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Advanced localization of massive black hole coalescences with LISA

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Ryan Lang### Advanced localization of massive black hole coalescences with LISA

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)

Ryan Lang, MIT

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?

- 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

- 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

- 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

Example: Polarization amplitude

Ryan Lang, MIT

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

Ryan Lang, MIT

Evolution of medians

Ryan Lang, MIT

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 precession

- Not much help for advanced localization
- LISA mission issue: download frequency

Ryan Lang, MIT

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

- 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

- 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

- 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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