How well do starlab and nbody4 compare? I. Simple models

N -body simulations are widely used to simulate the dynamical evolution of a variety of systems, among them star clusters. Much of our understanding of their evolution rests on the results of such direct N -body simulations. They provide insight in the structural evolution of star clusters, as well as into the occurrence of stellar exotica. Although the major pure N -body codes starlab/kira and nbody4 are widely used for a range of applications, there is no thorough comparison study yet.
Here, we thoroughly compare basic quantities as derived from simulations performed either with starlab/kira or nbody4 .
We construct a large number of star cluster models for various stellar mass function settings (but without stellar/binary evolution, primordial binaries, external tidal fields, etc.), evolve them in parallel with starlab/kira and nbody4 , analyse them in a consistent way and compare the averaged results quantitatively. For this quantitative comparison, we develop a bootstrap algorithm for functional dependencies.
We find an overall excellent agreement between the codes, both for the clusters' structural and energy parameters as well as for the properties of the dynamically created binaries. However, we identify small differences, like in the energy conservation before core collapse and the energies of escaping stars, which deserve further studies.
Our results reassure the comparability and the possibility to combine results from these two major N -body codes, at least for the purely dynamical models (i.e. without stellar/binary evolution) we performed. Further detailed comparison studies for more complex systems, e.g. including stellar/binary evolution, are required.     

A steady-state model of NEA binaries formed by tidal disruption of gravitational aggregates

We present results of a simulation of a steady-state binary near-Earth asteroid (NEA) population. This study combines previous work on tidal disruption of gravitational aggregates [Walsh, K.J., Richardson, D.C., 2006. Icarus 180, 201-216] with a Monte Carlo simulation of NEA planetary encounters. Evolutionary effects include tidal evolution and binary disruption from close planetary encounters. The results show that with the best known progenitor (small Main Belt asteroids) shape and spin distributions, and current estimates of NEA lifetime and encounter probabilities, that tidal disruption should account for approximately 1-2% of NEAs being binaries. Given the best observed estimate of a ∼15% binary NEA fraction, we conclude that there are other formation mechanisms that contribute significantly to this population. We also present the expected distribution of binary orbital and physical properties for the steady-state binary NEAs formed by tidal disruption. We discuss the effects on binary fraction and properties due to changes in the least constrained parameters, and other possible effects on our model that could account for differences between the presented results and the observed binary population. Finally, we model possible effects of a significant population of binaries migrating to the near-Earth population from the Main Belt.     

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.     

Gravitational and electromagnetic emission by magnetized coalescing binary systems

We discuss the possibility to obtain an electromagnetic emission accompanying the gravitational waves emitted in the coalescence of a compact binary system. Motivated by the existence of black hole configurations with open magnetic field lines along the rotation axis, we consider a magnetic dipole in the system, the evolution of which leads to (i) electromagnetic radiation, and (ii) a contribution to the gravitational radiation, the luminosity of both being evaluated. Starting from the observations on magnetars, we impose upper limits for both the electromagnetic emission and the contribution of the magnetic dipole to the gravitational wave emission. Adopting this model for the evolution of neutron star binaries leading to short gamma ray bursts, we compare the correction originated by the electromagnetic field to the gravitational waves emission, finding that they are comparable for particular values of the magnetic field and of the orbital radius of the binary system. Finally we calculate the electromagnetic and gravitational wave energy outputs which result comparable for some values of magnetic field and radius.     

Binary population synthesis for blue stragglers

In this talk, we will simply show the consequences of binary population synthesis for blue stragglers, such as the integrated spectral energy distribution (ISED), the color-magnitude diagram, the specific frequency, and the influences on colors. Blue stragglers have been found in all stellar populations and they are an important population component in both stellar evolution and star clusters. Much evidence shows that blue stragglers are relevant to primordial binaries. The binary population synthesis study shows that primordial binary evolution may produce blue stragglers at any given times. The specific frequency in this way decreases with time first, then increases when the age is larger than 10 Gyr, while that from angular momentum loss induced by magnetic braking in low-mass binaries increases with time and exceeds that of primordial binary evolution in a population older than 3 Gyr. Meanwhile, blue stragglers resulting from primordial binary evolution are dominant contributors to the ISEDs in ultraviolet and blue bands in a population between 0.3 and 2.0 Gyr. The mass fraction of the lost matter from the primary accreted by the secondary, β, significantly affects on the final results, e.g. the specific frequency of blue stragglers decreasing with β, blue stragglers produced from a high value of β being more massive, then contributing more to the ISEDs of the host clusters. For old open clusters, it is appropriate to adopt a higher value of β when the primary is in HG at the onset of mass transfer. Our study also shows that, for most Galactic open clusters, the specific frequency of blue stragglers obtained from our simulations is much lower than that of observations, which has been discussed in this talk.     

