Transcript LISA source modeling and data analysis at Goddard John Baker – NASA-GSFC

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LISA source modeling and data analysis
at Goddard
John Baker – NASA-GSFC
K. Arnaud, J. Centrella, R. Fahey,
B. Kelly, S. McWilliams, J. Van Meter
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John Baker
Binary Black Hole Mergers
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• A Key LISA Source
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Masses 10^4—10^7 MSun
Highest SNRs
May trace galaxy formation z>6
Standard candles: may provide redshift-distance information
Provide strong field GR test.
• Waveform Modeling
– PN, inspiral
– Numerical Relativity—Solving Einstein’s equations on a computer
• merger-ringdown simulations cover some parameter space
• Late-inspiral simulations beginning
• Merger-ringdown data analysis
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What can we learn from merger observations?
Power at higher frequencies—transfer function details
MLDC: Mergers to be represented in Round 3.
Preliminary steps at Goddard, based on X-ray data code.
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A Crucial Advance: Let the black holes move!
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…to realize a more suitable
coordinate system (i.e. gauge)
• Example: A single moving black
hole (v=c/2)
• General relativity gives freedom
to choose how coordinates will
evolve in time
 good choice is critical
for successful evolution!
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A previous approach:
– Typical “BEFORE” early 2005
– Begin with coordinate presciption to
minimize “gauge dynamics”
– Alter to force black holes not to move
(to avoid problems with black hole
interiors)
– …Problems develop
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BEFORE
NASA and UTB: ( “AFTER” )
– Begin with coordinate presciption to
minimize “gauge dynamics”
– Let black holes move through grid
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AFTER
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Better efficiency also helps…
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• Higher-order finite differencing
– Error reduced faster with increasing
resolution
– Now typically 4th order accurate
• Adaptive Mesh Refinement (AMR)
– Concentrate computational gridpoints
around black holes
– Move outer boundary far into the
wave zone
• Spectral Methods (Other groups)
– Exponential convergence
• These are large simulations!
– 10K to ~100K CPU-hours on
NASA-Ames’ Project Columbia
supercomputer
– Efficiency improving (~x10 per yr)
Project Columbia
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Waveform simulation progress
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• Simulations
– Equal mass/non-spinning
Dates: January, April, November
– Robust merger-ringdown
• ~ from -100M
• Exploring parameter space
– Late-inspiral
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• Last 15 (7.5 orbits) simulated
• Can compare with PN
John Baker
Merger-Ringdown progress
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• Merger-Ringdown covers
– Last few cycles from near ISCO
– Last ~100 M
– Factor of ~3 in frequency
• Robust results
– Robust ID independence
(equal-mass nonspinning, GSFC)
– Agreement among groups/approaches
(Pretorius, GSFC, UTB, PSU, AEI, Jena,…)
• Parameter Space Studies:
– Unequal-massKick (GSFC, Jena)
– Spin-Orbit coupling delay (UTB)
– Spin-Precession (UTB)
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Late-inspiral simulations
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• Simulations at 3 resolutions
– Equal-mass, non-spinning
– Same initial data
• log Ψ4 shown:
– waves grow by x10^2.5 fac
– GW freq grows by x10
• Phasing differences small:
– …between two highest resolutions
– …late half of simulations
– But, early timing differences!
• Better to compare phase v. freq
– Low-medium and medium-high
phase differences scaled for 4th
order convergence
– ~2 rad phase error est. (~14 cycles)
– Almost all before ω=0.08, t=-300
• Early part more difficult:
– slow energy loss crucial
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Phasing accuracy—PN Comparison
• Phasing Comparison
– NR phasing converges
on red curve
– Agrees best with 3PN φ(ω)
or 3.5PN dω/dt of ω
• Phasing Error
– NR error (red/black)
– NR best after ωM=0.08
– PN error (green) less earlier
3PN-3.5PN dω/dt of ω
– NR-extrap = 3.5PN to <1 rad
over ~900M to near ISCO
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PN-NR waveform matching
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• Best waveform estimate:
– NR after ωM=0.08 (circle), 3.5PN before
– Amplitude matches with no adjustment
– Est. 1rad phase error (over order of mag. in freq.)
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LISA Sensitivity
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• SNR based on equal-mass
waveform
• Top: Characteristic strain
– “Merger-ringdown”
starting 50M before peak
after square in curves
– “Late-inspiral”
starting 1000M before peak
after diamond in curves
• SNR vs. (1+z)M
– Highest SNRs dominated by
merger-ringdown… will be
reduced for unequal masses
– SNRs over 3x104 MSun
dominated by last 1000M
– Sky and orientation averaged
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What LISA may see
• Sensitivity contours
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SNR
– SNR vs. M and z
– SNR nearly independent of
distance for M~104 MSun
• Simulated LISA data
– Two 105 MSun BHs at z=15
– Unequal-arm Michelson “X”
– LISA Simulator (Cornish et al)
http://www.physics.montana.edu/LISA
– Plus white dwarf binary noise
(Barack-Cutler 2004)
– Inset shows a larger timescale
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LISA Data Analysis
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• Objectives
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Apply waveform simulation info in LISA DA studies
What can be measured from merger-only observations?
Enchance future MLDC Challenge models
Participate in future challenges
• First steps toward challenge participation
– XSPEC (X-ray data analysis code developed at Goddard)
– Used for thousands of papers and for several X-ray missions.
– First: Galactic binary identification
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GW data analysis with X-ray astronomy tools (Keith Arnaud)
XSPEC: Standard software used to fit models to X-ray energy spectra. Used for
thousands of published papers. Provides standard interface for adding models (which
can be done dynamically). Several options for fitting statistics and optimization
algorithms including Markov Chain Monte Carlo. (http://xspec.gsfc.nasa.gov)
Data fit is Real and Imaginary parts of FFT of A and E channels from MLDC. Model is
galactic binary using Cornish/Crowder fast code.
1-D marginalized
posterior PDF for
binary polarization
angle.
Re FFT of A
Im FFT of A
Re FFT of E
Im FFT of E
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2-D marginalized
posterior PDF for
source position
John Baker
What’s Next
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• Waveform modeling
– Covering Merger parameter space with waveform simulations
– Accurate empirical waveform model
• GW Data analysis
– Efficiency studies for LIGO burst techniques
– Parameter measurement accuracy estiamtes for LISA merger-only
observations
– ~Participate in MLDC Round 2
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John Baker