1. Black Hole Binaries Dynamically Formed in Globular Clusters
Dawoo Park, Chunglee Kim, Hyung Mok Lee,
Yeong-Bok Bae, and Krzysztof Belczynski
ICGAC-XIII & IK15, July 4th, 2017

2. BH binaries detected by LIGO
Belczynski et el., 2016
High mass BHs can exist in
low Z environment
BH mergers have wider mass
range than x-ray binaries
Spins are not aligned

3. GC Globular Cluster Spherical system containing 104-106 stars
High stellar density
Old stellar population
(low Z)

4. Mass segregation in GC
Dynamical friction make heavy particles (NS, BH) quickly collapse to center
Central high BH density region is an ideal place to dynamical interaction
Star, NS, BH
Bae et al. 2014

5. Dynamical binary formation scenario
GW capture
Three-body process
Energy loss by GW emission
Effective in galactic nuclei scale
Energy exchanged via interaction
Effective in GC scale

6. Binary-single interaction
Hard binaries tend to
be harder (Heggie 1975)
Eventually the binary
can be ejected

7. N-body simulation
Sample of initial model
We investigated BH binaries in GC via N-body simulation
Introduction of BH mass function
Binary properties
Binary formation efficiency

8. Binary hardening in GC Binary hardness (x) is proportional to t
‘tight’ subgroup is
the last binary, not
the highest mass
binary

9. Binary formation efficiency
Black line : initial BHs
Blue line : binary BHs
Binary formation efficiency increases along BH mass.
40 Msun BHs have ~7 times higher binary formation than 5 Msun BHs

10. BH mass ratio Mass ratio between individual BHs in binary
Nearly equal mass binary
favored
Less than 6% of binaries
have ratio > 2

11. Expected Event rate Merger fraction NBH Ejected binary fraction
BH-BH merging rate is estimated to be ~2.5 Gyr-1 per cluster. This corresponds to Gpc-3 yr-1
Have a range due to a conservative assumption
From confirmed observation : ~12 Gpc-3 yr-1 (Abbott et al., 2017)

12. summary We investigate BH binary formation and merging in GC
Higher mass BHs have higher binary formation efficiency, implying BH mass function from GW observation result can be biased.
The last BH binary at the cluster is retained relatively long time, then have short merging time.
BBH merging event rate is expected to 6.5 ~ 25 Gyr-3 per year
Nearly equal mass binaries are favored

13. Supplement slides

14. Binary formation and ejection
Higher mass binaries are ejected first
Ejected binaries undergo passive evolution due to gravitational wave emission
Certain fraction of ejected binaries can merge within Hubble time

15. Hardness distribution

16. Binary merging
‘merging’ binary fraction in all ejected binaries are not sensitive to the Binary mass
Peak value of MWGC

17. Binary formation efficiency
Higher mass BHs form binaries more efficiently
BH mass function from GW observation might be biased to higher mass

18. Our model N-body simulation NBODY6 code (Aarseth 2003)
Assuming GC, having ~ particles
Each model contains 100~200 BHs
Two-component BH mass case, 5 & 10 Msun or 10 & 20 Msun BHs
Continuous BH mass function case, 5 ~ 40 Msun
Totally ~140 runs performed