1. Le Fond Gravitationnel Stochastique Tania Regimbau ARTEMIS - OCA

2. The GW Stochastic Background 10 -43 s: gravitons decoupled (T = 10 19 GeV) 300000 yrs: photons decoupled (T = 0.2 eV)  Two contributions:  cosmological: signature of the early Universe inflation, 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. 3 Observational Constraints Maggiore, 2000

4. 4 Cosmological Predictions Cosmic Strings String Cosmology Electroweak phase transition inflation Maggiore, 2000

5. 5 Future Sensitivities Figure courtesy of Don Backer

6. 6 Astrophysical Stochastic Background 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 (H 0,  m  ) - The source rate - The individual energy spectral density Regimbau & de Freitas Pacheco, 2001-2005

7. 7  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  t ev >>  t : continuous  t ev ~  t : pop-corn  t ev <<  t : shot noise Astrophysical Stochastic Background

8. 8 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 Regimbau & de Freitas Pacheco, 2005, ApJ, 642, 455

9. 9 Population Synthesis  redshift of formation of massive binaries (Coward et al. 2002)  redshift of formation of NS/NS  coalescence time  redshift of coalescence  observed fluence Random selection of z f z b = z f -  z Random selection of  Compute z c Compute f  If z b < 0 If z c < z * x N=10 6 (uncertainty on  gw <0.1%) Last thousands seconds before the last stable orbit: 96% of the energy released, in the range [10-1500 Hz]

10. 10 Probability Event Horizon Coward et al., astro-ph/0510203

11. 11 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,

12. 12 Galactic CWDBs (HBW 90)  3 10 7 sources  intrinsic parameters: - masses m 1, m 2 - orbital period: P orb (t)  extrinsic parameters: - Inclination angle  polarisation  initial phase   - position: (d,,   signal: with:

13. 13 Galactic CWDBs (HBW 90)  masses: - initial mass of the first progenitor m 10 from Scalo IMF -WD masses (m 1 and m 2 ) calculated from m 10  age from uniform distribution  orbital period: -initial period from uniform distribution of log P o between [log P o,min ;log P o;max ], calculated from m 10 - final period P c calculated from m 10 - actual period:  position in the Galaxy (d, l, b), converted into ecliptic coordinate (d,   angles i,   from uniform distributions Random selection m 1 0 compute m 1, m 2, P 0,min, P 0,max, P c Random selection log P 0 Compute P(t) Compute (d,  ) If P < P c Random selection R, z, i Random selection i,   , Random selection t add GW signal X 10 7

14. 14 Galactic CWDBs (HBW 90)

15. 15 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 = and the noise by the variance s = Upper limit: the 90% confidence level upper limit is given by: Detection with Ground Based Interferometers

16. 16 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

17. 17 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 …..

18. 18 Thank you!