The large number of close binaries and high overall binary frequency are also completely inconsistent with published smoothed particle hydrodynamical modelling and argue against a dynamical origin for VLMs/BDs. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.