Objectives of the Research Program

GALNUC explores the dynamics of galactic nuclei by investigating the hierarchy of gravitational effects, building statistical physics and evolutionary models, and utilizing general methods often used in condensed matter physics. We use these models to explore fundamental questions about the collective behavior of a dense population of point masses and make observable predictions for electromagnetic surveys and also gravitational wave observatories like LIGO and VIRGO.

Introduction – The intriguing puzzles of the galactic center

The structure and evolution of galactic nuclei is among the most important open problems in astrophysics. Supermassive black holes (SMBHs) of mass 106 –109 Msun are found in the centers of most galaxies. These exotic objects are the engines that drive quasars and active galactic nuclei, and play an important role in galaxy formation through feedback to the interstellar medium. These massive objects are typically surrounded by a very dense population of stars. Due to its relative proximity, the center of the Milky Way provides a uniquely accessible laboratory to study the interactions between a massive black hole and the stellar system, to investigate the effects of extreme stellar number density with up to relativistic velocities, and to probe the central dark mass and post-Newtonian gravity in the weak- and strong-field limits.

Due to rapid technological advances, these environments become more and more accessible to observations, allowing us to test physical theories describing them (Alexander 2005, 2010). Our Galaxy contains a central black hole of mass 4x106 Msun associated with the radio source Sgr A*. Observations of the spatial distribution and kinematics of young massive stars in the Galactic center can be interpreted with the stars occupying one or possibly two disks between radii 0.05–0.5 pc (Genzel et al. 2010). The cluster also hosts a spherical population of old low-mass stars, and the innermost spherical population, called S-cluster.

FIGURE: Left: A schematic illustration of the dynamical components of galactic nuclei (Alexander 2010).

Right: Characteristic timescales of dynamical processes as a function of radius (Kocsis & Tremaine 2011)

The complexity of these systems arises due to the presence of several processes on vastly different temporal and spatial scales as shown in Figure 1 (right panel, adopted from Kocsis & Tremaine 2011). The most relevant processes are as follows:

1. First, the potential is dominated by the supermassive black hole; the corresponding orbit is the shortest timescale (1 – 104 yr). In the Keplerian approximation, the orbits are fixed, closed ellipses.
2. On longer timescales (104 – 105 yr), the spherical component of the Newtonian gravitational field of the cluster leads to the retrograde apsidal precession of the ellipses, and the first post- Newtonian relativistic correction leads to prograde precession, shown with magenta lines. The dotted magenta lines show the sum of these opposing effects. The Newtonian precession dominates outside of 0.007 pc.
3. On even longer timescales, the non-spherical gravitational field causes variations in the orientation of the orbital plane. This is due to the anisotropic Newtonian gravitational field of the stellar cluster and the post-Newtonian corrections for a spinning SMBH known as Lens-Thirring precession. The former is known as vector-resonant-relaxation (labeled “vector RR”, Rauch & Tremaine 1996). Over these timescales, the semimajor axis and eccentricity are still fixed.
4. On still longer timescales, the coherent gravitational torques that persist between stars on elliptic orbits lead to variations in the orbital eccentricity, a process known as scalar resonant relaxation (labeled "scalar RR").
5. Finally, the semimajor axis of the orbits can change due to two-body encounters on even longer timescales (108 –1010 yr, labeled "2 body").
6. Additional processes include the torques exerted by massive perturbers such as a molecular torus at ~1.5 pc, the two-body encounters between stars in a disk, collisions of stars, and tidal disruption of stars approaching the central SMBH.

The picture is yet more complex if the stellar cluster contains different mass stellar constituents. In this case, the heavier objects sink to the center at the expense of the lighter stars moving outwards on the dynamical friction timescale, which is proportional to the two body relaxation timescale times the inverse mass of the object relative to the average stellar mass in the cluster. Similar processes, which we may call resonant dynamical friction, lead to mass segregation in eccentricity and inclination. Note that 20,000 stellar mass black holes are expected to reside in the Galactic center, which have individually larger masses than typical stars, and thus might be expected to segregate to the inner parts of the cluster (O’Leary, Kocsis, & Loeb 2009).

The commonly assumed theoretical paradigm is strongly challenged by recent observations of the Galactic center (see below). The key open questions include the following (see Alexander 2005, 2010, Genzel et al. 2010).

1. Is the stellar system relaxed?
2. What is the origin of the stellar disk?
3. Is there a “dark cusp” or “dark disk” of black holes around the SMBH?
4. What is the origin of the S-stars?
5. Are there intermediate mass black holes (IMBHs) in the Galactic center?

These questions have a profound significance, as they lead to a deeper understanding of galaxy formation and the coevolution of supermassive black holes and dense stellar clusters, and have implications for future tests of General Relativity (GR) in the strong field limit and gravitational wave observations.

Moving Beyond Standard Methods of Astrophysical Dynamics

The large number of stars (107) and vast range of spatial and temporal scales (10-6 – 1 pc and 10 – 1010 yr), as well as the long-range spatial and temporal correlations of the forces involved in resonant relaxation, prohibit the accurate dynamical modeling of these environments using existing direct N-body, smoothed particle hydrodynamics (SPH) simulations, or Fokker-Planck diffusion models without additional insight (see reviews by Alexander 2005, 2010, Genzel 2010). Resonant effects play a major role, which are sensitive to the number, mass distribution, and radial range of stars, and the initial conditions. The effects of spatially varying numerical diffusion may substantially bias the result. However, the hierarchy of timescales in these stellar systems leads to adiabatic invariants, and algorithms that enforce their conservation can increase numerical accuracy and decrease computational demands. Similar symplectic algorithms are often employed in planetary dynamics (Wisdom & Holman 1991). Furthermore, these systems are expected to be chaotic, which evolve toward statistical equilibrium; great insight may be gained by exploring its statistical mechanics (see also Lynden-Bell & Wood 1968, Kocsis & Tremaine 2011). This calls for techniques well known in statistical and condensed matter physics, which are not often utilized in astrophysics. These include the mean field theory of canonical and microcanonical ensembles, Monte Carlo Markov Chains of the statistical equilibrium, quenched order/disorder, and molecular dynamics. We emphasize that these methods are very general; they only require the knowledge of the effective interaction Hamiltonian, but they are in no way limited to known systems of condensed matter physics.

