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Simon F. Portegies Zwart

Publications and source records attributed to Simon F. Portegies Zwart.

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The runaway growth of intermediate-mass black holes in dense star clusters

We study the growth rate of stars via stellar collisions in dense star clusters, calibrating our analytic calculations with direct N-body simulations of up to 65536 stars, performed on the GRAPE family of special-purpose computers. We find that star clusters with initial half-mass relaxation times of about 25 Myr are dominated by stellar collisions, the first collisions occurring at or near the point of core collapse, which is driven by the segregation of the most massive stars to the cluster center, where they end up in hard binaries. The majority of collisions occur with the same star, resulting in the runaway growth of a supermassive object. This object can grow up to about 0.1% of the mass of the entire star cluster and could manifest itself as an intermediate-mass black hole (IMBH). The phase of runaway growth lasts until mass loss by stellar evolution arrests core collapse. Star clusters older than about 5 Myr and with present-day half-mass relaxation times less than 100 Myr are expected to contain an IMBH.

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Runaway Collisions in Star Clusters

We study the occurrence of physical collisions between stars in young and compact star cluster. The calculations are performed on the GRAPE-4 with the starlab software environment which include the dynamical evolution and the nuclear evolution of all stars and binaries. The selection of the initial conditions is based on existing and well observed star clusters, such as R136 in the 30 Doradus region in the Large Magellanic Cloud and the Arches and Quintuplet star clusters in the vicinity of the Galactic center. Collisions between stars occurred rather frequently in our models. At any time a single star dominates the collision history of the system. The collision rate of this runaway merger scales with the initial relaxation time of the cluster and is independent on other cluster parameters, such as the initial mass function or the initial density profile of the cluster. Subsequent encounters result in a steady grow in mass of the coagulating star, until it escapes or explodes in a supernova. The collision rate in these models is about 0.00022 collisions per star per Myr for a cluster with an initial relaxation time of 1 Myr.

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Population synthesis for double white dwarfs I.Close detached systems

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.

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Is the Galactic center populated with young star clusters?

We study the evolution and observability of young and compact star clusters near the Galactic center, such as the Arches cluster and the Quintuplet. The star clusters are modeled with a combination of techniques; using direct N-body, integration to calculate the motions of all stars and detailed stellar and binary evolution to follow the evolution of the stars. The modeled star clusters dissolve within 10 to 60 million years in the tidal field of the Galaxy. The projected stellar density in the modeled clusters drops within 5% to 70% of the lifetime to a level comparable to the projected background density towards the Galactic center. And it will be very hard to distinguished these clusters at later age among the background stars. This effect is more severe for clusters at larger distance from the Galactic center but in projection at the same distance. Based on these arguments we conclude that the Galactic center easily hides 10 to 40 clusters with characteristics similar to the Arches and the Quintuplet cluster.

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Reconstructing the evolution of double helium white dwarfs: envelope loss without spiral-in

The unique core-mass - radius relation for giants with degenerate helium cores enables us to reconstruct the evolution of three observed double helium white dwarfs with known masses of both components. The last mass transfer phase in their evolution must have been a spiral-in. In the formalism proposed by Webbink (1984), we can constrain the efficiency of the deposition of orbital energy into the envelope to be $1 \la α\la 6$, for an envelope structure parameter $λ=0.5$. We find that the two standard mass transfer types (stable mass transfer and spiral-in) are both unable to explain the first phase of mass transfer for these three binaries. We use a parametric approach to describe mass transfer in low-mass binaries, where both stars are of comparable mass and find that the orbital characteristics of the observed double helium white dwarfs can be well reproduced if the envelope of the primary is lost with ~1.5 times the specific angular momentum of the initial binary. In this case no substantial spiral-in occurs.

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On the origin of the difference between the runaway velocities of the OB-supergiant X-ray Binaries and the Be/X-ray Binaries

The recent finding by Chevalier & Ilovaisky (1998) that OB-supergiant X-ray binaries have relatively large runaway velocities whereas Be/X-ray binaries have low runaway velocities, provides confirmation of the current models for the formation of these two types of systems. These predict a difference in runaway velocity of an order of magnitude. This difference basically results from the variation of the fractional helium core mass as a function of stellar mass, in combination with the conservation of orbital angular momentum during the mass transfer phase that preceded the formation of the compact object in the system. This combination results into: (i) Systematically narrower pre-supernova orbits in the OB-supergiant systems than in the Be-systems, and (ii) A larger fractional amount of mass ejected in the supernovae in high-mass systems relative to systems of lower mass. Regardless of possible kick velocities imparted to neutron stars at birth, this combination leads to a considerable difference in average runaway velocity between these two groups. The observed low runaway velocities of the Be/X-ray binaries confirm that in most cases not more than 1 to 2Msun was ejected in the supernovae that produced their neutron stars. This, in combination with the --on average-- large orbital eccentricities of these systems, indicates that their neutron stars must have received a velocity kick in the range 60 - 250 km/s at birth.

