LISA source modeling and data analysis at Goddard

1. 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

2. Binary Black Hole Mergers • A Key LISA Source • 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 • 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.

3. …to realize a more suitable coordinate system (i.e. gauge) General relativity gives freedom to choose how coordinates will evolve in time  good choice is critical for successful evolution! 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 NASA and UTB: ( “AFTER” ) Begin with coordinate presciption to minimize “gauge dynamics” Let black holes move through grid Example: A single moving black hole (v=c/2) A Crucial Advance: Let the black holes move! BEFORE AFTER

4. Better efficiency also helps… • Higher-order finite differencing • Error reduced faster with increasing resolution • Now typically 4th order accurate • Adaptive Mesh Refinement (AMR) • Concentrate computational gridpointsaround 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

5. Waveform simulation progress • Simulations • Equal mass/non-spinning Dates: January, April, November • Robust merger-ringdown • ~ from -100M • Exploring parameter space • Late-inspiral • Last 15 (7.5 orbits) simulated • Can compare with PN

6. Merger-Ringdown progress • 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)

7. Late-inspiral simulations • 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-highphase differences scaled for 4thorder convergence • ~2 rad phase error est. (~14 cycles) • Almost all before ω=0.08, t=-300 • Early part more difficult: • slow energy loss crucial

8. 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 earlier3PN-3.5PN dω/dt of ω • NR-extrap = 3.5PN to <1 radover ~900M to near ISCO

9. PN-NR waveform matching • 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.)

10. LISA Sensitivity • SNR based on equal-mass waveform • Top: Characteristic strain • “Merger-ringdown” starting 50M before peakafter square in curves • “Late-inspiral”starting 1000M before peakafter diamond in curves • SNR vs. (1+z)M • Highest SNRs dominated by merger-ringdown… will be reduced for unequal masses • SNRs over 3x104 MSundominated by last 1000M • Sky and orientation averaged

11. What LISA may see • Sensitivity contours • SNR vs. M and z • SNR nearly independent of distance for M~104 MSun SNR • 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

12. LISA Data Analysis • Objectives • 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

13. Re FFT of A Im FFT of A Re FFT of E Im FFT of E 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. GW data analysis with X-ray astronomy tools (Keith Arnaud) 1-D marginalized posterior PDF for binary polarization angle. 2-D marginalized posterior PDF for source position

14. What’s Next • 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