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Advanced localization of massive black hole coalescences with LISA

Ryan Lang Scott Hughes MIT 7 th International LISA Symposium June 17, 2008. Advanced localization of massive black hole coalescences with LISA. Overview. LISA source: coalescing massive black hole binaries Focus on the inspiral , circular orbits.

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Advanced localization of massive black hole coalescences with LISA

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  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

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