ALBERT

Description: According to Muñoz-Gutiérrez et al. the orbit of comet 1P/Halley is chaotic with a surprisingly small Lyapunov time-scale of order its orbital period. In this work we analyse the origin of chaos in Halley's orbit and the growth of perturbations, in order to get a better understanding of this unusually short time-scale. We perform N -body simulations to model Halley's orbit in the Solar system and measure the separation between neighbouring trajectories. To be able to interpret the numerical results, we use a semi-analytical map to demonstrate different growth modes, i.e. linear, oscillatory or exponential, and transitions between these modes. We find the Lyapunov time-scale of Halley's orbit to be of order 300 yr, which is significantly longer than previous estimates in the literature. This discrepancy could be due to the different methods used to measure the Lyapunov time-scale. A surprising result is that next to Jupiter, also encounters with Venus contribute to the exponential growth in the next 3000 yr. Finally, we note an interesting application of the sub-linear, oscillatory growth mode to an ensemble of bodies moving through the Solar system. Whereas in the absence of encounters with a third body the ensemble spreads out linearly in time, the accumulation of weak encounters can increase the lifetime of such systems due to the oscillatory behaviour.

Description: This paper describes an N -body model for the dynamical evolution of the nearby globular cluster M4. The initial conditions, with N  = 484 710 particles, were generated from a published study of this cluster with a Monte Carlo code. With the Monte Carlo code, these initial conditions led, after 12 Gyr of dynamical and stellar evolution, to a model which resembles M4 in terms of its surface brightness and velocity dispersion profiles, and its local luminosity function. Though the N -body model reported here is marred by some errors, its evolution can be compared with that of the published Monte Carlo model, with a result from the synthetic evolution code emacss , and with M4 itself.

Description: We investigate the dynamical evolution of a star cluster in an external tidal field by using N -body simulations, with focus on the effects of the presence or absence of neutron star natal velocity kicks. We show that, even if neutron stars typically represent less than 2 per cent of the total bound mass of a star cluster, their primordial kinematic properties may affect the lifetime of the system by up to almost a factor of 4. We interpret this result in the light of two known modes of star cluster dissolution, dominated by either early stellar evolution mass-loss or two-body relaxation. The competition between these effects shapes the mass-loss profile of star clusters, which may either dissolve abruptly (‘jumping’), in the pre-core-collapse phase, or gradually (‘skiing’), after having reached core collapse.

Description: Using a Monte Carlo code, we construct a dynamic evolutionary model of the Galactic globular cluster M22 (NGC 6656). The initial conditions are chosen so that, after about 12 Gyr of stellar and dynamical evolution, the model is an approximate fit to the surface brightness and velocity dispersion profiles of the cluster, to its mass function and to the current binary fraction. Depending on the distribution of black hole natal kicks, we predict that the present-day population of stellar-mass black holes ranges from about 40 (no kicks) down to essentially zero (kicks distributed like those of neutron stars). Provided that natal kicks do not eject all new black holes, it is suggested that clusters with a present-day half-mass relaxation time above about 1 Gyr are the ones that may still retain an appreciable population of black holes.

Description: We describe a major upgrade of a Monte Carlo code that has previously been used for many studies of dense star clusters. We outline the steps needed in order to calibrate the results of the new Monte Carlo code against N -body simulations for large- N systems, up to N  = 200 000. The new version of the Monte Carlo code (called MOCCA), in addition to the features of the old version, incorporates the direct Fewbody integrator for three- and four-body interactions, and a new treatment of the escape process based on work by Fukushige & Heggie. Now stars that fulfil the escape criterion are not removed immediately, but can stay in the system for a certain time that depends on the excess of the energy of the star above the escape energy. These stars are termed potential escapers. With the addition of the Fewbody integrator the code can follow all interaction channels that are important for the rate of creation of various types of objects observed in star clusters, and it is ensured that the energy generation by binaries is treated in a manner similar to in the N -body model. There are at most three new parameters that have to be adjusted against N -body simulations for large N : two (or one, depending on the chosen approach) connected with the escape process, and one responsible for the determination of the interaction probabilities. The values adopted for the free parameters have at most a weak dependence on N . They allow MOCCA to reproduce N -body results with reasonable precision, not only for the rate of cluster evolution and the cluster mass distribution, but also for the detailed distributions of mass and binding energy of binaries. In addition, the code can follow the rate of formation of blue stragglers and black hole–black hole binaries. The code computes interactions between binaries and single stars up to a maximum separation r pmax , and it is found that MOCCA needs a large value of r pmax to obtain agreement with the N -body simulations. In spite of some limitations, such as its spherical symmetry, a Monte Carlo code such as MOCCA is at present the most advanced code for simulations of real star clusters. It can follow the cluster evolution at a level of detail comparable to that in an N -body code, but orders of magnitude faster.

