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

Context: measurement of the Hubble constant ● Gravitatjonal-wave “standard sirens” Luminosity distance Redshif from electromagnetjc from GW observatjons observatjon (e.g., host galaxy) So far, only 1 point Infer Hubble constant in the z, D L plane (GW170817)! Error propagatjon : 10 oct 2019 Assemblée Générale GdR OG 2

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 10 oct 2019 Assemblée Générale GdR OG 3

Uncertainty estjmate ● Fisher informatjon matrix → Gaussian approx ● Require “beyond Gaussian” approx that – Encodes the degeneracies – Is analytjc (fast evaluatjon) Seminal paper: Cutler & Flanagan – 1994 Log likelihood: Gaussian approx is an oversimplifj fjcatj tjon Newtonian waveform (masses, merger tjme, sky positj tjon known) Free parameters: D L , inclinatjon, polarizatjon angle, merger phase 10 oct 2019 Assemblée Générale GdR OG 4

Cutler & Flanagan – 1994 A, B = + or x distance beam phase at merger polar angle inclinatjon patuern GW strain at detector: Efgectjve polarizatjon amplitudes: Rewrite scalar product: using efgectjve polarizatjons noise spectrum Mixing matrix of the scalar product: Diagonalize: 10 oct 2019 Assemblée Générale GdR OG 5 Note: error in CF94 afuer marginalizatjon

Degeneracy parameter ε d Two unknowns Two unknowns – two equatjons one equatjon Increase the number of detectors, decreases the number of degenerate cases 10 oct 2019 Assemblée Générale GdR OG 6

Efgect of degeneracy Non-degenerate ε d = 0 Degenerate ε d = 1 Posterior is Posterior is data driven prior driven D L D L 10 oct 2019 Assemblée Générale GdR OG 7

Uncertaintjes in the non-degenerate case SNR = 20 no golden spots Our predicted uncertaintjes for D L 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 ● 10 oct 2019 Assemblée Générale GdR OG 8

Applicatjon to GW170817 Computed using LAL Inf posteriors Based on analytjcal approx [CF’94] ε d = 0.8 SNR = 33 10 oct 2019 Assemblée Générale GdR OG 9

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 – ε d = 1 Risk of bias due to prior-driven posteriors when 10 oct 2019 Assemblée Générale GdR OG 10

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Cutler & Flanagan – 1994 Factor between our uncertainty predictjon on distance and that of CF94 (difgerence due to a mistake in the calculatjon that we have corrected) 10 oct 2019 Assemblée Générale GdR OG 13