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

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

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

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

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

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

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

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

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

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

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 6.5 - 25 Gpc-3 yr-1 Have a range due to a conservative assumption From confirmed observation : ~12 Gpc-3 yr-1 (Abbott et al., 2017)

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

Supplement slides

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

Hardness distribution

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

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

Our model N-body simulation NBODY6 code (Aarseth 2003) Assuming GC, having 25000 ~ 50000 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