Dynamical Evolution of the Mass Function of Globular Star Clusters

By S. M. Fall, Qing Zhang. 2001

306 citations recorded by the source corpus.

We present a series of simple, largely analytical models to compute the effects of disruption on the mass function of star clusters. Our calculations include evaporation by two-body relaxation and gravitational shocks and mass loss by stellar evolution. We find that, for a wide variety of initial conditions, the mass function develops a turnover or peak and that, after 12 Gyr, this is remarkably close to the observed peak for globular clusters, at Mp ≈ 2 × 105 M☉. Below the peak, the evolution is dominated by two-body relaxation, and the mass function always develops a tail of the form ψ(M) = const, reflecting that the masses of tidally limited clusters decrease linearly with time just before they are destroyed. This also agrees well with the empirical mass function of globular clusters in the Milky Way. Above the peak, the evolution is dominated by stellar evolution at early times and by gravitational shocks at late times. These processes shift the mass function to lower masses, while nearly preserving its shape. The radial variation of the mass function within a galaxy depends on the initial position-velocity distribution of the clusters. We find that some radial anisotropy in the initial velocity distribution, especially when this increases outward, is needed to account for the observed near-uniformity of the mass functions of globular clusters. This may be consistent with the observed near-isotropy of the present velocity distributions, because clusters on elongated orbits are preferentially destroyed. These results are based on models with static, spherical galactic potentials. We point out that there would be even more radial mixing of the orbits and hence more uniformity of the mass function if the galactic potentials were time-dependent and/or nonspherical.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/23d64cbf8fd377daed36cd7397a31eb1ff9c17ed

