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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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Ryan lang scott hughes mit 7 th international lisa symposium june 17 2008

Ryan Lang

Scott Hughes

MIT

7th International LISA Symposium

June 17, 2008

Advanced localization of massive black hole coalescences with LISA


Overview
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


Why sky position and distance
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


What kind of counterparts
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


Parameter estimation
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


Spin induced precession
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



Localization at merger
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


Time evolution of pixel
Time evolution of pixel

Ryan Lang, MIT


Evolution of medians
Evolution of medians

Ryan Lang, MIT


Influence of precession
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


Influence of precession1
Influence of precession

  • Not much help for advanced localization

  • LISA mission issue: download frequency

Ryan Lang, MIT


Summary of advanced localization
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


Position dependence of pixel
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



Future work
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


Conclusions
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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