Stochastic gravitational wave background from binary
black holes
Irina Dvorkin (Institut d’Astrophysique de Paris)
Joe Silk, Elisabeth Vangioni, Jean-Philippe Uzan, Enrico Barausse (IAP),
Keith Olive (U Minnesota)
MNRAS 461, 3877 [arXiv:1604.04288]
Phys. Rev. D 94, 103011 [arXiv:1607.06818]
IAP, 27 January 2017
Introduction
Colpi & Sesana (2016)
Introduction
Astrophysics with gravitational waves
S
Starting to measure the BH mass distribution
(LIGO/VIRGO Collaborations [1606.04856])
How to make a black hole
How to make a black hole
Core collapse SN/direct collapse to a BH
Mass prior to core collapse: determined by stellar winds
Explosion mechanism
How to make a black hole
How to make a black hole
Core collapse SN/direct collapse to a BH
Mass prior to core collapse: determined by stellar winds
Explosion mechanism
Supernova explosion and (partial) fallback of matter
Failed supernova: direct collapse into a BH
How to make a black hole
How to make a black hole
Core collapse SN/direct collapse to a BH
Mass prior to core collapse: determined by stellar winds
Explosion mechanism
Supernova explosion and (partial) fallback of matter
Failed supernova: direct collapse into a BH
Interactions in dense stellar environments
How to make a black hole
How to make a black hole
Core collapse SN/direct collapse to a BH
Mass prior to core collapse: determined by stellar winds
Explosion mechanism
Supernova explosion and (partial) fallback of matter
Failed supernova: direct collapse into a BH
Interactions in dense stellar environments
Population III stars (metal-free)
How to make a black hole
How to make a black hole
Core collapse SN/direct collapse to a BH
Mass prior to core collapse: determined by stellar winds
Explosion mechanism
Supernova explosion and (partial) fallback of matter
Failed supernova: direct collapse into a BH
Interactions in dense stellar environments
Population III stars (metal-free)
Primordial black holes
How to make a black hole
How to make a black hole
Core collapse SN/direct collapse to a BH
Mass prior to core collapse: determined by stellar winds
Explosion mechanism
Supernova explosion and (partial) fallback of matter
Failed supernova: direct collapse into a BH
Interactions in dense stellar environments
Population III stars (metal-free)
Primordial black holes
How to make a black hole
Core collapse: islands of ’explodability’ ?
The goal: MBH = f (Minitial , Z , ?)
Ugliano et al. (2012)
How to make a black hole
Core collapse: islands of ’explodability’ ?
The goal: MBH = f (Minitial , Z , ?)
Ugliano et al. (2012)
How to make a black hole
Common envelope evolution
Belczynski et al. (2016)
How to make a black hole
Isolated evolution of massive stars, MBH = f (Minitial , Z )
How to make a black hole
From massive stars to black holes
Mass prior to core collapse is determined by stellar winds
Vink (2008)
How to make a black hole
From massive stars to black holes
Mass prior to core collapse is determined by stellar winds
Belczynski et al. (2016)
How to make a black hole
Cosmic metallicity evolution
Damped Ly-α systems data from Rafelski et al. (2012)
0.5
0
−0.5
[M/H]
−1
−1.5
−2
−2.5
−3
0
1
2
3
Redshift
4
5
6
Dvorkin et al. (2015)
Chemical evolution of the interstellar matter
Self-consistent model of BBH birth rate: overview
Daigne et al. (2004, 2006), Vangioni et al. (2015), Dvorkin et al. (2015)
Input
Galaxy growth (inflow and outflow) prescriptions
Cosmic star formation rate
Stellar initial mass function
Stellar yields
Black hole mass as a function of initial stellar mass and metallicity
Chemical evolution of the interstellar matter
Self-consistent model of BBH birth rate: overview
Daigne et al. (2004, 2006), Vangioni et al. (2015), Dvorkin et al. (2015)
Input
Galaxy growth (inflow and outflow) prescriptions
Cosmic star formation rate
Stellar initial mass function
Stellar yields
Black hole mass as a function of initial stellar mass and metallicity
Constraints
Cosmic chemical evolution
Optical depth to reionization
Chemical evolution of the interstellar matter
Self-consistent model of BBH birth rate: overview
Daigne et al. (2004, 2006), Vangioni et al. (2015), Dvorkin et al. (2015)
Input
Galaxy growth (inflow and outflow) prescriptions
Cosmic star formation rate
Stellar initial mass function
Stellar yields
Black hole mass as a function of initial stellar mass and metallicity
