The study of how stars distribute themselves around a massive black hole (MBH) in the center of a galaxy is an important prerequisite for the understanding of many galactic-center processes. These include the observed overabundance of point X-ray sources at the Galactic center and the prediction of rates and characteristics of tidal disruptions of extended stars by the MBH and of inspirals of compact stars into the MBH, the latter being events of high importanceforthefuturespace-bornegravitationalwaveinterferometerLISA.Inrelativelysmallgalacticnucleihosting MBHs with masses in the range 10 5 –10 7 M� , the single most important dynamical process is two-body relaxation. It induces the formation of a steep density cusp around the MBH and strong mass segregation, as more massive stars loseenergytolighteronesand driftto thecentral regions. Usingaspherical stellardynamicalMonteCarlocode, we simulate the long-term relaxational evolution of galactic nucleus models with a spectrum of stellar masses. Our focus is the concentration of stellar black holes to the immediate vicinity of the MBH. We quantify this mass segregation for a variety of galactic nucleus models and discuss its astrophysical implications. Special attention is given to models developed to match the conditions in the Milky Way nucleus; we examine the presence of compact objects in connection to recent high-resolution X-ray observations. Subject headingg black hole physics — galaxies: nuclei — galaxies: star clusters — gravitational waves — methods: n-body simulations — stellar dynamics

/pdf/stellar-remnants-in-galactic-nuclei-mass-segregation-13u3mi9123.pdf

Stellar Remnants in Galactic Nuclei: Mass Segregation

We study the compact binary population in star clusters, focusing on binaries containing black holes, using a self-consistent Monte Carlo treatment of dynamics and full stellar evolution. We find that the black holes experience strong mass segregation and become centrally concentrated. In the core the black holes interact strongly with each other and black hole–black hole binaries are formed very efficiently. The strong interactions, however, also destroy or eject the black hole–black hole binaries. We find no black hole–black hole mergers within our simulations but produce many hard escapers that will merge in the Galactic field within a Hubble time. We also find several highly eccentric black hole–black hole binaries that are potential Laser Interferometer Space Antenna (LISA) sources, suggesting that star clusters are interesting targets for space-based detectors. We conclude that star clusters must be taken into account when predicting compact binary population statistics.

/pdf/compact-binaries-in-star-clusters-i-black-hole-binaries-432260t6uq.pdf

Compact binaries in star clusters – I. Black hole binaries inside globular clusters

The galactic population of globular clusters are old, dense star systems, with a typical cluster containing 104 - 106 stars. As an old population of stars, globular clusters contain many collapsed and degenerate objects. As a dense population of stars, globular clusters are the scene of many interesting close dynamical interactions between stars. These dynamical interactions can alter the evolution of individual stars and can produce tight binary systems containing one or two compact objects. In this review, we discuss the theoretical models of globular cluster evolution and binary evolution, techniques for simulating this evolution which lead to relativistic binaries, and current and possible future observational evidence for this population. Globular cluster evolution will focus on the properties that boost the production of hard binary systems and on the tidal interactions of the galaxy with the cluster, which tend to alter the structure of the globular cluster with time. The interaction of the components of hard binary systems alters the evolution of both bodies and can lead to exotic objects. Direct N-body integrations and Fokker-Planck simulations of the evolution of globular clusters that incorporate tidal interactions and lead to predictions of relativistic binary populations are also discussed. We discuss the current observational evidence for cataclysmic variables, millisecond pulsars, and low-mass X-ray binaries as well as possible future detection of relativistic binaries with gravitational radiation.

/pdf/relativistic-binaries-in-globular-clusters-296mh433rq.pdf

Relativistic Binaries in Globular Clusters

It is widely believed that globular clusters evolve over many two-body relaxation times toward a state of energy equipartition, so that velocity dispersion scales with stellar mass as \sigma ~ m^{-\eta} with \eta = 0.5. We show that this is incorrect, using direct N-body simulations with a variety of realistic IMFs and initial conditions. No simulated system ever reaches a state close to equipartition. Near the center, the luminous main-sequence stars reach a maximum \eta_{max} ~ 0.15 \pm 0.03. At large times, all radial bins convergence on an asymptotic value \eta_{\infty} ~ 0.08 \pm 0.02. The development of this "partial equipartition" is strikingly similar across our simulations, despite the range of initial conditions employed. Compact remnants tend to have higher \eta than main-sequence stars (but still \eta < 0.5), due to their steeper (evolved) mass function. The presence of an intermediate-mass black hole (IMBH) decreases \eta, consistent with our previous findings of a quenching of mass segregation under these conditions. All these results can be understood as a consequence of the Spitzer instability for two-component systems, extended by Vishniac to a continuous mass spectrum. Mass segregation (the tendency of heavier stars to sink toward the core) has often been studied observationally, but energy equipartition has not. Due to the advent of high-quality proper motion datasets from the Hubble Space Telescope, it is now possible to measure \eta. Detailed data-model comparisons open up a new observational window on globular cluster dynamics and evolution. Comparison of our simulations to Omega Cen observations yields good agreement, confirming that globular clusters are not generally in energy equipartition. Modeling techniques that assume equipartition by construction (e.g., multi-mass Michie-King models) are approximate at best.

