Marc Freitag

Formation of Massive Black Holes in Dense Star Clusters. I. Mass Segregation and Core Collapse

We review possible dynamical formation processes for central massive black holes in dense star clusters. We focus on the early dynamical evolution of young clusters containing a few thousand to a few million stars. One natural formation path for a central seed black hole in these systems involves the development of the Spitzer instability, through which the most massive stars can drive the cluster to core collapse in a very short time. The sudden increase in the core density then leads to a runaway collision process and the formation of a very massive merger remnant, which must then collapse to a black hole. Alternatively, if the most massive stars end their lives before core collapse, a central cluster of stellar-mass black holes is formed. This cluster will likely evaporate before reaching the highly relativistic state necessary to drive a runaway merger process through gravitational radiation, thereby avoiding the formation of a central massive black hole. We summarize the conditions under which these different paths will be followed, and present the results of recent numerical simulations demonstrating the process of rapid core collapse and runaway collisions between massive stars.

Stellar remnants in galactic nuclei: Mass segregation

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 importance for the future space-borne gravitational wave interferometer LISA. In relatively small galactic nuclei hosting MBHs with masses in the range 10–10 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 lose energy to lighter ones and drift to the central regions. Using a spherical stellar dynamicalMonte Carlo code, 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 MilkyWay nucleus; we examine the presence of compact objects in connection to recent high-resolution X-ray observations. Subject headingg s: black hole physics — galaxies: nuclei — galaxies: star clusters — gravitational waves — methods: n-body simulations — stellar dynamics Online material: color figuresThe 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

Intermediate and extreme mass-ratio inspirals — astrophysics, science applications and detection using LISA

Black hole binaries with extreme (gtrsim104:1) or intermediate (~102–104:1) mass ratios are among the most interesting gravitational wave sources that are expected to be detected by the proposed laser interferometer space antenna (LISA). These sources have the potential to tell us much about astrophysics, but are also of unique importance for testing aspects of the general theory of relativity in the strong field regime. Here we discuss these sources from the perspectives of astrophysics, data analysis and applications to testing general relativity, providing both a description of the current state of knowledge and an outline of some of the outstanding questions that still need to be addressed. This review grew out of discussions at a workshop in September 2006 hosted by the Albert Einstein Institute in Golm, Germany.

Runaway collisions in young star clusters – I. Methods and tests

We present the methods and preparatory work for our study of the collisional runaway scenario to form a very massive star (VMS, M∗ > 400 M� ) at the centre of a young, compact stellar cluster. In the first phase of the process, a very dense central core of massive stars (M∗ � 30‐120 M � ) forms through mass segregation and gravothermal collapse. This leads to a collisional stage, likely to result in the formation of a VMS (itself a possible progenitor for an intermediate-mass black hole) through a runaway sequence of mergers between the massive stars. In this paper, we present the runaway scenario in a general astrophysical context. We then explain the numerical method used to investigate it. Our approach is based on a Monte Carlo code to simulate the stellar dynamics of spherical star clusters, using a very large number of particles (a few 10 5 to several 10 6 ). Finally, we report on test computations carried out to ensure that our implementation of the important physics is sound. In a second paper, we present results from more than 100 cluster simulations realized to determine the conditions leading to the collisional formation of a VMS and the characteristics of the runaway sequences.

Red giant stellar collisions in the Galactic Centre

We show that collisions with stellar-mass black holes can partially explain the absence of bright giant stars in the Galactic Centre, first noted by Genzel et al. We show that the missing objects are low-mass giants and asymptotic giant branch stars in the range 1-3 M-circle dot. Using detailed stellar evolution calculations, we find that to prevent these objects from evolving to become visible in the depleted K bands, we require that they suffer collisions on the red giant branch, and we calculate the fractional envelope mass losses required. Using a combination of smoothed particle hydrodynamic calculations, restricted three-body analysis and Monte Carlo simulations, we compute the expected collision rates between giants and black holes, and between giants and main-sequence stars in the Galactic Centre. We show that collisions can plausibly explain the missing giants in the 10.5 < K < 12 band. However, depleting the brighter (K < 10.5) objects out to the required radius would require a large population of black hole impactors which would in turn deplete the 10.5 < K < 12 giants in a region much larger than is observed. We conclude that collisions with stellar-mass black holes cannot account for the depletion of the very brightest giants, and we use our results to place limits on the population of stellar-mass black holes in the Galactic Centre.

A comprehensive set of simulations of high-velocity collisions between main-sequence stars

We report on a very large set of simulations of collisions between two main-sequence (MS) stars. These computations were carried out with the smoothed particle hydrodynamics method. Realistic stellar structure models for evolved MS stars were used. In order to sample an extended domain of initial parameters space (masses of the stars, relative velocity and impact parameter), more than 14 000 simulations were carried out. We considered stellar masses ranging between 0.1 and 75 M ○. and relative velocities up to a few thousand km s -1 . To limit the computational burden, a resolution of 1000-32 000 particles per star was used. The primary goal of this study was to build a complete data base from which the result of any collision can be interpolated. This allows us to incorporate the effects of stellar collisions with an unprecedented level of realism into dynamical simulations of galactic nuclei and other dense stellar clusters. We make the data describing the initial condition and outcome (mass and energy loss, angle of deflection) of all our simulations available on the Internet. We find that the outcome of collisions depends sensitively on the stellar structure and that, in most cases, using polytropic models is inappropriate. Published fitting formulae for the collision outcomes, established from a limited set of collisions, prove of limited use because they do not allow robust extrapolation to other stellar structures or relative velocities.

