ADVANCED LOCALIZATION OF MASSIVE BLACK HOLE COALESCENCES WITH LISA

Ryan Lang

Scott Hughes

MIT

7th International LISA Symposium

June 17, 2008

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)

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Why sky position and distance? Can search the “3D pixel” for

electromagnetic counterparts.

Benefits of counterparts:Parameter estimation: helped by known positionAstrophysics: gas dynamics and accretionStructure formation: direct redshiftCosmology: “standard siren” Fundamental physics: photons vs. gravitons

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What kind of counterparts? Growing field of research! Worst to best:

No EM activity (Find the galaxy.)Delayed afterglow—gas swept awayTransients 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!

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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?

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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

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Example: Polarization amplitude

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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

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(ignoring weak lensing)

Time evolution of pixel

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Evolution of medians

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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 dayPrecession stronger closer to merger!Errors don’t track large SNR increase without

precession in waveform

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Influence of precession

Not much help for advanced localization

LISA mission issue: download frequency

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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 mergerz = 5: at merger only

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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

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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)

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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

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