New technologies for sensitivity improvement of current and future gravitational-wave detectors GRAN SASSO SCIENCE INSTITUTE 17th October 2019 Francesca Badaracco
• What a gravitational wave is • Why is it important to Astrophysics • How does a gravitational wave detector work? They are just like EM waves but they move in the 4D space-time modifying its structure. ∆𝑀 𝑀 = 10 − 21 1
• What a gravitational wave is • Why is it important to Astrophysics • How does a gravitational wave detector work? They are just like EM waves but they move in the 4D space-time modifying its structure. ∆𝑀 𝑀 = 10 − 21 1
• What a gravitational wave is • Why is it important to Astrophysics • How does a gravitational wave detector work? They are just like EM waves but they move in the 4D space-time modifying its structure. ∆𝑀 𝑀 = 10 − 21 1
• What a gravitational wave is • Why is it important to Astrophysics • How does a gravitational wave detector work? They are just like EM waves but they move in the 4D space-time modifying its structure. ∆𝑀 𝑀 = 10 − 21 1
• What a gravitational wave is • Why is it important to Astrophysics • How does a gravitational wave detector work? They are just like EM waves but they move in the 4D space-time modifying its structure. ∆𝑀 𝑀 = 10 − 21 1
• What a gravitational wave is • Why is it important to Astrophysics • How does a gravitational wave detector work? They are just like EM waves but they move in the 4D space-time modifying its structure. ∆𝑀 𝑀 = 10 − 21 1
• What a gravitational wave is • Why is it important to Astrophysics • How does a gravitational wave detector work? They are just like EM waves but they move in the 4D space-time modifying its structure. ∆𝑀 𝑀 = 10 − 21 1
• What a gravitational wave is • Why is it important to Astrophysics • How does a gravitational wave detector work? They are just like EM waves but they move in the 4D space-time modifying its structure. ∆𝑀 𝑀 = 10 − 21 1
• What a gravitational wave is • Why is it important to Astrophysics • How does a gravitational wave detector work? They are just like EM waves but Measure the change in length → they move in the 4D space-time Measure change in phase modifying its structure. ∆𝑀 ∝ ℎ𝑀 ∆𝑀 𝑀 = 10 − 21 Δ𝜚 ∝ ℎ𝑀 2
• What a gravitational wave is • Why is it important to Astrophysics • How does a gravitational wave detector work? Introduction of Fabry-Perot cavities (we indeed need interferometers 100 Km long) 𝜇 𝑥 𝑑 𝑀~ 2 = 2𝑔 𝑥 Measure the change in length → They are just like EM waves but Measure change in phase they move in the 4D space-time ∆𝑀 ∝ ℎ𝑀 modifying its structure. Δ𝜚 ∝ ℎ𝑀 ∆𝑀 𝑀 = 10 − 21 ℎ~10 − 21 2
• What a gravitational wave is • Why is it important to Astrophysics • How does a gravitational wave detector work? Introduction of Fabry-Perot cavities (we indeed need interferometers 100 Km long) 𝜇 𝑥 𝑑 𝑀~ 2 = 2𝑔 𝑥 Measure the change in length → They are just like EM waves but Measure change in phase they move in the 4D space-time ∆𝑀 ∝ ℎ𝑀 modifying its structure. Δ𝜚 ∝ ℎ𝑀 ∆𝑀 𝑀 = 10 − 21 ℎ~10 − 21 2
• What a gravitational wave is • Why is it important to Astrophysics • How does a gravitational wave detector work? Many different parts to reach the required sensitivity!!! Measure the change in length → They are just like EM waves but Measure change in phase they move in the 4D space-time ∆𝑀 ∝ ℎ𝑀 modifying its structure. Δ𝜚 ∝ ℎ𝑀 ∆𝑀 𝑀 = 10 − 21 ℎ~10 − 21 2
• What a gravitational wave is • Why is it important to Astrophysics • How does a gravitational wave detector work? Many different parts to reach the To be kept in mind: when I will required sensitivity!!! mention the ‘ TEST MASSES ’ I will refer to the end mirrors of the interferometer!!! Which are in free Measure the change in length → They are just like EM waves but fall along the arms direction. Measure change in phase they move in the 4D space-time ∆𝑀 ∝ ℎ𝑀 modifying its structure. Δ𝜚 ∝ ℎ𝑀 ∆𝑀 𝑀 = 10 − 21 ℎ~10 − 21 2
Plenty of different kinds of noises 3
