1. 1 GWDAW11 Dec 19, 2006 John Baker 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. 2 GWDAW11 Dec 19, 2006 John Baker Binary Black Hole Mergers A Key LISA Source –Masses 10^4—10^7 M Sun –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. 3 GWDAW11 Dec 19, 2006 John Baker A Crucial Advance: Let the black holes move! …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) BEFORE AFTER

4. 4 GWDAW11 Dec 19, 2006 John Baker Better efficiency also helps… Higher-order finite differencing –Error reduced faster with increasing resolution –Now typically 4 th 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

5. 5 GWDAW11 Dec 19, 2006 John Baker 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. 6 GWDAW11 Dec 19, 2006 John Baker 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. 7 GWDAW11 Dec 19, 2006 John Baker Late-inspiral simulations Simulations at 3 resolutions –Equal-mass, non-spinning –Same initial data log Ψ 4 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 4 th 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

8. 8 GWDAW11 Dec 19, 2006 John Baker 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

9. 9 GWDAW11 Dec 19, 2006 John Baker 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. 10 GWDAW11 Dec 19, 2006 John Baker LISA Sensitivity 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 3x10 4 M Sun dominated by last 1000M –Sky and orientation averaged

11. 11 GWDAW11 Dec 19, 2006 John Baker What LISA may see Sensitivity contours –SNR vs. M and z –SNR nearly independent of distance for M~10 4 M Sun SNR Simulated LISA data –Two 10 5 M Sun 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. 12 GWDAW11 Dec 19, 2006 John Baker 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. 13 GWDAW11 Dec 19, 2006 John Baker 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. Re FFT of A Im FFT of A Re FFT of E Im FFT of E 2-D marginalized posterior PDF for source position 1-D marginalized posterior PDF for binary polarization angle.

14. 14 GWDAW11 Dec 19, 2006 John Baker 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