Prospects for Stochastic Background Searches Using Virgo and LSC - - PowerPoint PPT Presentation

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)

11th Gravitational Wave Data Analysis Workshop

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary

Outline

1

SBGW detection on a network Isotropic background Anisotropic background

2

Numerical results Generalities Detection

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Outline

1

SBGW detection on a network Isotropic background Anisotropic background

2

Numerical results Generalities Detection

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Gaussian Case: Detection

Signal probability distribution dP = N e− 1

2 C−1 AB (f)s∗ A(f)sB(f) ∏

C,f

dsC(f) Detection problem: discriminate between C(0) =

• N11

N22

• and

C(1) =

• N11 + Sgw

γ12Sgw γ12Sgw

N22 + Sgw

• Solution: optimal correlator

Y12 ∝ Z s⋆

1(f) γ12(f)Sgw(f)

f 3N11(f)N22(f)s2(f)df

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Gaussian Case: Detection

Signal probability distribution dP = N e− 1

2 C−1 AB (f)s∗ A(f)sB(f) ∏

C,f

dsC(f) Detection problem: discriminate between C(0) =

• N11

N22

• and

C(1) =

• N11 + Sgw

γ12Sgw γ12Sgw

N22 + Sgw

• Solution: optimal correlator

Y12 ∝ Z s⋆

1(f) γ12(f)Sgw(f)

f 3N11(f)N22(f)s2(f)df

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Gaussian Case: Detection

Signal probability distribution dP = N e− 1

2 C−1 AB (f)s∗ A(f)sB(f) ∏

C,f

dsC(f) Detection problem: discriminate between C(0) =

• N11

N22

• and

C(1) =

• N11 + Sgw

γ12Sgw γ12Sgw

N22 + Sgw

• Solution: optimal correlator

Y12 ∝ Z s⋆

1(f) γ12(f)Sgw(f)

f 3N11(f)N22(f)s2(f)df

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Overlap Reduction Function γ(f)

SNR2 = 2F 2T Z ∞

0 γ2 12(f)

S2

gw(f)

N11(f)N22(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 ∗

AB = c

ℓAB

Best overlap with Virgo: Livingston & Hanford below 260 Hz GEO above 260 Hz

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Overlap Reduction Function γ(f)

SNR2 = 2F 2T Z ∞

0 γ2 12(f)

S2

gw(f)

N11(f)N22(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 ∗

AB = c

ℓAB

Best overlap with Virgo: Livingston & Hanford below 260 Hz GEO above 260 Hz

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Overlap Reduction Function γ(f)

SNR2 = 2F 2T Z ∞

0 γ2 12(f)

S2

gw(f)

N11(f)N22(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 ∗

AB = c

ℓAB

Best overlap with Virgo: Livingston & Hanford below 260 Hz GEO above 260 Hz

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Overlap Reduction Function γ(f)

SNR2 = 2F 2T Z ∞

0 γ2 12(f)

S2

gw(f)

N11(f)N22(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 ∗

AB = c

ℓAB

Best overlap with Virgo: Livingston & Hanford below 260 Hz GEO above 260 Hz

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Overlap Reduction Function γ(f)

SNR2 = 2F 2T Z ∞

0 γ2 12(f)

S2

gw(f)

N11(f)N22(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 ∗

AB = c

ℓAB

Best overlap with Virgo: Livingston & Hanford below 260 Hz GEO above 260 Hz

100 200 300 400 500 600 −1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 All−Sky Overlap Reduction Functions

f (Hz) γ(f)

LHO−LLO GEO600−Virgo LLO−Virgo LHO−Virgo

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Overlap Reduction Function γ(f)

SNR2 = 2F 2T Z ∞

0 γ2 12(f)

S2

gw(f)

N11(f)N22(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 ∗

AB = c

ℓAB

Best overlap with Virgo: Livingston & Hanford below 260 Hz GEO above 260 Hz

100 200 300 400 500 600 −1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 All−Sky Overlap Reduction Functions

f (Hz) γ(f)

LHO−LLO GEO600−Virgo LLO−Virgo LHO−Virgo

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Sensitivity Integrand

d SNR2

AB

df

= 2F 2Tγ2

AB(f)

