ABSTRACT
Black hole (BH) binary mergers formed through dynamical interactions in dense star clusters are believed to be one of the main sources of gravitational waves (GWs) for Advanced LIGO and ...Virgo. Here, we present a fast numerical method for simulating the evolution of star clusters with BHs, including a model for the dynamical formation and merger of BH binaries. Our method is based on Hénon’s principle of balanced evolution, according to which the flow of energy within a cluster must be balanced by the energy production inside its core. Because the heat production in the core is powered by the BHs, one can then link the evolution of the cluster to the evolution of its BH population. This allows us to construct evolutionary tracks of the cluster properties including its BH population and its effect on the cluster and, at the same time, determine the merger rate of BH binaries as well as their eccentricity distributions. The model is publicly available and includes the effects of a BH mass spectrum, mass-loss due to stellar evolution, the ejection of BHs due to natal and dynamical kicks, and relativistic corrections during binary–single encounters. We validate our method using direct N-body simulations, and find it to be in excellent agreement with results from recent Monte Carlo models of globular clusters. This establishes our new method as a robust tool for the study of BH dynamics in star clusters and the modelling of GW sources produced in these systems. Finally, we compute the rate and eccentricity distributions of merging BH binaries for a wide range of cluster initial conditions, spanning more than two orders of magnitude in mass and radius.
Black hole binaries formed dynamically in globular clusters are believed to be one of the main sources of gravitational waves in the Universe. Here, we use our new population synthesis code, CBHBd, ...to determine the redshift evolution of the merger rate density and masses of black hole binaries formed in globular clusters. We simulate ~ 2 million models to explore the parameter space that is relevant to real globular clusters and overall mass scales. We show that when uncertainties on the initial cluster mass function and their initial half-mass density are properly taken into account, they become the two dominant factors in setting the theoretical error bars on merger rates. Uncertainties in other model parameters (e.g., natal kicks, black hole masses, and metallicity) have virtually no effect on the local merger rate density, although they affect the masses of the merging black holes. Modeling the merger rate density as a function of redshift as R(z) = R0 (1 + z)κ at z < 2 , and marginalizing over uncertainties, we find: ... (90% credibility). The rate parameters for binaries that merge inside the clusters are ... and ... ~ 20 % of these form as the result of a gravitational-wave capture, implying that eccentric mergers from globular clusters contribute ≲ 0.4 Gpc−3 yr−1 to the local rate. A comparison to the merger rate reported by Laser Interferometer Gravitational Wave Observatory-Virgo shows that a scenario in which most of the detected black hole mergers are formed in globular clusters is consistent with current constraints and requires initial cluster half-mass densities ≳104 M⊙pc−3 . Interestingly, these models also reproduce the inferred black hole mass function in the range 13 – 30 M⊙ . However, all models underpredict the data outside this range, suggesting that other mechanisms might be responsible for the formation of these sources. (ProQuest: ... denotes formula omitted.)
Abstract
In a star cluster with a sufficiently large escape velocity, black holes (BHs) that are produced by BH mergers can be retained, dynamically form new BH binaries, and merge again. This ...process can repeat several times and lead to significant mass growth. In this paper, we calculate the mass of the largest BH that can form through repeated BH mergers and determine how its value depends on the physical properties of the host cluster. We adopt an analytical model in which the energy generated by the black hole binaries in the cluster core is assumed to be regulated by the process of two-body relaxation in the bulk of the system. This principle is used to compute the hardening rate of the binaries and to relate this to the time-dependent global properties of the parent cluster. We demonstrate that in clusters with initial escape velocity ${\gtrsim } 300\, {\rm km\, s}^{-1}$ in the core and density ${\gtrsim } 10^5\, \mathrm{ M}_\odot \rm pc^{-3}$, repeated mergers lead to the formation of BHs in the mass range $100\!-\!10^5 \, \mathrm{ M}_\odot$, populating any upper mass gap created by pair-instability supernovae. This result is independent of cluster metallicity and the initial BH spin distribution. We show that about $10{{\ \rm per\ cent}}$ of the present-day nuclear star clusters meet these extreme conditions, and estimate that BH binary mergers with total mass ${\gtrsim } 100\, \mathrm{ M} _\odot$ should be produced in these systems at a maximum rate ${\approx } 0.05 \, \rm Gpc^{-3} yr^{-1}$, corresponding to one detectable event every few years with Advanced LIGO/Virgo at design sensitivity.
The origin of the Milky Way globular clusters Renaud, Florent; Agertz, Oscar; Gieles, Mark
Monthly Notices of the Royal Astronomical Society,
03/2017, Letnik:
465, Številka:
3
Journal Article
Recenzirano
Odprti dostop
We present a cosmological zoom-in simulation of a Milky Way-like galaxy used to explore the formation and evolution of star clusters. We investigate in particular the origin of the bimodality ...observed in the colour and metallicity of globular clusters, and the environmental evolution through cosmic times in the form of tidal tensors. Our results self-consistently confirm previous findings that the blue, metal-poor clusters form in satellite galaxies that are accreted on to the Milky Way, while the red, metal-rich clusters form mostly in situ, or, to a lower extent, in massive, self-enriched galaxies merging with the Milky Way. By monitoring the tidal fields these populations experience, we find that clusters formed in situ (generally centrally concentrated) feel significantly stronger tides than the accreted ones, both in the present day, and when averaged over their entire life. Furthermore, we note that the tidal field experienced by Milky Way clusters is significantly weaker in the past than at present day, confirming that it is unlikely that a power-law cluster initial mass function like that of young massive clusters, is transformed into the observed peaked distribution in the Milky Way with relaxation-driven evaporation in a tidal field.
