1. 1/25 Current results and future scenarios for gravitational wave’s stochastic background G. Cella – INFN sez. Pisa

2. 2/25 Summary Introduction Introduction Data analysis strategies Data analysis strategies Current collaborations & projects Current collaborations & projects Current upper limits Current upper limits Some future perspectives Some future perspectives

3. 3/25 Stochastic background h  is a sum of statistically independent events We can describe h  using the correlation functions: Using the theory of point processes we can show that this scales with the rate as: As expected, at large rates h  becomes a Gaussian stochastic field (central limit theorem) Rate Burst Coalescence Pulsar Cosmological background Astrophysical background StochasticGaussian

4. 4/25 The gaussian case Every gravitational wave strain field can formally be developed in modes: Polarizations Frequencies Directions We do not know the amplitudes, so we can only give a probabilistic description. In the gaussian case only the second order correlations are relevant. They fully describe the stochastic field. Unpolarized Stationary Isotropic With these additional simplification the background is fully described by its power spectrum.

5. 5/25 Gaussian case: space correlations Space correlations can be evaluated analytically. They can be written as a sum over all the modes: When the phase factor oscillates strongly on the full solid angle. Correlations go to zero. These properties are detector independent. Now we must describe the real measurement. Always in phase Always out of phase

6. 6/25 Coupling to the detector A detector give us one or more projections of the strain h ij : SignalDetector tensor Strain at the detector position Example: for a bar aligned to the direction:

7. 7/25 Detector tensor: interferometer For the differential mode (arms along ): Common mode:

8. 8/25 Detector tensor: sphere

9. 9/25 Overlap reduction function The signal is a linear combination of the elements of the strain tensor. Gaussian Stationary, at least if D ij is time independent This can be written as where the overlap reduction function  AB is defined by Depends on distance (same features of strain correlations) Depends on orientation (via the overlap of detector tensors)

10. 10/25 ORF: examples Trigo:  =0.375 (frequency independent)

11. 11/25Detection Basic idea: two detectors. 1. noise not correlated with the signal 2. noise not correlated between the detectors (?) Determine the optimal correlation, which is of the form: Maximizing SNR…..

12. 12/25 Optimal correlation Can be seen as a matched filter for cross correlations. It depends on: theoretical PSD of stochastic background overlap reduction function noise PSD of the two detectors The optimal statistic is given by:

13. 13/25 Or, converting to theoretician’s units

14. 14/25 Many detectors Gaussian signals: optimal detector is a combination of optimal correlations from each pair. Not a large improvement factor, but Very important for ruling out spurious effects

15. 15/25 3 groups involved (Virgo, Auriga, ROG) Methodological study Software injection of simulated signal Use of real data (not syncronized) Validation of standard detection algorithm Noise power spectrum for the detectors involved : Overlap reduction function : (the coherence between detectors) Detection study in progress Impact of non stationarity Impact of non stationarity Study of vetoes Study of vetoes Comparison with simulated gaussian noise Comparison with simulated gaussian noise Application to C7 data Application to C7 data Perspectives: upper limit when at design sensitivity. Upper limit on the GW stochastic background energy density as a function of the upper frequency of the band: Virgo/Auriga/ROG collaborative data analysis: Stochastic background

16. 16/25 Virgo/LSC collaboration: the project concept Joint analysis between Virgo, LHO, LLO GEO600 Joint analysis between Virgo, LHO, LLO GEO600 Background above 200 Hz Background above 200 Hz Standard correlation (isotropic model) Standard correlation (isotropic model) Targeted search (map of sky gw luminosity) Targeted search (map of sky gw luminosity) Real data when comparable sensitivity will be reached Real data when comparable sensitivity will be reached Preparatory phase: work by project Preparatory phase: work by project Phase 1: simulated or technical data, pipeline test Phase 1: simulated or technical data, pipeline test Phase 2: A4/C7 data Phase 2: A4/C7 data

17. 17/25 Virgo/LSC: standard correlation analysis Design sensitivities, 4 months of data, 5% FA & FD: LHO/LLO and *LO/Virgo: same sensitivity above 200 Hz GEO/Virgo good above 200 Hz

18. 18/25Sensitivities  false alarm rate,  detection rate (constant  gw ) @ 900 Hz feasible with final sensitivity of Virgo & italian bars

19. 19/25Anisotropies Generalized statistics of mode amplitudes: Strategy: Expand in spherical harmonics Standard cross correlation analysis Signature: modulation generated by the earth rotation Detection of higher order harmonics requires larger SNR

20. 20/25

21. 21/25 Targeted search The idea: reconstruct a map of the gravitational wave luminosity in the sky. Recipe: 1.Decompose luminosity and detector response in spherical harmonics, in the sky and in the detector frames 2.Solve the inverse problem Detailed study needed (work in progress inside LSC) Virgo+WA 200 Hz At least 3 detectors needed to close the inverse problem. Angular resolution limited by

22. 22/25 Non gaussian signals Several astrophysical stochastic background are far from the gaussian limit They are interesting in itself, but also an obstacle for the detection of cosmological backgrounds Questions: Can they be optimally detected? Can they be disentangled from other backgrounds? Some proposals, but work in progress. Theoretical input is important.

23. 23/25 Detector sensitivities: 1 Virgo-like 2 Virgo-like Virgo+bar 2 Advanced LISA

24. 24/25 Upper limits 1 Virgo-like 2 Virgo-like Virgo+bar 2 Advanced LISA COBE Double pulsars ms pulsars Nucleosynthesis LIGO S3

25. 25/25Conclusions Other relevant points, not discussed: Detection of scalar fields (dilatons, moduli, …) How to deal with non gaussian and non stationary noise How to deal with noise correlations between detectors Template banks, simulation issues, pipeline implementation LISA Probably only upper limits with the current generation of detectors Good perspectives for advanced detectors Thank you!