Utilizing techniques of condensed matter physics in astrophysics

We investigate these questions from a new perspective using insights from statistical and condensed matter physics. First, we examine the dynamical evolution of a system of point masses neglecting gas effects, appropriate for galactic nuclei without a significant gas fraction, such as our own Galaxy at present. The stars in the stellar disk are a few million years old. To understand the dynamics on these timescales, one can focus on vector resonant relaxation (see discussion above), averaging the Hamiltonian over the shorter timescales, i.e. the Keplerian orbit and the apsidal precession, and neglecting the effects on much longer timescales, e.g. two-body relaxation. The result is a Hamiltonian, for which the semimajor axis and eccentricity are conserved for each star, but the orientations of the orbits (i.e. the angular momentum normal vectors \(\hat{L}_i\)) can slowly change. The Hamiltonian is the sum of the pairwise gravitational potential energy between the stellar orbits smeared out over their precessing orbits. The leading order terms are quadrupolar

$$H = {1 \over 2} \sum_{i,j} A_{ij} (\hat{L}_i \cdot \hat{L}_j)^2$$

where the sum runs over all pairs of stars, and \(A_{ij}\) are constant coefficients which depend on the semimajor axes, eccentricities, and masses. For circular orbits \(A_{ij} = -GM_i M_j r_{<}^2 / r_>^3\), where \(r_{<} = \min(r_i ,r_j )\) and \(r_{>} = \max(r_i ,r_j )  \). Upon inspection, this is reminiscent of the Heisenberg model of ferromagnetism, where L plays the role of the elementary spin of the lattice cell. The main difference is the second power exponent, due to the fact that the potential energy is invariant under the reversal of the orbital direction if averaging over the precession time. Coincidentally, this Hamiltonian is known as the Maier-Saupe model of liquid crystals in condensed matter physics (Maier & Saupe 1959). This connection is naturally explained by the fact that the geometry of axisymmetric liquid crystal molecules is similar to the stellar orbits smeared over a precession cycle, and the Coulomb and Newtonian gravitational interactions are very similar. The Maier-Saupe model neglects multipoles beyond quadrupolar and therefore gives the same Hamiltonian as the one given above.

This tantalizing analogy provides insight for understanding the collective behavior of stellar orbits in galactic nuclei. The phase diagram of liquid crystals is similar to that of ferromagnetism. In both cases, the ground state is the configuration in which the orientation vectors of the spins or liquid crystal molecules are aligned (or possibly antialigned for liquid crystals). Due to the large-scale alignment of spins, a macroscopic magnetic field is generated; this is the magnetized phase of ferromagnets. As the temperature increases, thermal motion, or entropy, competes with the ferromagnetic tendency for dipoles to align. Beyond a critical temperature, called the Curie temperature, the system can no longer maintain a spontaneous magnetization, it undergoes a phase transition as the spins become isotropically distributed. While the phase transition is continuous (second-order) for ferromagnets, it is abrupt (first-order) for liquid crystals.

A similar phase transition may be expected for the orientations of stellar orbits as a function of mass and radius. Assuming equipartition, different stars have the same interaction energy. The Hamiltonian given above for star \(i\) is proportional to \(-M_i \cos(I)^2 \), where \(I\) is the RMS inclination. To keep this product fixed, massive objects segregate into a thin disk with a smaller RMS inclination, at the expense of lighter stars going to a spherical distribution (Rauch & Tremaine 1996). Since liquid crystals exhibit first order phase transitions, we may expect the distribution to go from a disk-like structure to a spherical distribution very abruptly. These expectations are consistent with the observed distribution of stellar orbits in the Galactic center. Since black holes are more massive than typical stars, they are expected to settle to disk-like distributions, forming the densest population of compact objects in the centers of galaxies and in globular clusters.

Implications

This study has become particularly timely due to the recent detections of gravitational waves from mergers of black holes by LIGO and VIRGO. The recent discovery of gravitational waves opened new horizons for understanding the Universe and further developments are expected in the near future with new Earth and space-based instruments. The measurements have unveiled an abundant population of stellar mass black hole mergers in the Universe. The great challenge is to understand the possible astrophysical environments in which mergers may be most common. The GALNUC project aims to solve this challenge to gain a deeper understanding of the Universe.

