SBGW detection on a network Simulation results Summary Prospects for Stochastic Background Searches Using Virgo and LSC Interferometers Giancarlo Cella Carlo Nicola Colacino Elena Cuoco Angela Di Virgilio Tania Regimbau Emma L. Robinson John T. Whelan (for the LSC-Virgo working group on stochastic backgrounds) 11 th Gravitational Wave Data Analysis Workshop G. Cella Virgo/LSC SB search
SBGW detection on a network Simulation results Summary Outline SBGW detection on a network 1 Isotropic background Anisotropic background Numerical results 2 Generalities Detection G. Cella Virgo/LSC SB search
SBGW detection on a network Isotropic background Simulation results Anisotropic background Summary Outline SBGW detection on a network 1 Isotropic background Anisotropic background Numerical results 2 Generalities Detection G. Cella Virgo/LSC SB search
SBGW detection on a network Isotropic background Simulation results Anisotropic background Summary Gaussian Case: Detection Signal probability distribution A ( f ) s B ( f ) ∏ dP = N e − 1 2 C − 1 AB ( f ) s ∗ ds C ( f ) C , f Detection problem: discriminate between γ 12 S gw � � � � N 11 + S gw N 11 0 C ( 0 ) = C ( 1 ) = and γ 12 S gw N 22 + S gw 0 N 22 Solution: optimal correlator 1 ( f ) γ 12 ( f ) S gw ( f ) Z Y 12 ∝ s ⋆ f 3 N 11 ( f ) N 22 ( f ) s 2 ( f ) df G. Cella Virgo/LSC SB search
SBGW detection on a network Isotropic background Simulation results Anisotropic background Summary Gaussian Case: Detection Signal probability distribution A ( f ) s B ( f ) ∏ dP = N e − 1 2 C − 1 AB ( f ) s ∗ ds C ( f ) C , f Detection problem: discriminate between γ 12 S gw � � � � N 11 + S gw N 11 0 C ( 0 ) = C ( 1 ) = and γ 12 S gw N 22 + S gw 0 N 22 Solution: optimal correlator 1 ( f ) γ 12 ( f ) S gw ( f ) Z Y 12 ∝ s ⋆ f 3 N 11 ( f ) N 22 ( f ) s 2 ( f ) df G. Cella Virgo/LSC SB search
SBGW detection on a network Isotropic background Simulation results Anisotropic background Summary Gaussian Case: Detection Signal probability distribution A ( f ) s B ( f ) ∏ dP = N e − 1 2 C − 1 AB ( f ) s ∗ ds C ( f ) C , f Detection problem: discriminate between γ 12 S gw � � � � N 11 + S gw N 11 0 C ( 0 ) = C ( 1 ) = and γ 12 S gw N 22 + S gw 0 N 22 Solution: optimal correlator 1 ( f ) γ 12 ( f ) S gw ( f ) Z Y 12 ∝ s ⋆ f 3 N 11 ( f ) N 22 ( f ) s 2 ( f ) df G. Cella Virgo/LSC SB search
SBGW detection on a network Isotropic background Simulation results Anisotropic background Summary Overlap Reduction Function γ ( f ) Z ∞ S 2 gw ( f ) SNR 2 = 2 F 2 T 0 γ 2 12 ( f ) N 11 ( f ) N 22 ( f ) df γ express the coherence between the signals coupled to each detector SNR scales with γ γ Depends on detectors’ distance and orientation γ ’s Frequency scale: f ∗ c AB = ℓ AB Best overlap with Virgo: Livingston & Hanford below 260 Hz GEO above 260 Hz G. Cella Virgo/LSC SB search
SBGW detection on a network Isotropic background Simulation results Anisotropic background Summary Overlap Reduction Function γ ( f ) Z ∞ S 2 gw ( f ) SNR 2 = 2 F 2 T 0 γ 2 12 ( f ) N 11 ( f ) N 22 ( f ) df γ express the coherence between the signals coupled to each detector SNR scales with γ γ Depends on detectors’ distance and orientation γ ’s Frequency scale: f ∗ c AB = ℓ AB Best overlap with Virgo: Livingston & Hanford below 260 Hz GEO above 260 Hz G. Cella Virgo/LSC SB search
SBGW detection on a network Isotropic background Simulation results Anisotropic background Summary Overlap Reduction Function γ ( f ) Z ∞ S 2 gw ( f ) SNR 2 = 2 F 2 T 0 γ 2 12 ( f ) N 11 ( f ) N 22 ( f ) df γ express the coherence between the signals coupled to each detector SNR scales with γ γ Depends on detectors’ distance and orientation γ ’s Frequency scale: f ∗ c AB = ℓ AB Best overlap with Virgo: Livingston & Hanford below 260 Hz GEO above 260 Hz G. Cella Virgo/LSC SB search
SBGW detection on a network Isotropic background Simulation results Anisotropic background Summary Overlap Reduction Function γ ( f ) Z ∞ S 2 gw ( f ) SNR 2 = 2 F 2 T 0 γ 2 12 ( f ) N 11 ( f ) N 22 ( f ) df γ express the coherence between the signals coupled to each detector SNR scales with γ γ Depends on detectors’ distance and orientation γ ’s Frequency scale: f ∗ c AB = ℓ AB Best overlap with Virgo: Livingston & Hanford below 260 Hz GEO above 260 Hz G. Cella Virgo/LSC SB search
