Dynamical evolution of star clusters in tidal fields

By H. Baumgardt, J. Makino. 2002

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We report the results of a large set of N-body calculations aimed at studying the evolution of multimass star clusters in external tidal fields. Our clusters start with the same initial mass functions, but varying particle numbers, orbital types and density profiles. Our main focus is to study how the stellar mass function and other cluster parameters change under the combined influence of stellar evolution, two-body relaxation and the external tidal field. We find that the lifetimes of star clusters moving on similar orbits scale as T ∼ T x , where T rh is the relaxation time, and the exponent x depends on the initial concentration of the cluster and is around x ≈ 0.75. The scaling law does not change significantly if one goes from circular orbits to eccentric ones. From the results for the lifetimes, we predict that between 53 and 67 per cent of all Galactic globular clusters will be destroyed within the next Hubble time. Low-mass stars are preferentially lost and the depletion is strong enough to turn initially increasing mass functions into mass functions that decrease towards the low-mass end. The details of this depletion are insensitive to the starting condition of the cluster and can be characterized as a function of a single variable, such as, for example, the fraction of time spent until total cluster dissolution. The preferential depletion of low-mass stars from star clusters leads to a decrease of their mass-to-light ratios except for a short period close to final dissolution, when the mass fraction in the form of compact remnants starts to dominate. The fraction of compact remnants increases throughout the evolution. They are more strongly concentrated towards the cluster cores than main-sequence stars and their mass fraction in the centre can reach 95 per cent or more around and after core collapse. For a sample of Galactic globular clusters with well-observed parameters, we find a correlation between the observed slope of the mass function and the lifetimes predicted by us. It seems possible that Galactic globular clusters started with a mass function similar to what one observes for the average mass function of the Galactic disc and bulge.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/f1b07d34e9a28e32db1c2c83b987144833db9649

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Citations in the corpus

A catalogue of masses, structural parameters, and velocity dispersion profiles of 112 Milky Way globular clusters (2018, background): “This can be understood as a result of ongoing cluster dissolution which preferentially removes low-mass stars from the clusters (Vesperini & Heggie 1997; Baumgardt & Makino 2003).”
Young Massive Star Clusters (2010, background): “Baumgardt & Makino (2003) found that this scaling also holds for models of clusters with a stellar mass spectrum, stellar evolution, and for different types of orbits in a logarithmic potential.”
The mass function of young star clusters in spiral galaxies (2008, background): “Few clusters with initial masses less than ∼105 M would have survived for a Hubble time (Vesperini & Heggie 1997; Baumgardt & Makino 2003; Fall & Zhang 2001) and the shape of the low-mass end of the globular cluster MF is therefore strongly affected by dynamical evolution.”
The life cycle of star clusters in a tidal field (2011, methodology): “Because these clusters are faint, they could be close to final dissolution and might have stellar mass functions that are depleted in low mass stars (Baumgardt & Makino 2003).”
Gravitational N-Body Simulations (2003, methodology): “An ambitious survey of N -body models has recently been completed with NBODY 4 and a powerful GRAPE-6 configuration [Baumgardt & Makino, 2003].”
Massive Black Holes in Star Clusters. II. Realistic Cluster Models (2004, background): “Baumgardt & Makino (2003) and Gürkan et al. (2004) showed that mass segregation of high-mass stars proceeds on the same timescale as the evolution of the clusters toward core collapse.”
A complete N-body model of the old open cluster M67 (2005, background): “As a result, binary-rich open clusters are now within reach of direct N-body codes (Hurley & Shara 2003), as are larger single-star models (Baumgardt & Makino 2003).”
Evidence for top-heavy stellar initial mass functions with increasing density and decreasing metallicity (2012, result): “…initial mass function (IMF) and secular twobody relaxation driven evolution alone (Leigh et al. 2012), in agreement with earlier work that shows that an initially rising IMF with decreasing stellar mass can bend over in the course of a Hubble time (Vesperini & Heggie 1997; Baumgardt & Makino 2003).”
Star cluster disruption by giant molecular clouds (2006, background): “Note that the index γ is comparable, if we take the upper bound value of λ = 0.10 ± 0.03, since Baumgardt & Makino (2003) found tdis ∝ [Mc/ ln(Mc)]0.75.”
The dragon simulations: globular cluster evolution with a million stars (2016, unknown): “The important stepping stones were simulations of 10k (Spurzem & Aarseth 1996), 33k (Makino 1996), 100k (Baumgardt & Makino 2003), 200k (Hurley & Shara 2012), 263k (Sippel & Hurley 2013) and 485k (Heggie 2014) stars.”
Galactic Stellar and Substellar Initial Mass Function (2003, unknown): “…- contrarily to what seems to have been established from either Michie-King models or Fokker-Planck calculations - mass segregation or tidal shocks affect significantly the shape of the IMF even near the half-light radius, yielding a deficiency of low-mass stars (see e.g. Baumgardt & Makino 2003).”
Tidal tails of star clusters (2009, background): “3), which is expected, because the more eccentric the orbit the stronger is the average tidal field (Baumgardt & Makino 2003).”
Mean proper motions, space orbits, and velocity dispersion profiles of Galactic globular clusters derived fromGaiaDR2 data (2018, unknown): “10 and 12 of (Baumgardt & Makino 2003): TDiss [Myr] = 1.35 ( MIni ln(0.02NIni) )0.75 · RApo [kpc] · ( VG 240 km/sec · (1− ǫ) (5) and M(t) = 0.50MIni (1− t/TDiss) .”
Extragalactic Globular Clusters and Galaxy Formation (2006, result): “This appears to be consistent with results from more detailed N-body simulations (e.g., Baumgardt & Makino 2003).”
The stellar and sub-stellar IMF of simple and composite populations (2011, background): “Old star clusters evolve through energy equipartition driven evaporation of low-mass stars (Vesperini & Heggie 1997; Baumgardt & Makino 2003).”
Cluster Mass Functions in the Large and Small Magellanic Clouds: Fading and Size-of-Sample Effects (2003, methodology): “The dashed line in Figure 7 is the evaporation limit, given by the equation (Baumgardt & Makino 2003) tevap = R/kpc V/220 km s−1 ( N ln (0.02N) )0.8 My (8) for cluster number N = M/ (0.547 M ), galactocentric radius R, and galactic orbit speed V in the LMC.”
From star clusters to dwarf galaxies: the properties of dynamically hot stellar systems (2008, background): “Considering the lifetimes Baumgardt & Makino (2003) expect for a sample of MWGCs (while accounting for the tidal field of the Galaxy) and their results for the development of the M/L ratio as a function of the star cluster lifetime, a decrease of the M/L ratio by about 0.1 M⊙ L −1 ⊙ to 0.3 M⊙ L −1…”
On the star formation rate – brightest cluster relation: estimating the peak star formation rate in post-merger galaxies (2008, background): “…cluster in the galaxy, given here as an example of the uncertainties in the method. to correct for mass loss due to tidal/dynamical effects, which are expected to be relatively small since the mass loss is inversely related to cluster mass (e.g. Baumgardt & Makino 2003; Lamers et al. 2005).”