Transcript Document 7635664

Astrophysical Sources of Stochastic
Gravitational-Wave Background
Tania Regimbau
CNRS/ARTEMIS
GWDAW 12, Boston, Dec. 2008
LIGO-G070843-00-0
1
Stochastic Background
A stochastic background of gravitational waves (SGWB) has resulted from the
superposition of a large number of unresolved sources since the Big Bang.
We distinguish between two contributions:
 Cosmological SGWB:
signature of the early Universe
inflation, cosmic strings, phase transitions…
Astrophysical SGWB:
sources since the beginning of stellar
activity
compact binaries, supernovae, rotating NSs,
core-collapse to NSs or BHs, supermassive
BHs…
2
Plan of this talk
Spectral properties of Astrophysical Backgrounds (AGBs)
 Detection regimes (resolved sources, popcorn, continuous)
 Some predictions
 Astrophysical constraints with advanced detectors
3
Spectral properties of AGBs
fluence of single sources
source cosmic rate
zsup (n o )
8 G
dR o ( z )
W gw (n o )= 3 2 n o 
0
3c H 0
dz
dEgw
1
(n o ) dz
2
4 r ( z )(1  z ) dn
n max
n max

1
for
n


o
1  zmax
where zsup (n o )   n o
 z ~ 6 otherwise
 max
AGB spectra are determined by:
 the cosmological model (H0=70 km/s/Mpc, Wm =0.3, WL=0.7)
 the star formation history
 the spectral properties of individual sources dEgw /dn
4
Cosmic Star Formation Rate
0.25
h0=0.7 Wm WL
Madau & Pozzetti, 2000
Steidel et al., 1999
Blain et al., 1999
Hopkins & Beacom, 2006
-3
R* (Mo yr Mpc )
0.20
-1
0.15
0.10
0.05
0.00
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
z
5
Detection Regimes
The nature of AGBs is charaterized by the duty cycle, the ratio between the
average event duration to and the time interval between successive events Dto.
t o  (1  z ')t
o

z t ( z ')
1
o
D( z )  
dz ' where 
o


dR
0 Dt ( z ')
o
( z ') 
Dt ( z ')  
 dz '


resolved sources (D <<1):
burst data analysis, optimal filtering
popcorn noise (D~1)
Maximum Likelihood statistic (Drasco et al. 2003), Probability Event Horizon
(Coward et al. 2005)
 gaussian stochastic background (D>>1)
cross correlation statistic (isotropic/anisotropic)
6
Models
 Core collapse supernovae
•
Neutron star formation: Blair & Ju 1996, Coward et al. 2001-02, Howell et al. 2004, Buonanno et
al. 2005
•
Stellar Black Hole formation: Ferrari et al. 1999, de Araujo et al. 2000-04
 Neutron stars
•
•
•
tri-axial emission: Regimbau & de F. Pacheco 2001-06
bar or r-modes: Owen et al. 1998, Ferrari et al. 1999, Regimbau 2001
phase transitions: Sigl 2006
 Stellar Compact Binaries
•
near coalescence (NS, BH): Regimbau et al. 2006-07 , Coward et al. 2005 (BNS), Howell et al.
2007 (BBH)
•
low frequency inspiral phase: Ferrari et al. 2002, Farmer & Phinney 2002, Cooray 2004 (WD-NS)
 Capture of compact objects by SMBHs : Barack & Cutler 2004
7
Spectra
The shape of AGBs is characterized by:
cutoff at the maximal emission frequency nmax
maximum which depends on the shape of the SFR and nmax
often well approximated by power laws at low frequency
core collapse to BH: ringdown
1E-8
1E-9
3H 02 3
n o W gw (n o )
4 2
1E-49
NS-NS
Regimbau et al. gr-qc/07074327
NS phase transition
Sigl astro-ph/0602345
1E-10
1E-50
1E-51
1E-52
magnetars
1E-11
1E-53
1E-12
1E-54
SN II: Buonnano et al.
astro-ph/0412277
1E-55
-1
r modes
1E-13
ShHz
Wgw
spectal energy density: Sh (n o ) 
de Sitter inflation
1E-14
1E-56
1E-57
1E-58
slow roll inflation
1E-59
1E-15
1E-60
bar modes
Maclauren/Dedekind
1E-16
pulsars
1E-17
1E-61
1E-62
1E-63
10
1E-18
10
100
1000
100
1000
no(Hz)
no(Hz)
8
Tri-axial Neutron Stars
 source rate:
follows the star formation rate (fast evolution of massive stars)
dR 0
R * ( z ) dV
( z)  p
( z)
dz
(1  z ) dz
 p = mass fraction of NS progenitors in the range 8-40 M
 *
 R ( z ) = cosmic star formation rate
 spectral energy density:
192 4GI 3
2

