The DRAGON globular cluster simulations: a million stars, black holes and gravitational waves

An international team of experts from China and Europe has performed the first simulations of globular clusters with a million stars on the high-performance GPU cluster of the Max Planck Computing and Data Facility. These – up to now - largest and most realistic simulations can not only reproduce observed properties of stars in globular clusters at unprecedented detail but also shed light into the dark world of black holes. The computer models produce high-quality synthetic data comparable to Hubble Space Telescope observations. They also predict nuclear clusters of single and binary black holes. The recently detected gravitational wave signal might have originated from a binary black hole merger in the center of a globular cluster.


Globular clusters are truly enigmatic objects. They consist of hundreds of thousands luminous stars and their remnants, which are confined to a few tens of parsecs (up to 100 lightyears) – they are the densest and oldest gravitationally bound stellar systems in the Universe. Their central star densities can reach a million times the stellar density near our Sun. About 150 globular clusters orbit the Milky Way but more massive galaxies can have over 10,000 gravitationally bound globular clusters. As their stars have mostly formed at the same time but with different masses, globular clusters are ideal laboratories for studies of stellar dynamics and stellar evolution.


The dynamical evolution of globular clusters, however, is very complex. Unlike in galaxies, the stellar densities are so high that stars can interact in close gravitational encounters or might even physically collide with each other. Because of these interactions there are more tightly bound binary stars than for normal galactic field stars. Moreover, in a process called mass-segregation more massive stars sink to the center of the system.


The evolution of a globular cluster as a whole is further complicated by the life cycle of both individual and binary stars. In the early phases, massive stars (with more than 8 solar masses) suffer significant mass-loss in a stellar wind phase and end their lifetime in core-collapse supernova explosions. The remnants of these long-gone stars are neutron stars or black holes; the latter with masses in the range of ten to fifty solar masses. They are invisible for normal electromagnetic observations and, until recently, could only be detected indirectly.

The light from globular clusters is dominated by just a few hundred very bright red giant stars. Most of the other stars in the systems have a much lower mass than our Sun and very low luminosity. This is why the Hubble Space Telescope has been a preferred instrument to observe the stellar population of globular clusters. Color-magnitude diagrams (CMD) obtained by Hubble have superior quality compared to ground-based instruments due to very low photometric errors (creating sharp structures like the main sequence or giant or white dwarf branches) and very high sensitivity. Hubble for the first time observed low-luminosity white dwarf features and low mass main sequences in high quality.


It has been a long-standing challenge to follow the evolution of a massive globular cluster with self-consistent numerical simulations. For the first time a team led by international experts at Peking University, MPA, the Chinese Academy of Sciences and has carried out the – up to now – most realistic simulations of the evolution of a globular cluster with initially one million stars orbiting in the tidal field of the Milky Way for about 12 billion years. The simulations carried out at the Hydra Supercomputer at the Max Planck Computing and Data Facility (MPCDF) as part of the international DRAGON project set a new standard in globular cluster modeling.


They have been possible after significant improvements of the simulation software on the laohu supercomputer of the Center of Information and Computing at National Astronomical Observatories, Chinese Academy of Sciences. The code has excellent parallel performance using, simultaneously, multi-node parallelization, OpenMP on the nodes and general-purpose Kepler K20 graphic cards acceleration (GPGPUs) to compute the gravitational forces between the stars. A typical DRAGON star cluster simulation used 8 nodes of Hydra with 160 CPU cores and about 32k GPU threads, for a consecutive computing time of the order of one year (8000 wall-clock hours).


The evolution of the stellar population of a globular cluster can now be followed in great detail through all its dynamical and stellar evolution phases, including the loss of stars in the tidal field of the Milky Way. The evolution of single and binary stars with a large range of masses (0.08 -100 solar masses) are followed through their major evolutionary phases. The DRAGON simulations have also been used to prepare synthetic color magnitude diagrams (CMD) as observed by Hubble.


In the DRAGON simulations the black holes – remnants of massive stars with masses of ten to fifty solar masses – form a dense nuclear cluster in the center of the system. In classical astronomy this black hole cluster can only be observed indirectly by its gravitational influence on the luminous – and observable – stars. A few dozen black holes form binaries and lose energy by gravitational radiation, a process included in our simulations.


Recently the LIGO collaboration has detected gravitational wave emission from a binary black hole coalescence (black hole masses of 36 and 29 solar masses) at a distance of 410 Mpc. Our DRAGON clusters produce such binary black hole mergers with similar parameters; about ten events in each cluster. Therefore we expect that more events will be observed in the coming months or years. A more detailed prediction for gravitational wave events from our models is under way. It depends not only on the internal evolution but also the number and distribution of globular clusters in the Universe. However, we predict that globular clusters – similar to our DRAGON clusters – are a possible origin of the recently observed spectacular gravitational wave event.


The now detected black hole merger event is probably only the tip of the iceberg. The dynamical evolution of the central regions of the simulated clusters is dominated by hundreds (if not thousands) of single and binary stellar mass black holes. Future studies should examine whether such clusters of stellar mass black holes exist in centers of most globular clusters rather than the predicted intermediate mass black holes.


The DRAGON project


The DRAGON project ( is a supercomputing initiative of NAOC/CAS and KIAA/PKU (Beijing), MPA (Garching), CAMK (Warsaw) and IoA (Cambridge) to investigate the evolution of globular clusters with GPU supported high-performance simulations. The team consists of Rainer Spurzem (supported by the Thousand Talents Program of People's Republic of China at National Astronomical Observatories of China (NAOC), Beijing and University of Heidelberg), Long Wang and Thijs (M.B.N.) Kouwenhoven (Kavli Institute for Astronomy and Astrophysics, Peking University), Peter Berczik (NAOC and Main Astronomical Observatory of National Academy of Sciences of Ukraine in Kiev), Sverre Aarseth (Institute of Astronomy, Cambridge), Mirek Giersz and Abbas Askar (Nicolaus Copernicus Astronomical Center, Warsaw), Thorsten Naab and Riko Schadow (Max-Planck-Institute for Astrophysics, Garching), and further students and collaborators. Computations are performed at the Max Planck Computing and Data Facility; software development and preliminary simulations at KIAA and the laohu cluster of NAOC.


Original Source:


Published papers


Wang, Long; Spurzem, Rainer; Aarseth, Sverre; Giersz, Mirek; Askar, Abbas; Berczik, Peter; Naab, Thorsten; Schadow, Riko; & Kouwenhoven & M.B.N.,  Monthly Notices of the Royal Astronomical Society, 458, 1450, 2016

The DRAGON simulations: globular cluster evolution with a million stars


Wang, Long; Spurzem, Rainer; Aarseth, Sverre; Nitadori, Keigo; Berczik, Peter; Kouwenhoven, M.B.N. & Naab, Thorsten, Monthly Notices of the Royal Astronomical Society, 450, 4070, 2015

NBODY6++GPU: ready for the gravitational million-body problem