SBGW detection on a network Isotropic background Simulation results Anisotropic background Summary Overlap Reduction Function γ ( f ) Z ∞ S 2 gw ( f ) SNR 2 = 2 F 2 T 0 γ 2 12 ( f ) N 11 ( f ) N 22 ( f ) df All−Sky Overlap Reduction Functions γ express the coherence between 0.4 the signals coupled to each 0.2 detector 0 SNR scales with γ −0.2 γ Depends on detectors’ γ (f) −0.4 distance and orientation γ ’s Frequency scale: f ∗ c LHO−LLO AB = ℓ AB −0.6 GEO600−Virgo LLO−Virgo −0.8 Best overlap with Virgo: LHO−Virgo Livingston & Hanford below 260 Hz −1 0 100 200 300 400 500 600 f (Hz) GEO above 260 Hz G. Cella Virgo/LSC SB search
SBGW detection on a network Isotropic background Simulation results Anisotropic background Summary Overlap Reduction Function γ ( f ) Z ∞ S 2 gw ( f ) SNR 2 = 2 F 2 T 0 γ 2 12 ( f ) N 11 ( f ) N 22 ( f ) df All−Sky Overlap Reduction Functions γ express the coherence between 0.4 the signals coupled to each 0.2 detector 0 SNR scales with γ −0.2 γ Depends on detectors’ γ (f) −0.4 distance and orientation γ ’s Frequency scale: f ∗ c LHO−LLO AB = ℓ AB −0.6 GEO600−Virgo LLO−Virgo −0.8 Best overlap with Virgo: LHO−Virgo Livingston & Hanford below 260 Hz −1 0 100 200 300 400 500 600 f (Hz) GEO above 260 Hz G. Cella Virgo/LSC SB search
SBGW detection on a network Isotropic background Simulation results Anisotropic background Summary Sensitivity Integrand S 2 d SNR 2 gw ( f ) = 2 F 2 T γ 2 AB AB ( f ) N AA ( f ) N BB ( f ) df df Stochastic Sensitivity Integrand for S gw =10 −48 Hz −1 4 months of data 0.02 G1−V2 design sensitivity 0.018 L1−V2 H1−V2 H2−V2 Low frequency: worse than 0.016 H1/L1 (orientation) 0.014 d(SNR 2 )/df (Hz −1 ) 0.012 200 − 300 Hz : comparable sensitivities 0.01 0.008 High frequency: GEO/Virgo pair can do better (smaller 0.006 separation) 0.004 0.002 0 0 100 200 300 400 500 600 Frequency (Hz) G. Cella Virgo/LSC SB search
SBGW detection on a network Isotropic background Simulation results Anisotropic background Summary Sensitivity Integrand S 2 d SNR 2 gw ( f ) = 2 F 2 T γ 2 AB AB ( f ) N AA ( f ) N BB ( f ) df df Stochastic Sensitivity Integrand for S gw =10 −48 Hz −1 −3 9 x 10 4 months of data G1−V2 design sensitivity L1−V2 8 H1−V2 Low frequency: worse than H2−V2 7 H1/L1 (orientation) 6 200 − 300 Hz : comparable d(SNR 2 )/df (Hz −1 ) 5 sensitivities 4 High frequency: GEO/Virgo pair can do better (smaller 3 separation) 2 1 0 200 250 300 350 400 Frequency (Hz) G. Cella Virgo/LSC SB search
SBGW detection on a network Isotropic background Simulation results Anisotropic background Summary Sensitivity Integrand S 2 d SNR 2 gw ( f ) = 2 F 2 T γ 2 AB AB ( f ) N AA ( f ) N BB ( f ) df df Stochastic Sensitivity Integrand for S gw =10 −48 Hz −1 −3 9 x 10 4 months of data G1−V2 design sensitivity L1−V2 8 H1−V2 Low frequency: worse than H2−V2 7 H1/L1 (orientation) 6 200 − 300 Hz : comparable d(SNR 2 )/df (Hz −1 ) 5 sensitivities 4 High frequency: GEO/Virgo pair can do better (smaller 3 separation) 2 1 0 200 250 300 350 400 Frequency (Hz) G. Cella Virgo/LSC SB search
SBGW detection on a network Isotropic background Simulation results Anisotropic background Summary Sensitivity Integrand S 2 d SNR 2 gw ( f ) = 2 F 2 T γ 2 AB AB ( f ) N AA ( f ) N BB ( f ) df df Stochastic Sensitivity Integrand for S gw =10 −48 Hz −1 −3 9 x 10 4 months of data G1−V2 design sensitivity L1−V2 8 H1−V2 Low frequency: worse than H2−V2 7 H1/L1 (orientation) 6 200 − 300 Hz : comparable d(SNR 2 )/df (Hz −1 ) 5 sensitivities 4 High frequency: GEO/Virgo pair can do better (smaller 3 separation) 2 1 0 200 250 300 350 400 Frequency (Hz) G. Cella Virgo/LSC SB search
SBGW detection on a network Isotropic background Simulation results Anisotropic background Summary Sensitivity Integrand S 2 d SNR 2 gw ( f ) = 2 F 2 T γ 2 AB AB ( f ) N AA ( f ) N BB ( f ) df df Stochastic Sensitivity Integrand for S gw =10 −48 Hz −1 −3 9 x 10 4 months of data G1−V2 design sensitivity L1−V2 8 H1−V2 Low frequency: worse than H2−V2 7 H1/L1 (orientation) 6 200 − 300 Hz : comparable d(SNR 2 )/df (Hz −1 ) 5 sensitivities 4 High frequency: GEO/Virgo pair can do better (smaller 3 separation) 2 1 0 200 250 300 350 400 Frequency (Hz) G. Cella Virgo/LSC SB search
SBGW detection on a network Isotropic background Simulation results Anisotropic background Summary Combined sensitivity SNR 2 are additive: We can define a combined sensitivity integrand d SNR 2 = ∑ SNR 2 AB df A > B Overall improvement of a factor 2-3 with combined analysis Virgo contributes better when spectrum grows with frequency G. Cella Virgo/LSC SB search
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