Looking to the Future: LISA and Beyond

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Looking to the Future LISA and Beyond

• Neil Cornish

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Bill Hiscock
Ron Hellings
Matt Benacquista
Dan Bambeck
Joe Plowman
Neil Cornish
Louis Rubbo Jeff Crowder Paul
Schladensky Joey Shaipro Vincent Corbin
Seth Timpano
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Montana Harvest

• Forward Modeling
• The LISA Simulator
• Adiabatic Approximation
• TDI with a flexing array
• Synthetic Galactic Background
• Inverse Problem
• The LISA Calculator
• Parameter estimation with multiple sources
• Detecting CGB, Resolution of the BBO
• Signal Demodulation
• gCLEAN
• A prescription for LISA data analysis

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Forward Modeling
LISA
GW Source
Earth
Sun

• N. J. Cornish and L. J. Rubbo, Phys. Rev. D 67,
  022001 (2003)

http/www.physics.montana.edu/LISA
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AM - FM - Stereo
Channel 2
Channel 1
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SMBH Inspiral at z 1
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SMBH Inspiral at z 1
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Adiabatic Approximation
Neglects Flexing Aberration. Works in mixed
Time-Frequency domain
L. Rubbo, N. Cornish O. Poujade, gr-qc/0311069
Low Freq. Approx.
Adiabatic Approx.
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Galactic Background
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Confusion Noise
Main noise source for LISA is signal
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Synthetic Galactic Background
Timpano, Rubbo Cornish
Multiple Realizations to be placed on the
AstroGravs Mock Data Challenge Website (with the
answer keys)
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Galactic Background
Timpano, Rubbo Cornish. (Similar work by
Benacquista)
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Source Parameter Estimation
Can estimate parameter resolution using Fisher
Information Matrix (Cutler, Hellings Moore,
Vecchio, Seto, Hughes, Cutler Barack)
Source Parameters
Whitened LISA data streams
(Whitening )
Fisher Matrix
Variance-Covariance Matrix
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LISA Angular Resolution
Doppler modulation
Amplitude modulation
Monochromatic Binaries. Fixed SNR10
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Source Confusion
Multiple Sources
How does source interference affect parameter
resolution? Example Two non-chirping binaries,
14 x 14 Fisher Matrix.
Crowder Cornish
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Extended Observation Time Key
Source confusion decays much faster than familiar
for incoherent noise. Extended mission
lifetime is key.
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LISA Angular Resolution
Z1, Final Year
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Big Bang Observatory
P.I. Phinney. Co.Is Bender, Buchman, Cornish,
Fritschel, Folkner, Merkowitz.
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Big Bang Observatory
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BBO Angular Resolution(For foreground
Subtraction)
Z1, Final Year
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LISA Data Analysis

• Simple Waveforms (generally)
• Long Duration and Continuous Sources
• Orbital Signal Modulation
• Multiple Overlapping Sources

Optimal signal processing uses matched filters
(Wiener) But, optimal filter for LISA is
Huge parameter space Under determined problem
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A prescription for LISA data analysis
(Cornish Hellings)

• Approximate solution using demodulation
  accelerated gCLEAN
• Refinement using linear least squares

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Forward Modeling Redux
Stereo Signal Vector
Wave Strain Vector
Modulation Matrix
Single Source
Multiple Sources Noise
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Power Demodulation
Can directly solve for source parameters
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Accelerated gCLEAN

• Power Demodulation for initial guess
• Refine using single source templates
• gCLEAN Procedure
• Identify Best Match
• Subtract small fraction of best match
• Record what is subtracted
• Repeat steps 1 through 3
• Reconstruct individual sources

N. Cornish S. Larson Phys. Rev. D67 103001
(2003)
Output of gCLEAN is an approximate solution for
all the sources resolved by LISA
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gCLEAN v1.0
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Linear Least Squares Improvement
gCLEAN yields approximate solution
The residual is a combination of detector
noise and undetected sources (confusion
background)
The variance is minimized by
Have to invert a dimensional
Fisher matrix (easy)
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Some Open Questions

• How well can we solve the cocktail party
  problem?
• What is the computational cost?
• How do we incorporate complex sources?
• Can we say something about un-modeled sources?