This document summarizes the PhD work of Brunetto M. Ziosi on simulating the formation and evolution of compact object binaries in young star clusters. Using N-body simulations with stellar evolution at different metallicities, Ziosi found that: 1) The number of black hole-black hole binaries formed depends only slightly on metallicity, but lower metallicity leads to earlier formation of more stable binaries. 2) Orbital properties of binaries span a wide range, with neutron star-neutron star binaries having smaller minimum separations critical for merger. 3) Higher black hole masses are allowed at lower metallicity due to direct collapse, leading to higher chirp masses. 4) Only a small fraction

1. time
VIRGO/
LIGO
LISA
Gravitational waves
from the nursery of stars:
simulating
the formation and evolution of
compact-object binaries
in young star clusters
PhD student: Brunetto M. Ziosi
Supervisors: Dr. M. Mapelli, Prof. G. Tormen
PhD Defense PD/2015-11-16

2. My work
How do ...
1
... dynamics and metallicity...
2
... different initial structural
properties of SCs...
3
... a galactic tidal field...
impact on the population of double
compact-object binaries?
Introduction
Gravitational
Waves
Dynamics
Stellar
evolution
Outline

3. Gravitational waves
Gravitational
Waves
Dynamics
Stellar
evolution

4. GWs | What?
"... perturbations in the spacetime propagating at the speed of light... "
They propagate as waves
Spacetime is stretched by their passage
Predicted but never observed directly
2 / 38

5. Gw | PSR B1913+16
A.K.A. Hulse-Taylor binary pulsar
Provided the first indirect GW evidence
Discovered in 1974, Nobel prize in 1993
NS + pulsar system
Credits: Dr. K. Y. Michael WONG
3 / 38

6. GWs emission causes decrease
decrease
Very good measurement of the
period change
In perfect agreement with GR
predictions
Gw | PSR B1913+16
A.K.A. Hulse-Taylor binary pulsar
Provided the first indirect GW evidence
a
⇒ Pb
4 / 38

7. GWs emission causes decrease
decrease
Very good measurement of the
period change
In perfect agreement with GR
predictions
0
−5
−10
−15
−20
−25
−30
−35
−40
Cumulativeperiodshift(s)
1975 1980 1985 1990 1995 2000 2005
Year
Credits: Public domain
Gw | PSR B1913+16
A.K.A. Hulse-Taylor binary pulsar
Provided the first indirect GW evidence
a
⇒ Pb
4 / 38

8. Observations | NS-NS binaries
The Hulse-Taylor pulsar is not the only one observed
Few pulsar-NS system since 1974
from Duncan R. Lorimer 2008, Binary and Millisecond Pulsars
Hulse-Taylor
J0737-3039
5 / 38

9. Gw | Sources summary
Credits: NASA
6 / 38

10. GWs | Virgo/LIGO
Ground based GW detector: huge Michelson interferometer
Baseline required for these GWs observations: 100 km
impractical
Virgo arms ~ 3 km advanced optics tricks
Avd. LIGO already started scientific runs, Adv. Virgo starting in 2016!!
→
⇐
7 / 38

11. Double compact
object binaries are
expected to emit
detectable GWs
during inspiral and
merger events
Inspiral Merger Ringdown
Gw | Compact Binary Coalescence
8 / 38

12. Double compact
object binaries are
expected to emit
detectable GWs
during inspiral and
merger events
Inspiral Merger Ringdown
Gw | Compact Binary Coalescence
During the inspiral:
GW frequency:
Relative deformation (strain)
On the distance Earth-Sun it correspond to the diameter of an
Hydrogen atom
= 2ωGW ωorb
∼ 1 ×hGW 10
−21
( )
mchirp
M⊙
5/3
( )Pb
hours
−2/3
( )d
1 kpc
−1
with chirp mass =mchirp
(m1 m2 )
3/5
( +m1 m2 )
1/5
8 / 38

