Abstract
In order to investigate the formation rate of binary black holes (BBHs) in stellar clusters with a mass comparable to open clusters, we performed a series of direct N-body simulations of ...open clusters with a mass of 2.5 × 103 (Model A) and $10^4 \, \mathrm{M}_{\odot }$ (Model B). Since such low-mass clusters would have been more populous than globular clusters when they were born, low-mass clusters are also candidates as the origin of BBHs which are the source of the gravitational waves. In model A, most of BBHs merged within 10 Gyr formed via dynamically formed main-sequence binary stars and stable and unstable mass transfer between them since open clusters collapse within the main-sequence lifetime of massive stars. These binaries, therefore, have little eccentricities. The fraction of such binaries among all merging BBHs increases as the cluster mass decreases due to the shorter relaxation time. In our simulations, 4.0 × 10−5 and 1.7 × 10−5 BBHs per solar mass merged within 10 Gyr for models A and B, respectively. These values correspond to ∼20–50 per cent of the number of mergers per solar mass originated from globular clusters with a mass of 105–$10^6\, \mathrm{M}_{\odot }$. Thus, the contribution of BBHs originated from open clusters is not negligible. The estimated mergers rate density in the local Universe is about 0.3 yr−1 Gpc−3 assuming a cluster mass function with a power of −2.
ABSTRACT
Several binary black holes (BBHs) have been observed using gravitational wave detectors. For the formation mechanism of BBHs, two main mechanisms, isolated binary evolution and dynamical ...formation in dense star clusters, have been suggested. Future observations are expected to provide more information about BBH distributions, and it will help us to distinguish the two formation mechanisms. For the star cluster channel, globular clusters have mainly been investigated. However, recent simulations have suggested that BBH formation in open clusters is not negligible. We estimate a local merger rate density of BBHs originated from open clusters using the results of our N-body simulations of open clusters with four different metallicities. We find that the merger rate per cluster is the highest for our 0.1 solar metallicity model. Assuming a cosmic star formation history and a metallicity evolution with dispersion, we estimate the local merger rate density of BBHs originated from open clusters to be ∼70 yr−1 Gpc−3. This value is comparable to the merger rate density expected from the first and second observation runs of LIGO and Virgo. In addition, we find that BBH mergers obtained from our simulations can reproduce the distribution of primary mass and mass ratio of merging BBHs estimated from the LIGO and Virgo observations.
Abstract
We study the formation of massive black holes in the first star clusters. We first locate star-forming gas clouds in protogalactic haloes of ≳107 M⊙ in cosmological hydrodynamics simulations ...and use them to generate the initial conditions for star clusters with masses of ∼105 M⊙. We then perform a series of direct-tree hybrid N-body simulations to follow runaway stellar collisions in the dense star clusters. In all the cluster models except one, runaway collisions occur within a few million years, and the mass of the central, most massive star reaches ∼400–1900 M⊙. Such very massive stars collapse to leave intermediate-mass black holes (IMBHs). The diversity of the final masses may be attributed to the differences in a few basic properties of the host haloes such as mass, central gas velocity dispersion and mean gas density of the central core. Finally, we derive the IMBH mass to cluster mass ratios, and compare them with the observed black hole to bulge mass ratios in the present-day Universe.
ABSTRACT
Observations found that star clusters contain a large fraction of binaries. Tight binaries are an important heating source that influences the long-term dynamical evolution of star clusters. ...However, due to the limitation of N-body tool, previous theoretical modelling for globular clusters (GCs) by using direct N-body simulations has not investigated how a large fraction of primordial binaries affect their long-term evolution. In this work, by using the high-performance N-body code, petar, we carry out star-by-star models for intermediate massive GCs (N = 100 000) with the primordial binary fraction varying from 0 to 1. We find that when a stellar-mass black hole (BH) subsystem exists, the structural evolution of GCs (core and half-mass radii) only depends on the properties of massive primordial binaries, because they affect the number of BH binaries (BBHs), which dominate the binary heating process. Low-mass binaries including double white dwarf binaries (BWDs) have almost no influence on the dynamics. Meanwhile, only gravitational wave mergers from BBHs are strongly affected by dynamical interactions, while low-mass mergers from BWDs show no difference in the isolated environment (field) and in GCs. Low-mass binaries become important only after most BHs escape and the core collapse of light stars occurs. Our result suggests that for N-body modelling of GCs with a BH subsystem dominating binary heating, it is not necessary to include low-mass binaries. These binaries can be studied separately by using standalone binary stellar evolution codes. This way can significantly reduce the computing cost.