Constraints
Cosmic chemical evolution
Optical depth to reionization
Output
Birth rate of black holes per unit mass
Chemical evolution of the interstellar matter
Self-consistent model of BBH birth rate: overview
Daigne et al. (2004, 2006), Vangioni et al. (2015), Dvorkin et al. (2015)
Input
Galaxy growth (inflow and outflow) prescriptions
Cosmic star formation rate
Stellar initial mass function
Stellar yields
Black hole mass as a function of initial stellar mass and metallicity
Constraints
Cosmic chemical evolution
Optical depth to reionization
Output
Birth rate of black holes per unit mass
Note: to get merger rate we need to assume time delay distribution
Chemical evolution of the interstellar matter
Self-consistent model of BBH birth rate: overview
Input
Galaxy growth (inflow and outflow) prescriptions
Cosmic star formation rate
Stellar initial mass function
Stellar yields
Black hole mass as a function of initial stellar mass and metallicity
Dvorkin et al. [1604.04288]
Chemical evolution of the interstellar matter
Black hole mass as a function of stellar mass and
metallicity
Woosley & Weaver (1995): piston-driven explosion, assuming an
explosion energy
Fryer et al. (2012) : analytic model, assume time delay, calculate the
explosion energy and fallback mass
Kinugawa et al. (2014) : MBH = f (Mcore ) from Herant et al. (1994);
Belczynski et al. (2002)
Chemical evolution of the interstellar matter
Metallicity
1
Fryer
WWp
WWp + PopIII
WWp + GRB-based SFR
WWp + steep IMF
0.5
0
-0.5
[M/H]
-1
-1.5
-2
-2.5
-3
-3.5
-4
0
2
4
6
8
Redshift
10
12
14
Merger rates of binary black holes
Total merger rates
Normalized to the observed merger rate: R = 10−7 Mpc−3 yr−1
10 -6
Fryer
WWp
WWp + PopIII
WWp + GRB-based SFR
WWp + steep IMF
Mpc -3 yr -1
10 -7
10 -8
10 -9
0
2
4
6
Redshift
8
10
Merger rates of binary black holes
Merger rates vs. mass
Normalized to the observed merger rate: R = 10−7 Mpc−3 yr−1
Fryer
WWp
WWp + K + PopIII
WWp + GRB-based SFR
WWp + steep IMF
10 -8
Mpc -3 yr -1 M -1
sun
10 -9
10 -10
10 -11
10 -12
5
10
15
20
25
30
BH Mass
35
40
45
50
Gravitational wave background from merging binaries
Stochastic gravitational wave background
The background due to unresolved mergers of binary BHs
Gravitational wave background from merging binaries
Stochastic gravitational wave background
The background due to unresolved mergers of binary BHs
Dimensionless density parameter (energy density in units of ρc per
unit logarithmic frequency)
8πG
Ωgw (fo ) = 2 3 fo
3c H0
Z
dmbh
Z
dz
Rsource (z, mbh ) dE gw (mbh )
(1 + z)EV (z)
df
Rsource (z, mbh ) is the merger rate, dEgw /df is the emitted spectrum
Gravitational wave background from merging binaries
Stochastic gravitational wave background
10 -7
LIGO Fiducial
LIGO Fiducial + uncertainty
Dvorkin et al. (2016)
Dvorkin et al. (2016) + uncertainty
O1: 2015-16
O2: 2016-17
O5: 2020-22
ΩGW
10 -8
10 -9
10 -10
10 1
10 2
Frequency [Hz]
Gravitational wave background from evolving binaries
BH binaries number density (simple case)
Gravitational wave background from evolving binaries
BH binaries number density (simple case)
If all BH are in binaries, and all merger products remain single, the number
density nX of binaries in a certain mass M and orbital parameters bin is
set by: [where w = (a, e)]
The formation rate of BH (determined from stellar physics) RX (M, t)
The initial distribution of orbital parameters PX (w )
The evolution in time of the orbital parameters of the binary dw /dt
Gravitational wave background from evolving binaries
Evolution of the orbital parameters
General case (w = (a, e)):
dw
= f (w , M)
dt
A merger occurs when
w
= wmerger
Gravitational wave background from evolving binaries
Evolution of the orbital parameters
General case (w = (a, e)):
dw
= f (w , M)
dt
A merger occurs when
w
= wmerger
Example: evolution due to emission of GW [Peters & Mathews (1963)]
37 4
73 2
da
64 G 3 µm2 1 + 24 e + 96 e
=−
dt
5 c 5 a3
(1 − e 2 )7/2
121 2
304 G 3 µm2 e 1 + 304 e
de
=−
dt
15 c 5 a4 (1 − e 2 )5/2
Gravitational wave background from evolving binaries
Continuity equation
Hydrodynamics (matter density ρ, coordinate x, velocity u = dx/dt):
dρ
d
.[ρu ] = 0
+
dt
dx
Gravitational wave background from evolving binaries
Continuity equation
Hydrodynamics (matter density ρ, coordinate x, velocity u = dx/dt):
dρ
d
.[ρu ] = 0
+
dt
dx
Binaries (number density nX , coordinate
