Deanna Emery Mentor: Dick Gustafson A Coherent Three Dimensional FFT Based Search Scheme for Gravitational Waves from Binary Neutron Star Systems Deanna Emery Mentor: Dick Gustafson LIGO Scientific Collaboration

LIGO Scientific Collaboration Basic Idea http://planetquest.jpl.nasa.gov/system/media_files/binaries/7/original/doppler1.jpg?1321291255 http://ironbark.xtelco.com.au/subjects/DC/lectures/7/fig_2010_07_08.jpg LIGO Scientific Collaboration

Phase Modulated Signal ω = carrier frequency (frequency of gravitational wave) Ω = modulation frequency (orbital frequency of binary system) Γ = modulation index/ modulation amplitude (representing the Doppler shift) Assuming circular motion LIGO Scientific Collaboration

LIGO Scientific Collaboration Search Limits LIGO looks for signals between 10 to 2000 Hz Target binary neutron stars with orbital frequencies of around 0.1 to 10-6 Hz Modulation index ranges from 0.1 to 500,000 LIGO Scientific Collaboration

LIGO Scientific Collaboration Program Strategy Factor the phase modulation out of the signal Work in the frequency domain Convolution Theorem Perform a search over the three parameters LIGO Scientific Collaboration

LIGO Scientific Collaboration The Program LIGO Scientific Collaboration

The Jacobi-Anger Expansion LIGO Scientific Collaboration

LIGO Scientific Collaboration Outline of Program Sample a phase modulated signal Take the FFT and plot it Perform search through parameters Generate 3D plot and find values of the three parameters General steps of program LIGO Scientific Collaboration

LIGO Scientific Collaboration Results Plot for candidate value of Γ Gives values for all three parameters Baseline features Took just over 4 mins N = 1 Million 500 Million steps total in search Size of bins: each bin is 0.01 Hz w- 0:500 Hz (steps of 0.01)– 500,000 steps W- 0:1 Hz (steps of 0.01)– 100 steps g- 5:15 (steps of 1)– 10 steps For g- 45:55, T = 10s N = 100,000 Took 5 seconds T = 100 Took 10 mins LIGO Scientific Collaboration

First Try At Adding Noise fc = 100 Hz, fm = 0.5 Hz, Γ = 5 LIGO Scientific Collaboration

LIGO Scientific Collaboration Adding Noise Γ = 5 fc = 100 Hz fm = 0.5 Hz LIGO Scientific Collaboration

LIGO Scientific Collaboration Possible Limitations N (number of elements in the data array) Size of search Number of Jacobi-Anger expansion terms Phase of neutron star More than one signal Several phase modulated signals can be found A regular sinusoidal signal is picked up by sidebands LIGO Scientific Collaboration

Further Investigation Effects of noise Non-Gaussian noise (with spikes) Address annoying baseline features Computing realties All-sky search stratagems LIGO Scientific Collaboration