n 3 with n  [0; 2 / P0 ]
2 6
2
2
dn
5c R
Bdip sin 
dEgw
Population synthesis (Regimbau & de F. Pacheco 2000, Faucher-Giguere & Kaspi 2006) :
•
initial period: normal distribution with <Po>~250 -300 ms and s~80 -150ms
•
magnetic field: log-normal distribution with <log B>~13 G
9
Energy density spectrum
Spectrum from the cosmological population of rotating NSs, assuming initial period and
magnetic field distributions derived from population synthesis.
1E-13
13
-6
B = 10 G,  = 10
Pmin=0.8 ms
Pmin=0.5 ms
1E-14
Wgw
1E-15
 v04
1E-16
1E-17
1E-18
10
100
1000
no(Hz)
10
Constraints on B*
Constraints given by coaligned and coincident detectors (ex: H1-H2), for T=3 yrs of observation,
in the range 10-500 Hz.
Advanced detectors (Ad LIGO sensitivity)
3rd generation detectors (Einstein Telescope)
0.01
0.01
1E-3
1E-3
Excluded region
Excluded region

1E-4

1E-4
1E-5
SNR=5
1E-5
SNR=5
SNR=1
1E-6
1E-6
SNR=1
1E-7
1E11
1E12
1E13
<Beff> (Gauss)
1E14
1E-7
1E11
1E12
1E13
1E14
<Beff> (Gauss)
*2-D projection, assuming the distribution of initial period derived from population synthesis.
11
Double Neutron Stars
Last thousands seconds before the last stable orbit in [10-1500 Hz]: 96% of the energy released.
 source rate:
R* (tc  td )
dR 0
dV
( z )  fb  ns  p 
P(td )dtd
( z)
dz
1 z f
dz
 p = mass fraction of NS progenitors in the range 8-40 M

 fb : fraction of massive binaries formed among all stars

  NS :fraction of massive binaries that remain bounded after the second supernova
 *
 R ( z ) = cosmic star formation rate
 P(td ): probability for a newly formed NS/NS to coalesce in a timescale t d
 spectral energy density:
m1m2
( G )2/3

n 1/3 with n  [10 Hz;n lso ]
1/3
dn
3 (m1  m2 )
dEgw
12
Cosmic coalescence rate
P(td )  td with minimal delay t o
0.20
star formation rate
 = 1, t=20 Myr
 = 3/2, t=20 Myr
 = 1/2, t=20 Myr
 = 1, t=100 Myr
-3
-1
R* (MoMpc yr )
0.15
0.10
0.05
0.00
0
1
2
3
4
5
6
z
13
Energy density spectrum
Spectrum for the three regimes (resolved sources, popcorn noise and gaussian background),
assuming a galactic coalescence rate Rmw=3. 10-5 yr-1 and a coalescence time distribution with
parameter =1 and t0=20Myr.
1E-9
all sources
z >0.26 (popcorn)
z >0.52 (continuous)
resolved sources
popcorn noise
100
D(z)
continuous background
1
Wgw
10
gaussian background
popcorn noise
0.1
resolved sources
0.01
1E-10
0.1
1
z
10
100
1000
no(Hz)
14
Constraints on fb-ns*
Constraints given on the fractions fb and ns for T= 3 years and SNR=1.
-4
-1
-5
-1
Ad H1L1: Rmw=4.5 10 yr
1
Ad H1H2: Rmw=2.4 10 yr
-6
-1
-6
-1
3rd gen. H1L1: Rmw=4.5 10 yr
3rd gen. H1H2: Rmw=1.7 10 yr
ns
0.1
-4
-1
-5
-1
-6
-1
Rmw=10 yr
0.01
Rmw=10 yr
1E-3
Rmw=10 yr
1E-4
0.0
0.2
0.4
0.6
0.8
1.0
fb
*2D projection, assuming a coalescence time distribution with parameter =1 and t0=20Myr.
15
Summary and Conclusions
Why are AGBs important (and need to be modeled accurately)?
carry information about the star formation history, the statistical properties of source
populations.
 may be a noise for the cosmological background
How do AGBs differ from the CGB (and need specific detection strategies)?
 anisotropic in the local universe (directed searches)
different regimes: shot noise, popcorn noise and gaussian
(maximum likelihood statistic, Drasco et al.; probability event horizon Coward et al.)
spectrum characterized by a maximum and a cutoff frequency
 Advanced detectors may be able to put interesting constraints
NS ellipticity, magnetic field, initial period
rate of compact binaries
….
16
Extra Slides
17
Sensitivity
1E-20
1E-21
LIGO SDR 4K
hn(f)
Ad LIGO
1E-22
1E-23
EGO
1E-24
10
100
1000
f Hz
18
Magnetars
 about 10-20% of the radio pulsar population
 super-strong crustal magnetic fields (Bdip~1014 – 1016 G) formed by dynamo action
in proto neutron stars with millisecond rotation period P0 ~0.6 – 3 ms (break up
limit - convective overturn).
 strong magnetic fields can induce significant equatorial deformation
•
pure poloidal field (Bonazzola 1996)
R8 B 2 sin 2 
B  g
4GI 2
2 2
3.7 104 g100 R108 I 45
B15
The distortion parameter g depends on both the EOS and the geometry of the magnetic field:
g~1-10 (non-superconductor), g~100-1000 (type I superconductor), g>1000-10000 (type II superconductor,
counter rotating electric current)
•
internal field dominated by the toroidal component (Cutler 2002, dall’Osso et al. 2007):
 B ~ 1.6 104  Bt2,16 2 when Bt  Bp
 spectral energy density
K


