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LIGO Laboratory 1 LIGO-G030395-00-E Simulating the LIGO Laser Phase Change Resulting from Gravitational Waves Simulate GW generation and detection Make use of real physics Implement in e2e Jeff Jauregui SURF Student – Caltech Mentor: Dr. Hiro Yamamoto

LIGO-G030395-00-E LIGO Laboratory1 Simulating the LIGO Laser Phase Change Resulting from Gravitational Waves Simulate GW generation and detection Make

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LIGO Laboratory 1LIGO-G030395-00-E

Simulating the LIGO Laser Phase Change Resulting from Gravitational Waves

Simulate GW generation and detection

Make use of real physics

Implement in e2e

Jeff JaureguiSURF Student – Caltech

Mentor: Dr. Hiro Yamamoto

LIGO Laboratory 2LIGO-G030395-00-E

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 3LIGO-G030395-00-E

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

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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 5LIGO-G030395-00-E

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

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Is the Solution Valid?

Accuracy of laser phase shift approximation)cos()( 0 tAt

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Implement in e2e

New modules

h+

hx

timer

m1

m2

h+

hx

timet_fm1

m2

h+

hx

xy

GW signal generation Detection

Binary, circular orbit Inspiralling binary Interferometer

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Some Results

Binary system» Two 1.5Msun stars

» 1000 km apart

» 10 Mpc from Earth

» 0o, 0o incidence

Detector» LHO

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More Results

Inspiral system» 10Msun each

» 10Mpc from Earth

http://www.phys.latech.edu/official/research/ligo.htm

LIGO Laboratory 10LIGO-G030395-00-E

Future Improvements

More signal types:» Supernova

» Black hole formation

Signal delay between two detectorshttp://www.mpa-garching.mpg.de/Hydro/RGRAV/

LIGO-G020007

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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

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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

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Acknowledgements

Dr. Hiro Yamamoto SURF Program LIGO Project

Thanks to: