1. 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

2. LIGO Scientific Collaboration
Basic Idea
LIGO Scientific Collaboration

3. 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

4. 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

5. 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

6. LIGO Scientific Collaboration
The Program
LIGO Scientific Collaboration

7. The Jacobi-Anger Expansion
LIGO Scientific Collaboration

8. 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

9. 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

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

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

12. 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

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