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Inﬂuence of dynamics and metallicity
on the formation and evolution of
black-hole binaries in star clusters
Brunetto M. Ziosi
(University of Padova, INAF-Padova)
Collaborators: Michela Mapelli (INAF-Padova), Marica Branchesi
(University of Urbino), Giuseppe Tormen (Univ. Padova)
Gravasco, W2 workshop
Paris, 2013-11-08
B. Ziosi (Univ. of Padova) W2, 2013-11-08

Dynamics, Z and DCOBs
Outline
1 Overview
DCOBs and GWs
Stellar evolution and BH mass
Star cluster dynamics
2 Tools
Direct N-body simulations
3 Results
DCOB population
Life-times & Exchanges
Orbital properties distribution
Mass distribution
Coalescence times
4 Conclusions
B. Ziosi (Univ. of Padova) W2, 2013-11-08

Dynamics, Z and DCOBs Overview
Why DCOBs?
• DCO binaries during inspiral and
merger events produce GWs we
could observe in the near future
• Simulations provide theoretical
models to interpret Advanced
Virgo/LIGO upcoming data
• Key quantities:
• Number of DCOBs
• BH mass spectrum
• Binary orbital properties
B. Ziosi (Univ. of Padova) W2, 2013-11-08 1 / 12

Why stellar evolution and metallicity (Z)?
• Massive stars lose mass by stellar
winds
• Winds eﬃciency depends on
metallicity
• Stars with Mﬁn ≥ 40M are
expected to collapse to a BH
without SN explosion
(Fryer 1999, Fryer&Kalogera 2001)
• BHs formed from direct collapse
are more massive than BHs
formed from SN
• Metal-poor stars lose less mass by
stellar winds ⇒ more likely to
collapse to BH directly

Why dynamics? Why YSCs?
• YSCs are birthplace for > 80% of
stars in the local universe (Lada&Lada, 2003)
• (Collisional) YSCs are
• young (< 100 Myr)
• relatively massive (103
− 107
M ),
• dense (103
− 106
/pc3
)
groups of stars
• YSCs are sites of intense dynamical
activity: central trelax < 10 Myr

• Focus on 3-body encounters: close
encounters between a single object and
a binary
• If kinetic energy is tranferred from the
binary to the single object ⇒ SMA
decrease (hardening)
• ”Hard” binary: Gm1m2
a ≥ 1
2 m σ2
• Hard binaries tend to become harder,
soft binaries tend to become softer as
eﬀect of three-body encounters
(Heggie 1975)
• If msingle ≥ m2 ⇒ the single star can
take the place of one of the stars in the
binary ⇒ exchange

• Dynamics enhances the formation of
hard compact-object binaries
(exhanges also produces very high
eccentricity binaries)
• Key processes:
• mass segregation
• 3-body exchanges
• hardening

Dynamics, Z and DCOBs Tools
Tools
• 200 N-body realizations of the same cluster
for each Z = 0.01, 0.1, 1Z
• StarLab: Kira (GPU) + SeBa (CPU)
(Portegies Zwart et al. 2001)
• Our simulations combines dynamics +
up-to-date recipes for Z-dependent
stellar evolution
• Custom recipes:
• accurate metallicity-dependent
stellar evolution (Hurley et al. 2000) and
stellar winds (Vink et al. 2001; Vink & de Koter
2005; Belczynski et al. 2010)
• the possibility of massive BHs
formation by direct collapse (Fryer et al.
2012; Mapelli et al. 2013)
600 simulations
Parameter Value
W0 5
N∗ 5500
Mtot ∼ 3500M
rc [pc] 0.4
c = rt/rc 1.03
IMF Kroupa (2001)
mmin [M ] 0.1
mmax [M ] 150
fPB 0.1
Z [Z ] 0.01, 0.1, 1
Sim. time 100 Myr
MW typical, e.g. Orion Nebula Cluster

