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Simulating the LIGO Laser Phase Change Resulting from Gravitational Waves

This research project aims to simulate the generation and detection of gravitational waves (GW) using real physics. The focus is on simulating the laser phase shift caused by GWs at the LIGO laboratory in Hanford, WA. The results will help understand LIGO's response to different GW signals and improve data analysis techniques.

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Simulating the LIGO Laser Phase Change Resulting from Gravitational Waves

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  1. Simulating the LIGO Laser Phase Change Resulting from Gravitational Waves Jeff Jauregui SURF Student – Caltech Mentor: Dr. Hiro Yamamoto • Simulate GW generation and detection • Make use of real physics • Implement in e2e Hanford, WA, 8/14/03 LIGO Laboratory

  2. Physics Background • Essential physics: how GW’s affect optical path length of FP cavity • Extract GW polarization components parallel to arms • Convert strain into laser phase shift LIGO Laboratory

  3. e2e Background • e2e: time-domain simulation designed for LIGO • A modeled system is described in terms of interacting modules • Design new modules: GW sources and detector • Example: F-P cavity LIGO Laboratory

  4. Let’s Approach the Problem • What factors must we consider? • GW properties, source location • LIGO location and orientation • How do we take them into account? • Transform GW to LIGO coordinate system • Numerically compute phase shift of laser at each time step • How can we integrate the results with other modules? • Dynamically pass laser phase information to EM-field propagators LIGO Laboratory

  5. Outline of Solution • Express GW and LIGO in Earth coordinate system • Rotate GW (from TT) to achieve z-incidence • Translate strain into laser phase shift • Analytic formula for sinusoidal GW’s (P-980007-00, D. Sigg) • Approximation for general GW’s • Write a program to handle computation LIGO Laboratory

  6. Is the Solution Valid? • Accuracy of laser phase shift approximation LIGO Laboratory

  7. Implement in e2e • New modules GW signal generation Detection Binary, circular orbit Inspiralling binary Interferometer LIGO Laboratory

  8. Some Results • Binary system • Two 1.5Msun stars • 1000 km apart • 10 Mpc from Earth • 0o, 0o incidence • Detector • LHO LIGO Laboratory

  9. More Results • Inspiral system • 10Msun each • 10Mpc from Earth http://www.phys.latech.edu/official/research/ligo.htm LIGO Laboratory

  10. Future Improvements • More signal types: • Supernova • Black hole formation • Signal delay between two detectors http://www.mpa-garching.mpg.de/Hydro/RGRAV/ LIGO-G020007 LIGO Laboratory

  11. Applications • Study properties of LIGO with incident GW’s • Learn how imperfections distort signal • What types of noise are most detrimental? • Data analysis • View photodetector output for signal, embedded in realistic noise • Test existing data analysis techniques LIGO Laboratory

  12. Conclusion • Now e2e has GW detection functionality • Can generate variety of signals and study LIGO’s response • Will be able to compare responses of multiple LIGO sites LIGO Laboratory

  13. Acknowledgements Thanks to: • Dr. Hiro Yamamoto • SURF Program • LIGO Project LIGO Laboratory

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