w,
velocity
d
dnX
.[nX f ] = 0
+
dt
dw
f
= dw /dt):
Gravitational wave background from evolving binaries
Continuity equation
Hydrodynamics (matter density ρ, coordinate x, velocity u = dx/dt):
dρ
d
.[ρu ] = 0
+
dt
dx
Binaries (number density nX , coordinate
w,
velocity
f
= dw /dt):
d
dnX
.[nX f ] = 0
+
dt
dw
Assuming ∂/∂t = 0 (stationary distribution of binaries in the galaxy) −→
stochastic GW emission from coalescing binary NS
Buitrago, Moreno-Garrido & Mediavilla (1994); Moreno-Garrido, Mediavilla & Buitrago
(1995); Ignatiev et al. (2001)
Gravitational wave background from evolving binaries
Continuity equation
Hydrodynamics (matter density ρ, coordinate x, velocity u = dx/dt):
dρ
d
.[ρu ] = 0
+
dt
dx
Binaries (number density nX , coordinate
w,
velocity
d
dnX
.[nX f ] = RX
+
dt
dw
No stationarity
Source function RX is given by astrophysics
f
= dw /dt):
Gravitational wave background from evolving binaries
Continuity equation (single population)
dw
dt
=
f (w , M)
Gravitational wave background from evolving binaries
Continuity equation (single population)
dw
dt
(1)
dnX (M, t)
dt
=
f (w , M)
= S M ′, M ′, t
Gravitational wave background from evolving binaries
Continuity equation (single population)
dw
dt
(1)
dnX (M, t)
dt
(2)
dnX (M, M, w , t)
dt
=
f (w , M)
= S M ′, M ′, t
=
−
1
RX (M, t)PX (w )
2
∂
(2)
.[f (w , M) nX (M, M, w , t)]
∂w
Gravitational wave background from evolving binaries
Continuity equation (single population)
dw
dt
(1)
dnX (M, t)
dt
(2)
dnX (M, M, w , t)
dt
=
f (w , M)
= S M ′, M ′, t
=
−
1
RX (M, t)PX (w )
2
∂
(2)
.[f (w , M) nX (M, M, w , t)]
∂w
S is source term due to mergers
All the merger products remain single, all objects are born in binaries
Gravitational wave background from evolving binaries
Initial distribution of orbital parameters
Sana et al. (2012); de Mink & Belczynski (2015)
Joint distribution: PX (w ) = P(e)P(a)
P(e) ∝ e −0.42
P(log T ) ∝ (log T )−0.5 in T ∈ (Tmin , Tmax )
Gravitational wave background from evolving binaries
Initial distribution of orbital parameters
Sana et al. (2012); de Mink & Belczynski (2015)
Joint distribution: PX (w ) = P(e)P(a)
P(e) ∝ e −0.42
P(log T ) ∝ (log T )−0.5 in T ∈ (Tmin , Tmax )
Gravitational wave background from evolving binaries
Time to coalescence
amin chosen so as to fit the observed merger rate (τmerger ∝ a4 )
1
0.9
Rapid mergers
M =5
M =10
M =30
M =50
0.8
Eccentricity
0.7
0.6
0.5
0.4
0.3
Slow mergers
0.2
0.1
0
-1.5
-1
-0.5
Log10(a/AU)
0
0.5
1
Gravitational wave background from evolving binaries
Initial distribution of orbital parameters
Sana et al. (2012); de Mink & Belczynski (2015)
Joint distribution: PX (w ) = P(e)P(a)
P(e) ∝ e −0.42
P(log T ) ∝ (log T )−0.5 in T ∈ (Tmin , Tmax )
Gravitational wave background from evolving binaries
GW background from BH binaries
Dvorkin et al. [1607.06818]
10 -7
This work, a
min
=0.2 AU
10 -8
This work, a
10 -9
Mergers only (D16)
LIGO O5
eLISA
min
=0.15-0.3 AU
Ω GW
10 -10
10 -11
10 -12
10 -13
10 -14
10 -15
10 -6
10 -4
10 -2
Frequency [Hz]
10 0
10 2
Massive BH binaries
Massive BH binaries
Massive BHs M ∼ 106 − 1010 M⊙ exist in the centers of galaxies
Galaxy mergers should create binaries that emit GW
Massive BH binaries
Massive BH binaries
Massive BHs M ∼ 106 − 1010 M⊙ exist in the centers of galaxies
Galaxy mergers should create binaries that emit GW
Shannon et al. 2016
Massive BH binaries
Estimated SNR with SKA
Assuming timing accuracy of 30 ns [PRELIMINARY RESULTS!!!]
200
15
10
5
3
180
20
140
15
120
10
5
3
No. of pulsars
160
100
10
80
5
60
3
40
5
5
10
observation time [yr]
15
Conclusions and outlook
Summary
Future GW observations can provide constraints on stellar physics:
SN explosion mechanism
PopIII stars
Properties of compact binary systems
Conclusions and outlook
Summary
Future GW observations can provide constraints on stellar physics:
SN explosion mechanism
PopIII stars
Properties of compact binary systems
... and galaxy-MBH co-evolution:
Formation of MBH binaries
Binary evolution, merger rates
Conclusions and outlook
Summary
Future GW observations can provide constraints on stellar physics:
SN explosion mechanism
PopIII stars
Properties of compact binary systems
... and galaxy-MBH co-evolution:
Formation of MBH binaries
Binary evolution, merger rates
More detections to come soon: need tools to analyze them and
extract astrophysical information