Jarrod R. Hurley

Comprehensive analytic formulae for stellar evolution as a function of mass and metallicity

We present analytic formulae that approximate the evolution of stars for a wide range of mass M and metallicity Z. Stellar luminosity, radius and core mass are given as a function of age, M and Z, for all phases from the zero-age main sequence up to, and including, the remnant stages. For the most part we find continuous formulae accurate to within 5 per cent of detailed models. These formulae are useful for purposes such as population synthesis that require very rapid but accurate evaluation of stellar properties, and in particular for use in combination with N-body codes. We describe a mass-loss prescription that can be used with these formulae, and investigate the resulting stellar remnant distribution.

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.

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

Summary 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 10 4 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 sub-population. 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.

ON THE MAXIMUM MASS OF STELLAR BLACK HOLES

We present the spectrum of compact object masses: neutron stars and black holes (BHs) that originate from single stars in different environments. In particular, we calculate the dependence of maximum BH mass on metallicity and on some specific wind mass loss rates (e.g., Hurley et al. and Vink et al.). Our calculations show that the highest mass BHs observed in the Galaxy M bh ~ 15 M ☉ in the high metallicity environment (Z = Z ☉ = 0.02) can be explained with stellar models and the wind mass loss rates adopted here. To reach this result we had to set luminous blue variable mass loss rates at the level of ~10–4 M ☉ yr–1 and to employ metallicity-dependent Wolf-Rayet winds. With such winds, calibrated on Galactic BH mass measurements, the maximum BH mass obtained for moderate metallicity (Z = 0.3 Z ☉ = 0.006) is M bh,max = 30 M ☉. This is a rather striking finding as the mass of the most massive known stellar BH is M bh = 23-34 M ☉ and, in fact, it is located in a small star-forming galaxy with moderate metallicity. We find that in the very low (globular cluster-like) metallicity environment the maximum BH mass can be as high as M bh,max = 80 M ☉ (Z = 0.01 Z ☉ = 0.0002). It is interesting to note that X-ray luminosity from Eddington-limited accretion onto an 80 M ☉ BH is of the order of ~1040 erg s–1 and is comparable to luminosities of some known ultra-luminous X-ray sources. We emphasize that our results were obtained for single stars only and that binary interactions may alter these maximum BH masses (e.g., accretion from a close companion). This is strictly a proof-of-principle study which demonstrates that stellar models can naturally explain even the most massive known stellar BHs.

A complete N-body model of the old open cluster M67

The old open cluster M67 is an ideal testbed for current cluster evolution models because of its dynamically evolved structure and rich stellar populations that show clear signs of interaction between stellar, binary and cluster evolution. Here, we present the first truly direct N-body model for M67, evolved from zero age to 4 Gyr taking full account of cluster dynamics as well as stellar and binary evolution. Our preferred model starts with 36 000 stars (12 000 single stars and 12 000 binaries) and a total mass of nearly 19 000 M � , placed in a Galactic tidal field at 8.0 kpc from the Galactic Centre. Our choices for the initial conditions and for the primordial binary population are explained in detail. At 4 Gyr, the age of M67, the total mass has reduced to 2000 Mas a result of mass loss and stellar escapes. The mass and half-mass radius of luminous stars in the cluster are a good match to observations, although the model is more centrally concentrated than observations indicate. The stellar mass and luminosity functions (LFs) are significantly flattened by preferential escape of low-mass stars. We find that M67 is dynamically old enough that information about the initial mass function (IMF) is lost, both from the current LF and from the current mass fraction in white dwarfs (WDs). The model contains 20 blue stragglers (BSs) at 4 Gyr, which is slightly less than the 28 observed in M67. Nine are in binaries. The blue stragglers were formed by a variety of means and we find formation paths for the whole variety observed in M67. Both the primordial binary population and the dynamical cluster environment play an essential role in shaping the population. A substantial population of short-period primordial binaries (with periods less than a few days) is needed to explain the observed number of BSs in M67. The evolution and properties of two-thirds of the BSs, including all found in binaries, have been altered by cluster dynamics and nearly half would not have formed at all outside the cluster environment. On the other hand, the cluster environment is also instrumental in destroying potential BSs from the primordial binary population, so that the total number is in fact slightly smaller than what would be expected from evolving the same binary stars in isolation. Ke yw ords: stellar dynamics - methods: N-body simulations - binaries: close - blue stragglers - stars: evolution - open clusters and associations: general.

