1. LIGO Response to High Frequency Gravitational Waves Implications for Calibration Hunter Elliott Mentors: Rick Savage, Greg Mendell, Malik Rakhmanov

2. High f behavior and calibration Current calibration is affected at high frequencies by two approximations:  Single-pole length response approximation  Long wavelength approximation

3. Angular Dependence (Antenna Paterns) Detector’s response to gravitational waves depends on source location: X y Y X

4. Angular Dependence (Continued) Sensitivity also depends on source polarization/orientation: X y X y Plus (+) Polarized Cross (+) Polarized

5. 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)

6. Antenna Patterns Complete θ and φ dependence visualized through three dimensional plots: Thanks to Malik Rakhmanov for Matlab scripts. Plus Polarized Cross Polarized

7. Antenna Patterns & Calibration Currently assumed to be frequency independent (Long Wavelength Approximation) Patterns Do vary with frequency: Frame frequency

8. Antenna Patterns & Calibration Deviation increases with frequency.

9. 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°

10. Detector Length Response Peaks are FSR frequencies

11. Length Response & Calibration Currently Approximated

12. Antenna Patterns at FSR Average AP value decreased by ~ factor of 7 Plus Polarized Cross Polarized

13. Overall Sensitivity Combination of antenna pattern and length response frequency dependence

14. 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

15. 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

16. 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)