Observatjons gravitatjonnelles et incertjtudes dans la mesure de - - PowerPoint PPT Presentation

Observatjons gravitatjonnelles et incertjtudes dans la mesure de distance

Eric Chassande-Mottjn

CNRS/IN2P3 AstroPartjcule et Cosmologie in collaboratjon with Konstantjn Leyde, Simone Mastrogiovanni, Danièle Steer

Basé sur arXiv:1906.02670 – accepté dans Phys Rev D

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Context: measurement of the Hubble constant

• Gravitatjonal-wave “standard sirens”

Infer Hubble constant Luminosity distance from GW observatjons Redshif from electromagnetjc

• bservatjon (e.g., host galaxy)

So far, only 1 point in the z, DL plane (GW170817)! Error propagatjon :

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Initjal intuitjons

• Uncertainty largely due to distance/inclinatjon degeneracy
• Two polarizatjons may help to resolve this degeneracy

Ex: GW170817 with signifjcant SNR in both LIGO HL and Virgo

• Sky locatjons where distance uncertainty is smaller?

“Golden spots” for H0 measurement?

Abbotu et al. Phys. Rev. X 9, 011001 2019

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Uncertainty estjmate

• Fisher informatjon matrix → Gaussian approx
• Require “beyond Gaussian” approx that

– Encodes the degeneracies – Is analytjc (fast evaluatjon)

Seminal paper: Cutler & Flanagan – 1994

Gaussian approx is an oversimplifj fjcatj tjon

Log likelihood:

Newtonian waveform (masses, merger tjme, sky positj tjon known) Free parameters: DL, inclinatjon, polarizatjon angle, merger phase

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Cutler & Flanagan – 1994

GW strain at detector: Efgectjve polarizatjon amplitudes: Rewrite scalar product:

using efgectjve polarizatjons

inclinatjon polar angle distance phase at merger

Mixing matrix of the scalar product:

noise spectrum beam patuern

Diagonalize: A, B = + or x

Note: error in CF94 afuer marginalizatjon

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Degeneracy parameter εd

Two unknowns – two equatjons Two unknowns

• ne equatjon

Increase the number of detectors, decreases the number of degenerate cases

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Efgect of degeneracy

Degenerate εd = 1 Non-degenerate εd = 0 DL DL Posterior is prior driven Posterior is data driven

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Uncertaintjes in the non-degenerate case

Our predicted uncertaintjes for DL or inclinatjon ί are consistent with:

• Simulated binary neutron-star signals estjmated using LAL Inf (nested sampling)
• Similar results in the literature obtained through simulatjons

SNR = 20

no golden spots

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Applicatjon to GW170817

εd = 0.8 SNR = 33

Based on analytjcal approx [CF’94] Computed using LAL Inf posteriors

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Concluding remarks

• Analytjcal predictjon for the distance uncertaintjes

– Able to capture the distance/inclinatjon degeneracy – Consistent results with Bayesian estjmates – Can be used for future projectjons of H0 measurements (200 BNS+)

• Positjon-dependent predictjons applied to the full sky

– No “golden” spots – Evidences the existence of degenerate sky locatjons – εd = 1

Risk of bias due to prior-driven posteriors when

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Cutler & Flanagan – 1994

Factor between our uncertainty predictjon

• n distance and that of CF94 (difgerence

due to a mistake in the calculatjon that we have corrected)