Circular binary star and an interstellar interloper: The analytical solution

We consider an interstellar interloper moving at a relatively large distance from a circular binary star. We use the analytical method of separating rapid and slow subsystems, the rapid subsystem being the binary and the slow subsystem being the interstellar interloper. We show that due to the higher than geometrical symmetry of the problem, in addition to the conservation of the energy and the projection of the angular momentum on the axis of the rotation of the binary, the square of the angular momentum is also conserved. In the course of the time evolution, the vector of the angular momentum rotates about that axis at the constant angle to the axis. After obtaining this general counterintuitive result, we focus at the case where the interstellar interloper is coplanar with the binary. We provide an explicit equation of the motion of the interloper. Then we calculate analytically the angle of deflection of the interloper from the straight line. We analyze the difference in the angle of deflection between this three-body problem and the corresponding two-body problem: we show that this difference remains almost constant (a negative constant) at the range of the eccentricities of the interloper trajectory relatively close to unity and linearly increases (by the absolute value, remaining negative) with the eccentricity as the latter becomes much greater than unity.     

Another channel to detect close-in binary companions via gravitational microlensing

Gaudi & Gould showed that close companions of remote binary systems can be efficiently detected by using gravitational microlensing via the deviations in the lensing light curves induced by the existence of the lens companions. In this paper, we introduce another channel to detect faint close-in binary companions by using microlensing. This method utilizes a caustic-crossing binary lens event with a source also composed of binary stars, where the companion is a faint star. Detection of the companion is possible because the flux of the companion can be highly amplified when it crosses the lens caustic. The detection is facilitated since the companion is more amplified than the primary because it, in general, has a smaller size than the primary, and thus experiences less finite source effect. The method is an extension of the previous one suggested to detect close-in giant planets by Graff & Gaudi and Lewis & Ibata and further developed by Ashton & Lewis. From the simulations of realistic Galactic bulge events, we find that companions of K-type main-sequence or brighter stars can be efficiently detected from the current type of microlensing follow-up observations by using the proposed method. We also find that compared with the method of detecting lens companions for which the efficiency drops significantly for binaries with separations ≲0.2 of the angular Einstein ring radius, θ _E, the proposed method has an important advantage of being able to detect companions with substantially smaller separations down to ∼     .     

Dynamo saturation in direct simulations of the multi‐phase turbulent interstellar medium

The ordered magnetic field observed via polarised synchrotron emission in nearby disc galaxies can be explained by a mean‐field dynamo operating in the diffuse interstellar medium (ISM). Additionally, vertical‐flux initial conditions are potentially able to influence this dynamo via the occurrence of the magnetorotational instability (MRI). We aim to study the influence of various initial field configurations on the saturated state of the mean‐field dynamo. This is motivated by the observation that different saturation behaviour was previously obtained for different supernova rates. We perform direct numerical simulations (DNS) of three‐dimensional local boxes of the vertically stratified, turbulent interstellar medium, employing shearing‐periodic boundary conditions horizontally. Unlike in our previous work, we also impose a vertical seed magnetic field. We run the simulations until the growth of the magnetic energy becomes negligible. We furthermore perform simulations of equivalent 1D dynamo models, with an algebraic quenching mechanism for the dynamo coefficients. We compare the saturation of the magnetic field in the DNS with the algebraic quenching of a mean‐field dynamo. The final magnetic field strength found in the direct simulation is in excellent agreement with a quenched α) dynamo. For supernova rates representative of the Milky Way, field losses via a Galactic wind are likely responsible for saturation. We conclude that the relative strength of the turbulent and regular magnetic fields in spiral galaxies may depend on the galaxy's star formation rate. We propose that a mean field approach with algebraic quenching may serve as a simple sub‐grid scale model for galaxy evolution simulations including a prescribed feedback from magnetic fields. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reconstructing the evolution of white dwarf binaries: further evidence for an alternative algorithm for the outcome of the common-envelope phase in close binaries

We determine the possible masses and radii of the progenitors of white dwarfs in binaries from fits to detailed stellar evolution models and use these to reconstruct the mass-transfer phase in which the white dwarf was formed. We confirm the earlier finding that in the first phase of mass transfer in the binary evolution leading to a close pair of white dwarfs, the standard common-envelope formalism (the α-formalism) equating the energy balance in the system (implicitly assuming angular momentum conservation) does not work. An algorithm equating the angular momentum balance (implicitly assuming energy conservation) can explain the observations. This conclusion is now based on 10 observed systems rather than three. With the latter algorithm (the γ-algorithm) the separation does not change much for approximately equal-mass binaries. Assuming constant efficiency in the standard α-formalism and a constant value of γ, we investigate the effect of both methods on the change in separation in general and conclude that when there is observational evidence for strong shrinkage of the orbit, the γ-algorithm also leads to this. We then extend our analysis to all close binaries with at least one white dwarf component and reconstruct the mass-transfer phases that lead to these binaries. In this way we find all possible values of the efficiency of the standard α-formalism and of γ that can explain the observed binaries for different progenitor and companion masses. We find that all observations can be explained with a single value of γ, making the γ-algorithm a useful tool to predict the outcome of common-envelope evolution. We discuss the consequences of our findings for different binary populations in the Galaxy, including massive binaries, for which the reconstruction method cannot be used.     