S2

gw(f)

NAA(f)NBB(f) df

100 200 300 400 500 600 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 Stochastic Sensitivity Integrand for Sgw=10−48 Hz−1

Frequency (Hz) d(SNR2)/df (Hz−1)

G1−V2 L1−V2 H1−V2 H2−V2

4 months of data design sensitivity Low frequency: worse than H1/L1 (orientation) 200− 300Hz: comparable sensitivities High frequency: GEO/Virgo pair can do better (smaller separation)

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Sensitivity Integrand

d SNR2

AB

df

= 2F 2Tγ2

AB(f)

S2

gw(f)

NAA(f)NBB(f) df

200 250 300 350 400 1 2 3 4 5 6 7 8 9 x 10

−3

Stochastic Sensitivity Integrand for Sgw=10−48 Hz−1

Frequency (Hz) d(SNR2)/df (Hz−1)

G1−V2 L1−V2 H1−V2 H2−V2

4 months of data design sensitivity Low frequency: worse than H1/L1 (orientation) 200− 300Hz: comparable sensitivities High frequency: GEO/Virgo pair can do better (smaller separation)

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Sensitivity Integrand

d SNR2

AB

df

= 2F 2Tγ2

AB(f)

S2

gw(f)

NAA(f)NBB(f) df

200 250 300 350 400 1 2 3 4 5 6 7 8 9 x 10

−3

Stochastic Sensitivity Integrand for Sgw=10−48 Hz−1

Frequency (Hz) d(SNR2)/df (Hz−1)

G1−V2 L1−V2 H1−V2 H2−V2

4 months of data design sensitivity Low frequency: worse than H1/L1 (orientation) 200− 300Hz: comparable sensitivities High frequency: GEO/Virgo pair can do better (smaller separation)

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Sensitivity Integrand

d SNR2

AB

df

= 2F 2Tγ2

AB(f)

S2

gw(f)

NAA(f)NBB(f) df

200 250 300 350 400 1 2 3 4 5 6 7 8 9 x 10

−3

Stochastic Sensitivity Integrand for Sgw=10−48 Hz−1

Frequency (Hz) d(SNR2)/df (Hz−1)

G1−V2 L1−V2 H1−V2 H2−V2

4 months of data design sensitivity Low frequency: worse than H1/L1 (orientation) 200− 300Hz: comparable sensitivities High frequency: GEO/Virgo pair can do better (smaller separation)

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Sensitivity Integrand

d SNR2

AB

df

= 2F 2Tγ2

AB(f)

S2

gw(f)

NAA(f)NBB(f) df

200 250 300 350 400 1 2 3 4 5 6 7 8 9 x 10

−3

Stochastic Sensitivity Integrand for Sgw=10−48 Hz−1

Frequency (Hz) d(SNR2)/df (Hz−1)

G1−V2 L1−V2 H1−V2 H2−V2

4 months of data design sensitivity Low frequency: worse than H1/L1 (orientation) 200− 300Hz: comparable sensitivities High frequency: GEO/Virgo pair can do better (smaller separation)

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Combined sensitivity

SNR2 are additive: We can define a combined sensitivity integrand d SNR2 df

= ∑

A>B

SNR2

AB

Overall improvement of a factor 2-3 with combined analysis Virgo contributes better when spectrum grows with frequency

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Combined sensitivity

SNR2 are additive: We can define a combined sensitivity integrand d SNR2 df

= ∑

A>B

SNR2

AB

Overall improvement of a factor 2-3 with combined analysis Virgo contributes better when spectrum grows with frequency

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Combined sensitivity

SNR2 are additive: We can define a combined sensitivity integrand d SNR2 df

= ∑

A>B

SNR2

AB

Overall improvement of a factor 2-3 with combined analysis Virgo contributes better when spectrum grows with frequency

100 200 300 400 500 600 0.02 0.04 0.06 0.08 0.1 0.12 Stochastic Sensitivity Integrand for Sgw=10−48 Hz−1

Frequency (Hz) d(SNR2)/df (Hz−1)

L1−H1 LLO−LHO best pair all pairs

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Combined sensitivity

SNR2 are additive: We can define a combined sensitivity integrand d SNR2 df

= ∑

A>B

SNR2

AB

Overall improvement of a factor 2-3 with combined analysis Virgo contributes better when spectrum grows with frequency

