Evolution Of Dense Stellar Systems Research Articles

Introducing a new multi-particle collision method for the evolution of dense stellar systems

Context.In a previous paper we introduced a new method for simulating collisional gravitationalN-body systems with linear time scaling onN, based on the multi-particle collision (MPC) approach. This allows us to easily simulate globular clusters with a realistic number of stellar particles (105 − 106) in a matter of hours on a typical workstation.Aims.We evolve star clusters containing up to 106stars to core collapse and beyond. We quantify several aspects of core collapse over multiple realizations and different parameters while always resolving the cluster core with a realistic number of particles.Methods.We run a large set ofN-body simulations with our new code MPCDSS. The cluster mass function is a pure power law with no stellar evolution, allowing us to clearly measure the effects of the mass spectrum on core collapse.Results.Leading up to core collapse, we find a power-law relation between the size of the core and the time left to core collapse. Our simulations thus confirm the theoretical self-similar contraction picture but with a dependence on the slope of the mass function. The time of core collapse has a non-monotonic dependence on the slope, which is well fitted by a parabola. This also holds for the depth of core collapse and for the dynamical friction timescale of heavy particles. Cluster density profiles at core collapse show a broken-power-law structure, suggesting that central cusps are a genuine feature of collapsed cores. The core bounces back after collapse, with visible fluctuations, and the inner density slope evolves to an asymptotic value. The presence of an intermediate-mass black hole inhibits core collapse, making it much shallower, irrespective of the mass-function slope.Conclusions.We confirm and expand on several predictions of star cluster evolution before, during, and after core collapse. Such predictions were based on theoretical calculations or small-size directN-body simulations. Here we put them to the test in MPC simulations with a much larger number of particles, allowing us to resolve the collapsing core.

Introducing a new multi-particle collision method for the evolution of dense stellar systems

Context. Stellar systems are broadly divided into collisional and non-collisional categories. While the latter are large-N systems with long relaxation timescales and can be simulated disregarding two-body interactions, either computationally expensive direct N-body simulations or approximate schemes are required to properly model the former. Large globular clusters and nuclear star clusters, with relaxation timescales of the order of a Hubble time, are small enough to display some collisional behaviour and big enough to be impossible to simulate with direct N-body codes and current hardware. Aims. We aim to introduce a new method to simulate collisional stellar systems and validate it by comparison with direct N-body codes on small-N simulations. Methods. The Multi-Particle Collision for Dense Stellar Systems (MPCDSS) code is a new code for evolving stellar systems with the multi-particle collision method. Such a method amounts to a stochastic collision rule that makes it possible to conserve the exact energy and momentum over a cluster of particles experiencing the collision. The code complexity scales with N log N in the number of particles. Unlike Monte Carlo codes, MPCDSS can easily model asymmetric, non-homogeneous, unrelaxed, and rotating systems, while allowing us to follow the orbits of individual stars. Results. We evolved small (N = 3.2 × 104) star clusters with MPCDSS and with the direct-summation code NBODY6, finding a similar evolution of key indicators. We then simulated different initial conditions in the 104 − 106 star range. Conclusions. MPCDSS bridges the gap between small collisional systems that can be simulated with direct N-body codes and large non-collisional systems. In principle, MPCDSS allows us to simulate globular clusters such as Ω Centauri and M 54, and even nuclear star clusters, which is beyond the limits of current direct N-body codes in terms of the number of particles.

A new, efficient stellar evolution code for calculating complete evolutionary tracks

We present a new stellar evolution code and a set of results, demonstrating its capability at calculating full evolutionary tracks for a wide range of masses and metallicities. The code is fast and efficient, and is capable of following through all evolutionary phases, without interruption or human intervention. It is meant to be used also in the context of modelling the evolution of dense stellar systems, for performing live calculations for both normal star models and merger products. The code is based on a fully implicit, adaptive-grid numerical scheme that solves simultaneously for structure, mesh and chemical composition. Full details are given for the treatment of convection, equation of state, opacity, nuclear reactions and mass loss. Results of evolutionary calculations are shown for a solar model that matches the characteristics of the present sun to an accuracy of better than 1 per cent; a 1 M⊙ model for a wide range of metallicities; a series of models of stellar Populations I and II, for the mass range 0.25 to 64 M⊙, followed from pre-main-sequence to a cool white dwarf or core collapse. An initial–final mass relationship is derived and compared with previous studies. Finally, we briefly address the evolution of non-canonical configurations, merger products of low-mass main-sequence parents.