Publications

1. Disrupted Globular Clusters Can Explain the Galactic Center Gamma Ray Excess
   T. Brandt, B. Kocsis
   The Astrophysical Journal, Volume 812, article id. 15 (2015) [arXiv] [Scientific American] [Blog] [Zenodo]
2. Dynamical Formation Signatures of Black Hole Binaries in the First Detected Mergers by LIGO
   R. M. OLeary, Y. Meiron, B. Kocsis
   The Astrophysical Journal Letters, Volume 824, article id. L12 (2016) [arXiv] [Blogs]
3. Merging binaries in the Galactic Center: the eccentric Kozai-Lidov mechanism with stellar evolution
   A. P. Stephan, S. Naoz, A. M. Ghez, G. Witzel, B. N. Sitarski, T. Do, B. Kocsis
   Monthly Notices of the Royal Astronomical Society, Volume 460, Issue 3494 (2016) [arXiv]
4. The influence of mergers and ram-pressure stripping on black hole-bulge correlations
   Y. B. Ginat, Y. Meiron, N. Soker
   Monthly Notices of the Royal Astronomical Society, Volume 461, Issue 3533 (2016) [arXiv]
5. Star-disc interaction in galactic nuclei: orbits and rates of accreted stars
   G. F. Kennedy, Y. Meiron, B. Shukirgaliyev, T. Panamarev, P. Berczik, A. Just, R. Spurzem
   Monthly Notices of the Royal Astronomical Society, Volume 460, Issue 240 (2016) [arXiv]
6. Rapid and Bright Stellar-mass Binary Black Hole Mergers in Active Galactic Nuclei
   I. Bartos, B. Kocsis, Z. Haiman, S. Márka
   The Astrophysical Journal, Volume 835, article id. 165 (2017) [arXiv]
7. Detecting Triple Systems with Gravitational Wave Observations
   Y. Meiron, B. Kocsis, A. Loeb
   The Astrophysical Journal, Volume 834, article id. 200 (2017) [arXiv]
8. Isotropic-Nematic Phase Transitions in Gravitational Systems
   Z. Roupas, B. Kocsis, S. Tremaine
   The Astrophysical Journal, Volume 842, article id. 90 (2017) [arXiv]
9. Testing the binary hypothesis: pulsar timing constraints on supermassive black hole binary candidates
   A. Sesana, Z. Haiman, B. Kocsis, L. Z. Kelley
   The Astrophysical Journal, Volume 856, article id. 42 (2018) [arXiv]
10. Accuracy of Estimating Highly Eccentric Binary Black Hole Parameters with Gravitational-Wave Detections
    L. Gondán, B. Kocsis, P. Raffai, Z. Frei
    The Astrophysical Journal, Volume 855, article id. 34 (2018) [arXiv]
11. Eccentric Black Hole Gravitational-Wave Capture Sources in Galactic Nuclei: Distribution of Binary Parameters
    L. Gondán, B. Kocsis, P. Raffai, Z. Frei
    The Astrophysical Journal, Volume 860, article id. 5 (2018) [arXiv]
12. Black Hole Mergers in Galactic Nuclei Induced by the Eccentric Kozai-Lidov Effect
    B. Hoang, S. Naoz, B. Kocsis, F. A. Rasio, F. Dosopoulou
    The Astrophysical Journal, Volume 856, article id. 140 (2018) [arXiv] [astrobites]
13. Gamma-ray and X-ray emission from the Galactic centre: hints on the nuclear star cluster formation history
    M. Arca-Sedda, B. Kocsis, T. Brandt
    Monthly Notices of the Royal Astronomical Society, Volume 479, Issue 900 (2018) [arXiv]
14. Hidden universality in the merger rate distribution in the primordial black hole scenario
    B. Kocsis, T. Suyama, T. Tanaka, S. Yokoyama
    The Astrophysical Journal, Volume 854, article id. 41 (2018) [arXiv]
15. Gravitational Waves and Intermediate-Mass Black Hole Retention in Globular Clusters
    G. Fragione, I. Ginsburg, B. Kocsis
    The Astrophysical Journal, Volume 856, article id. 92 (2018) [arXiv]
16. Isotropic-Nematic Phase Transitions in Gravitational Systems II: Higher Order Multipoles
    A. Takács, B. Kocsis
    The Astrophysical Journal, Volume 856, article id. 113 (2018) [arXiv]
17. Diffusion and mixing in globular clusters
    Y. Meiron, B. Kocsis
    The Astrophysical Journal, Volume 855, article id. 87 (2018) [arXiv]
18. Spiral arms, warping, and clumps formation in the Galactic center young stellar disk
    H. B. Perets, A. Mastrobuono-Battisti, Y. Meiron, A. Gualandris
    submitted to Science (2018) [arXiv]
19. Star-disc interaction in galactic nuclei: formation of a central stellar disc
    T. Panamarev, B. Shukirgaliyev, Y. Meiron, P. Berczik, A. Just, R. Spurzem, C. Omarov, E. Vilkoviskij
    Monthly Notices of the Royal Astronomical Society, Volume 476, Issue 4224 (2018) [arXiv]
20. Merger of multiple accreting black holes concordant with gravitational wave events
    H Tagawa, M. Umemura
    The Astrophysical Journal, Volume 856, article id. 47 (2018) [arXiv] [astrobites]
21. Metallicity dependence of the Hercules stream in Gaia/RAVE data -- explanation by non-closed orbit
    K. Hattori, N. Gouda, T. Yano, N. Sakai, H. Tagawa, J. Baba, J. Kumamoto
    Monthly Notices of the Royal Astronomical Society, Volume 484, Issue 4 (2018) [arXiv]
22. Compact object mergers driven by gas fallback
    H. Tagawa, B. Kocsis, T. R. Saitoh
    Physical Review Letters, 120, 261101 (2018) [arXiv]