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Citations in the corpus

Globular Cluster Systems in Brightest Cluster Galaxies: Bimodal Metallicity Distributions and the Nature of the High-Luminosity Clusters (2005, background): “Recent simulations accounting for this (e.g. Fall & Zhang 2001; Vesperini et al. 2003) indicate that these most massive clusters would, however, still take up ∼ 20 percent or more of the GCS mass at earlier times.”
Implications for the formation of star clusters from extragalactic star formation rates (2004, background): “Smaller clusters dissolve fast through dynamical effects (gas expulsion, stellardynamical heating, galactic tidal field) and only massive clusters survive for a significant fraction of a Hubble time (Vesperini 1998; Fall & Zhang 2001; Baumgardt & Makino 2003).”
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 Luminosity Function of Star Clusters in Spiral Galaxies (2002, background): “The low-mass end of the old GC mass spectrum is likely to be strongly affected by dynamical evolution (Fall & Zhang 2001; Vesperini 2000, 2001), but for masses above 105 M the mass distribution is well approximated by a power-law with slope about 1.9 (Kissler et al. 1994; Kissler-Patig, Richtler,…”
Globular cluster systems in nearby dwarf galaxies – III. Formation efficiencies of old globular clusters (2010, background): “…cluster relaxation), which shapes the initial power-law to the observed, present-day Gaussian globular cluster luminosity function (GCLF, see e.g. Fall & Zhang 2001; Goudfrooij et al. 2004, 2007; Gieles et al. 2006; McLaughlin & Fall 2008; Kruijssen & Portegies Zwart 2009; Elmegreen 2010, and…”
The life cycle of star clusters in a tidal field (2011, background): “Since in the homologous phaseτrh ∝ M , there should also be a uniform distribution ofM at low mass, ordN/dM ≃ const (Hénon 1961; Fall & Zhang 2001), which is indeed found in many galaxies (Jordán et al. 2007).”
STELLAR FEEDBACK IN MOLECULAR CLOUDS AND ITS INFLUENCE ON THE MASS FUNCTION OF YOUNG STAR CLUSTERS (2009, background): “For young clusters, such a feature is not observed (as noted above), while for globular clusters, it arises from almost any initial conditions as a consequence of stellar escape driven by two-body relaxation over ∼ 1010 yr (Fall & Zhang 2001; McLaughlin & Fall 2008, and references therein).”
On the fraction of star formation occurring in bound stellar clusters (2012, background): “…clusters would then be caused by differences in the birth environment (e.g. Kravtsov & Gnedin 2005; Elmegreen 2010; Shapiro, Genzel & Förster Schreiber 2010; Kruijssen et al. 2012b) and a Hubble time of dynamical evolution (e.g. Elmegreen & Efremov 1997; Fall & Zhang 2001; Vesperini 2001).”
The Age Distribution of Massive Star Clusters in the Antennae Galaxies (2005, background): “This causes the mass function of the clusters, although initially a power law, to evolve in a Hubble time into one with a peak or turnover at Mp ≈ 2 × 10 5 M⊙, similar to that of old globular clusters (Fall & Zhang 2001 and references therein).”
Young Massive Star Clusters (2010, background): “…then could originate from the long timescale phase-3 dynamical evolution, this evolution could severre the relatively low-mass (M <∼ MTO) clusters more whereas it leaves the high-mass (M >∼ MTO) clusters unaffected (Elmegreen & Efremov 1997, Vesperini 1997, Baumgardt 1998, Fall & Zhang 2001, ?).”
Dynamical evolution of star clusters in tidal fields (2002, background): “Similarly, Fall & Zhang (2001) found by semi-analytical modeling that at present between 5 to 8% of all globular clusters are destroyed per Gyr, which corresponds to 7 to 11 clusters.”
THE ANTENNAE GALAXIES (NGC 4038/4039) REVISITED: ADVANCED CAMERA FOR SURVEYS AND NICMOS OBSERVATIONS OF A PROTOTYPICAL MERGER (2010, methodology): “Based on Fall & Zhang (2001) we might expect this turnover to occur around MV ≈ −4, assuming that most of the outer clusters are 100–300 yr old and that two-body relaxation is the dominant process.”
Formation of Globular Clusters in Hierarchical Cosmology (2003, background): “Fall & Zhang (2001) have demonstrated that these processes naturally transform the initial power law into the observed truncated mass function of old GCs.”
The ACS Virgo Cluster Survey. XII. The Luminosity Function of Globular Clusters in Early-Type Galaxies (2007, methodology): “The mass function of such a cluster ensemble with any aget is then related to the initial one as in equation (11) of Fall & Zhang (2001): dN dM(t) = dN dM0 @M0 @M = dN dM0 : (6) Thus, simply making the substitutionM0 = M + evt in the functional form of the original GC mass function gives the…”
Extragalactic Globular Clusters and Galaxy Formation (2006, methodology): “Vesperini et al. (2003) explored M87 in detail, and (reminiscent of Fall & Zhang 2001) found that the observed log-normal GCLF, which has a constant turnover with radius (see also Harris et al. 1998), could only evolve from a power-law initial GCLF if there were (unobserved) strong radial…”
Multiple populations in globular clusters (2012, background): “These mechanisms might have transformed a power law (Fall and Zhang 2001; Vesperini and Zepf 2003; Boley et al. 2009; Elmegreen 2010) or a Press–Schechter (Ricotti 2002) initial distribution of masses, generally found for young objects (see the review in Gieles 2009), into the currently observed app”
Star Cluster Demographics. I. A General Framework and Application to the Antennae Galaxies (2006, methodology): “3 of Fall & Zhang 2001) andM87 (Waters et al. 2006) agree with this functional form.”
Globular clusters as the relics of regular star formation in ‘normal’ high-redshift galaxies (2015, methodology): “…insensitivity of the GCMF peak mass and the specific frequency to the host galaxy mass or the galactocentric radius (at fixed metallicity), unless the strong environmental dependence of evaporationis ignored (as in e.g.Fall & Zhang 2001; Prieto & Gnedin 2008; Katz & Ricotti 2014; Li & Gnedin 2014).”
Star cluster formation and disruption time-scales — I. An empirical determination of the disruption time of star clusters in four galaxies (2002, background): “Theoretical and dynamical simulations (e.g. Spitzer 1957; Portegies Zwart et al. 1999; Fall & Zhang 2001) both suggest that disruption results in a linear decrease of the mass of a cluster with time, rather than the sudden disappearance that we adopted in this study.”