After the Supernova: Runaway Stars and Massive X-ray Binary Populations with Metallicity

One of the main pathways by which massive runaways are thought to be produced is by the disruption of a binary system after the supernova (SN) of one of its components. Under such a scenario, the populations of runaway stars in different phases should reflect the input binary population and its evolution. Conversely, if the system stays together after the SN, a High Mass X-Ray Binary (HMXB) may result. We present simulations exploring the behaviour of such runaway and HMXB populations with metallicity, and compare them to observations. As many as two-thirds of massive runaway stars may be produced by supernovae in binaries. Decreasing metallicity lowers the fraction of O stars which are runaway, but increases the Wolf-Rayet runaway fractions and the number of potential HMXBs.     

Limit-Cycle Behaviour of Thermally Unstable Accretion Flows on to Black Holes

Non-linear time-dependent calculations are being carried out in order to study the evolution of vertically integrated models of non-self-gravitating, transonic accretion discs around black holes. In this paper we present results from a new calculation for a high-α model similar to one studied previously by Honma, Matsumoto &38; Kato who found evidence for limit-cycle behaviour connected with thermal instability. Our results are in substantial agreement with theirs but, in our calculation, the disc material does not always remain completely optically thick and we include a suitable treatment for this. We followed the evolution for several cycles and determined the period of the cycle as being about 780 s. Advective cooling is dominant in the region just behind the outward-moving peak of surface density. The behaviour of this model is significantly different from what we saw earlier for low-α models (which we discussed in a previous paper) and we contrast and compare the two situations.     

Evolution of X-ray cavities

A wide range of recent observations have shown that active galactic nuclei (AGN) driven cavities may provide the energy source that balances the cooling observed in the centres of 'cool-core' galaxy clusters. One tool for better understanding the physics of these cavities is their observed morphological evolution, which is dependent on such poorly understood properties as the turbulent density field and the impact of magnetic fields. Here, we combine numerical simulations that include subgrid turbulence and software that produces synthetic X-ray observations to examine the evolution of X-ray cavities in the absence of magnetic fields. Our results reveal an anisotropic size evolution of the cavities that is dramatically different from simplified, analytical predictions. These differences highlight some of the key issues that must be accurately quantified when studying AGN-driven cavities, and help to explain why the inferred pV energy in these regions appears to be correlated with their distance from the cluster centre. Interpreting that X-ray observations will require detailed modelling of effects, including mass entrainment, distortion by drag forces and projection. Current limitations do not allow a discrimination between purely hydrodynamic and magnetically dominated models for X-ray cavities.     

Constrained simulations of the local universe – II. The nature of the local Hubble flow

Using a suite of N -body simulations in different cold dark matter (CDM) scenarios, with cosmological constant (ΛCDM) and without (OCDM, SCDM), we study the Hubble flow (σ_H) in Local Volumes (LV) around Local Group (LG) like objects found in these simulations, and compare the numerical results with the most recent observations. We show that ΛCDM and OCDM models exhibit the same behaviour of σ_H. Hence, we demonstrate that the observed coldness of the Hubble flow is not likely to be a manifestation of the dark energy, contrary to previous claims. The coldness does not constitute a problem by itself but it poses a problem to the standard ΛCDM model only if the mean density within the LV is greater than twice the mean matter cosmic density. The lack of blueshifted galaxies in the LV, outside of the LG can be considered as another manifestation of the coldness of the flow. Finally, we show that the main dynamical parameter that affects the coldness of the flow is the relative isolation of the LG, and the absence of nearby Milky Way like objects within a distance of about  3 Mpc  .     