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Star cluster ecology IVa: Dissection of an open star cluster---photometry

The evolution of star clusters is studied using N-body simulations in which the evolution of single stars and binaries are taken self-consistently into account. Initial conditions are chosen to represent relatively young Galactic open clusters, such as the Pleiades, Praesepe and the Hyades. The calculations include a realistic mass function, primordial binaries and the external potential of the parent Galaxy. Our model clusters are generally significantly flattened in the Galactic tidal field, and dissolve before deep core collapse occurs. The binary fraction decreases initially due to the destruction of soft binaries, but increases later because lower mass single stars escape more easily than the more massive binaries. At late times, the cluster core is quite rich in giants and white dwarfs. There is no evidence for preferential evaporation of old white dwarfs, on the contrary the formed white dwarfs are likely to remain in the cluster. Stars tend to escape from the cluster through the first and second Lagrange points, in the direction of and away from the Galactic center. Mass segregation manifests itself in our models well within an initial relaxation time. As expected, giants and white dwarfs are much more strongly affected by mass segregation than main-sequence stars. Open clusters are dynamically rather inactive. However, the combined effect of stellar mass loss and evaporation of stars from the cluster potential drives its dissolution on a much shorter timescale than if these effects are neglected. The often-used argument that a star cluster is barely older than its relaxation time and therefore cannot be dynamically evolved is clearly in error for the majority of star clusters.

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The characteristics of high velocity O and B stars which are ejected from supernovae in binary systems

We perform binary population synthesis calculations to study the origin and the characteristics of runaway O and B stars which are ejected by the supernova explosion of the companion star in a binary system. The number of OB runaways can be explained from supernova ejections only if: high mass stars are preferentially formed in binaries, the initial mass ratio distribution is strongly peaked to unity and stars are rejuvenated to zero age upon accretion of mass from a companion star. Taking these requirements into consideration we conclude that at most 30% of the runaway O stars but possibly all runaway B stars obtain high velocities due to supernovae in evolving binaries. Stars which obtain high velocities via supernova ejections have the following characteristics: 1) at least 10% of the high velocity B stars and half the O stars have a mass greater than the turn off mass of the cluster in which they are born and would be observed as blue stragglers in the parent cluster, 2) their equatorial rotational velocities are proportional to their space velocity and 3) between 20% and 40% of the runaways have neutron star companions but less than 1% are visible as radio pulsars in part of the orbit.

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Gravitational waves from cosmological compact binaries

We consider gravitational waves emitted by various populations of compact binaries at cosmological distances. We use population synthesis models to characterize the properties of double neutron stars, double black holes and double white dwarf binaries as well as white dwarf-neutron star, white dwarf-black hole and black hole-neutron star systems. We use the observationally determined cosmic star formation history to reconstruct the redshift distribution of these sources and their merging rate evolution. The gravitational signals emitted by each source during its early-inspiral phase add randomly to produce a stochastic background in the low frequency band with spectral strain amplitude between 10^{-18} Hz^{-1/2} and 5 10^{-17} Hz^{-1/2} at frequencies in the interval [5 10^{-6}-5 10^{-5}] Hz. The overall signal which, at frequencies above 10^{-4}Hz, is largely dominated by double white dwarf systems, might be detectable with LISA in the frequency range [1-10] mHz and acts like a confusion limited noise component which might limit the LISA sensitivity at frequencies above 1 mHz.

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The Evolution of Globular Clusters in the Galaxy

We investigate the evolution of globular clusters using N-body calculations and anisotropic Fokker-Planck (FP) calculations. The models include a mass spectrum, mass loss due to stellar evolution, and the tidal field of the parent galaxy. Recent N-body calculations have revealed a serious discrepancy between the results of N-body calculations and isotropic FP calculations. The main reason for the discrepancy is an oversimplified treatment of the tidal field employed in the isotropic FP models. In this paper we perform a series of calculations with anisotropic FP models with a better treatment of the tidal boundary and compare these with N-body calculations. The new tidal boundary condition in our FP model includes one free parameter. We find that a single value of this parameter gives satisfactory agreement between the N-body and FP models over a wide range of initial conditions. Using the improved FP model, we carry out an extensive survey of the evolution of globular clusters over a wide range of initial conditions varying the slope of the mass function, the central concentration, and the relaxation time. The evolution of clusters is followed up to the moment of core collapse or the disruption of the clusters in the tidal field of the parent galaxy. In general, our model clusters, calculated with the anisotropic FP model with the improved treatment for the tidal boundary, live longer than isotropic models. The difference in the lifetime between the isotropic and anisotropic models is particularly large when the effect of mass loss via stellar evolution is rather significant. On the other hand the difference is small for relaxation- dominated clusters which initially have steep mass functions and high central concentrations.

