The life cycle of star clusters in a tidal field

By M. Gieles, Douglas Heggie, HongSheng Zhao IoA Cambridge, Edinburgh, S. Andrews. 2011

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The evolution of globular clusters due to 2-body relaxation results in an outward flow of energy and at some stage all clusters need a central energy source to sustain their evolution. Henon provided the insight that we do not need to know the details of the energy production in order to understand the relaxation-driven evolution of the cluster, at least outside the core. He provided two self-similar solutions for the evolution of clusters based on the view that the cluster as a whole determines the amount of energy that is produced in the core: steady expansion for isolated clusters, and homologous contraction for clusters evaporating in a tidal field. We combine these models: the half-mass radius increases during the first half of the evolution, and decreases in the second half; while the escape rate approaches a constant value set by the tidal field. We refer to these phases as `expansion dominated' and `evaporation dominated'. These simple analytical solutions immediately allow us to construct evolutionary tracks and isochrones in terms of cluster half-mass density, cluster mass and galacto-centric radius. From a comparison to the Milky Way globular clusters we find that roughly 1/3 of them are in the second, evaporation-dominated phase and for these clusters the density inside the half-mass radius varies with the galactocentric distance R as rho_h ~ 1/R^2. The remaining 2/3 are still in the first, expansion-dominated phase and their isochrones follow the environment-independent scaling rho_h ~ M^2; that is, a constant relaxation time-scale. We find substantial agreement between Milky Way globular cluster parameters and the isochrones, which suggests that there is, as Henon suggested, a balance between the flow of energy and the central energy production for almost all globular clusters.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/8629fcc9de357ced772b8e1e6d666679f6b91caa

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Citations in the corpus

THE RELATIONSHIPS AMONG COMPACT STELLAR SYSTEMS: A FRESH VIEW OF ULTRACOMPACT DWARFS (2011, methodology): “This tidal model may explain the observed sizedistance relation of Milky Way halo clusters, with β ∼ 0.4–0.5 (van den Bergh et al. 1991; McLaughlin 2000; Larsen & Brodie 2003; Mackey & van den Bergh 2005; Baumgardt et al. 2010; cf Gieles et al. 2011).”
Black hole growth through hierarchical black hole mergers in dense star clusters: implications for gravitational wave detections (2018, background): “The constant ζ ≃ 0.1 (Gieles et al. 2011; Alexander & Gieles 2012), and τrh is the average relaxation time-scale within rh which is given by (e.g., Spitzer & Hart 1971) τrh = 0.138 √ Mclr 3 h G 1 〈m⋆〉ψ lnΛ .”
CO-EVOLUTION OF GALACTIC NUCLEI AND GLOBULAR CLUSTER SYSTEMS (2013, background): “…the evaporation time in isolation as a multiple of the half-mass relaxation time,trh: tiso(M) = trh 2.5ξe ≈ 17Gyr [ M(t) 2×105M⊙ ] , (5) whereξe = 0.0074 is the Ambartsumian (1938) rate for a single stellar mass model, and the factor 2.5 corrects it for multimass models (e.g., Gieles et al. 2011).”