What is Newtonian Noise (NN): Perturbation of the gravity field due to a variation in the density ( δρ ) of the surrounding media. Example of NN in Virgo: 4
# What is Newtonian Noise (NN): What can we do about Perturbation of the gravity field due to a variation in the density ( δρ ) of the surrounding media. Newtonian Noise? Example of NN in Virgo: Estimation of the noise Subtraction 4
# What is Newtonian Noise (NN): What can we do about Perturbation of the gravity field due to a variation in the density ( δρ ) of the surrounding media. Newtonian Noise? Example of NN in Virgo: Estimation of the noise HOW?!? Subtraction 4
Wiener filter is the way Assumptions: • Stationary signal 𝑄−1 • Linear relationship: x ∝ 𝑧 𝑦 𝑛 = ො 𝑥 𝑙 𝑧(𝑛 − 𝑙) 𝑙=0 Estimated value of Measured signal ( seismic the Newtonian Noise Wiener filter displacement ) coefficients 𝐸𝐵𝑈𝐵 − ො 𝑦 Subtraction 5
Factor 10 How much Factor 3 deep? Surface Underground Suppression up to a factor 10 6
OPTIMIZATION of: CPSDs between Cross Power Spectral seismometers and Densities (CPSDs) Power Spectral test mass between Density of test mass seismometers Isotropic & Homogeneous Single example seismic field hypothesis + & k P,S a << 1 + Gravitational coupling model: mirror <-> field 7
OPTIMIZATION of: CPSDs between Cross Power Spectral seismometers and Densities (CPSDs) Power Spectral test mass between Density of test mass seismometers Isotropic & Homogeneous Single example seismic field hypothesis + & k P,S a << 1 + Gravitational coupling model: mirror <-> field 7
OPTIMIZATION of: CPSDs between Cross Power Spectral seismometers and Densities (CPSDs) Power Spectral test mass between Density of test mass seismometers Isotropic & Homogeneous Single example seismic field hypothesis + & k P,S a << 1 + Gravitational coupling model: mirror <-> field 7
Succesful mission: factor 10 of reduction already with 13 seismometers per test mass 8
Succesful mission: factor 10 of reduction already with 13 seismometers per test mass Factor 10 Factor 3 8
Validation: Analytical solution for N = 1 Global minimum Seismometers self noise limitation curve: Τ R min = 1 𝑂 ∗ 𝑇𝑂𝑆 Bigger slope: NO 9
N= 15 sensors 𝜇 = 700𝑛 → Δ = 49𝑛 Still a factor 3 of reduction 10
Broadband optimization: 11
Broadband optimization: 11
Broadband optimization: 11
Virgo: Newtonian Noise from body AND surface seismic waves Virgo end buildings are complex. A fitted model is not enough. We can base our optimization on seismic data 12
Virgo: Newtonian Noise from body AND surface seismic waves Virgo end buildings are complex. A fitted model is not enough. Work in progress… We can base our optimization on seismic data 70% 12
Future perspectives: • Finishing the work on the array optimization for Virgo • Starting a new project on the calibration of Virgo. Very technical thing but with It will give me the chance to deeper important consequences on the understand the fundamental astrophysics functioning of the interferometer I’ll need to collaborate with a group in France which is working on the calibration 13
Than hank k you you for for you your atten r attention tion
Optimization algorithms: Differential Evolution: Basin Hopping: Perturbed Mutation Configuration Crossover Rejected Selection minima Local minima no 1) Perturbation Stopping Criterion 2) Local minimization (convergence of 3) Acceptance/Rejection population) yes Global minimum Metropolis
Rayleigh, N = 6 Already limited by the self noise This entails a worse NN 𝜇 = 200𝑛 → Δ = 20𝑛 reduction for a degraded array configuration
What about 4d interpolation? Convolution theorem: CPSD (s1, s2) = <(Fx 1 ( ω )*Fx 2 ( ω ))> For each seismometer take N samples in the data → FFT For each sample period calculate the interpolation of the FFT(ω) in the 2D space Calculate CPSD (s1, s2) = CPSD (x1,y1,x2,y2) (just one element of the matrix) CPSD of the 30 ° sensor
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