23. Tidal Disruption Events and Gravitational Waves from Intermediate Mass Black Holes in Evolving Globular Clusters Across Space and Time
    G. Fragione, N. Leigh, I. Ginsburg, B. Kocsis
    The Astrophysical Journal, Volume 856, article id. 92 (2018) [arXiv]
24. Black hole disks in galactic nuclei
    Á. Szölgyén, B. Kocsis
    Physical Review Letters, 121, 101101 (2018) [arXiv] [astronomy.com] [news]
25. Black hole mergers from an evolving population of globular clusters
    G. Fragione, B. Kocsis
    Physical Review Letters, 121, 161103 (2018) [arXiv]
26. Black holes, gravitational waves and fundamental physics: a roadmap
    L. Barack, et al.; chapter I.5 by A. Askar and B. Kocsis
    Classical and Quantum Gravity, Volume 36, Issue 14 (2019) [arXiv]
27. Resonant relaxation in globular clusters
    Y. Meiron, B. Kocsis
    The Astrophysical Journal, Volume 878, article id. 138 (2019) [arXiv]
28. Hypervelocity Stars from a Supermassive Black Hole-Intermediate Mass Black Hole binary
    A. Rasskazov, G. Fragione, N. W. C. Leigh, H. Tagawa, A. Sesana, A. Price-Whelan, E. M. Rossi
    The Astrophysical Journal, Volume 878, article id. 17 (2019) [arXiv]
29. The impact of stripped Nuclei on the Super-Massive Black Hole number density in the local Universe
    K. T. Voggel, A. C. Seth, H. Baumgardt, S. Mieske, J. Pfeffer, A. Rasskazov
    The Astrophysical Journal, Volume 871, article id. 159 (2019) [arXiv]
30. Measurement Accuracy of Inspiraling Eccentric Neutron Star and Black Hole Binaries Using Gravitational Waves
    L. Gondán, B. Kocsis
    The Astrophysical Journal, Volume 871, article id. 178 (2019) [arXiv]
31. Localization of Binary Black-Hole Mergers with Known Inclination
    K. R. Corley, I. Bartos, L. P. Singer, A. R. Williamson, Z. Haiman, B. Kocsis, S. Nissanke, Z. Márka, S. Márka
     Monthly Notices of the Royal Astronomical Society, Volume 488, Issue 3 (2019) [arXiv]
32. The rate of stellar mass black hole scattering in galactic nuclei
    A. Rasskazov, B. Kocsis
    The Astrophysical Journal, Volume 881, article id. 20 (2019) [arXiv]
33. Detecting Supermassive Black Hole-Induced Binary Eccentricity Oscillations with LISA
    B-M. Hoang, S. Naoz, B. Kocsis, W. Farr, J. McIver
    The Astrophysical Journal Letters, Volume 875, article id. L31 (2019) [arXiv]
34. AGN Disks Harden the Mass Distribution of Stellar-mass Binary Black Hole Mergers
    Y. Yang, I. Bartos, Z. Haiman, B. Kocsis, Z. Marka, N. C. Stone, S. Marka
    The Astrophysical Journal, Volume 876, article id. 122 (2019) [arXiv]
35. Black Hole Mergers from Quadruples
    G. Fragione, B. Kocsis
    Monthly Notices of the Royal Astronomical Society, Volume 486, Issue 4 (2019) [arXiv]
36. Anisotropic Mass Segregation in Rotating Globular Clusters
    Á. Szölgyén, Y. Meiron, B. Kocsis
    The Astrophysical Journal, Volume 887, article id. 123 (2019) [arXiv]
37. Tidal disruption events onto stellar black holes in triples
    G .Fragione, N. W. C. Leigh, R. Perna, B. Kocsis
    Monthly Notices of the Royal Astronomical Society, Volume 489, Issue 1 (2019) [arXiv]
38. Hierarchical Black Hole Mergers in Active Galactic Nuclei
    Y. Yang, I. Bartos, V. Gayathri, S. Ford, Z. Haiman, S. Klimenko, B. Kocsis, S. Márka, Z. Márka, B. McKernan, R. O'Shaugnessy Physical Review Letters, 123, 181101 (2019) [arXiv]
39. Effective spin distribution of black hole mergers in triples
    G .Fragione, B. Kocsis
    Monthly Notices of the Royal Astronomical Society, Volume 493, Issue 3 (2019) [arXiv]
40. Electromagnetic transients and gravitational waves from white dwarf disruptions by stellar black holes in triple systems
    G. Fragione, B. D. Metzger, R. Perna, N. W. C. Leigh, B. Kocsis
    Monthly Notices of the Royal Astronomical Society, Volume 495, Issue 1, pp.1061-1072 (2020) [arXiv]
41. Intermediate-mass black holes' effect on compact object binaries
    B. Deme, Y. Meiron, B. Kocsis
    The Astrophysical Journal, Volume 892, Issue 2, id.130, 10 pp. (2020) [arXiv]
42. Binary intermediate-mass black hole mergers in globular clusters
    A. Rasskazov, G. Fragione, B. Kocsis
    The Astrophysical Journal, Volume 899, Issue 2, id.149 (2020) [arXiv]
43. Formation and Evolution of Compact Object Binaries in AGN Disks
    H. Tagawa, Z. Haiman, B. Kocsis
    The Astrophysical Journal, Volume 898, Issue 1, id.25 (2020) [arXiv]
44. Making a supermassive star by stellar bombardment
    H. Tagawa, Z. Haiman, B. Kocsis
    The Astrophysical Journal, Volume 892, article id. 36 (2020) [arXiv]
45. GW170817A as a Hierarchical Black Hole Merger
    V. Gayathri, I. Bartos, Z. Haiman, S. Klimenko, B. Kocsis, S. Marka, Y. Yang
    The Astrophysical Journal Letters, Volume 890, article id. L20 (2020) [arXiv]