 Kn 3 1  2 n 2 
dn
  I 
dEgw
1
37 2
2

3.9 10 g100 B15 (pure poloidal field)
where K ~ 
36 4
2

7.110 Bt ,16 B15 (toroidal internal field)
19
Energy density spectrum
Spectrum from the cosmological population of magnetars, assuming an initial period Pi =1 ms
and a galactic rate Rmw=0.1 per century.
pure poloidal magnetic field
1E-6
toroidal internal magnetic field
1E-7
15
Beff=10 G ; g=100
saturation: GW spin-down
16
Beff=10 G ; g=1000
1E-7
17
15
16
14
16
15
Bt=10 G Beff=10 G
1E-8
1E-9
1E-9
1E-10
1E-10
1E-11
1E-11
1E-12
Wgw
Wgw
14
17
Bt=10 G Beff=10 G
Beff=10 G ; g=10000
1E-12
1E-14
1E-14
1E-15
1E-15
1E-16
1E-16
1E-17
1E-17
100
no(Hz)
1000
Bt=10 G Beff=10 G
1E-13
1E-13
10
17
Bt=10 G Beff=10 G
1E-8
1E-18
10
100
no(Hz)
1000
20
Constraints on g-B
Constraints given by coaligned and coincident detectors (H1-H2), for T=3 yrs of observation,
, in the range 10-500 Hz.
Advanced detectors (Ad LIGO sensitivity)
3rd generation detectors (Einstein Telescope)
1E18
1E18
SNR=1
SNR=10
GW spindown:
SNR~1.5 I45 RMW;0.1 (saturation)
1E17
1E17
GW spindown:
SNR~16 I45 RMW;0.1 (saturation)
SNR=5
SNR=1
1E16
Beff G
Beff G
1E16
<B>SGR
<B>AXP
1E15
<B>SGR
<B>AXP
1E15
magnetic spindown:
-1
magnetic spindown:
2
SNR~0.002 I45 RMW;0.1(g100B15)
1E14
10
normal interior
-1
100
superconductor I
g
1000
superconductor II
or currents
10000
2
SNR~0.01 I45 RMW;0.1(g100B15)
1E14
magnetar limit
10
normal interior
magnetar limit
100
superconductor I
g
1000
10000
superconductor II
or currents
If no detection, we can rule out the model of spindown dominated by GW emission
21
Constraints on BtB
Constraints given by coaligned and coincident detectors (ex: H1-H2), for T=3 yrs of
observation, in the range 10-500 Hz.
Advanced detectors (Ad LIGO sensitivity)
3rd generation detectors (Einstein Telescope)
1E17
1E17
SNR=1
magnetic spindown:
magnetic spindown:
2
SNR~0.04 (B16 /B14)
3
2
SNR~0.22 I45 RMW;0.1(B16 /B14)
2
2
SNR=5
1E16
1E16
SNR=10
<B>SGR
<B>SGR
1E15
Beff (G)
Beff (G)
SNR=1
<B>AXP
1E15
<B>AXP
1E14
1E14
magnetar limit
1E15
magnetar limit
GW spindown (saturation)
SNR~1.5
1E16
1E17
Bt (G)
1E18
1E15
GW spindown (saturation)
SNR~16 I45 RMW;0.1
1E16
1E17
1E18
Bt (G)
If no detection, we can rule out the model of spindown dominated by GW emission
22
NS Initial Instabilities
 source rate:
Only the small fraction of NS born fast enough to enter the instability window:
dR 0
R * ( z ) dV
( z )   p
( z)
dz
(1  z ) dz
 p = mass fraction of NS progenitors in the range 40-100 M