Dynamics, Z and DCOBs Results
DCOB population
• DBH distribution
• Mean number of DBHs: ∼ 3
• Max number of DBHs: 18
• # NS ∼ 4 # BH but
• # DBH ∼ 10 # DNS due to
dynamics
• Negligible dependence on Z,
but... (see after)
Ziosi et al., in prep

DBH population in time
Low-Z case vs higher metallicities:
• Build up the DBH population before high-Z case
• Higher DBH mass allowed ⇒ earlier DBHBs formation
• But mean # and mean # in time of DBHs do not agree
• Higher DBH mass allowed ⇒ more stable binaries & longer lifetime

Exchanges & mean DCOB life time
• Z=0.01 Z DBHBs live longer
than at higher Z but the avg
number of exchanges is similar
• Z=0.1, 1 Z DBHBs tend to
break-up
• DNS are 10 times less
numerous but are much more
stable
Avg exchanges per CO and Z
Type 0.01Z 0.1 Z Z
DBH 9.92 9.91 10.14
DNS 0.00 0.5 0.26
• 97% of all the DBHBs come
from exchanges
Distribution of DBHBs lifetimes

Orbital properties
• Distribution of orbital
parameters at minimum
semi-major axis
• Critical for coalescence times
and mergers detection
• SMA and period span a wide
range
• Eccentricity follows the
thermal distribution
f (e) ∝ 2e but
• excess in e ∼ 0: GW and tidal
circularization
• DNS (grey) are 10 times less
numerous but have small SMA
and short periods
Z=0.01 Z๏
Total#ofbinaries
100
101
102
sma [AU]
10−3
100
103
106
Z=0.01 Z๏
Total#ofbinaries
100
period [yr]
10−6
10−3
100
103
106
Z=0.01 Z๏
Total#ofbinaries
100
ecc
0 0.2 0.4 0.6 0.8 1
Z=0.1Z๏
Total#ofbinaries
100
101
102
sma [AU]
10−3
100
103
106
Z=0.1Z๏
Total#ofbinaries
100
period [yr]
10−6
10−3
100
103
106
Z=0.1Z๏
Total#ofbinaries
100
ecc
0 0.2 0.4 0.6 0.8 1
Z=1Z๏
Total#ofbinaries
100
101
102
sma [AU]
10−3
100
103
106
Z=1Z๏
Total#ofbinaries
100
period [yr]
10−6
10−3
100
103
106
Z=1Z๏
Total#ofbinaries
100
ecc
0 0.2 0.4 0.6 0.8 1

Masses
• High BH masses because of direct collapse at low metallicity
• Chirp mass mchirp = (m1m2)3/5
(m1+m2)1/5
• Why chirp mass:
• νGW ∝ m
−5/8
chirp, hGW ∝ m
5/3
chirp
• So from observations we can reconstruct mchirp
• In our model mchirp strongly depends on Z
⇒ Z-dependent BH mass model test
• But: in black chirp mass distribution of the best merger-candidates

Coalescence times
• Time to reach SMA=0
considering only GW
emission
• tGW ∝ a4
(1−e2
)7/2
m1m2mtot
(Peters, 1964)
• GW emission: SMA shrink
and orbit circularization
• Dynamical outlier: signal
detectability depends on e
• 7 DBHs with tGW < 13
Gyr (0 for Z=Z )
• 17 DNSs with tGW < 13
Gyr, 11 DNS mergers
during the simulations

Dynamics, Z and DCOBs Conclusions
Conclusions
• DCOBs during mergers emits GWs likely to be detected in the near future
• Metallicity is important:
• Heavier BHs form at low Z
• They tend to form DBHBs at early times
• and these binaries are more stable ⇒ BHBs lifetimes are longer at low
Z
• Dynamics is important
• Dynamics enhances the formation of DCOBs: 97% of DBHBs come
from exchanges
• Dynamics hardens binaries and can modify the eccentricity ⇒
increase detection probability
• DNSBs are 10 times less numerous but are harder
• Fewer exchanges and shorter coalescence times than DBHBs
• Selection eﬀect

Dynamics, Z and DCOBs Conclusions
Thank you

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2013-11-08-Gravasco-Ziosi_NO_appendix

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