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Register a new userRelativistic Binaries in Globular Clusters
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Matthew Benacquista
Publication date
2011
fields
Physics
and research's language is
English
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Galactic globular clusters are old, dense star systems typically containing 10super{4}--10super{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.
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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 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.
The stellar encounter rate Gamma has been shown to be strongly correlated with the number of X-ray binaries in clusters and also to the number of radio pulsars. However, the pulsar populations in different clusters show remarkably different characteristics: in some GCs the population is dominated by binary systems, in others by single pulsars and exotic systems that result from exchange encounters. In this paper, we describe a second dynamical parameter for globular clusters, the encounter rate for a single binary, gamma. We find that this parameter provides a good characterization of the differences between the pulsar populations of different globular clusters. The higher gamma is for any particular globular cluster the more isolated pulsars and products of exchange interactions are observed. Furthermore, we also find that slow and young pulsars are found almost exclusively in clusters with a high gamma; this suggests that these kinds of objects are formed by the disruption of X-ray binaries, thus halting the recycling of a previously dead neutron star. We discuss the implications of this for the nature of young pulsars and for the formation of neutron stars in globular clusters.
We investigate properties of black hole (BH) binaries formed in globular clusters via dynamical processes, using direct N-body simulations. We pay attention to effects of BH mass function on the total mass and mass ratio distributions of BH binaries ejected from clusters. Firstly, we consider BH populations with two different masses in order to learn basic differences from models with single-mass BHs only. Secondly, we consider continuous BH mass functions adapted from recent studies on massive star evolution in a low metallicity environment, where globular clusters are formed. In this work, we consider only binaries that are formed by three-body processes and ignore stellar evolution and primordial binaries for simplicity. Our results imply that most BH binary mergers take place after they get ejected from the cluster. Also, mass ratios of dynamically formed binaries should be close to one or likely to be less than 2:1. Since the binary formation efficiency is larger for higher-mass BHs, it is likely that a BH mass function sampled by gravitational-wave observations would be weighed toward higher masses than the mass function of single BHs for a dynamically formed population. Applying conservative assumptions regarding globular cluster populations such as small BH mass fraction and no primordial binaries, the merger rate of BH binaries originated from globular clusters is estimated to be at least 6.5 per yr per Gpc^3. Actual rate can be up to more than several times of our conservative estimate.
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 $sim 2$ million models to explore the parameter space that is relevant to real clusters and over all mass scales. We show that when uncertainties on the initial cluster mass function and density are properly taken into account, they become the two dominant factors in setting the theoretical error bars on merger rates. Other model parameters (e.g., natal kicks, black hole masses, metallicity) have virtually no effect on the local merger rate density, although they affect the masses of the merging black holes. Modelling the merger rate density as a function of redshift as $R(z)=R_0(1+z)^kappa$ at $z<2$, and marginalizing over uncertainties, we find: $R_0=7.2^{+21.5}_{-5.5}{rm Gpc^{-3}yr^{-1}}$ and $kappa=1.6^{+0.4}_{-0.6}$ ($90%$ credibility). The rate parameters for binaries that merge inside the clusters are ${R}_{rm 0,in}=1.6^{+1.9}_{-1.0}{rm Gpc^{-3}yr^{-1}}$ and $kappa_{rm in}=2.3^{+1.3}_{-1.0}$; $sim 20%$ of these form as the result of a gravitational-wave capture, implying that eccentric mergers from globular clusters contribute $lesssim 0.4 rm Gpc^{-3}yr^{-1}$ to the local rate. A comparison to the merger rate reported by LIGO-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 $gtrsim 10^4 M_odot rm pc^{-3}$. Such models also reproduce the inferred primary black hole mass distribution for masses $13-30 M_odot$, but under-predict the data outside this range.
The intermediate mass-ratio inspiral of a stellar compact remnant into an intermediate mass black hole (IMBH) can produce a gravitational wave (GW) signal that is potentially detectable by current ground-based GW detectors (e.g., Advanced LIGO) as well as by planned space-based interferometers (e.g., eLISA). Here, we present results from a direct integration of the post-Newtonian $N$-body equations of motion describing stellar clusters containing an IMBH and a population of stellar-mass black holes (BHs) and solar mass stars. We take particular care to simulate the dynamics closest to the IMBH, including post-Newtonian effects up to order $2.5$. Our simulations show that the IMBH readily forms a binary with a BH companion. This binary is gradually hardened by transient 3-body or 4-body encounters, leading to frequent substitutions of the BH companion, while the binarys eccentricity experiences large amplitude oscillations due to the Lidov-Kozai resonance. We also demonstrate suppression of these resonances by the relativistic precession of the binary orbit. We find an intermediate mass-ratio inspiral in one of the 12 cluster models we evolved for $sim 100$ Myr. This cluster hosts a $100 M_odot$ IMBH embedded in a population of 32 $10M_odot$ BH and 32,000 $1M_odot$ stars. At the end of the simulation, after $sim 100$ Myr of evolution, the IMBH merges with a BH companion. The IMBH--BH binary inspiral starts in the eLISA frequency window ($gtrsim 1rm mHz$) when the binary reaches an eccentricity $1-esimeq 10^{-3}$. After $simeq 10^5$ years the binary moves into the LIGO frequency band with a negligible eccentricity. We comment on the implications for GW searches, with a possible detection within the next decade.
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