Pmax


fraction
of
newborn
NS
that
enter
the
instability
(

=

Pmin g ( P0 )dP0 )

 R * ( z ) = cosmic star formation rate
Population synthesis ((Regimbau & de F. Pacheco 2000, Faucher-Giguere & Kaspi 2006) :
• initial period: normal distribution with <Po>~250 -300 ms and s~80 -150ms
 spectral energy density:
r-modes: E0  DEK
dE 2 E0
 2 n 
dn n sup
bar-modes: E0  EMacLauren  EDedekind
23
Instability windows
Bar modes:
R modes:
secular instability: 0.14< <0.27
|tgw(W)|tv (W,T)
-R=10 km: Po ~0.8-1.1 ms (~2e-5)
-R=10 km: Po ~0.7-9 ms (~5e-4)
-R=12.5 km: Po ~ 1.1-1.6 ms (~3e-5)
-R=12.5 km: Po ~1-12 ms (~8e-4)
1.6
R=12.5 km
1.5
GW emission
1.4
P (ms)
1.3
1.2
R=10 km
1.1
1.0
0.9
0.076
viscosity
0.8
0.14
0.16
0.18
0.20
=T/W
0.22
0.24
0.26
24
Energy density spectrum
Spectrum from the cosmological population of newborn NSs that enter the bar and r-modes
instability windows.
Bar modes:
R modes:
1E-8
-8
10
R=10 km (shot noise DC<<1)
R=12.5 km (shot noise DC<<1)
1% of NS born with P0~1ms (continuous)
-9
10
1E-10
-11
1E-11
10
Wgw
Wgw
1E-9
-10
10
R=10 km
R=12.5 km
1% of NS born with Wmax
-12
1E-12
-13
1E-13
-14
1E-14
10
10
10
-15
1E-15
10
10
100
no(Hz)
10
100
1000
no(Hz)
25
Constraints on 
Constraints on the fraction of NS that enter the instability window of bar modes and R modes
near the Keplerian velocity for T= 3 years and SNR=1-5.
Bar modes:
R modes:
sensitivity
H1L1
H1H2
sensitivity
H1L1
H1H2
Advanced
-
2-4%
Advanced
-
2-5%
4-9%
0.2-0.4%
4-10%
0.2-0.5%
3rd gen.
3rd gen.
26
Core collapse to BH (ringdown)
 source rate:
follows the star formation rate (fast evolution of massive stars)
dR 0
R * ( z ) dV
( z)  p
( z)
dz
(1  z ) dz
 p = mass fraction of NS progenitors in the range 40-100 M
 *
 R ( z ) = cosmic star formation rate
 spectral energy density:
All the energy is emitted at the same frequency (Thorne, 1987)
dEgw
  M c c 2 (n n * ( M c )) with n * (kHz) ~ 13 / M c (M )
dn
mass of the BH: M c   M p with  ~ 10  20%
efficiency:  <7 104
27
Energy density spectrum
Spectrum from the cosmological population of newborn distorted BHs. The resulted background
is not gaussian but rather a shot noise with a duty cycle DC~0.01.
-4
=7.10
1.40E-008
Mmin=40 Ms =10%
Mmin=40 Ms =20%
Mmin=30 Ms =10%
Mmin=30 Ms =20%
1.20E-008
1.00E-008
Wgw
8.00E-009
6.00E-009
4.00E-009
2.00E-009
0.00E+000
0
500
1000
1500
2000
2500
3000
3500
4000
4500
no(Hz)
28