Advanced localization of massive black hole coalescences with LISA

1. Ryan Lang Scott Hughes MIT 7th International LISA Symposium June 17, 2008 Advanced localization of massive black hole coalescences with LISA

2. Overview • LISA source: coalescing massive black hole binaries • Focus on the inspiral, circular orbits. • Key question: What is the expected accuracy with which LISA can measure parameters of the source? • 15 parameters (masses, spins, orbital orientation, merger time and phase, sky position, luminosity distance) Ryan Lang, MIT

3. Why sky position and distance? • Can search the “3D pixel” for electromagnetic counterparts. • Benefits of counterparts: • Parameter estimation: helped by known position • Astrophysics: gas dynamics and accretion • Structure formation: direct redshift • Cosmology: “standard siren” • Fundamental physics: photons vs. gravitons Ryan Lang, MIT

4. What kind of counterparts? • Growing field of research! • Worst to best: • No EM activity (Find the galaxy.) • Delayed afterglow—gas swept away • Transients during coalescence • Mass loss and potential change • Recoil of hole • Variable source during inspiral • Easiest ID and best science when we can localize the source in advance! Ryan Lang, MIT

5. Parameter estimation • Statistical errors only (not systematic) • Fisher matrix analysis • Covariance matrix: • Fisher matrix: • Inner product: • Key assumption: “Gaussian approximation” • Good for “high SNR,” but what does this mean? Ryan Lang, MIT

6. Spin-induced precession • Spins precess: • So does orbital plane: • Creates amplitude and phase modulations which help break degeneracies between the sky position, the distance, and the binary’s orientation Ryan Lang, MIT

7. Example: Polarization amplitude Ryan Lang, MIT

8. Localization at merger • Sky position major axis: • ~ 15-45 arcminutes (z = 1) • ~ 3-5 degrees (z = 5) • Sky position minor axis: • ~ 5-20 arcminutes (z = 1) • ~ 1-3 degrees (z = 5) • Luminosity distance (DDL/DL): • ~ 0.002-0.007 (z = 1) • ~ 0.025-0.05 (z = 5) • Factors of 2-7 improvement with precession (ignoring weak lensing) Ryan Lang, MIT

9. Time evolution of pixel Ryan Lang, MIT

10. Evolution of medians Ryan Lang, MIT

11. Influence of precession • Great improvement in final day before merger. • Turns out to be due mostly to precession effects! • LISA orbital motion small in single day • Precession stronger closer to merger! • Errors don’t track large SNR increase without precession in waveform Ryan Lang, MIT

12. Influence of precession • Not much help for advanced localization • LISA mission issue: download frequency Ryan Lang, MIT

13. Summary of advanced localization • Sky position metric: LSST 10 degree field • z = 1: as far back as a month (most masses) • z = 3: few days before merger (small/int.) • z = 5: at most a day (few cases) • Distance metric: < 5% (lensing limit) • z = 1: as far back as a month (most masses) • z = 3: few days to a week before merger • z = 5: at merger only Ryan Lang, MIT

14. Position dependence of pixel • Pixel size may also depend on sky position of source • Assumptions: • Vary either polar or azimuthal angle consistently, Monte Carlo the other • Final merger time is random => relative azimuth is random • Azimuthal dependence is thus (mostly) washed out • Can make other choices Ryan Lang, MIT

15. Ryan Lang, MIT

16. Future work • Tests of Gaussian approximation: • analytic (S. Hughes, M. Vallisneri), • compared to MCMC (N. Cornish, SH, RL, and S. Nissanke) • Is stationary phase OK? (SH and RL) • Add higher harmonics (NC, E. Porter, SH, RL, and SN) • Effects of higher PN phase and precession terms (S. O’Sullivan) Ryan Lang, MIT

17. Conclusions • Observing EM counterparts to MBHB coalescences probes lots of astrophysics/physics. • Advanced localization of a source possible at low redshift, worse at high z • Precession drives large improvement in final days • Best pixels found outside galactic plane Ryan Lang, MIT