GW Backgound from extragalactic Double Neutron Stars
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GW Backgound from extragalactic Double Neutron Stars Tania Regimbau Virgo/ARTEMIS-OCA
description
GW Backgound from extragalactic Double Neutron Stars. Tania Regimbau Virgo/ARTEMIS-OCA. Plan. Monte Carlo simulations in the frequency band of: Ground-based interferometers: last 1000 s before the LSO LISA band: low frequency inspiral signal. - PowerPoint PPT Presentation
Transcript of GW Backgound from extragalactic Double Neutron Stars
GW Backgound from extragalactic Double Neutron
Stars
Tania Regimbau
Virgo/ARTEMIS-OCA
2
Plan
Monte Carlo simulations in the frequency band of:
Ground-based interferometers: last 1000 s before the LSO
LISA band: low frequency inspiral signal
23
20
( ) 4( ) = ( )
(ln ) 3gw
gw hc
d ff f S f
d f H
The GW Stochastic Background
10-43s: gravitons decoupled (T = 1019 GeV)
300000 yrs: photons decoupled (T = 0.2 eV)
Two contributions:
cosmological: signature of the early Universeinflation, cosmic strings, phase transitions…
astrophysical: superposition of all the sources since the beginning of the stellar activity:Compact binairies, supernovae, BH ring down, supermassive BH …
characterized by the energy density parameter:
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Astrophysical Stochastic Backgrounds
sup0
0
0
3 200
sup
supsup
1 1( )= with ( )
4
6 if 7where (14)
1 otherwise
z gwgw
critical L
o
o
F dEf F dR z
c d d
z
To model astrophysical backgrounds one needs to know:
The cosmological model (H0, m):737 cosmology: flat Einstein de Sitter Universe with h0=0.7, m=0.3,
The source rate dR(z)
The individual energy spectral density gwdE
d
5
Ground-based interferometer frequency band
5 100.087( ) with [2 10 ;2 10 yr]P
8( ) with 10 yrb f b bz z z
*
5
0
( )( ) with ( )
1( )
f f ff f f f p
f f f
R z R dVP z R z
z dzR z dz
redshift of formation of massive binaries (Coward et al. 2002)
redshift of formation of NS/NS
coalescence time
redshift of coalescence
0
1
(1 ) ( )
b
c
z
z
dz
H z E z
observed fluence
o
1/3
2 2 4/30
1
4 4 ( )(1 )gw o
L c c
dE Kf
d d r z z
Last thousands seconds before the last stable orbit:
96% of the energy released, in the range [10-1500 Hz]
Random selection of zf
zb = zf - z
Random selection of
Compute zc
Compute f
If zb < 0
If zc < z*
x N=106
(uncertainty on gw <0.1%)
0
0 0
0
31
( )= with DNS
NN i
gw Nic
Ff F f
c
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Detection Regimes
The duty cycle characterizes the nature of the background.
= 1000 s, which corresponds to 96% of the energy released, between 10-1500 Hz
D >1: continuous (z>0.1, 96%) The time interval between successive events is short compared to the duration of a single event
D <1: shot noise (z<0.01) The time interval between successive events is long compared to the duration of a single event
D ~1: popcorn (0.01<z<0.1) The time interval between successive events is of the same order as the duration of a single event
0( ) (1 ') ( ') '
z
cD z z R z dz
7
10 100 1000
1E-9
1E-8
1E-7
D(z=0.1)=1
D(z=0.01)=0.1
D(z=0.62)=10continuous background
popcorn noise
shot noise
o Hz
gw
Regimbau & de Freitas Pacheco, 2005, ApJ, 642, 455
8
10 100 1000 100001E-20
1E-18
1E-16
1E-14
1E-12
1E-10
1E-8
1E-6
magnetars superconducting
bar mode
BHNS/NS
pulsars
2 LIGO ad
magnetars
slow roll inflation
de Sitter inflation
string theory
cosmic strings
gw
o Hz
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Because the stochastic background cannot be distinguished from the instrumental noise background, the optimal detection strategy is to correlate the outputs of two (or more) detectors.
hypothesis:
isotropic, gaussian, stationnary
signal and noise, detector noises uncorrelated
Cross correlation statistic:
combine the signal outputs using an optimal filter to optimize the signal to noise ratio
Signal to noise ratio:
2 colocated/coaligned advanced detectors (LIGO ad): S/N ~0.652 colocated/coaligned 3rd generation detectors (EGO):S/N ~10
1 21 2
( ) ( )
( ) ( ) ( ) ( )( )
with( )hf S f
Y s f Q f s f df Q fP f P f
Detection
2 22 22
1 2 1 2
( ) ( )( ) ( ) 2( ) 2 2 where =
( ) ( ) ( ) ( ) 5effh
eff h
f S ff S fST T S S
N P f P f P f P f
10
LISA frequency band
8/3 3/8( ( ( , )) /(1 ) o l e eso c bzK zz
redshift of emission
observed fluence
o
1/3
2 2 4/30
1
4 4 ( )(1 )e e
gw o
L
dE Kf
d r z zd
Random selection of zf
zb = zf - z
Random selection of
Compute ze
Compute f
If zb < 0
x N=106
0
0 0
0
31
( )= with DNS
NN i
gw Nic
Ff F f
c
min max0 0 0for in [ , ]
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1E-5 1E-4 1E-3 0.01 0.1 11E-23
1E-21
1E-19
1E-17
1E-15
d > 25 Mpc (Virgo cluster) d > 100 Mpc (Great Attractor)
galactic WD-WD
LISA
Hz
Sh1/
2 Hz-1
/2
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Summary
GBased interferometers (1000s before LSO):- 3 regimes: resolved (z<0.01), popcorn (0.01<z<0.1), continuous (z>0.1)- continuous contribution reaches a maximum of around 930 Hz
- S/R~0.65 (~10) for second (third) generation of interferometers
LISA band (low frequency inspiral phase):- may dominate the LISA instrumental noise between 0.7-6 mHz (or 0.3-10 mHz
for the less conservative estimate), and the galactic double white dwarf confusion noise after 2 mHz.
- however, the resulting reduction in the sensitivity should be less than a factor 4 and thus shouldn't affect significantly signal detection.
97 10gw
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EXTRA SLIDES
14
0 1 2 3 4 5 6
0.000
0.005
0.010
0.015
0.020
0.025
0.030 coalescence formation
Rz
z
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LISA frequency band
8/3 3/8( ( ( , )) /(1 ) o l e eso c bzK zz
max
min
6
6
0
( ; ( , ))
( ) ( ') ( ') '( ) where
and ( ') ( )b
fz
Max z z
N z R z z dzN N z dz
z P d
8/3 5/3min 8/3 3/8 1 2
5 1/31 2
8/3 3/8cmax
256( ) /(1 ) with
5 ( )
( ( (0, )) /(1 ) if z 0
if z 0
o lso c b
lso c b co
lso c
mmGK z K
c m m
K z z
observed frequency range
redshift of emission
observed fluence
o
1/3
2 2 4/30
1
4 4 ( )(1 )e e
gw o
L
dE Kf
d r z zd
number of sources present today
Random selection of zf
zb = zf - z
Random selection of
Compute ze
Compute f
If zb < 0
x N=106
0
0 0
0
31
( )= with DNS
NN i
gw Nic
Ff F f
c
min max0 0 0for in [ , ]