46. On the eccentricity evolution of massive black hole binaries in stellar backgrounds
    M. Bonetti, A. Rasskazov, A. Sesana, M. Dotti, F. Haardt, N. W. C. Leigh, M. Arca Sedda, G. Fragione, E. Rossi
    Monthly Notices of the Royal Astronomical Society: Letters, Volume 493, Issue 1, p.L114-L119 (2020) [arXiv]
47. Cosmic Evolution of Stellar-mass Black Hole Merger Rate in Active Galactic Nuclei
    Y. Yang, I. Bartos, Z. Haiman, B. Kocsis, S. Márka, H. Tagawa
    The Astrophysical Journal, Volume 896, Issue 2, id.138, 5 pp. (2020) [arXiv]
48. Detecting Kozai-Lidov Imprints on the Gravitational Waves of Intermediate-mass Black Holes in Galactic Nuclei
    B. Deme, B.-M. Hoang, S. Naoz, B. Kocsis
    The Astrophysical Journal, Volume 901, Issue 2, id.125 (2020)[arXiv]
49. Spin Evolution of Stellar-mass Black Hole Binaries in Active Galactic Nuclei
    H. Tagawa, Z. Haiman, I. Bartos, B. Kocsis
    The Astrophysical Journal, Volume 899, Issue 1, id.26 (2020)
50. A Canonical Transformation to Eliminate Resonant Perturbations. I.
    B. Deme, B. Kocsis
    The Astronomical Journal, Volume 162, Issue 1, id.22, 11 pp. (2021)
51. Eccentric Black Hole Mergers in Active Galactic Nuclei
    H. Tagawa, B. Kocsis, Z. Haiman, I. Bartos, K. Omukai, J. Samsing
    The Astrophysical Journal Letters, Volume 907, Issue 1, id.L20 (2021)
52. Mass-gap Mergers in Active Galactic Nuclei
    H. Tagawa, B. Kocsis, Z. Haiman, I. Bartos, K. Omukai, J. Samsing
    The Astrophysical Journal, Volume 908, Issue 2, id.194 (2021)
53. Order in the chaos. Eccentric black hole binary mergers in triples formed via strong binary-binary scatterings
    M. Arca-Sedda, G. Li, B. Kocsis
    Astronomy & Astrophysics, Volume 650, id.A189 (2021)
54. Thermal equilibrium of an ideal gas in a free-floating box
    S. Tremaine, B. Kocsis, A. Loeb
    American Journal of Physics, Volume 89, Issue 8, p.789-792 (2021)
55. High eccentricities and high masses characterize gravitational-wave captures in galactic nuclei as seen by Earth-based detectors
    L. Gondán, B. Kocsis
    Monthly Notices of the Royal Astronomical Society, Volume 506, Issue 2, pp.1665-1696 (2021)
56. Resonant Dynamical Friction in Nuclear Star Clusters: Rapid Alignment of an Intermediate-mass Black Hole with a Stellar Disk
    Á. Szölgyén, G. Máthé, B. Kocsis
    The Astrophysical Journal, Volume 919, Issue 2, id.140 (2021)
57. First- and second-generation black hole and neutron star mergers in 2+2 quadruples: population statistics
    A. S. Hamers, G. Fragione, P. Neunteufel, B. Kocsis
    Monthly Notices of the Royal Astronomical Society, Volume 506, Issue 4, pp.5345-5360 (2021)
58. Signatures of hierarchical mergers in black hole spin and mass distribution
    H. Tagawa, Z. Haiman, I. Bartos, B. Kocsis, K. Omukai
    Monthly Notices of the Royal Astronomical Society, Volume 507, Issue 3, pp.3362-3380 (2021)
59. Formation of supermassive black hole seeds in nuclear star clusters via gas accretion and runaway collisions
    Das, Arpan; Schleicher, Dominik R. G.; Leigh, Nathan W. C.; Boekholt, Tjarda C. N.
    Monthly Notices of the Royal Astronomical Society, Volume 503, Issue 1, pp.1051-1069 (2021)
60. Stellar collisions in flattened and rotating Population III star clusters
    Vergara, M. Z. C.; Schleicher, D. R. G.; Boekholt, T. C. N.; Reinoso, B.; Fellhauer, M.; Klessen, R. S.; Leigh, N. W. C.
    Astronomy & Astrophysics, Volume 649, id.A160, 10 pp. (2021)
61. Effect of mass-loss due to stellar winds on the formation of supermassive black hole seeds in dense nuclear star clusters
    Das, Arpan; Schleicher, Dominik R. G.; Basu, Shantanu; Boekholt, Tjarda C. N.
    Monthly Notices of the Royal Astronomical Society, Volume 505, Issue 2, pp.2186-2194 (2021)
62. Relativistic Pythagorean three-body problem
    Boekholt, Tjarda C. N.; Moerman, Arend; Portegies Zwart, Simon F.
    Physical Review D, Volume 104, Issue 8, article id.083020 (2021)
63. Astrophysical Gravitational-Wave Echoes from Galactic Nuclei
    L. Gondán, B. Kocsis
    submitted to MNRAS
64. Active Galactic Nuclei as Factories for Eccentric Black Hole Mergers
    J. Samsing, I. Bartos, D. J. D'Orazio, Z. Haiman, B. Kocsis, N. W. C. Leigh, B. Liu, M. E. Pessah, H. Tagawa
    submitted to Nature
65. Stellar triples on the edge; Comprehensive overview of the evolution of destabilised triples leading to stellar and binary exotica
    Toonen, S.; Boekholt, T. C. N.; Portegies Zwart, S.
    submitted
66. Chaos in self-gravitating many-body systems: Lyapunov time dependence of N and the influence of general relativity
    Portegies Zwart, Simon F. ; Boekholt, Tjarda C. N. ; Por, Emiel ; Hamers, Adrian S. ; McMillan, Steve L. W.
    submitted