The solar neighbourhood age-metallicity relation - Does it exist?

We test the hypothesis that the spread in the age-metallicity plot of the solar neighborhood is due to a mixture of stars belonging to kinematically different sub-populations of the Galactic disk, i.e., the thin and the thick disk. We use a kinematic subsample of similar to 600 stars from a sample of similar to 6000 dwarf and subgiant stars from the Hipparcos catalog. All of these stars have a full set of stellar parameters determined, including good ages. We find that a significant spread in [Me/H] is present in both kinematic populations, especially at large stellar ages. This implies that a simple one-to-one relation between ages and metallicities is not possible. In fact, there are stars that are-truly old and at the same time have [Me/H] > 0.2 dex. (Less)

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 = 10000 simulations in order to quantify the rate of escape of stars from a cluster subject to the Galactic tidal field.

Ratios of star cluster core and half‐mass radii: a cautionary note on intermediate‐mass black holes in star clusters

There is currently much interest in the possible presence of intermediate-mass black holes (IMBHs) in the cores of globular clusters (GCs). Based on theoretical arguments and simulation results it has previously been suggested that a large core radius - or particularly a large ratio of the core radius to half-mass radius - is a promising indicator for finding such a black hole (BH) in a star cluster. In this study N-body models of 100 000 stars with and without primordial binaries are used to investigate the long-term structural evolution of star clusters. Importantly, the simulation data are analysed using the same processes by which structural parameters are extracted from observed star clusters. This gives a ratio of the core and half-mass (or half-light) radii that are directly comparable to the Galactic GC sample. As a result, it is shown that the ratios observed for the bulk of this sample can be explained without the need for an IMBH. Furthermore, it is possible that clusters with large core to half-light radius ratios harbour a BH binary (comprising stellar mass BHs) rather than a single massive BH. This work does not rule out the existence of IMBHs in the cores of at least some star clusters.

An age difference of two billion years between a metal-rich and a metal-poor globular cluster

Globular clusters trace the formation history of the spheroidal components of our Galaxy and other galaxies, which represent the bulk of star formation over the history of the Universe. The clusters exhibit a range of metallicities (abundances of elements heavier than helium), with metal-poor clusters dominating the stellar halo of the Galaxy, and higher-metallicity clusters found within the inner Galaxy, associated with the stellar bulge, or the thick disk. Age differences between these clusters can indicate the sequence in which the components of the Galaxy formed, and in particular which clusters were formed outside the Galaxy and were later engulfed along with their original host galaxies, and which were formed within it. Here we report an absolute age of 9.9 ± 0.7 billion years (at 95 per cent confidence) for the metal-rich globular cluster 47 Tucanae, determined by modelling the properties of the cluster’s white-dwarf cooling sequence. This is about two billion years younger than has been inferred for the metal-poor cluster NGC 6397 from the same models, and provides quantitative evidence that metal-rich clusters like 47 Tucanae formed later than metal-poor halo clusters like NGC 6397.

The Core Binary Fractions of Star Clusters from Realistic Simulations

We investigate the evolution of binary fractions in star clusters using N-body models of up to 100,000 stars. Primordial binary frequencies in these models range from 5% to 50%. Simulations are performed with the NBODY4 code and include a full mass spectrum of stars, stellar evolution, binary evolution, and the tidal field of the Galaxy. We find that the overall binary fraction of a cluster almost always remains close to the primordial value, except at late times when a cluster is near dissolution. A critical exception occurs in the central regions, where we observe a marked increase in binary fraction with time—a simulation starting with 100,000 stars and 5% binaries reached a core binary frequency as high as 40% at the end of the core-collapse phase (occurring at 16 Gyr with ~20,000 stars remaining). Binaries are destroyed in the core by a variety of processes as a cluster evolves, but the combination of mass segregation and creation of new binaries in exchange interactions produces the observed increase in relative number. We also find that binaries are cycled into and out of cluster cores in a manner that is analogous to convection in stars. For models of 100,000 stars we show that the evolution of the core radius up to the end of the initial phase of core collapse is not affected by the exact value of the primordial binary frequency (for frequencies of 10% or less). We discuss the ramifications of our results for the likely primordial binary content of globular clusters.