Le Fond Gravitationnel Stochastique
description
Transcript of Le Fond Gravitationnel Stochastique
Le Fond Gravitationnel Stochastique
Tania Regimbau
ARTEMIS - OCA
2 3
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( ) 4( ) ( )
(ln ) 3gw
gw gwc
d f ff 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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Observational Constraints
Maggiore, 2000
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Cosmological Predictions
Cosmic Strings
String Cosmology
Electroweak phase transition
inflation
Maggiore, 2000
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Future Sensitivities
Figure courtesy of Don Backer
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Astrophysical Stochastic Background
max0
0
0
3 200
1 1( )= ou ( )
4
z gwgw
critical L
F dEf F dR z
c d d
Superposition of all the sources since the beginning of the stellar activity:
periodic (compact binaries, pulsars…) bursts (supernovae, oscillation modes, collapse, BH ringdown …)
Astrophysical backgrounds spectrum are determined by:
- The cosmological model (H0, m)- The source rate - The individual energy spectral density
1 10 100 1000 100001E-20
1E-18
1E-16
1E-14
1E-12
1E-10
1E-8
1E-6
bar modes
BH
DNS (z>0.27)
pulsars
magnetars
slow roll inflation
de Sitter inflation
string theory
cosmic strings
gw
o Hz
Regimbau & de Freitas Pacheco, 2001-2005
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1 10 100 1000 100001E-20
1E-18
1E-16
1E-14
1E-12
1E-10
1E-8
1E-6
bar modes
BH
DNS (z>0.27)
pulsars
magnetars
slow roll inflation
de Sitter inflation
string theory
cosmic strings
gw
o Hz
periodic sources: Continuous stochastic background when the number of sources per resolution frequency interval is >>1.
bursts: the nature of the stochastic backgroud is determined by the ratio between the mean duration of a single event and the mean time interval between successive events
tev >> t : continuous
tev ~ t : pop-corn
tev<< t : shot noise
Astrophysical Stochastic Background
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Detection Regimes (ex, DNSs)
The duty cycle characterizes the nature of the background.
= 1000 s, which corresponds to 96% of the energy released, in the frequency range [10-1500 Hz]
D >1: continuous (z>0.23, 96%)
The time interval between successive events is short compared to the duration of a single event. D <1: shot noise (z<0.027)The time interval between successive events is long compared to the duration of a single event D ~1: popcorn (0.027<z<0.23)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
10 100 10001E-12
1E-11
1E-10
1E-9
1E-8
D = 10 (z*=1.05)
D = 1 (z*=0.23)
continuous background
popcorn noise
shot noise
D = 0.1 (z*=0.027)
gw
HzRegimbau & de Freitas Pacheco, 2005, ApJ, 642, 455
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Population Synthesis
5 100.087( ) with [2 10 ;2 10 yr]P
8( ) with 10 yrb f b bz z z
*
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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
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
Last thousands seconds before the last stable orbit:
96% of the energy released, in the range [10-1500 Hz]
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Probability Event Horizon
Coward et al., astro-ph/0510203
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Galactic Confusion Foreground
Between 0.2-3 mHz LISA is expected to be limited by the galactic foreground, essentially the WD binary contribution, rather than by the instrumental noise.
Hils, Bender & Webbink, 1990, ApJ, 360, 75,
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Galactic CWDBs (HBW 90)
3 107 sources
intrinsic parameters:
- masses m1, m2
- orbital period: Porb(t)
extrinsic parameters:
- Inclination angle polarisationinitial phase
- position: (d, ,
signal:
with:
0 0
0 0
cos(2 )cos(2 ) sin(2 )sin(2 )
sin(2 )cos(2 ) cos(2 )sin(2 )
h A t A t
h A t A t
2 21/3 21 2
41 2
2 21/31 2
41 2
2( ) (1 cos )
( )
4( ) cos
( )
G m mA i
c r G m m
G m mA i
c r G m m
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Galactic CWDBs (HBW 90)
masses:
- initial mass of the first progenitor m10 from Scalo IMF-WD masses (m1 and m2) calculated from m10
age from uniform distribution
orbital period:
-initial period from uniform distribution of log Po between [log Po,min;log Po;max], calculated from m10
- final period Pc calculated from m10
- actual period:
position in the Galaxy (d, l, b), converted into ecliptic coordinate (d,
angles i, from uniform distributions
8/3 8/3 5/3 3/80 5
256( ) (2 ) ( ) )
5orbP t P GM tc
0( , ) exp( / 2.5)exp( / 0.1)R z R z
Random selection m10
compute m1, m2, P0,min , P0,max, Pc
Random selection log P0
Compute P(t)
Compute (d, ) If P < Pc
Random selection R, z, i
Random selection i,,
Random selection t
add GW signal
X 107
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-4.5 -4.0 -3.5 -3.0 -2.5 -2.0
-19.0
-18.5
-18.0
-17.5
-17.0 BHW Code LISA
Sqr
t Sh
Hz1
/2
log Hz
Galactic CWDBs (HBW 90)
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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 (cosmological origin)
signal and noise, detector noises uncorrelated
Cross correlation statistic:
combine the signal outputs using an optimal filter to optimize the signal to noise ratio
the signal is given by the mean m = <Y> and the noise by the variance s = <(Y – m)2>
Upper limit:
the 90% confidence level upper limit is given by:
1 21 2
( ) ( )
( ) ( ) ( ) ( )( )
with) (
gwf S fY s f Q f s f df Q f
P f P f
Detection with Ground Based Interferometers
2100 1.26gwh
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Michelson: ~f-2
Seach signal
Symmetrized Sagnac: ~f-3 monitor noise
The three Michelson interferometers share common spacecrafts, therefore the instumental noise is not removed by cross correlating the signal outputs.
The idea is to use the Sagnac configuration, almost insensitive to the GW signal, to estimate the instrumental noise background and substract it to the standard configuration.
Detection with LISA
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LISA Mock Data Challenge
Small group:Nelemans (Nijmegen), Regimbau (OCA), Romano (Cardiff), Ungarelli (Italy),
Whelan (AEI)
But lot of work
• Simulation of the galactic foregrounds• Simulation of the Cosmological background• Detection methods
…..
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Thank you!