Characterizing the Gravitational Wave Background using LISA Seth

Characterizing the Gravitational Wave Background using LISA Seth Timpano Louis Rubbo Neil Cornish

Outline • • Motivation Galactic Sources of Gravitational Waves Modeling a Source LISA and Detector Simulations The Full Modulated Signal Bright Sources Confusion Background Tests of Normality

Galactic Sources of Gravitational Radiation • Binaries have time varying quadrupole moments • Large number of binaries • Galactic Sources – – – Unevolved Binaries: 7 1010 Catacylsmics: 1. 8 106 WUMa: 3 107 Neutron Star Binaries: 1 106 Neutron Star/Black Hole: 5 105 Close White Dwarfs: 3 106 • 3 107 ? ? ? D. Hils, P. Bender, and R. F. Webbink, Astrophys. J. 360, 75, 1990

Modeling an Individual Source • General Gravitational Wave • Polarization Coefficients • Amplitudes

Galactic Model • Galactic Disk • Sun-Centered Ecliptic Coordinates

Barycenter Combine all source types to arrive at a total barycenter background.

Source Number Density Number of sources per Frequency bin versus frequency.

LISA • NASA/ESA mission • 2014 • Orbital Configuration – – 1 AU 60 degree inclination 3 spacecraft 5 e 6 km arm-length • Sensitive to both + & x • Frequency Response – 10 -5 to 100 Hz • Sources – Galactic Binaries – SMBH Mergers – EMRIs

Signal Modulation – Frequency Modulation • Doppler Effect – Amplitude Modulation • Time Varying Antenna Patterns – Phase Modulation • +, x sensitivity

Extended Low Frequency Approximation • Arbitrary Observation Time: • Frequency Evolution: • Arm Response Functions: • Total Response:

Correlations Low Frequency Approximation Rigid Adiabatic Approximation Extended Low Frequency Approximation

The Accelerated LISA Simulator f < 3 m. Hz Low Frequency Approximation f < 7 m. Hz Extended Low Frequency Approximation f < 100 m. Hz Rigid Adiabatic Approximation

The Simulated Background

The Barycenter Background

The Simulated Background

Noise Co-added to Signal

Outlier Removal • Exact Removal • Removal Procedure – Determine initial Confusion Background – Remove all sources with SNR > 5 – Update Confusion Background – Remove all sources with SNR > 5 – Repeat 4 more times

Confusion Background • Definition of the Confusion Background • Estimate of the Confusion Background

Outlier Properties • Source Number and Type • Distance versus Frequency • Source Density

Gaussian? . . . No Are the Fourier coefficients of the power spectrum normally distributed? Fails to be Gaussian due to outliers in the tails of the distribution. Central Limit Theorem?

Gaussian? . . . Yes What happens when we remove all the bright sources? The Confusion background is Gaussian.

Summary • Galactic Model of Gravitational Radiation • Detector Simulation • Identification of Outliers and Source Removal • Distinguish Background from Noise