LISA Aperture Synthesis for Searching Binary Compact Objects

1. LISA Aperture Synthesis for Searching Binary Compact Objects Aaron Rogan Washington State University roganelli@wsu.edu Collaborator: Sukanta Bose GWDAW 2003 Space-Based Detectors II Analysis Methods Supported by NASA: NASA-NAG5-12837

2. Introduction • LISA is a network of three detectors • 2 are independent • Total of 6 elementary data streams • Main Sources of Noise: • Laser Frequency Fluctuation • Relative Craft Motion • Time delay interferometry can eliminate much of the dominating noise

3. Introduction Cont’d • Lasers aborad LISA will have a frequency stability of a few parts in 10-13. • Desired sensitivity range at least a few parts in 10-20 • Time delay interferometry uses time shift operators, Ei. • The time shift operator described by: Eif(t) = f(t-Li/c) • Using these generators or pseudo-strains LISA can achieve the desired levels of sensitivity

4. Introduction Cont’d • The pseudo-strains do not span a vector space • They use data from all six data streams to cancel noise • Act as a network of 3 independent detectors • The pseudo-strains have different sensitivities to the same sky position • An optimal combination of the pseudo-strains is needed to: • Maintain the highest signal-to-noise ratio possible over the entire orbit • Maintain the highest level of sensitivity for all sky positions • Maintain the most efficient search over all sky positions

5. The Problem • To obtain the optimal combination of the data streams one must consider: • The pseudo-strains are a function of the orbital position of LISA • How to weight each pseudo-strain for a given orbital position • The advantages of an optimal combination are: • Maintaining the maximum sensitivity to a wider range of {θ,Φ} values • Maintaining the maximum sensitivity for all points on LISA’s orbit

6. How to Approach the Problem? • Identify the time domain polarization amplitudes, h+(t) and hx(t). • Derive the appropriate Fourier domain polarization amplitudes • Combine the 3 weighted pseudo-strains to obtain the complete signal, hA(Ω). • Analytically maximize over the following parameters: {Ψ,ε,δ} • Obtain the optimal statistic, λ|Ψ,Є,δ . • Develop a template bank over remaining parameters, namely {θ,Ф}. • Determine the computational feasibility of a search

7. The Optimal Statistic • The matched filter is used to obtain the optimal detection statistic. Before maximization it takes the following form: • Now maximizing over the source polarization and inclination angles can be achieved

8. Signal-To-Noise Ratio • The SNR for a each pseudo-strain is plotted to the right. • The holes indicate directions that minimize the SNR • Compare the optimal SNR to the SNR for a given pseudo-strain • The optimal statistic improves the SNR for all orbital positions

9. Network Sensitivity • The optimal statistic also greatly improves the sensitivity of LISA • Although a single pseudo-strain spans all {θ,Ф} values • It does not obtain a maximum sensitivity to all {θ,Ф} • At any given point in the orbit, the sensitivity is very limited • The optimal statistic advantages are: • All {θ,Ф} values are maximized at some point in the orbit • The likelihood of finding a source is increased

10. Developing the Template Bank • Develop a metric on the parameter space {Ω,θ,Ф} as outlined by Owen • Project out Ω from the 3-dimensional metric • This new metric will define the overall volume of your parameter space • Decide on a Minimal Mismatch (MM) • The Minimal Mismatch will fix the number density of the templates • Determine the grid spacing within this volume • Finally determine the number of templates

11. I Would Like to Thank The Following Individuals and Organizations for Their Direct Contributions to My Research: • Shawn Seader • Rajesh Kumble Nayak • Washington State University Physics Department • National Aeronautics and Space Administration

12. If not for the previous work by the following individuals I would not be here today • S. Bose • S. Dhurandhar • K. R Nayak • J-Y Vinet • A. Pai • M. Tinto • B. Owen • B. Schutz • T. Price • S. Larson • J.W. Armstrong • A. Eastabrook

13. Signal-To-Noise Ratio for the Optimal Statistic and a single Pseudo-Strain

14. Sensitivity of the a single Pseudo-Strain and the Optimal Statistic for the Entire Orbit