Seth Timpano Louis Rubbo Neil Cornish
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Transcript of Seth Timpano Louis Rubbo Neil Cornish
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