A New, Efficient Stellar Evolution Code for Calculating Complete Evolutionary Tracks

AbstractWe report on the development of a new stellar evolution code, and provide a taste of results, showing its capability to calculate full evolutionary tracks for a wide range of masses and metalicities. The code is fast and efficient, and is capable of following through all evolutionary phases, including core/shell flashes and thermal pulses, without any interruption or intervention. It is meant to be used also in the context of modeling the evolution of dense stellar systems, for performing live calculations for both ‘normal’ ZAMS/PRE-MS models, but mainly for ‘non-canonical’ stellar configurations (i.e. merger-products). We show a few examples of evolutionary calculations for stellar populations I and II, and for masses in the range 0.25–64 M⊙.

The Formation and Evolution of Very Massive Stars in Dense Stellar Systems

AbstractThe early evolution of dense stellar systems is governed by massive single star and binary evolution. Core collapse of dense massive star clusters can lead to the formation of very massive objects through stellar collisions (M≥ 1000M⊙). Stellar wind mass loss determines the evolution and final fate of these objects, and determines whether they form black holes (with stellar or intermediate mass) or explode as pair instability supernovae, leaving no remnant. We present a computationally inexpensive evolutionary scheme for very massive stars that can readily be implemented in an N-body code. Using our new N-body code ‘Youngbody’ which includes a detailed treatment of massive stars as well as this new scheme for very massive stars, we discuss the formation of intermediate mass and stellar mass black holes in young starburst regions. A more detailed account of these results can be found in Belkus, Van Bever & Vanbeveren (2007).

Embryo to Ashes Complete Evolutionary Tracks, Hands-off

AbstractWe present a new stellar evolution code and a set of results, showing its capability to calculate full evolutionary tracks for a wide range of masses and metalicities. The code is meant to be used also in the context of modeling the evolution of dense stellar systems, for performing live evolutionary calculations both for ‘normal’ ZAMS/PRE-MS models, but mainly for ‘non-canonical’ (i.e. merger-products) stellar configurations. For such tasks, it has to be robust and efficient, capable to run through all phases of stellar evolution without interruption or intervention. Here we show a few examples of evolutionary calculations for stellar populations I and II, and for masses in the range 0.25–64 M⊙.

The Early Evolution of Dense Stellar Systems

AbstractThe early evolution of dense stellar systems is dominated by the majority mass component – the gas – and so any credible modeling of the first Myr or so of a cluster's life inevitably involves hydrodynamical simulations. Such simulations have increased considerably in sophistication over the last few years and are now beginning to incorporate the effects of stellar feedback, thus enabling one, for the first time, to model the formation of populous clusters. In this review I focus on two issues that have arisen from the simulations – the relationship between maximum stellar mass and cluster mass, and the issue of the maximum density that is attainable during the cluster formation process. I also report on the first results of new simulations that model feedback from ionising radiation.

The formation, disruption and properties of pressure-supported stellar systems and implications for the astrophysics of galaxies

AbstractMost stars form in dense star clusters deeply embedded in residual gas. These objects must therefore be seen as the fundamental building blocks of galaxies. With this contribution some physical processes that act in the very early and also later dynamical evolution of dense stellar systems in terms of shaping their later appearance and properties, and the impact they have on their host galaxies, are highlighted. Considering dense systems with increasing mass, it turns out that near 106M⊙ their properties change fundamentally: stellar populations become complex, a galaxial mass–radius relation emerges and the median two-body relaxation time becomes longer than a Hubble time. Intriguingly, only systems with a two-body relaxation time longer than a Hubble time show weak evidence for dark matter, whereby dSph galaxies form total outliers.

Direct physical collisions and the evolution of dense stellar systems

This paper formulates kinetic equations to describe the destruction of stars via direct physical collisions, assumed characterized by a constant geometric cross section, which are valid for spherically-symmetric systems both in Newtonian gravity and general relativity. An ‘orbit averaging’ prescription is then used to formulate simpler equations for the evolution of an ‘average’ distribution function involving only the specific energyE, angular momentumJ, and time. If one supposes that, in the absence of physical collisions, the distribution would be stationary, it is easy to identify a collision time-scalet C associated with the stationary distribution that depends only uponE andJ. These relations assume especially simple forms in the limit that all the stars have vanishing angular momentum and follow radial trajectories: the analysis of physical collisions then reduces effectively to a one-dimensional problem. As a concrete example, one may suppose in this case that the stationary distribution corresponds to a gaussian distribution of radial velocities. The time-scalet C (E) then reduces to a single quadrature that involves the radial distribution of stars, whose asymptotic forms corroborate one's naive expectations.