200 250 300 350 400 0.005 0.01 0.015 0.02 0.025 0.03 Stochastic Sensitivity Integrand for Sgw=10−48 Hz−1

Frequency (Hz) d(SNR2)/df (Hz−1)

L1−H1 LLO−LHO best pair all pairs

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Combined sensitivity

SNR2 are additive: We can define a combined sensitivity integrand d SNR2 df

= ∑

A>B

SNR2

AB

Overall improvement of a factor 2-3 with combined analysis Virgo contributes better when spectrum grows with frequency

200 250 300 350 400 0.005 0.01 0.015 0.02 0.025 0.03 Stochastic Sensitivity Integrand for Sgw=10−48 Hz−1

Frequency (Hz) d(SNR2)/df (Hz−1)

L1−H1 LLO−LHO best pair all pairs

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Combined sensitivity

SNR2 are additive: We can define a combined sensitivity integrand d SNR2 df

= ∑

A>B

SNR2

AB

Overall improvement of a factor 2-3 with combined analysis Virgo contributes better when spectrum grows with frequency

200 250 300 350 400 0.005 0.01 0.015 0.02 0.025 0.03 Stochastic Sensitivity Integrand for Sgw=10−48 Hz−1

Frequency (Hz) d(SNR2)/df (Hz−1)

L1−H1 LLO−LHO best pair all pairs

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Astrophysical Models

(see T. Regimbau talk) 10

1

10

2

10

3

10

−9

10

−8

Frequency (Hz) h100

2

ΩGW(f) DNS Magnetars

Magnetars:

ΩGW ∼ f 4

Double Neutron Stars:

ΩGW ∼ f 2/3

Amplitudes well below the current sensitivities

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Sensitivity integrands

100 200 300 400 500 600 0.5 1 x 10

−9

DNS spectrum

f (Hz)

dSNR2/df L1−H1 LLO−LHO best pair all pairs 100 200 300 400 500 600 0.5 1 1.5 2 x 10

−14

magnetar spectrum

f (Hz)

dSNR2/df L1−H1 LLO−LHO best pair all pairs

Improvement of a factor 2-3 with the “full” network

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Sensitivity integrands

200 250 300 350 400 0.2 0.4 0.6 0.8 1 x 10

−11

DNS spectrum

f (Hz)

dSNR2/df L1−H1 LLO−LHO best pair all pairs 200 250 300 350 400 0.5 1 x 10

−14

magnetar spectrum

f (Hz)

dSNR2/df L1−H1 LLO−LHO best pair all pairs

Improvement of a factor 2-3 with the “full” network

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Sensitivity integrands

200 250 300 350 400 0.2 0.4 0.6 0.8 1 x 10

−11

DNS spectrum

f (Hz)

dSNR2/df L1−H1 LLO−LHO best pair all pairs 200 250 300 350 400 0.5 1 x 10

−14

magnetar spectrum

f (Hz)

dSNR2/df L1−H1 LLO−LHO best pair all pairs

Improvement of a factor 2-3 with the “full” network

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Upper limits

100 200 300 400 500 600 Frequency (Hz) 10

• 6

10

• 4

10

• 2

10 Upper limit h100

2 ΩGW

H1-L1 G1-V2 H1-V2 L1-V2

Flat ΩGW Current sensitivity (S5,WSR1) Design sensitivity Improvement in the “high frequency” region

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Upper limits

100 200 300 400 500 600 Frequency (Hz) 10

• 6

10

• 4

10

• 2

10 Upper limit h100

2 ΩGW

H1-L1 G1-V2 H1-V2 L1-V2

Flat ΩGW Current sensitivity (S5,WSR1) Design sensitivity Improvement in the “high frequency” region

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Upper limits

100 200 300 400 500 600 Frequency (Hz) 10

• 6

10

• 4

10

• 2

10 Upper limit h100

2 ΩGW

H1-L1 G1-V2 H1-V2 L1-V2

Flat ΩGW Current sensitivity (S5,WSR1) Design sensitivity Improvement in the “high frequency” region

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Outline

1

SBGW detection on a network Isotropic background Anisotropic background

2

Numerical results Generalities Detection

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Anisotropic background

Not much to say until now, mainly question marks Sensitivity? Blind reconstruction or template-driven one?

