astrophysical sources of stochastic gravitational-wave background tania regimbau cnrs/artemis gwdaw...
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Astrophysical Sources of Stochastic Gravitational-Wave Background
Tania Regimbau CNRS/ARTEMIS
GWDAW 12, Boston, Dec. 2008
1LIGO-G070843-00-0
Stochastic Background
2
Cosmological SGWB: signature of the early Universeinflation, cosmic strings, phase transitions…
Astrophysical SGWB: sources since the beginning of stellar activitycompact binaries, supernovae, rotating NSs, core-collapse to NSs or BHs, supermassive BHs…
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:
Plan of this talk
3
Spectral properties of Astrophysical Backgrounds (AGBs)
Detection regimes (resolved sources, popcorn, continuous)
Some predictions
Astrophysical constraints with advanced detectors
Spectral properties of AGBs
4
AGB spectra are determined by:
the cosmological model (H0=70 km/s/Mpc, m =0.3, =0.7)
the star formation history
the spectral properties of individual sources dEgw /d
sup
fluence of single sourcessource cosmic rate
( )
3 2 200
max max
maxsup
max
8 ( ) 1( )= ( )
3 4 ( )(1 )
1 for 1where ( )
~ 6 otherwise
ooz gw
gw o o o
ooo
dEG dR zdz
c H dz r z z d
zz
z
Cosmic Star Formation Rate
5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00.00
0.05
0.10
0.15
0.20
0.25
h0=0.7
m
Madau & Pozzetti, 2000 Steidel et al., 1999 Blain et al., 1999 Hopkins & Beacom, 2006
R* (
Mo
yr-1 M
pc-3)
z
Detection Regimes
6
The nature of AGBs is charaterized by the duty cycle, the ratio between the average event duration and the time interval between successive events t.
0
(1 ')( ') 1( ) ' where( ') ( ') ( ')
'
o
ozo
o o
zz
D z dz dRt z t z zdz
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)
Models
7
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
Spectra
8
The shape of AGBs is characterized by:cutoff at the maximal emission frequencymax
maximum which depends on the shape of the SFR and max
often well approximated by power laws at low frequency
10 100 10001E-18
1E-17
1E-16
1E-15
1E-14
1E-13
1E-12
1E-11
1E-10
1E-9
1E-8
de Sitter inflation
slow roll inflation
bar modesMaclauren/Dedekind
r modesSN II: Buonnano et al. astro-ph/0412277
NS phase transitionSigl astro-ph/0602345
magnetars
pulsars
core collapse to BH: ringdown
NS-NSRegimbau et al. gr-qc/07074327
(Hz)
gw
10 100 10001E-63
1E-62
1E-61
1E-60
1E-59
1E-58
1E-57
1E-56
1E-55
1E-54
1E-53
1E-52
1E-51
1E-50
1E-49
(Hz)
ShH
z-1
230
2
3spectal energy density: ( ) ( )
4h o o gw o
HS
Tri-axial Neutron Stars
9
source rate:follows the star formation rate (fast evolution of massive stars)
spectral energy density:
Population synthesis (Regimbau & de F. Pacheco 2000, Faucher-Giguere & Kaspi 2006) :
• initial period: normal distribution with <Po>~250 -300 ms and ~80 -150ms
• magnetic field: log-normal distribution with <log B>~13 G
4 3 23
02 6 2 2
192 with [0;2 / ]
5 singw
dip
dE GIP
d c R B
0 *
*
( )( ) ( )
(1 )
= mass fraction of NS progenitors in the range 8-40 M
( ) = cosmic star formation rate
p
p
dR R z dVz z
dz z dz
R z
Energy density spectrum
10
10 100 1000
1E-18
1E-17
1E-16
1E-15
1E-14
1E-13
B = 1013
G, = 10-6
Pmin
=0.8 ms P
min=0.5 ms
gw
(Hz)
Spectrum from the cosmological population of rotating NSs, assuming initial period and magnetic field distributions derived from population synthesis.
0
4v
Constraints on B*
11
1E11 1E12 1E13 1E141E-7
1E-6
1E-5
1E-4
1E-3
0.01
SNR=1
SNR=5
Excluded region
<Beff
> (Gauss)
1E11 1E12 1E13 1E141E-7
1E-6
1E-5
1E-4
1E-3
0.01
SNR=1
SNR=5
Excluded region
<Beff
> (Gauss)
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)
*2-D projection, assuming the distribution of initial period derived from population synthesis.