Description: In this paper, globular star clusters which contain a subsystem of stellar mass black holes (BH) are investigated. This is done by considering two-component models, as these are the simplest approximation of more realistic multimass systems, where one component represents the BH population and the other represents all the other stars. These systems are found to undergo a long phase of evolution where the centre of the system is dominated by a dense BH subsystem. After mass segregation has driven most of the BH into a compact subsystem, the evolution of the BH subsystem is found to be influenced by the cluster in which it is contained. The BH subsystem evolves in such a way as to satisfy the energy demands of the whole cluster, just as the core of a one-component system must satisfy the energy demands of the whole cluster. The BH subsystem is found to exist for a significant amount of time. It takes approximately 10 t rh,i , where t rh,i is the initial half-mass relaxation time, from the formation of the compact BH subsystem up until the time when 90 per cent of the subsystem total mass is lost (which is 10 3 times the half-mass relaxation time of the BH subsystem at its time of formation). Based on theoretical arguments, the rate of mass-loss from the BH subsystem (M 2 ) is predicted to be –β M /(α t rh ), where M is the total mass, t rh is the half-mass relaxation time and α, β, are three dimensionless parameters (see Section  2 of the main text for details). An interesting consequence of this is that the rate of mass-loss from the BH subsystem is approximately independent of the stellar mass ratio ( m 2 / m 1 ) and the total mass ratio ( M 2 / M 1 ) (in the range m 2 / m 1   10 and M 2 / M 1  ~ 10 –2 , where m 1 and m 2 are the masses of individual low-mass and high-mass particles, respectively, and M 1 and M 2 are the corresponding total masses). The theory is found to be in reasonable agreement with most of the results of a series of N -body simulations, and with all of the models if the value of is suitably adjusted. Predictions based on theoretical arguments are also made about the structure of BH subsystems. Other aspects of the evolution are also considered such as the conditions for the onset of gravothermal oscillation.

Description: We present the results of a photometric search for variable stars in the core of the Galactic globular cluster Messier 4 (M 4). The input data are a large and unprecedented set of deep Hubble Space Telescope WFC3 images (large programme GO-12911; 120 orbits allocated), primarily aimed at probing binaries with massive companions by detecting their astrometric wobbles. Though these data were not optimized to carry out a time-resolved photometric survey, their exquisite precision, spatial resolution and dynamic range enabled us to firmly detect 38 variable stars, of which 20 were previously unpublished. They include 19 cluster-member eclipsing binaries (confirming the large binary fraction of M 4), RR Lyrae and objects with known X-ray counterparts. We improved and revised the parameters of some among published variables.

Description: Recent observational evidence, numerical simulations and theoretical arguments seem to indicate that stellar mass black holes (BH) persist in stellar systems such as globular star clusters for much longer than previously thought. Previously, theory implied that the BH would segregate into a compact system with short dynamical time-scales, and that the BH would escape long before the present. But stellar systems can exist in a state of balanced evolution , where the energy generated in the core is regulated by the process of two-body relaxation in the bulk of the system. If the system has a centrally concentrated BH subsystem and there is no massive central BH, then the energy is generated by three-body encounters in the core of this subsystem. Therefore, in balanced evolution, the evolution of the BH subsystem is regulated by the much longer time-scales of the host system. In the present paper the implications of these results for idealized nuclear star clusters (NSC) are discussed. Though previous theory implied that BH would be almost absent from many NSC – those with relatively short dynamical time-scales – it is argued here that, based on the results of idealized models, many such NSC could still be host to substantial BH subsystems.

Description: The M 4 Core Project with HST is designed to exploit the Hubble Space Telescope ( HST ) to investigate the central regions of M 4, the Globular Cluster closest to the Sun. In this paper we combine optical and near-infrared photometry to study multiple stellar populations in M 4. We detected two sequences of M-dwarfs containing ~38 per cent ( MS I ) and ~62 per cent ( MS II ) of MS stars below the main-sequence (MS) knee. We compare our observations with those of NGC 2808, which is the only other GCs where multiple MSs of very low-mass stars have been studied to date. We calculate synthetic spectra for M-dwarfs, assuming the chemical composition mixture inferred from spectroscopic studies of stellar populations along the red giant branch, and different helium abundances, and we compare predicted and observed colours. Observations are consistent with two populations, one with primordial abundance and another with enhanced nitrogen and depleted oxygen.