astrophysical sources of stochastic gravitational-wave background
DESCRIPTION
Astrophysical Sources of Stochastic Gravitational-Wave Background. Tania Regimbau CNRS/ARTEMIS GWDAW 12, Boston, Dec. 2008. LIGO-G070843-00-0. Stochastic Background. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/1.jpg)
Astrophysical Sources of Stochastic Gravitational-Wave Background
Tania Regimbau CNRS/ARTEMIS
GWDAW 12, Boston, Dec. 2008
1LIGO-G070843-00-0
![Page 2: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/2.jpg)
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:
![Page 3: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/3.jpg)
Plan of this talk
3
Spectral properties of Astrophysical Backgrounds (AGBs)
Detection regimes (resolved sources, popcorn, continuous)
Some predictions
Astrophysical constraints with advanced detectors
![Page 4: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/4.jpg)
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
![Page 5: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/5.jpg)
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
![Page 6: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/6.jpg)
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)
![Page 7: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/7.jpg)
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
![Page 8: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/8.jpg)
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
![Page 9: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/9.jpg)
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
![Page 10: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/10.jpg)
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
![Page 11: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/11.jpg)
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.
![Page 12: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/12.jpg)
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
![Page 13: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/13.jpg)
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
![Page 14: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/14.jpg)
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.
![Page 15: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/15.jpg)
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.
![Page 16: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/16.jpg)
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….
![Page 17: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/17.jpg)
Extra Slides
17
![Page 18: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/18.jpg)
Sensitivity
18
10 100 1000
1E-24
1E-23
1E-22
1E-21
1E-20
LIGO SDR 4K
EGO
Ad LIGO
h n(f)
f Hz
![Page 19: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/19.jpg)
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
![Page 20: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/20.jpg)
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.
![Page 21: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/21.jpg)
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)
![Page 22: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/22.jpg)
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)
![Page 23: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/23.jpg)
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
![Page 24: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/24.jpg)
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
![Page 25: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/25.jpg)
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.
![Page 26: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/26.jpg)
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:
![Page 27: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/27.jpg)
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
![Page 28: Astrophysical Sources of Stochastic Gravitational-Wave Background](https://reader036.vdocuments.net/reader036/viewer/2022062322/5681479d550346895db4d2aa/html5/thumbnails/28.jpg)
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.