13. GW frequency:
Strain:
Double compact
object binaries are
expected to emit
detectable GWs
during inspiral and
merger events
Inspiral Merger Ringdown
Gw | Compact Binary Coalescence
An example
= 11.5m1 M⊙
= 15.0m2 M⊙
a = 10.5 × km10
6
= 1.4 daysPb
d set to 1 Mpc
= 2 = 1.6 × HzfGW [ ]
G( )m1 m2
4π2
a3
1/2
10
−5
∼ = 6.1 ×hGW 10
−21
m5/3
chirp
P−2/3
b
d−1
10
−22
8 / 38

14. GW frequency:
Strain:
Double compact
object binaries are
expected to emit
detectable GWs
during inspiral and
merger events
Inspiral Merger Ringdown
Gw | Compact Binary Coalescence
An example (just before the merger: ISCO)
= 11.5m1 M⊙
= 15.0m2 M⊙
= 224 kmaISCO
= 0.004 sPb,ISCO
d set to 1 Mpc
= = 546.9 HzfGW,ISCO
c3
πG6
3/2
1
+m1 m2
= = 3.1 ×hGW,ISCO
G
c2
1
d
m1 m2
+m1 m2
10
−19
8 / 38

15. Dynamics
Gravitational
Waves
Dynamics
Stellar
evolution

16. Dynamics | Environment
Young Star Clusters are birthplace for ∼ 80% of stars in the local universe
(Lada&Lada, 2003)
They are building blocks of the galactic disks
Previous studies: Monte Carlo or population synthesis for the field
First study of YSCs with direct N-body simulations
9 / 38

17. Dynamics | YSC Facts
Young Star Clusters are birthplace for ∼ 80% of stars in the local universe
(Lada&Lada, 2003)
Previous studies: Monte Carlo or population synthesis for the field
(Collisional) YSCs are
young (< 100 Myr)
relatively massive ( ),
dense ( pc )
self-gravitating systems of stars
Dense YSCs are sites of intense dynamical activity:
Myr
−103
105
M⊙
−103
106 −3
∼ 10 − 100trelax
10 / 38

18. Dynamics | Relevant processes
11 / 38

19. 3-body exchanges:
A single star take the place of
one of the binary members
higher probability if
BHs can acquire a
companion
Dynamics | Relevant processes
>mintruder mi
11 / 38

20. 3-body encounters:
A single star take the place of
one of the binary members
higher probability if
BHs can acquire a
companion
Hardening: kinetic energy
transfer from the binary to the
perturber
semi-major axis decreases
effective GW sources in
shorter times
Dynamics | Relevant processes
>mintruder mi
11 / 38

21. Stellar evolution
Gravitational
Waves
Dynamics
Stellar
evolution
11 / 38

22. Massive stars lose mass by
stellar winds depending on
Compact object formation | Metallicity
Z
12 / 38

23. Massive stars lose mass by
stellar winds depending on
MS winds (Vink+2001)
LBV (Belczynski+2010, Humphreys+1994)
WR (Belczynski+2010)
Naked helium giants with
Compact object formation | Metallicity
Z
log ∝ f(L)M˙ 10
−6
( )Z
z⊙
0.86
M⊙ yr−1
> 6 × , ( ) >
L
L⊙
10
5 R
R⊙
( )L
L⊙
0.5
10
5
⇒ ∼ 1.5 ×M˙ 10
−4
M⊙ yr−1
> 25mZAMS M⊙
⇒ ∼M˙ 10
−5
( )L
10
5
L⊙
1.5
( )Z
Z⊙
0.86
M⊙ yr−1
12 / 38

24. Massive stars lose mass by
stellar winds depending on
MS winds (Vink+2001)
LBV (Belczynski+2010, Humphreys+1994)
WR (Belczynski+2010)
Naked helium giants with
Direct collapse to a BH without
SN explosion if
(Fryer 1999, Fryer&Kalogera 2001)
Direct collapse ⇒ more massive
BHs
Metal-poor stars ⇒ more likely
to collapse to BH directly
Metal poor stars can form more
massive remnants
Compact object formation | Metallicity
Z
log ∝ f(L)M˙ 10
−6
( )Z
z⊙
0.86
M⊙ yr−1
> 6 × , ( ) >
L
L⊙
10
5 R
R⊙
( )L
L⊙
0.5
10
5
⇒ ∼ 1.5 ×M˙ 10
−4
M⊙ yr−1
> 25mZAMS M⊙
⇒ ∼M˙ 10
−5
( )L
10
5
L⊙
1.5
( )Z
Z⊙
0.86
M⊙ yr−1
≥ 40 M ⊙Mfin
12 / 38