Abstract
Binary black hole (BBH) systems detected via gravitational-wave emission are a recently opened astrophysical frontier with many unknowns and uncertainties. Accurate reconstruction of the ...binary distribution with as few assumptions as possible is desirable for inference of formation channels and environments. Most population analyses have, though, assumed a power law in binary mass ratio
q
, and/or assumed a universal
q
distribution regardless of primary mass. Methods based on kernel density estimation allow us to dispense with such assumptions and directly estimate the joint binary mass distribution. We deploy a self-consistent iterative method to estimate this full BBH mass distribution, finding local maxima in primary mass consistent with previous investigations and a secondary mass distribution with a partly independent structure, inconsistent both with a power law and with a constant function of
q
. We find a weaker preference for near-equal-mass binaries than in most previous investigations; instead, the secondary mass has its own “spectral lines” at slightly lower values than the primary, and we observe an anticorrelation between primary and secondary masses around the ∼10
M
⊙
peak.
The life cycle of star clusters in a tidal field Gieles, Mark; Heggie, Douglas C.; Zhao, HongSheng
Monthly Notices of the Royal Astronomical Society,
June 2011, Letnik:
413, Številka:
4
Journal Article
Recenzirano
Odprti dostop
The evolution of globular clusters due to two-body relaxation results in an outward flow of energy and at some stage all clusters need a central energy source to sustain their evolution. Hénon ...provided the insight that we do not need to know the details of the energy production in order to understand the relaxation-driven evolution of the cluster, at least outside the core. He provided two self-similar solutions for the evolution of clusters based on the view that the cluster as a whole determines the amount of energy that is produced in the core: steady expansion for isolated clusters, and homologous contraction for clusters evaporating in a tidal field. The amount of expansion or evaporation per relaxation time-scale is set by the instantaneous radius or number of stars, respectively. We combine these two approximate models and propose a pair of Unified Equations of Evolution (UEE) for the life cycle of initially compact clusters in a tidal field. The half-mass radius increases during the first part (roughly half) of the evolution, and decreases in the second half, while the escape rate approaches a constant value set by the tidal field. We refer to these phases as 'expansion dominated' and 'evaporation dominated'. These simple analytical solutions of the UEE immediately allow us to construct evolutionary tracks and isochrones in terms of cluster half-mass density, cluster mass and galactocentric radius. From a comparison to the Milky Way globular clusters we find that roughly one-third of them are in the second, evaporation-dominated phase and for these clusters the density inside the half-mass radius varies with the galactocentric distance R
G as ρh∝R
−2
G. The remaining two-thirds are still in the first, expansion-dominated phase and their isochrones follow the environment-independent scaling ρh∝M
2, where M is the cluster mass; that is, a constant relaxation time-scale. We find substantial agreement between Milky Way globular cluster parameters and the isochrones, which suggests that there is, as Hénon suggested, a balance between the flow of energy and the central energy production for almost all globular clusters.
We present a model for the concurrent formation of globular clusters (GCs) and supermassive stars (SMSs, ≳103M⊙) to address the origin of the HeCNONaMgAl abundance anomalies in GCs. GCs form in ...converging gas flows and accumulate low-angular momentum gas, which accretes on to protostars. This leads to an adiabatic contraction of the cluster and an increase of the stellar collision rate. A SMS can form via runaway collisions if the cluster reaches sufficiently high density before two-body relaxation halts the contraction. This condition is met if the number of stars ≳106 and the gas accretion rate ≳105M⊙ Myr-1, reminiscent of GC formation in high gas-density environments, such as - but not restricted to - the early Universe. The strong SMS wind mixes with the inflowing pristine gas, such that the protostars accrete diluted hot-hydrogen burning yields of the SMS. Because of continuous rejuvenation, the amount of processed material liberated by the SMS can be an order of magnitude higher than its maximum mass. This 'conveyor-belt' production of hot-hydrogen burning products provides a solution to the mass budget problem that plagues other scenarios. Additionally, the liberated material is mildly enriched in helium and relatively rich in other hot-hydrogen burning products, in agreement with abundances of GCs today. Finally, we find a super-linear scaling between the amount of processed material and cluster mass, providing an explanation for the observed increase of the fraction of processed material with GC mass. We discuss open questions of this new GC enrichment scenario and propose observational tests.
Young Massive Star Clusters Portegies Zwart, Simon F.; McMillan, Stephen L.W.; Gieles, Mark
Annual review of astronomy and astrophysics,
01/2010, Letnik:
48, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Young massive clusters (YMCs) are dense aggregates of young stars that form the fundamental building blocks of galaxies. Several examples exist in the Milky Way Galaxy and the Local Group, but they ...are particularly abundant in starburst and interacting galaxies. The few YMCs that are close enough to resolve are of prime interest for studying the stellar mass function and the ecological interplay between stellar evolution and stellar dynamics. The distant unresolved clusters may be effectively used to study the star-cluster mass function, and they provide excellent constraints on the formation mechanisms of young cluster populations. YMCs are expected to be the nurseries for many unusual objects, including a wide range of exotic stars and binaries. So far only a few such objects have been found in YMCs, although their older cousins, the globular clusters, are unusually rich in stellar exotica. In this review, we focus on star clusters younger than ~100 Myr, more than a few current crossing times old, and more massive than ...10...M...; the size of the cluster and its environment are considered less relevant as distinguishing parameters. We describe the global properties of the currently known young massive star clusters in the Local Group and beyond, and discuss the state of the art in observations and dynamical modeling of these systems. In order to make this review readable by observers, theorists, and computational astrophysicists, we also review the cross-disciplinary terminology. (ProQuest: ... denotes formulae/symbols omitted.)
PDF