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Isotropic background Anisotropic background

Anisotropic background

Not much to say until now, mainly question marks Sensitivity? Blind reconstruction or template-driven one?

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Generalities Detection

Outline

1

SBGW detection on a network Isotropic background Anisotropic background

2

Numerical results Generalities Detection

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Generalities Detection

Signal Generation

Strategy: Factorization of the covariance array, frequency by frequency

Cholesky or SVD

Vectorial filter applied to white noise streams

Overlap and Add to avoid boundary effects

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Generalities Detection

Signal Generation

Strategy: Factorization of the covariance array, frequency by frequency

Cholesky or SVD

Vectorial filter applied to white noise streams

Overlap and Add to avoid boundary effects

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Generalities Detection

Signal Generation

Strategy: Factorization of the covariance array, frequency by frequency

Cholesky or SVD

Vectorial filter applied to white noise streams

Overlap and Add to avoid boundary effects

Checks: in the noiseless case C(1)

AB

• C(1)

AA C(1) BB

=

SGWγAB

• (SGW + NAA)(SGW + NBB)

→ γAB

C(1)

AA → SGW

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Generalities Detection

Signal Generation Checks

Time domain (flat ΩGW )

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Generalities Detection

Signal Generation Checks

Overlap reduction function recostruction (γ2

AB)

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Generalities Detection

Outline

1

SBGW detection on a network Isotropic background Anisotropic background

2

Numerical results Generalities Detection

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Generalities Detection

Detection: Flat ΩGW

Hanford & Virgo Data injected in project1a noise at different SNR ratios Results agree with expectations with all the used pipelines (both for simulation & detection)

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Generalities Detection

Detection: Flat ΩGW

Hanford & Virgo Data injected in project1a noise at different SNR ratios Results agree with expectations with all the used pipelines (both for simulation & detection)

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Generalities Detection

Detection: Flat ΩGW

Hanford & Virgo Data injected in project1a noise at different SNR ratios Results agree with expectations with all the used pipelines (both for simulation & detection)

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Generalities Detection

Detection: Astrophysical Models

10 100 1000 Frequency (Hz) 1e-52 1e-48 Power Sectrum (Hz

• 1)

Numerical LHO Numerical Virgo Theoretical 10 100 1000 Frequency (Hz) 1e-55 1e-54 1e-53 Power Spectrum (Hz

• 1)

Numerical LHO Numerical Virgo Theoretical

Project1a + LLO Magnetars & DNS spectrum scaled to different SNR ratios Analysis in progress

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Generalities Detection

Detection: Astrophysical Models

10 100 1000 Frequency (Hz) 1e-52 1e-48 Power Sectrum (Hz

• 1)

Numerical LHO Numerical Virgo Theoretical 10 100 1000 Frequency (Hz) 1e-55 1e-54 1e-53 Power Spectrum (Hz

• 1)

Numerical LHO Numerical Virgo Theoretical

Project1a + LLO Magnetars & DNS spectrum scaled to different SNR ratios Analysis in progress

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary Generalities Detection

Detection: Astrophysical Models

10 100 1000 Frequency (Hz) 1e-52 1e-48 Power Sectrum (Hz

• 1)

Numerical LHO Numerical Virgo Theoretical 10 100 1000 Frequency (Hz) 1e-55 1e-54 1e-53 Power Spectrum (Hz

• 1)

Numerical LHO Numerical Virgo Theoretical

Project1a + LLO Magnetars & DNS spectrum scaled to different SNR ratios Analysis in progress

• G. Cella

Virgo/LSC SB search

SBGW detection on a network Simulation results Summary

Summary

Virgo/LSC collaboration can improve the sensitivity and the robustness

• f stochastic background search.

We are far from the perspective of a real detection, but we can improve upper limits and work in the perspective of second generation interferometers. Future steps:

Analysis of project1b data Real data (as soon as MOU will be signed)

Non stationarity Non gaussianity

Start with radiometer research

• G. Cella

Virgo/LSC SB search