Double Neutron Stars
12
Last thousands seconds before the last stable orbit in [10-1500 Hz]: 96% of the energy released.
source rate:
spectral energy density:2/3
1/31 21/3
1 2
( ) with [10 Hz; ]
3 ( )gw
lso
dE m mG
d m m
*0 ( )( ) ( ) ( )
1
= mass fraction of NS progenitors in the range 8-40 M
: fraction of massive binaries formed among all stars
:fraction of massive binaries that remain
c db ns p d d
f
p
b
NS
R t tdR dVz f P t dt z
dz z dz
f
*
bounded after the second supernova
( ) = cosmic star formation rate
( ): probability for a newly formed NS/NS to coalesce in a timescale td d
R z
P t
13
Cosmic coalescence rate
0 1 2 3 4 5 60.00
0.05
0.10
0.15
0.20
star formation rate = 1, =20 Myr = 3/2, =20 Myr = 1/2, =20 Myr = 1, =100 Myr
R* (
MoM
pc-3yr
-1)
z
( ) with minimal delay d d oP t t
Energy density spectrum
14
0.1 1
0.01
0.1
1
10
100
continuous background
resolved sources
popcorn noiseD(z
)
z
10 100 1000
1E-10
1E-9
popcorn noise
resolved sources
gaussian background gw
(Hz)
all sources z >0.26 (popcorn) z >0.52 (continuous)
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 0=20Myr.
Constraints on fb-ns*
15
0.0 0.2 0.4 0.6 0.8 1.0
1E-4
1E-3
0.01
0.1
1
Rmw
=10-5 yr-1
Rmw
=10-6 yr-1
Rmw
=10-4 yr-1
Ad H1L1: Rmw
=4.5 10-4 yr-1
Ad H1H2: Rmw
=2.4 10-5 yr-1
3rd gen. H1L1: Rmw
=4.5 10-6 yr-1
3rd gen. H1H2: Rmw
=1.7 10-6 yr-1
ns
fb
Constraints given on the fractions fb and ns for T= 3 years and SNR=1.
*2D projection, assuming a coalescence time distribution with parameter =1 and 0=20Myr.
Summary and Conclusions
16
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 periodrate of compact binaries….
Magnetars
1919
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)
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):
spectral energy density
8 2 24 8 2 2
100 10 45 152
sin3.7 10
4B
R Bg g R I B
GI
4 2 2,16~ 1.6 10 when B t t pB B B
100
37 2 21153 2
2 36 4 2,16 15
3.9 10 (pure poloidal field)1 where ~
7.1 10 (toroidal internal field)
gw
t
g BdE KK K
d I B B
Energy density spectrum
20
10 100 10001E-17
1E-16
1E-15
1E-14
1E-13
1E-12
1E-11
1E-10
1E-9
1E-8
1E-7
1E-6saturation: GW spin-down Beff=10
15G ; g=100
Beff=1016
G ; g=1000
Beff=1017
G ; g=10000
gw
(Hz)10 100 1000
1E-18
1E-17
1E-16
1E-15
1E-14
1E-13
1E-12
1E-11
1E-10
1E-9
1E-8
1E-7
(Hz)
Bt=10
17G B
eff=10
14G
Bt=10
17G B
eff=10
15G
Bt=10
16G B
eff=10
14G
Bt=10
16G B
eff=10
15G
gw
pure poloidal magnetic field toroidal internal magnetic field
Spectrum from the cosmological population of magnetars, assuming an initial period P i =1 ms and a galactic rate Rmw=0.1 per century.
Constraints on g-B
21
10 100 1000 10000
1E14
1E15
1E16
1E17
1E18
SNR=1
normal interior superconductor II or currents
superconductor I
magnetic spindown:
SNR~0.002 I45
-1 RMW;0.1
(g100
B15
)2
GW spindown: SNR~1.5 I
45 R
MW;0.1 (saturation)
<B>AXP
<B>SGR
magnetar limit
Bef
f G
g
If no detection, we can rule out the model of spindown dominated by GW emission
10 100 1000 10000
1E14
1E15
1E16
1E17
1E18
SNR=10
SNR=5
SNR=1
normal interior superconductor II or currents
superconductor I
magnetic spindown:
SNR~0.01 I45
-1 RMW;0.1(g100B15)2
GW spindown: SNR~16 I45 RMW;0.1 (saturation)
<B>AXP
<B>SGR
magnetar limit
Bef
f G
g
Constraints given by coaligned and coincident detectors (H1-H2), for T=3 yrs of observation, , in the range 10-500 Hz.