No energy equipartition in globular clusters

Galactic globular clusters are old, dense star systems typically containing 10\super{4}--10\super{7} stars. As an old population of stars, globular clusters contain many collapsed and degenerate objects. As a dense population of stars, globular clusters are the scene of many interesting close dynamical interactions between stars. These dynamical interactions can alter the evolution of individual stars and can produce tight binary systems containing one or two compact objects. In this review, we discuss theoretical models of globular cluster evolution and binary evolution, techniques for simulating this evolution that leads to relativistic binaries, and current and possible future observational evidence for this population. Our discussion of globular cluster evolution will focus on the processes that boost the production of hard binary systems and the subsequent interaction of these binaries that can alter the properties of both bodies and can lead to exotic objects. Direct {\it N}-body integrations and Fokker--Planck simulations of the evolution of globular clusters that incorporate tidal interactions and lead to predictions of relativistic binary populations are also discussed. We discuss the current observational evidence for cataclysmic variables, millisecond pulsars, and low-mass X-ray binaries as well as possible future detection of relativistic binaries with gravitational radiation.

/pdf/relativistic-binaries-in-globular-clusters-4hk74dardy.pdf

We address the dynamical evolution of an isolated self-gravitating system with two stellar mass groups. We vary the individual ratio of the heavy to light bodies, μ from 1.25 to 50 and alter also the fraction of the total heavy mass M h from 5 to 40 per cent of the whole cluster mass. Clean-cut properties of the cluster dynamics are examined, like core collapse, the evolution of the central potential, as well as escapers. We present in this work collisional N-body simulations, using the high-order integrator NBODY6++ with up to Ν * = 2 x 10 4 particles improving the statistical significancy of the lower-N * simulations by ensemble averages. Equipartition slows down the gravothermal contraction of the core slightly. Beyond a critical value of μ ≈ 2, no equipartition can be achieved between the different masses; the heavy component decouples and collapses. For the first time, the critical boundary between Spitzer-stable and Spitzer-unstable systems is demonstrated in direct N-body models. We also present the measurements of the Coulomb logarithm and discuss the relative importance of the evaporation and ejection of escapers.

/pdf/a-comprehensive-nbody-study-of-mass-segregation-in-star-231f9nv1yz.pdf

A comprehensive nbody study of mass segregation in star clusters: energy equipartition and escape

We address the dynamical evolution of an isolated self--gravitating system with two stellar mass groups. We vary the individual ratio of the heavy to light bodies, $\mu$ from 1.25 to 50 and alter also the fraction of the total heavy mass $\MH$ from 5% to 40% of the whole cluster mass. Clean-cut properties of the cluster dynamics are examined, like core collapse, the evolution of the central potential, as well as escapers. We present in this work collisional $N$-body simulations, using the high--order integrator NBODY6++ with up to ${\cal N}_{\star}=2\cdot 10^4$ particles improving the statistical significancy of the lower--${\cal N}_{\star}$ simulations by ensemble averages. Equipartition slows down the gravothermal contraction of the core slightly. Beyond a critical value of $\mu \approx 2$, no equipartition can be achieved between the different masses; the heavy component decouples and collapses. For the first time the critical boundary between Spitzer--stable and --unstable systems is demonstrated in direct $N$-body models.

A comprehensive Nbody study of mass segregation in star clusters: Energy equipartition and escape

We present high-accuracy N-body simulations of isolated star clusters consisting of two distinct mass components, m 1 and m 2, and vary their relative ratio μ =m 2/m 1. The mass fraction of the more massive component relative to the total mass, q = M 2/M tot, is set equal to 0.1 in all cases. We determine the average star mass within a fixed ‘Lagrangian shell’. It is found that the time of first core collapse is reduced by the ratio μ with respect to a cluster with uniform masses.

Emil Khalisi

Papers

A comprehensive nbody study of mass segregation in star clusters: energy equipartition and escape

A comprehensive Nbody study of mass segregation in star clusters: Energy equipartition and escape

Shortening of core collapse time in star clusters with two mass components