Eccentricity Distribution of Coalescing Black Hole Binaries Driven by the Kozai Mechanism in Globular Clusters. Linqing Wen. Overview Globular clusters Binary black hole (BH) mergers in GC Mergers driven by Kozai mechanism. Evolution of merger systems under Kozai mechanism & others
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Eccentricity Distribution of CoalescingBlack Hole Binaries Driven by the Kozai Mechanism in Globular Clusters
Linqing Wen
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Overview
Globular clusters
Binary black hole (BH) mergers in GC
Mergers driven by Kozai mechanism
Evolution of merger systems under Kozai mechanism & others
Eccentricities
GW Frequencies
Implications to LIGO detections
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MBH~4000 Msun 20,000 Msun
(stolen from the STScI web site)
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e.g., ~12 billion yrs old
* LIGO, LISA sources
(medium-size)
MBH~4000 Msun 20,000 Msun
(stolen and modified from the STScI web site)
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2-body relaxation, energy equipartition, mass segregation:
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Binary Merger Time Scale
* a: semi-major axis, ε = 1-e2 , m0, m1: masses
* quadrupole approximation for gravitational radiation
* Need to reduce a or ε to have TGR < Hubble time
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(Miller & Hamilton 2002)
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These merger systems are associated with extremely high eccentricities !
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II. Evolution of Individual Triple System
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(Kozai 1962)
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* Lidov (1976)+ Peters (1964)
+PN effect (Miller & Hamilton 2002)
* KG << KE
* ΘPN ~a-4
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* ε=1-e2
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Dashed line: predicted lower and upper limits
II. Merge within one Kozai cycle
* I0 ~Ic
* x--- : predicted evolution
* typical case of extreme eccentricity
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f mGW =nm f orb
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III. Eccentricity Distribution
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* the system should have enough time to reach extreme eccentricity
* merge should occur before the system is disrupted by encounters with field stars
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a2/a1 = 20 10 5 3
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e >0.1 : 30 %,
e~1 : 2 %
Eccentricity might be important for advanced LIGO
e<0.2
e<0.04
* Consistent with e ~ f mGW-19/18
* Eccentricity is probably irrelevant for initial LIGO for this type of mergers.
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