Le Fond Gravitationnel Stochastique

Tania Regimbau

ARTEMIS - OCA

2 3

20

( ) 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:

3

Observational Constraints

Maggiore, 2000

4

Cosmological Predictions

Cosmic Strings

String Cosmology

Electroweak phase transition

inflation

Maggiore, 2000

5

Future Sensitivities

Figure courtesy of Don Backer

6

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

*

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

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]

10

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!