Seth Timpano

Louis Rubbo

Neil Cornish

Characterizing the Gravitational WaveBackground using LISA

OutlineOutline

• 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: 71010

– Catacylsmics: 1.8106

– WUMa: 3107

– Neutron Star Binaries: 1106

– Neutron Star/Black Hole: 5105

– Close White Dwarfs: 3106

• 3107 ???

D. Hils, P. Bender, and R.F. Webbink, Astrophys. J. 360, 75, 1990

Modeling an Individual Source

• General Gravitational Wave

• Polarization Coefficients

• Amplitudes1

2 321 2

1 2

2[1 cos ( )]

M MA

r M M

12 3

1 2

1 2

4cos( )

M MA

r M M

( ) ( ) ( )h h h e e

0 0cos(2 )cos(2 ) sin(2 )sin(2 )h A t A t

0 0cos(2 )sin(2 ) sin(2 )cos(2 )h A t A t

Galactic Model

• Galactic Disk

• Sun-Centered Ecliptic Coordinates

00 0

( , ) exp expzr

r zr z

Barycenter

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

2/1

1

22 )(2

1

bN

iinet AAh

Source Number Density

Number of sources perFrequency bin versus frequency.

LISA

• NASA/ESA mission• 2014 • Orbital Configuration

– 1 AU– 60 degree inclination– 3 spacecraft – 5e6 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:

obsm T

f1

1*

f

f

m

mk

kn

nli

ll

iq cJacAepAes o )()(

2

1 2/3

)2cos()()( 2tftftAts oo

CorrelationsLow Frequency Approximation Rigid Adiabatic

Approximation

Extended Low Frequency Approximation

The Accelerated LISA Simulator

0 1 2, , , , , , , ,M M r

Low Frequency Approximation

Extended Low Frequency Approximation

Rigid Adiabatic Approximation

f < 3mHz f < 7mHz f < 100mHz

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?...NoGaussian?...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?...YesGaussian?...Yes

What happens when we remove all the bright sources?

The Confusion background is Gaussian.

• Galactic Model of Gravitational Radiation

• Detector Simulation

• Identification of Outliers and Source Removal

• Distinguish Background from Noise

SummarySummary