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Gamma-ray bursts and density evolution of neutron star binary mergers

The evolution of the comoving cosmic merger-rate density of neutron star binaries n_c(z) is calculated using a distribution of their merging times provided by population-synthesis computations of binary stars. We adopt an exponential law for the star formation rate with various timescales for different morphological types of galaxies. For elliptical galaxies also an initial burst of star formation, lasting one Gyr, is considered. The resulting n_c(z) of most models agree with the form n_c(z) \propto (1+z)^{1.5-2} for z < 2, which has been proposed for the source population of gamma-ray bursts. Assuming a standard candle luminosity, the computed brightness distribution is consistent with the BATSE results if bursts at the peak flux threshold, P = 0.4 photons cm^{-2}/s, are located at a limiting redshift of 1.9 to 3.3. Progenitors of the systems producing gamma-ray bursts at small redshift (bright) are likely to host in spiral galaxies and star forming regions whereas these at high redshift (dim) reside mainly in elliptical galaxies. The location of a burst may be up to a Mpc away from the host galaxy.

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Evolution of Close Binaries: Formation and Merger of Neutron Star Binaries

We discuss the formation and evolution of binaries which contain neutron stars or black holes. It is shown that in a stellar system which for $10^{10}$ yr had star formation rate similar to the current one in the Galactic disc, the rate of neutron star mergers is $\sim 2 \times 10^{-5} yr{-1}$, consistent with the observational estimates. The rate of black hole and neutron star mergers is by an order of magnitude lower. The pairs of black holes form but do not merge because heavy mass loss by their progenitors efficiently moves the binary components apart.

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Formation and Evolution of Binary Neutron Stars

The formation and evolution of binaries which contain two neutron stars or a neutron star with a black hole are discussed in detail. The evolution of the distributions in orbital period and eccentricity for neutron star binaries are studied as a function of time. In the model which fits the observations of high mass binary pulsars best the deposition of orbital energy into common envelopes has to be very efficient and a kick velocity distribution has to contain a significant contribution of low velocity kicks. The estimated age of the population has to be between several 100 Myr and 1 Gyr. The birthrate of binary neutron stars is about 3.4 10^{-5} per year (assuming 100% binarity) and their merger rate is about 2 x 10^{-5} per year. The merger rate of neutron star binaries is consistent with the estimated rate of gamma-ray bursts, if the latter are beamed into an opening angle of a few degrees. We argue that PSR B2303+46 is possibly formed in a scenario in which the common envelope is avoided while for the other three known high-mass binary pulsars a common envelope is required to explain their orbital period.

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Stellar Evolution and Dynamics in Star Clusters

Dynamical models of star clusters are maturing in the sense that effects other than simple point particle dynamics are taken into account. We summarize the relevance of and prospects for this new generation of N-body models.

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Formation of Low-mass Black Hole X-ray Transients

We study the formation of low-mass X-ray binaries with a black hole as accreting object. The performed semi-analytic analysis reveals that the formation rate of black holes in low-mass X-ray binaries is about two orders of magnitude smaller than that of systems with a neutron star as accretor. This is contradicted by the six observed systems, which are all transients, which suggest that the majority of these systems has not been seen jet. The birthrate for both type of objects are expected to be similar (for reviews see Cowley 1992, Tanaka & Lewin 1995). Solution of this conundrum requires either that stars with masses less than 20~\msun can evolve into black holes, or that stellar wind from a member of a binary is accompanied by a much larger loss of angular momentum than hitherto assumed.

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Star Cluster Ecology II: Binary evolution with single-star encounters

Three-body effects greatly complicate stellar evolution. We model the effects of encounters of binaries with single stars, based on parameters chosen from conditions prevalent in the cores of globular clusters. For our three-body encounters, we start with a population of primordial binaries, and choose incoming stars from the evolving single star populations of Portgies Zwart, Hut and Verbunt (1997). In addition, we study the formation of new binaries through tidal capture among the single stars. In subsequent papers in this series, we will combine stellar evolution with the dynamics of a full N-body system.

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Star Cluster Ecology I: A Cluster Core with Encounters between Single Stars

Star clusters with a high central density contain an ecological network of evolving binaries, affected by interactions with passing stars, while in turn affecting the energy budget of the cluster as a whole by giving off binding energy. This is the first paper in a series aimed at providing the tools for increasingly realistic simulations of these ecological networks.

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The formation of black-holes in low-mass X-ray binaries

We calculate the formation rates of low-mass X-ray binaries with a black hole. Both a semi-analytic and a more detailed model predict formation rates two orders of magnitude lower than derived from the observations. Solution of this conundrum requires either that stars with masses less than 20M$_\odot$ can evolve into a black hole, or that stellar wind from a member of a binary is accompanied by a much larger loss of angular momentum than hitherto assumed.

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