3rd generation detectors (Einstein Telescope)Advanced detectors (Ad LIGO sensitivity)
Constraints on BtB
22
If no detection, we can rule out the model of spindown dominated by GW emission
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)
1E15 1E16 1E17 1E18
1E14
1E15
1E16
1E17
SNR=1
magnetic spindown:
SNR~0.04 (B16
2/B14
)2
GW spindown (saturation)SNR~1.5
<B>AXP
<B>SGR
magnetar limit
Bef
f (G
)
Bt (G)
1E15 1E16 1E17 1E18
1E14
1E15
1E16
1E17
SNR=5
SNR=10
SNR=1magnetic spindown:
SNR~0.22 I45
3 RMW;0.1
(B16
2/B14
)2
GW spindown (saturation)SNR~16 I
45 R
MW;0.1
<B>AXP
<B>SGR
magnetar limit
Bef
f (G
)
Bt (G)
NS Initial Instabilities
23
source rate:Only the small fraction of NS born fast enough to enter the instability window:
Population synthesis ((Regimbau & de F. Pacheco 2000, Faucher-Giguere & Kaspi 2006) :
• initial period: normal distribution with <Po>~250 -300 ms and ~80 -150ms
spectral energy density:
max
min
0 *
0 0
*
( )( ) ( )
(1 )
= mass fraction of NS progenitors in the range 40-100 M
fraction of newborn NS that enter the instability ( = ( ) )
( ) = cosmic star formation rate
p
p
P
P
dR R z dVz z
dz z dz
g P dP
R z
002
0sup
r-modes: 2
bar-modes: K
MacLauren Dedekind
E EEdE
E E Ed
Instability windows
24
Bar modes:
secular instability: 0.14< <0.27-R=10 km: Po ~0.8-1.1 ms (~2e-5)
-R=12.5 km: Po ~ 1.1-1.6 ms (~3e-5)
R modes:
gwv ,T)
-R=10 km: Po ~0.7-9 ms (~5e-4)
-R=12.5 km: Po ~1-12 ms ~8e-4)
GW emission
viscosity
0.14 0.16 0.18 0.20 0.22 0.24 0.260.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
R=10 km
R=12.5 km
P (m
s)
=T/W
0.076
Energy density spectrum
25
10 10010
-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
R=10 km (shot noise DC<<1) R=12.5 km (shot noise DC<<1) 1% of NS born with P0~1ms (continuous)
gw
(Hz)
10 100 10001E-15
1E-14
1E-13
1E-12
1E-11
1E-10
1E-9
1E-8
(Hz)
gw
R=10 km R=12.5 km 1% of NS born with
max
Bar modes: R modes:
Spectrum from the cosmological population of newborn NSs that enter the bar and r-modes instability windows.
Constraints on
26
Bar modes:
sensitivity H1L1 H1H2
Advanced - 2-5%
3rd gen.
4-10% 0.2-0.5%
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.
R modes:
Core collapse to BH (ringdown)
272727
source rate:follows the star formation rate (fast evolution of massive stars)
spectral energy density:All the energy is emitted at the same frequency (Thorne, 1987)
2* *
4
( ( )) with (kHz) ~ 13 / (M )
mass of the BH: with ~ 10 20%
efficiency: <7 10
gwc c c
c p
dEM c M M
dM M
0 *
*
( )( ) ( )
(1 )
= mass fraction of NS progenitors in the range 40-100 M
( ) = cosmic star formation rate
p
p
dR R z dVz z
dz z dz
R z
0 500 1000 1500 2000 2500 3000 3500 4000 45000.00E+000
2.00E-009
4.00E-009
6.00E-009
8.00E-009
1.00E-008
1.20E-008
1.40E-008 =7.10-4 Mmin=40 Ms =10% Mmin=40 Ms =20% Mmin=30 Ms =10% Mmin=30 Ms =20%
gw
Hz
Energy density spectrum
28
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.