Monte Carlo Simulations of Star Clusters - VII. The globular cluster 47 Tuc

We describe Monte Carlo models for the dynamical evolution of the massive globular cluster 47 Tuc (NGC 104). The code includes treatments of two-body relaxation, most kinds of three- and four-body interactions involving primordial binaries and those formed dynamically, the Galactic tide, and the internal evolution of both single and binary stars. We arrive at a set of initial parameters for the cluster which, after 12Gyr of evolution, gives a model with a fairly satisfactory match to surface brightness and density profiles, the velocity dispersion profile, the luminosity function in two fields, and the acceleration of pulsars. Our models appear to require a relatively steep initial mass function for stars above about turnoff, with an index of about 2.8 (where the Salpeter mass function has an index of 2.35), and a relatively flat initial mass function (index about 0.4) for the lower main sequence. According to the model, the current mass is estimated at 0.9 million solar masses, of which about 34% consists of remnants. We find that primordial binaries are gradually taking over from mass loss by stellar evolution as the main dynamical driver of the core. Despite the high concentration of the cluster, core collapse will take at least another 20Gyr.

💡 Research Summary

The paper presents a comprehensive Monte‑Carlo study of the massive Galactic globular cluster 47 Tucanae (NGC 104), aiming to reproduce its present‑day structural and kinematic properties after 12 Gyr of dynamical evolution. The authors employ a sophisticated Monte‑Carlo code that simultaneously treats two‑body relaxation, a wide range of three‑ and four‑body interactions (including those involving primordial binaries and dynamically formed binaries), the external Galactic tidal field, and the internal stellar evolution of both single stars and binaries. By varying the initial total mass, half‑mass radius, primordial binary fraction, and especially the shape of the initial mass function (IMF), they search for a set of initial conditions that yields a model matching multiple observational constraints: surface‑brightness and density profiles, the line‑of‑sight velocity‑dispersion profile, luminosity functions measured in two distinct fields, and the measured accelerations of millisecond pulsars in the core.

A key outcome is that the best‑fit IMF must be steeper than the classic Salpeter law for stars above the turn‑off mass, with a power‑law index of ≈ 2.8 (Salpeter = 2.35), while the low‑mass end must be unusually flat, with an index of ≈ 0.4. This combination yields a present‑day cluster mass of roughly 9 × 10⁵ M⊙, of which about 34 % is in compact remnants (white dwarfs, neutron stars, and black holes). The high remnant fraction reflects the initially top‑heavy IMF and the cumulative mass loss from stellar evolution over a Hubble time.

The dynamical analysis shows that, although early evolution is dominated by mass loss from stellar winds and supernovae, the long‑term driver of core dynamics switches to the heating supplied by primordial binaries. As the cluster ages, binaries sink toward the centre via mass segregation, and their frequent three‑ and four‑body encounters inject kinetic energy into the core, counteracting the tendency toward core collapse. Consequently, despite the cluster’s high concentration, the model predicts that core collapse will not occur for at least another ~20 Gyr. This delayed collapse underscores the importance of binary heating in massive, dense clusters and suggests that many Galactic globular clusters may be in a prolonged pre‑collapse phase.

The inclusion of the Galactic tidal field does not significantly alter the inner structure, indicating that internal processes dominate the present configuration of 47 Tuc. Moreover, the agreement with pulsar acceleration data demonstrates that the spatial distribution of massive remnants is realistically reproduced, lending confidence to the model’s treatment of mass segregation and dynamical friction.

Overall, the study demonstrates that a Monte‑Carlo approach, when equipped with realistic treatments of stellar evolution, binary dynamics, and external tides, can successfully reproduce the multi‑observable properties of a complex system like 47 Tuc. The findings highlight the sensitivity of present‑day cluster characteristics to the assumed IMF and binary fraction, and they provide a valuable benchmark for future simulations of other dense globular clusters.