25. Compact object formation | Metallicity
13 / 38

26. (Portegies Zwart+2001)
N-body on GPU + stellar
evolution
Each particle is a star
(with its physics)
Updated to take into account
different metallicities
(Mapelli+2013)
Methods |StarLab
14 / 38

27. (Portegies Zwart+2001)
N-body on GPU + stellar
evolution
Each particle is a star
(with its physics)
Updated to take into account
different metallicities
(Mapelli+2013)
Methods |StarLab
N-body: kira
4th order Predictor-Corrector Hermite integrator
Approximate solution
Language: C++ and GRAPE / CUDA (Sapporo, Gaburov+2009)
15 / 38

28. (Portegies Zwart+2001)
N-body on GPU + stellar
evolution
Each particle is a star
(with its physics)
Updated to take into account
different metallicities
(Mapelli+2013)
Methods |StarLab
Stellar evolution: SeBa public version
MS stellar winds: only at
Post MS stellar winds: only at
Stellar parameters: at (Portegies Zwar+2001)
Z = Z⊙
Z = Z⊙
R, T, L = f(M) Z⊙
16 / 38

29. (Portegies Zwart+2001)
N-body on GPU + stellar
evolution
Each particle is a star
(with its physics)
Updated to take into account
different metallicities
(Mapelli+2013)
Methods |StarLab
Stellar evolution: SeBa Mapelli+2013
MS stellar winds: -dependent fitting formulas (Vink+2001)
Post MS stellar winds: LBV and WR evolution (Belczynski+2010,
Humphreys+1994)
Stellar parameters: polinomial fitting formulas
(Hurley+2000)
Z
R, T, L = f(M, Z)
17 / 38

30. Go(lang) wrapper for StarLab +
cluster monitors + simulation
management
Python seeker to extract the
binaries + analysis routines
Trace the complete history of
compact objects (BH, NS) in
binary
Move to database to include
positions and to simplify and
speed up future analyses
Methods |SlTools
(on GitHub)
18 / 38

31. time
VIRGO/
LIGO
LISA
My results

32. Ziosi et al. (2014)
600 N-body realizations of the
same cluster at
D&M | Simulations
Z = 0.01, 0.1, 1Z⊙
19 / 38

33. Ziosi et al. (2014)
600 N-body realizations of the
same cluster at
D&M | Simulations
Simulations parameters
Z = 0.01, 0.1, 1Z⊙
19 / 38

34. Mean number of
BH-BHs:
# BH-BH 10 # NS-
NS due to dynamics
# NS 4 # BH
Max number of
BH-BHs: 18
Negligible
dependence on Z,
but... (see after)
D&M | How many BH-BH?
∼ 3
∼
∼
20 / 38

35. D&M | BH-BH evolution in time
Lower Z case...
... build up the BH-BH population before...
have more stable binaries & longer lifetime than...
... higher metallicities ones because higher BH masses are allowed
BH­BH
Ziosi+2014
21 / 38

36. Distributions of
minimum semi-
major axis
spans a wide
range
NS-NS are 10 times
less numerous but
have small
Critical for
coalescence times
and merger
detection
D&M | Orbital properties ( )a
a
a
a
22 / 38

37. D&M | Masses
Higher BH masses at low Z because of direct collapse
Ziosi+2014
23 / 38

38. Chirp mass
Why chirp mass:
,
From observations we can
reconstruct
In our model
depends on Z test the
model
In black, of the best
merger candidates
Ziosi+2014
D&M | Chirp masses
=mchirp
(m1m2)
3/5
( +m1 m2)
1/5
∝νGW m−5/8
chirp
∝hGW m5/3
chirp
mchirp
mchirp
⇒
mchirp
24 / 38