ABSTRACT
Dynamically formed black hole (BH) binaries (BBHs) are important sources of gravitational waves (GWs). Globular clusters (GCs) provide a major environment to produce such BBHs, but the total ...mass of the known GCs is small compared to that in the Galaxy; thus, the fraction of BBHs formed in GCs is also small. However, this assumes that GCs contain a canonical initial mass function (IMF) similar to that of field stars. This might not be true because several studies suggest that extreme dense and metal-poor environment can result in top-heavy IMFs, where GCs may originate. Although GCs with top-heavy IMFs were easily disrupted or have become dark clusters, the contribution to the GW sources can be significant. Using a high-performance and accurate N-body code, petar, we investigate the effect of varying IMFs by carrying out four star-by-star simulations of dense GCs with the initial mass of 5 × 105 M⊙ and the half-mass radius of 2 pc. We find that the BBH merger rate does not monotonically correlate with the slope of IMFs. Due to a rapid expansion, top-heavy IMFs lead to less efficient formation of merging BBHs. The formation rate continuously decreases as the cluster expands because of the dynamical heating caused by BHs. However, in star clusters with a top-heavier IMF, the total number of BHs is larger, and therefore, the final contribution to merging BBHs can still be more than that from clusters with the standard IMF, if the initial cluster mass and density are higher than those used in our model.
Abstract
We study the stellar dynamics of the first star clusters after intermediate-mass black holes (IMBHs) are formed via runaway stellar collisions. We use the outputs of cosmological simulations ...of Sakurai et al. to follow the star cluster evolution in a live dark matter (DM) halo. Mass segregation within a cluster promotes massive stars to be captured by the central IMBH occasionally, causing tidal disruption events (TDEs). We find that the TDE rate scales with the IMBH mass as $\dot{N}_{\rm TDE}\sim 0.3\, {\rm Myr} ^{-1}(M_{\rm IMBH}/1000\, {\rm M}_{\odot })^2$. The DM component affects the star cluster evolution by stripping stars from the outer part. When the DM density within the cluster increases, the velocity dispersion of the stars increases, and then the TDE rate decreases. By the TDEs, the central IMBHs grow to as massive as $700\hbox{--}2500\, {\rm M}_{\odot }$ in 15 million years. The IMBHs are possible seeds for the formation of supermassive BHs observed at $z$ ≳ 6–7, if a large amount of gas is supplied through galaxy mergers and/or large-scale gas accretion, or they might remain as IMBHs from the early epochs to the present-day Universe.
The Origin of OB Runaway Stars Fujii, Michiko S.; Zwart, Simon Portegies
Science,
12/2011, Letnik:
334, Številka:
6061
Journal Article
Recenzirano
Odprti dostop
About 20% of all massive stars in the Milky Way have unusually high velocities, the origin of which has puzzled astronomers for half a century. We argue that these velocities originate from strong ...gravitational interactions between single stars and binaries in the centers of star clusters. The ejecting binary forms naturally during the collapse of a young (≤ 1 milion years old) star cluster. This model replicates the key characteristics of OB runaways in our galaxy, and it explains the presence of runaway stars of ≥ 100 solar masses (M ⊚ ) around young star clusters, such as R136 and Westerlund 2. The high proportion and the distributions in mass and velocity of runaways in the Milky Way are reproduced if the majority of massive stars are born in dense and relatively low-mass (5000 to 10,000 M ⊚ ) clusters.