Conference presentations

1. Bence Kocsis, contributed talk, “Disrupted globular clusters explain gamma-ray excess in the Galactic center”,
    28th Texas Symposium on Relativistic Astrophysics, Geneva, Switzerland, December 2015
2. Bence Kocsis, invited talk, “Liquid crystals of stars and black holes at the centers of galaxies”,
   Dynamics and accretion at the Galactic Center, Aspen, CO, February 2016
3. Bence Kocsis, contributed talk, “Liquid crystals of stars and black holes at the centers of galaxies”,
   MTA Statistical Physics Day, Hungarian Academy of Sciences, Hungary, April 2016
4. Bence Kocsis, invited talk, “Liquid crystals of stars and gravitational resonant phase transitions”,
   The secular evolution of self-gravitating systems over cosmic ages, Paris, France, May 2016
5. Bence Kocsis, invited talk, “Gravitational wave astrophysics, the dawn of a new era”,
   Discovery of gravitational waves, Hungarian Academy of Sciences, Hungary, May 2016
6. Yohai Meiron, contributed talk, “Dynamical formation signatures of black hole binaries”,
   Star Clusters – Dynamics and Observations, Heidelberg, June 2016
7. Zacharias Roupas, poster presentation, “Isotropic nematic phase transitions in gravitating systems”,
   Long-Range Interacting Many-Body Systems, Trieste, Italy, July 2016
8. Bence Kocsis, invited plenary talk, “Gravitational wave astrophysics, the dawn of a new era”,
   Hungarian Physicist Meeting, Szeged, Hungary, August 2016.
9. Zacharias Roupas, contributed talk, “Gravitational liquid crystals”,
   NEB-17 Recent Developments in Gravity, Mykonos, Greece, September 2016
10. Yohai Meiron, conference participation, "Perspectives of GPU Computing in Science", September 2016
11. Bence Kocsis, invited talk, “Sources of Gravitational Waves”,
    100 years of relativity, NKE, Budapest, Hungary, November 2016.
12. Bence Kocsis, invited talk,  “Disentangling LIGO sources in dense stellar systems”,
    The Dawning Era of Gravitational Wave Astrophysics, Aspen, CO, February 2017.
13. Bence Kocsis, contributed talk, “Liquid crystals of stars and black holes at the centers of galaxies”,
    MTA Statistical Physics Day, Hungarian Academy of Sciences, Hungary, April 2017.
14. Bence Kocsis, contributed talk, “Gravitational wave sources in galactic nuclei and dense systems”,
    MODEST17, Prague, Czechia, September 2017
15. Yohai Meiron, contributed talk, “Relaxation and mixing in globular clusters”,
    MODEST17, Prague, Czechia, September 2017
16. Alexander Rasskazov, contributed talk,
    “Evolution of massive black hole binaries in rotating stellar nuclei and its implications for gravitational wave detections”, MODEST17, Prague, Czechia, September 2017
17. Bence Kocsis, contributed talk, “Gravitational wave sources in galactic nuclei”,
    Stellar Dynamics in Galactic Nuclei, Institute for Advanced Study, Princeton, USA, November 2017
18. Yohai Meiron, poster presentation, “Stellar dynamics with N-body simulations”,
    Stellar Dynamics in Galactic Nuclei, Institute for Advanced Study, Princeton, USA, November 2017
19. Alexander Rasskazov, poster presentation,
    “Evolution Of Massive Black Hole Binaries In Rotating Stellar Nuclei: Implications For Gravitational Wave Detection”,
    Stellar Dynamics in Galactic Nuclei, Institute for Advanced Study, Princeton, USA, November 2017
20. Bence Kocsis, invited talk, Gravity@Malta 2018 COST Action
    "Gravitational Waves, Black Holes and Fundamental Physics", Malta, January 2018
21. Hiromichi Tagawa, contributed talk, "Compact object mergers driven by gas fallback",
    Gravitational wave physics and astronomy: Genesis, University of Tokyo, Japan, March 2018
22. Bence Kocsis, invited talk, “EM counterparts for LISA sources”,
    Sackler Conference 2018: Gravitational Wave Astrophysics, Harvard University, Cambridge, MA, USA, May 2018
23. Idan Ginsburg, poster presentation, “Gravitational waves and Intermediate Mass Black Hole retention in Globular Clusters”, Sackler Conference 2018: Gravitational Wave Astrophysics, Harvard University, Cambridge, MA, USA, May 2018
24. Bence Kocsis, contributed talk, “Distinguishing Source Populations with LIGO/VIRGO”,
    MODEST-18 Dense Stellar Systems in the Era of Gaia, LIGO, & LISA, Santorini, Greece, June 2018
25. Alexander Rasskazov, contributed talk, “The Rate of GW Capture of Stellar-mass BHs in Nuclear Star Clusters”,
    MODEST-18 Dense Stellar Systems in the Era of Gaia, LIGO, & LISA, Santorini, Greece, June 2018
26. Ákos Szölgyén, contributed talk, “Disks of Black Holes in Galactic Nuclei”,
    MODEST-18 Dense Stellar Systems in the Era of Gaia, LIGO, & LISA, Santorini, Greece, June 2018
27. Giacomo Fragione, contributed talk, “IMBHs in GCs – Retention, GWs and Tidal Disruption Events”,
    MODEST-18 Dense Stellar Systems in the Era of Gaia, LIGO, & LISA, Santorini, Greece, June 2018
28. Hiromichi Tagawa, poster presentation, “Compact Object Mergers Driven by Gas Fallback”,
    MODEST-18 Dense Stellar Systems in the Era of Gaia, LIGO, & LISA, Santorini, Greece, June 2018
29. Yohai Meiron, poster presentation, “Resonant Relaxation in Globular Clusters”,
    MODEST-18 Dense Stellar Systems in the Era of Gaia, LIGO, & LISA, Santorini, Greece, June 2018
30. Yohai Meiron, invited talk, “Resonant relaxation in globular clusters”,
    Star Clusters around the Milky Way and in the Local Group, Heidelberg, Germany, August 2018
31. Ákos Szölgyén, invited talk, “Anisotropic mass segregation in stellar systems”,
    Star Clusters around the Milky Way and in the Local Group, Heidelberg, Germany, August 2018
32. Hiromichi Tagawa, poster presentation, “Compact Object Mergers Driven by Gas Fallback”,
    IAU General Assembly, Vienna, Austria, August 2018
33. Bence Kocsis, contributed talk,
    “Gravitational waves and high energy electromagnetic waves from disrupted globular clusters”,
    MWStreams: Survival of Dense Star Clusters in the Milky Way System, MPIA Heidelberg, Germany, November 2018
34. Alexander Rasskazov, contributed talk,
    “Hypervelocity stars from a supermassive black hole-intermediate mass black hole binary”,
    MWStreams: Survival of Dense Star Clusters in the Milky Way System, MPIA Heidelberg, Germany, November 2018
35. Bence Kocsis, invited talk, “Gravitation al waves from disrupted globular clusters”,
    Astrophysics with Gravitational-Wave Populations, Aspen, USA, February 2019
36. Hiromichi Tagawa, contributed talk, “Formation and evolution of compact object binaries in active galactic nuclei”,
    Astrophysics with Gravitational-Wave Populations, Aspen, USA, February 2019
37. Alexander Rasskazov, poster presentation, “The Rate of GW Capture of Stellar- mass BHs in Nuclear Star Clusters”, Astrophysics with Gravitational-Wave Populations, Aspen, USA, February 2019
38. Ákos Szölgyén, poster presentation, "Anisotropic Mass Segregation in Rotating Globular Clusters",
    MODEST-19 Star Clusters: from the Milky Way to the Early Universe, Bologna, Italy, May 2019
39. Barnabás Deme, poster presentation, "Black hole binary disruptions via intermediate mass black holes"
    MODEST-19 Star Clusters: from the Milky Way to the Early Universe, Bologna, Italy, May 2019
40. Bence Kocsis, invited talk, "On the Origin of Gravitational Wave Sources observed by LIGO/VIRGO"
    Modern theories of gravity, Hungarian Academy of Sciences, Budapest, Hungary, May 2019
41. Alexander Rasskazov, contributed talk, "Hypervelocity stars from a supermassive black hole - intermediate mass black hole binary", Stars on the run II, Potsdam, Germany, August 2019
42. Hiromichi Tagawa, contributed talk, “Keep Growing to Super Massive Star via Runaway Collision”,
    Cosmic Evolution of Quasars: from the First Light to Local Relics, China, October 2019
43. Alexander Rasskazov, contributed talk, "Merger rate of binary intermediate-mass black holes",
    The new faces of black holes, Annapolis MD, USA, November 2019
44. Alexander Rasskazov, contributed talk, "Hypervelocity star production by a supermassive black hole - intermediate mass black hole binary and its dynamical evolution",
    The Origins of Black Hole Mergers and Gravitational Waves, Leiden, Netherlands, December 2019
45. Tjarda Boekholt, contributed talk, "Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length",
    AAS Division on Dynamical Astronomy meeting #52, June 2021
46. Tjarda Boekholt, colloquium talk, "Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length", University of Coimbra, 21 April 2021
47. Tjarda Boekholt, colloquium talk, "Chaotic triples and their irreversibility to the Planck length",
    TRENDY-3, 24 March 2021