39. D&M | Coalescence
timescale
Time a binary needs to merge
only for GWs emission (Peters 1964):
5 BH-BH merging in less than
over 600
simulations
17 NS-NS with ,
11 NS-NS merge during the
simulations
Starting point to compute the
merger and detection rates
∝tGW
(1−a4
e2
)
7/2
m1m2mT
∼ 14 GyrtH
<tGW tH
25 / 38

40. What else?
The results I obtained, however, stand on two critical assumptions:
Random realizations of a single SC model
SCs live unperturbed in isolation for 100 Myr
Both these assumptions can heavily affect my estimate of BH-BH
demographics.
26 / 38

41. Impact of YSC structural parameters on DCOBs
Grid of ~ simulations
Number of stars :
Central adimensional potential : 3, 5, 9
Virial radius [pc]: 1, 3, 5
Metallicity [Z ]: 0.1, 1
Primordial binaries fraction : 0.05, 0.1, 0.2
103
N∗ 1 × 104
W0
rv
Z ⊙
fPB
27 / 38

42. Sanity check
No BH-BH observations
Few NS-NS
from Duncan R. Lorimer 2008,
Binary and Millisecond Pulsars
Good agreement
Observations | NS-NS binaries
28 / 38

43. Consistent with
Ziosi+2014
~ 4 BH-BH / SC
but ~ 1 hard BH-BH /
SC
The soft binaries
dominate the
statistics
BH-BH favoured by
high density, high
concentration, low
Demographics | Average number of BH-BH
fPB
29 / 38

44. ~ 0.1 NS-NS / SC
but 0 soft NS-NS / SC:
selection effect!
Higher favour
NS-NS
reflects
(no NS-NS from
dynamics)
BH-NS averages are
similar to NS-NS
ones
Demographics | Average number of NS-NS
Z
⟨nNS−NS⟩SC
fPB
30 / 38

45. High density favour
stable BH-BH
formation
High concentration
too
Small differences
between different
in the new
simulations
Vertical lines
highlight the core
collapse
Demographics | Average BH-BH per cluster per timestep
Z
∼ 2 Myrtcc [ ]
rvir
0.8 pc
3/2
[ ]
Mtot
3500 M⊙
1/2
31 / 38

46. All DCOB systems with
(BMCs)
BH-BH and NS-NS BMCs are in
agreement with Ziosi+2014
NS-NS are harder than BH-BH
shorter
Presence of BH-NS BMCs in the
new simulations
14 BH-BH and 45 NS-NS merging
within (in total)
34 NS-NS merging within 100
Myr
Demographics | Coalescence timescales
≤tGW tH
⇒ tGW
tH
32 / 38

47. BH-BH merger rate
shows no significant
dependence on the
YSC structural
properties
Errors through
MonteCarlo
approach
(underestimated)
Demographics | Merger rate
33 / 38

48. Demographics | Merger rate comparison with literature
34 / 38

49. BH-BH detection
rates are higher at:
higher densities
higher
concentrations
NS-NS and BH-NS
detection rates
follow the trends of
the merger rates
Demographics | Detection rate
∼ O(1 )Rdet yr−1
35 / 38

50. Starlab public version
Spherical bulge (Plummer) only
My upgraded version
Bulge + disk + halo
(Milky Way-like potential)
(Allen&Santillan 1991)
Tidal field | Before and after
36 / 38

51. Tidal field Example
37 / 38

52. Summary & Future prospects
➡ Adv. Virgo/LIGO are starting their science runs NOW!!
✔ BHs are likely to acquire a companion through dynamical exchanges
✔ Low metallicity favours the early formation of heavy and stable BH-BH
✔ Higher density and concentration and smaller favour BH-BH formation
✔ Good agreement with NS-NS observations
✔ Merger and detection rates do not depend on cluster properties
significantly and are compatible with literature
➡ Tidal field routines ready to investigate the role of tidal field
➡ Increase statistical sample
➡ Add Mikkola's regularization
➡ Multiple systems
➡ SC formation from a gas cloud
fPB
O(1 )yr−1
38 / 38

53. time
VIRGO/
LIGO
LISA
Thanks!! 恀