Le Fond Gravitationnel Stochastique

1. Le Fond Gravitationnel Stochastique Tania Regimbau ARTEMIS - OCA

2. The GW Stochastic Background 10-43s: gravitons decoupled (T = 1019 GeV) • 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: 300000 yrs:photonsdecoupled (T = 0.2 eV)

3. Observational Constraints Maggiore, 2000

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

5. Future Sensitivities Figure courtesy of Don Backer

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 (H0, Wm , Wn) • The source rate • The individual energy spectral density Regimbau & de Freitas Pacheco, 2001-2005

7. Astrophysical Stochastic Background • 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 >> Dt : continuous • tev ~ Dt : pop-corn • tev<< Dt : shot noise

8. Detection Regimes (ex, DNSs) The duty cycle characterizes the nature of the background. <t> = 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 shortcompared 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. Random selection of zf zb = zf - Dz If zb < 0 Random selection of t Compute zc If zc < z* Compute fn0 Last thousands seconds before the last stable orbit: 96% of the energy released, in the range [10-1500 Hz] Population Synthesis • redshift of formation of massive binaries (Coward et al. 2002) • redshift of formation of NS/NS x N=106 (uncertainty on Wgw <0.1%) • coalescence time • redshift of coalescence • observed fluence

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

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. Galactic CWDBs (HBW 90) • 3 107 sources • intrinsic parameters: - masses m1, m2 - orbital period: Porb(t) • extrinsic parameters: • - Inclination angle i, polarisationy, initial phase j0 • - position: (d, l, d) • signal: with:

13. Random selection m10 compute m1, m2, P0,min , P0,max, Pc X 107 Random selection log P0 Random selection R, z, i Random selection t Compute P(t) If P < Pc Random selection i, j0, y, Compute (d, a, d) add GW signal 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,a,d): • angles i, y, j0 from uniform distributions

14. Galactic CWDBs (HBW 90)

15. Detection with Ground Based Interferometers • 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 meanm = <Y> and the noise by the variances = <(Y – m)2> Upper limit: the 90% confidence level upper limit is given by:

16. Detection with LISA 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. Symmetrized Sagnac: ~f-3 monitor noise Michelson: ~f-2 Seach signal

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. Thank you!