Workshop presentations

1. Bence Kocsis, invited talk, “Dynamics in nuclear star clusters”,
   Galactic nuclei at high resolution in many dimensions, Alajar Meeting, Alajar, Spain, October 2015
2. Bence Kocsis and Yohai Meiron, Dense Stellar Environments as a Probe of Astrophysics and General Relativity: What can we learn from the first GW detection?, Benasque, June 2016
3. Bence Kocsis, invited talk, “Eccentric LIGO sources”,
   Astrophysics of Gravitational Radiation Sources and Multimessenger Astronomy in the Era of LIGO Detections,
   Aspen, CO, July 2017
4. Gergely Máthé, student talk, “Statistical physics of gravitational systems”,
   The 16th international scientific Baikal Summer School on Physics of Elementary Particles and Astrophysics,
   Russia, July 2016
5. Gergely Máthé, poster presentation, “A numerical study the statistical physics of vector resonant relaxation”,
   48th Saas-Fee course: Black hole formation and growth, Saas-Fee, Switzerland, January 2018
6. Ákos Szölgyén, poster presentation, “Anisotropic Mass Segregation of Black Hole Orbits in Galactic Nuclei”,
   48th Saas-Fee course: Black hole formation and growth, Saas-Fee, Switzerland, January 2018
7. Bence Kocsis, invited talk, “The origin of black hole mergers seen by LIGO”,
   Eötvös Loránd Physics Society Summer School, Matrahaza, Hungary, September 2018
8. Bence Kocsis, invited talk, "Populations & Dynamics in Galactic Nuclei",
   CCA workshop on stellar mass black hole mergers in AGN disks, Flatiron Insitute, USA, March 2019
9. Gergely Máthé, Kavli RISE Summer School on Gravitational Waves,
   University of Cambridge, Cambridge, United Kingdom, September 2019
10. Ákos Szölgyén, Kavli RISE Summer School on Gravitational Waves,
    University of Cambridge, Cambridge, United Kingdom, September 2019
11. Hiromichi Tagawa, contributed talk, “Formation and Evolution of Compact Object Binaries in Active Galactic Nuclei”,
    Multi-Messenger Astrophysics in the Gravitational Wave Era, Kyoto, Japan, October 2019

