Ryan Lang Scott Hughes MIT 7 th 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 ID: 496021
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Slide1
Advanced localization of massive black hole coalescences with LISA
Ryan Lang
Scott Hughes
MIT
7
th
International LISA Symposium
June 17, 2008Slide2
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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2
Ryan Lang, MITSlide3
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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3
Ryan Lang, MITSlide4
What kind of counterparts?
Growing field of research!
Worst to best:
No EM activity (Find the galaxy.)Delayed afterglow—gas swept awayTransients during coalescenceMass loss and potential changeRecoil of holeVariable source during inspiralEasiest ID and best science when we can localize the source in advance!
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Ryan Lang, MITSlide5
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?6/17/2008Ryan Lang, MIT
5Slide6
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 6/17/2008Ryan Lang, MIT
6Slide7
Example: Polarization amplitude
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Ryan Lang, MITSlide8
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
6/17/2008
8Ryan Lang, MIT
(ignoring weak
lensing
)Slide9
Time evolution of pixel
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Ryan Lang, MITSlide10
Evolution of medians
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10
Ryan Lang, MITSlide11
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 waveform6/17/2008Ryan Lang, MIT
11Slide12
Influence of precession
Not much help for
advanced
localizationLISA mission issue: download frequency6/17/2008
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Ryan Lang, MITSlide13
Summary of advanced localization
Sky position metric:
LSST
10 degree fieldz = 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 6/17/2008
13
Ryan Lang, MITSlide14
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 otherFinal merger time is random => relative azimuth is randomAzimuthal dependence is thus (mostly) washed outCan make other choices6/17/200814
Ryan Lang, MITSlide15
6/17/2008
15
Ryan Lang, MITSlide16
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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Ryan Lang, MIT
16Slide17
Conclusions
Observing
EM
counterparts to MBHB coalescences probes lots of astrophysics/physics.Advanced localization of a source possible at low redshift, worse at high zPrecession drives large improvement in final daysBest pixels found outside galactic plane6/17/200817
Ryan Lang, MIT