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LIGO Response to High Frequency Gravitational Waves Implications for Calibration Hunter Elliott Mentors: Rick Savage, Greg Mendell, Malik Rakhmanov
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High f behavior and calibration Current calibration is affected at high frequencies by two approximations: Single-pole length response approximation Long wavelength approximation
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Angular Dependence (Antenna Paterns) Detector’s response to gravitational waves depends on source location: X y Y X
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Angular Dependence (Continued) Sensitivity also depends on source polarization/orientation: X y X y Plus (+) Polarized Cross (+) Polarized
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Antenna Patterns Angular dependence is visualized with antenna patterns. Patterns give normalized sensitivity. Distance from origin to pattern is sensitivity in that direction. antenna pattern for φ = 0, plus polarized (X-Z Plane)
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Antenna Patterns Complete θ and φ dependence visualized through three dimensional plots: Thanks to Malik Rakhmanov for Matlab scripts. Plus Polarized Cross Polarized
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Antenna Patterns & Calibration Currently assumed to be frequency independent (Long Wavelength Approximation) Patterns Do vary with frequency: Frame frequency
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Antenna Patterns & Calibration Deviation increases with frequency.
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Origin of Antenna Pattern Frequency Dependence Above DC forward and return trips differ GW Strain is not constant over a photon round-trip X y Φ=135° θ = 90°
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Detector Length Response Peaks are FSR frequencies
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Length Response & Calibration Currently Approximated
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Antenna Patterns at FSR Average AP value decreased by ~ factor of 7 Plus Polarized Cross Polarized
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Overall Sensitivity Combination of antenna pattern and length response frequency dependence
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Calibration & Injection Changes Current software injection process: Simulate Source Strain Apply Directional Dependence using F + (θ,φ,ψ) and F x (θ,φ,ψ) calculated at DC h +SF (t) h xSF (t) Choose Source Sky Location and Orientation (θ,φ,ψ ) Select Raw Data Stream for Injection. AS_Q(t) AS_Q(f) 1+ G(f) Remove Effect of Cavity Length Response using Single Pole Approximation LD(f)LD(f) h +DF (t) h xDF (t) hD(t)hD(t) Inverse Fourier Transform hI(t)hI(t) Analysis Pipeline Remove effect of Digital Gain / Filters Fourier Transform hD(f)hD(f) L -1 Yellow Injector Blue Calibration team
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Calibration & Injection Changes Proposed software injection scheme: Simulate Source Strain Apply Directional Dependence using E + (θ,φ,ψ, f) and E x (θ,φ,ψ, f) h +SF (t) h xSF (t) Choose Source Sky Location and Orientation (θ,φ,ψ ) Select Raw Data Stream for Injection. AS_Q(t) AS_Q(f) 1+ G(f) Remove Effect of Cavity Length Response using Full H L (f) LD(f)LD(f) h +DF (t) h xDF (t) hD(t)hD(t) Inverse Fourier Transform hI(t)hI(t) Analysis Pipeline Fourier Transform h +SF (f) h xSF (f) Inverse Fourier Transform h +DF (f) h xDF (f) Remove effect of Digital Gain / Filters Fourier Transform L -1 hD(f)hD(f) Green : Matlab script E.m Yellow Injector Blue : Calibration team
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Conclusions For high frequency injection antenna patterns should be dynamic. Can be performed by Matlab script (E.m) Full analytical length response should be used. (Will be in place for S4 analysis)
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