Institutional talks, other talks

1. Bence Kocsis, invited institutional talk, “Liquid crystals of stars and black holes at the centers of galaxies”,
   Ortvay Colloquium, Eötvös University, Hungary, September 2015
2. Bence Kocsis, invited institutional talk, “Liquid crystals of stars and black holes at the centers of galaxies”,
   Astrophysics Colloquium, Leiden, Netherlands, October 2015
3. Bence Kocsis, invited institutional talk, “Liquid crystals of stars and black holes at the centers of galaxies”,
   Astrophysics Seminar, Konkoly Observatory, Hungary, November 2015
4. Bence Kocsis, invited institutional talk, “Gravitational wave astrophysics”,
   Physics Seminar, Bolyai College, Hungary, March 2016
5. Yohai Meiron, invited institutional talk, “Interaction between stars and disks around supermassive black holes”,
   Astrophysics Seminar, Konkoly Observatory, Hungary, March 2016
6. Bence Kocsis, invited institutional talk, “Astrophysical liquid crystals”,
   Statistical Physics Seminar, Eötvös University, Hungary, April 2016
7. Bence Kocsis, invited institutional talk, “Liquid crystals of stars and black holes at the centers of galaxies",
   RESCEU Colloquium, University of Tokyo, Japan, June 2016
8. Bence Kocsis, invited institutional talk, “Liquid crystals of stars and black holes at the centers of galaxies”,
   Astrophysics Colloquium, Kyoto University, Japan, July 2016
9. Yohai Meiron, invited institutional talk, “Triple companion in gravitational wave signals”,
   Galaxies and Cosmology Seminar, Max-Planck-Institut für Astronomie, Germany, July 2016
10. Yohai Meiron, invited institutional talk, “Triple companion in gravitational wave signals”,
    Silk Road Tea Seminar, Zentrum für Astronomie (Astronomisches Rechen-Institut), Germany, August 2016
11. Yohai Meiron, invited institutional talk, “Triple companion in gravitational wave signals”,
    KIAA Lunch talk, Peking University (Kavli Institute), China, September 2016
12. Yohai Meiron, invited institutional talk, “Triple companion in gravitational wave signals”,
    Seminar, Academy of Mathematics and Systems Science, China, September 2016
13. Bence Kocsis, invited institutional talk, “Phase transitions in astrophysical liquid crystals”,
    Wigner SZFI Seminar, Wigner Institute, Hungary, October 2016
14. Bence Kocsis, invited institutional talk, “Astrophysical implications of LIGO gravitational wave detections”,
    Physics Colloquium, University of Bern, Switzerland, October 2016
15. Bence Kocsis, invited institutional talk, “Dynamical origin of black hole mergers”,
    Physics Seminar, Sapienza University of Rome, Italy, November 2016
16. Bence Kocsis, invited institutional talk, “Dynamical origin of black hole mergers”, Particle Physics Seminar,
    Eötvös University, Hungary, November 2016
17. Yohai Meiron, invited institutional talk, “Triple companion in gravitational wave signals”,
    Astrophysics seminar, Technion, Israel, January 2017
18. Bence Kocsis, invited institutional talk, “Black hole disks at the centers of galaxies”,
    Black Hole Initiative Colloquium, Harvard University, USA, February 2017
19. Yohai Meiron, invited institutional talk, “Triple companion in gravitational wave signals”,
    Particle Physics Seminar, Eotvos University, Hungary, May 2017
20. Yohai Meiron, invited institutional talk, “Triple companion in gravitational wave signals”,
    Seminar, University of Waterloo, Canada, June 2017
21. Yohai Meiron, invited institutional talk, “Status of the hybrid code and mixing in clusters”,
    Silk Road Tea Seminar, Zentrum für Astronomie (Astronomisches Rechen-Institut), Germany, July 2017
22. Yohai Meiron, invited institutional talk, “Relaxation and mixing of constants of motion in globular clusters”,
    Seminar, Peking University (Kavli Institute), China, September 2017
23. Bence Kocsis, invited institutional talk, “Gravitational wave sources in galactic nuclei and dense systems”,
    DARK seminar, Niels Bohr Institute, Copenhagen, Denmark, Oct. 2017
24. Bence Kocsis, invited institutional talk, “Eccentric sources of gravitational waves”,
    Bahcall Lunch, Institute for Advanced Study, Princeton, USA, November 2017
25. Ákos Szölgyén, invited student talk, “Gravitational waves: a beginning of a new astronomy”,
    Bolyai János High School, December 2017
26. Bence Kocsis, invited institutional talk, “Open questions on the interpretation of black hole mergers seen by LIGO”,
    GALNUC Seminar, Eötvös University, Hungary, March 2018.
27. Bence Kocsis, invited institutional talk, “Stellar Dynamics and Gravitational wave astrophysics in the GALNUC Project”,
    ELTE Astronomy Talent Day, Eötvös University, Hungary, April 2018
28. Bence Kocsis, invited institutional talk, “Liquid crystals of stars and black holes at the centers of galaxies”,
    CERN Cosmo Coffee, Geneva, Switzerland, January 2019
29. Bence Kocsis, invited institutional talk, “On the Origin of Gravitational Wave Sources Observed by LIGO/VIRGO”,
    CERN Particle and Astro-particle Seminar, Geneva, Switzerland, January 2019.
30. Bence Kocsis, invited institutional talk, “On the Origin of Gravitational Wave Sources Observed by LIGO/VIRGO”,
    Astrophys. and Cosm. Relativity Seminar, AEI, Potsdam, Germany, March 2019
31. Barnabás Deme, invited institutional talk, "Restricted and hierarchical three-body problem",
    Research Group Seminar, UCLA, Los Angeles, USA, March 2019
32. Bence Kocsis, invited institutional talk, "Liquid crystals of stars and black holes at the centers of galaxies",
    Special seminar, Oxford Department of Physics, May 2019
33. Bence Kocsis, invited institutional talk, “Compact object mergers due to gas fall back”,
    Santa Barbara Astro Lunch, UCSB, Santa Barbara, USA, May 2019
34. Bence Kocsis, invited institutional talk, “On the Origin of Gravitational Wave Sources observed by LIGO/VIRGO”,
    Astrophysics Colloquium, Kyoto University, Kyoto, Japan, July 2019
35. Bence Kocsis, invited institutional talk, “On the Origin of Gravitational Wave Sources observed by LIGO/VIRGO",
    Physics Seminar, Bolyai College, Hungary, October 2019
36. Alexander Rasskazov, invited institutional talk, "Observational signatures of intermediate-mass black holes",
    CIERA theory seminar, Northwestern University, Chicago, USA, November 2019
37. Hiromichi Tagawa, invited institutional talk, “Formation and evolution of compact object binaries in active galactic nuclei",
    Theoretical Seminar, Tohoku University, Japan, January 2020
38. Bence Kocsis, invited institutional talk, "On the Origin of Gravitational Wave Sources Observed by LIGO/VIRGO",
    Konkoly Seminar, Hungary, February 2020
39. Bence Kocsis, invited institutional talk, "On the Origin of Gravitational Wave Sources Observed by LIGO/VIRGO",
    CSH-CEH Virtual Seminar Series, University of Bern, Switzerland, virtual, April 2020
40. Bence Kocsis, invited institutional talk, "Mergers in AGN",
    Informal Astrophysics Coffee Seminar, Institute for Advanced Study, USA, virtual, September 2020
41. Bence Kocsis, invited institutional talk, "On the Origin of Gravitational Wave Sources Observed by LIGO/VIRGO",
    Astrophysics Colloquium, Oxford, virtual, November 2020
42. Bence Kocsis, invited institutional talk, "On the AGN Origin of Gravitational Wave Sources Observed by LIGO/VIRGO",
    ITC Colloquium, Harvard, virtual, November 2020
43. Bence Kocsis, invited institutional talk, "On the AGN Origin of Gravitational Wave Sources Observed by LIGO/VIRGO",
    Astrophysics Colloquium, KIAA Peking University, virtual, November 2020
44. Bence Kocsis, invited institutional talk, "On the AGN Origin of Gravitational Wave Sources Observed by LIGO/VIRGO",
    Astrophysics Seminar, Brno University, virtual, April 2021
45. Bence Kocsis, invited institutional talk, "On the AGN Origin of Gravitational Wave Sources Observed by LIGO/VIRGO",
    Astrophysics Colloquium, Georgia Tech, virtual, September 2021
46. Bence Kocsis, invited institutional talk, "On the AGN Origin of Gravitational Wave Sources Observed by LIGO/VIRGO",
    Astrophysics Seminar, Institut d'Astrophysique de Paris, virtual, September 2021
47. Bence Kocsis, invited institutional talk, "On the AGN Origin of Gravitational Wave Sources Observed by LIGO/VIRGO",
    Astrophysical Fluid Dynamics Seminar, Cambridge, virtual, October 2021