Accretion of stars on to a massive black hole: a realistic diffusion model and numerical studies

We present a study of the secular evolution of a spherical stellar system with a central star-accreting black hole (BH) using the anisotropic gaseous model. This method solves numerically moment equations of the full Fokker–Planck equation, with Boltzmann–Vlasov terms on the left-hand side and collisional terms on the right-hand side. We study the growth of the central BH due to star accretion at its tidal radius and the feedback of this process on to the core collapse as well as the post-collapse evolution of the surrounding stellar cluster in a self-consistent manner. Diffusion in velocity space into the loss cone is approximated by a simple model. The results show that the self-regulated growth of the BH reaches a certain fraction of the total mass cluster and agrees with other methods. Our approach is much faster than competing ones (Monte Carlo, N-body) and provides detailed information about the time- and space-dependent evolution of all relevant properties of the system. In this paper we present the method and study simple models (equal stellar masses, no stellar evolution or collisions). None the less, a generalization to include such effects is conceptually simple and under way.

Binary encounters with supermassive black holes: Zero-eccentricity LISA events

Current simulations of the rate at which stellar-mass compact objects merge with supermassive black holes (called extreme mass ratio in-spirals, or EMRIs) focus on two-body capture by emission of gravitational radiation. The gravitational wave signal of such events will likely involve a significant eccentricity in the sensitivity range of the Laser Interferometer Space Antenna(LISA). We show that tidal separation of stellar-mass compact object binaries by supermassive black holes will instead produce events whose eccentricity is nearly zero in the LISA band. Compared to two-body capture events, tidal separations have a high cross section and result in orbits that have a large pericenter and small apocenter. Therefore, the rate of interactions per binary is high, and the resulting systems are very unlikely to be perturbed by other stars into nearly radial plunges. Depending on the fraction of compact objects that are in binaries within a few parsecs of the center, the rate of low-eccentricity LISA events could be comparable to or larger than the rate of high-eccentricity events. Subject headings: binaries: general — galaxies: nuclei — gravitational waves — relativity

A new Monte Carlo code for star cluster simulations - I. Relaxation

We have developed a new simulation code aimed at studying the stellar dynamics of a galactic central star cluster surrounding a massive black hole. In order to include all the relevant physical ingredients (2-body relaxation, stellar mass spectrum, collisions, tidal disruption, ...) , we chose to revive an umerical scheme pioneered by H enon in the 70s (H enon 1971b,a; H enon 1973. It is basically a Monte Carlo resolution of the Fokker-Planck equation. It can cope with any stellar mass spectrum or velocity distribution. Being a particle-based method, it also allows one to take stellar collisions into account in a very realistic way. This rst paper covers the basic version of our code which treats the relaxation-driven evolution of a stellar cluster without a central BH. A technical description of the code is presented, as well as the results of test computations. Thanks to the use of a binary tree to store potential and rank information and of variable time steps, cluster models with up to 2 10 6 particles can be simulated on a standard personal computer and the CPU time required scales as Np ln(Np) with the particle number Np. Furthermore, the number of simulated stars needs not be equal to Np but can be arbitrarily larger. A companion paper will treat further physical elements, mostly relevant to galactic nuclei.

Intermediate-mass black holes in colliding clusters : Implications for lower frequency gravitational-wave astronomy

Observations suggest that star clusters often form in binar ies or larger bound groups. Therefore, mergers between two clusters are likely to occur. If these clusters both harbor an interme diate-mass black hole (IMBH; ∼ 10 2-4 M⊙) in their center, they can become a strong source of gravitational waves when the black holes merge with each other. In order to understand the dynamical processes that operate in such a scenario, one has to study the evolution of the merger of two such young massive star clusters, and more specifically, their respective IMBHs. We employ the direct-summation NBODY4 numerical tool on special-purpose GRAPE6 hardware to simulate a merger of two stellar clusters each containing 63,000 particles and a central IMBH. This allows us to study accurately the orbital evolution of the collidin g clusters and the embedded massive black holes. Within ∼ 7 Myr the clusters have merged and the IMBHs constitute a hard binary. The final coalescence happens in ∼ 10 8 yrs. The implication of our analysis is that intermediate-mass black holes merging as the result of coalescence of young dense clusters could provide a source for the Laser Interferometer Space Antenna (LISA) space-based gravitational wave detector mission. We find t hat interactions with stars increase the eccentricity of the IMBH binary to about 0.8. Although the binary later circularizes by emission of gravitational waves, the residual eccentricity can be dete ctable through its influence on the phase of the waves if the la st few years of inspiral are observed. For proposed higher-frequency space-based missions such as the Big Bang Observer (BBO), whose first purpose is to search for an inflation-generated gr avitational waves background in the 10 -1 - 1 Hz range, binary IMBH inspirals would be a foreground noise source. However, we fin d that the inspiral signals could be characterized accurate ly enough that they could be removed from the data stream and in the process provide us with detailed information about these astrophysical events. Subject headings:Black hole physics, gravitational waves, stellar dynamics, methods: N-body simulations