ABSTRACT Recent observations have revealed a variety of young star clusters, including embedded systems, young massive clusters, and associations. We study the formation and dynamical evolution of ...these clusters using a combination of simulations and theoretical models. Our simulations start with a turbulent molecular cloud that collapses under its own gravity. The stars are assumed to form in the densest regions in the collapsing cloud after an initial free-fall time of the molecular cloud. The dynamical evolution of these stellar distributions is continued by means of direct N-body simulations. The molecular clouds typical of the Milky Way Galaxy tend to form embedded clusters that evolve to resemble open clusters. The associations were initially considerably more clumpy, but they lost their irregularity in about a dynamical timescale, due to the relaxation process. The densest molecular clouds, which are absent in the Milky Way but are typical in starburst galaxies, form massive, young star clusters. They indeed are rare in the Milky Way. Our models indicate a distinct evolutionary path from molecular clouds to open clusters and associations or to massive star clusters. The mass-radius relation for both types of evolutionary tracks excellently matches the observations. According to our calculations, the time evolution of the half-mass-radius relation for open clusters and associations follows , whereas for massive star clusters . Both trends are consistent with the observed age-mass-radius relation for clusters in the Milky Way.
Abstract
Most stars are formed as star clusters in galaxies, which then disperse into galactic disks. Upcoming exascale supercomputational facilities will enable simulations of galaxies and their ...formation by resolving individual stars (star-by-star simulations). This will substantially advance our understanding of star formation in galaxies, star cluster formation, and assembly histories of galaxies. In previous galaxy simulations, a simple stellar population approximation was used. It is, however, difficult to improve the mass resolution with this approximation. Therefore, a model for forming individual stars that can be used in simulations of galaxies must be established. In this first paper of a series from the SIRIUS (SImulations Resolving IndividUal Stars) project, we demonstrate a stochastic star formation model for star-by-star simulations. An assumed stellar initial mass function (IMF) is randomly assigned to newly formed stars in this model. We introduce a maximum search radius to assemble the mass from surrounding gas particles to form star particles. In this study, we perform a series of N-body/smoothed particle hydrodynamics simulations of star cluster formations from turbulent molecular clouds and ultra-faint dwarf galaxies as test cases. The IMF can be correctly sampled if a maximum search radius that is larger than the value estimated from the threshold density for star formation is adopted. In small clouds, the formation of massive stars is highly stochastic because of the small number of stars. We confirm that the star formation efficiency and threshold density do not strongly affect the results. We find that our model can naturally reproduce the relationship between the most massive stars and the total stellar mass of star clusters. Herein, we demonstrate that our models can be applied to simulations varying from star clusters to galaxies for a wide range of resolutions.
We perform a set of cosmological simulations of early structure formation incorporating baryonic streaming motions. We present a case where a significantly elongated gas cloud with ∼104 solar mass (M ...) is formed in a pre-galactic (∼107 M ) dark halo. The gas streaming into the halo compresses and heats the massive filamentary cloud to a temperature of ∼10,000 Kelvin. The gas cloud cools rapidly by atomic hydrogen cooling, and then by molecular hydrogen cooling down to ∼400 Kelvin. The rapid decrease of the temperature and hence of the Jeans mass triggers fragmentation of the filament to yield multiple gas clumps with a few hundred solar masses. We estimate the mass of the primordial star formed in each fragment by adopting an analytic model based on a large set of radiation hydrodynamics simulations of protostellar evolution. The resulting stellar masses are in the range of ∼50-120 M . The massive stars gravitationally attract each other and form a compact star cluster. We follow the dynamics of the star cluster using a hybrid N-body simulation. We show that massive star binaries are formed in a few million years through multi-body interactions at the cluster center. The eventual formation of the remnant black holes will leave a massive black hole binary, which can be a progenitor of strong gravitational wave sources similar to those recently detected by the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO).
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