Ultraviolet Studies Of Interacting Binaries

Interacting Binaries consist of a variety of stellar objects in different stages of evolution and those containing accreting compact objects still represent a major challenge to our understanding of not only close binary evolution but also of the chemical evolution of the Galaxy. These end-points of binary star evolution are ideal laboratories for the study of accretion and outflow processes, and provide insight on matter under extreme physical conditions. One of the key-questions of fundamental relevance is the nature of SN Ia progenitors. The study of accreting compact binary systems relies on observations over the entire electromagnetic spectrum and we outline here those unresolved questions for which access to the ultraviolet range is vital, as they cannot be addressed by observations in any other spectral region.An erratum to this article can be found at     

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 de-excited energy of electron capture in accreting neutron star crusts

When a daughter nucleus produced by electron capture takes part in a level transition from an excited state to its ground state in accreting neutron star crusts, thermal energy will be released and heat the crust, increasing crust temperature and changing subsequent carbon ignition conditions. Previous studies show that the theoretical carbon ignition depth is deeper than the value inferred from observations because the thermal energy is not sufficient. In this paper, we present the de-excited energy from electron capture of rp-process ash before carbon ignition, especially for the initial evolution stage of rp-process ash, by using a level-to-level transition method. We find the theoretical column density of carbon ignition in the resulting superbursts and compare it with observations. The calculation of the electron capture process is based on a more reliable level-to-level transition, adopting new data from experiments or theoretical models(e.g., large-scale shell model and proton-neutron quasi-particle random phase approximation). The new carbon ignition depth is estimated by fitting from previous results of a nuclear reaction network. Our results show the average de-excited energy from electron capture before carbon ignition is ~0.026 Me V/u, which is significantly larger than the previous results. This energy is beneficial for enhancing the crust's temperature and decreasing the carbon ignition depth of superbursts.     

Winds from clusters with non-uniform stellar distributions

We present the analytic and numerical models of the 'cluster wind' resulting from the multiple interactions of the winds ejected by the stars of a dense cluster of massive stars. We consider the case in which the distribution of stars (i.e. the number of stars per unit volume) within the cluster is spherically symmetric, has a power-law radial dependence, and drops discontinuously to zero at the outer radius of the cluster. We carry out comparisons between an analytic model (in which the stars are considered in terms of a spatially continuous injection of mass and energy) and 3D gasdynamic simulations (in which we include 100 stars with identical winds, located in 3D space by statistically sampling the stellar distribution function). From the analytic model, we find that for stellar distributions with steep enough radial dependencies, the cluster wind flow develops a very high central density and a non-zero central velocity, and for steeper dependencies, it becomes fully supersonic throughout the volume of the cluster (these properties are partially reproduced by the 3D numerical simulations). Therefore, the wind solutions obtained for stratified clusters can differ dramatically from the case of a homogeneous stellar distribution (which produces a cluster wind with zero central velocity, and a fully subsonic flow within the cluster radius). Finally, from our numerical simulations, we compute predictions of X-ray emission maps and luminosities, which can be directly compared with observations of cluster wind flows.     

Hydrodynamical Simulations of Molecular Dynamics in Supersonic Turbulent Flow

Here we present results from simulations of turbulence in star forming environments obtained by coupling three-dimensional hydrodynamical models with appropriate chemical processes. We investigate regimes of decaying high-speed molecular turbulence. Here we analyse PDFs of density for the volume, mass, molecular mass and the energy distribution over the range of scales. We compare our results to those previously obtained for isothermal turbulence and suggest possible explanations.     

Formation of Asteroid Families by Catastrophic Disruption: Simulations with Fragmentation and Gravitational Reaccumulation

This paper builds on preliminary work in which numerical simulations of the collisional disruption of large asteroids (represented by the Eunomia and Koronis family parent bodies) were performed and which accounted not only for the fragmentation of the solid body through crack propagation, but also for the mutual gravitational interaction of the resulting fragments. It was found that the parent body is first completely shattered at the end of the fragmentation phase, and then subsequent gravitational reaccumulations lead to the formation of an entire family of large and small objects with dynamical properties similar to those of the parent body. In this work, we present new and improved numerical simulations in detail. As before, we use the same numerical procedure, i.e., a 3D SPH hydrocode to compute the fragmentation phase and the parallel N-body code pkdgrav to compute the subsequent gravitational reaccumulation phase. However, this reaccumulation phase is now treated more realistically by using a merging criterion based on energy and angular momentum and by allowing dissipation to occur during fragment collisions. We also extend our previous studies to the as yet unexplored intermediate impact energy regime (represented by the Flora family formation) for which the largest fragment's mass is about half that of the parent body. Finally, we examine the robustness of the results by changing various assumptions, the numerical resolution, and different numerical parameters. We find that in the lowest impact energy regime the more realistic physical approach of reaccumulation leads to results that are statistically identical to those obtained with our previous simplistic approach. Some quantitative changes arise only as the impact energy increases such that higher relative velocities are reached during fragment collisions, but they do not modify the global outcome qualitatively. As a consequence, these new simulations confirm previous main results and still lead to the conclusion that: (1) all large family members must be made of gravitationally reaccumulated fragments; (2) the original fragment size distribution and their orbital dispersion are respectively steeper and smaller than currently observed for the real families, supporting recent studies on subsequent evolution and diffusion of family members; and (3) the formation of satellites around family members is a frequent and natural outcome of collisional processes.