Gravitational waves from compact object binaries

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1 Gravitational waves from compact object binaries Laboratoire Univers et Théories Observatoire de Paris / CNRS aligo, avirgo, KAGRA, elisa, ( DECIGO, ET,... (

2 Main sources of gravitational waves (GW) elisa LIGO/Virgo Binary neutron stars (2 1.4M ) Stellar mass black hole binaries (2 1M ) Supermassive black hole binaries (2 1 6 M ) Extreme mass ratio inspirals ( 1M M )

3 Methods to compute GW templates for compact binaries log 1 (r /m) 4 1 (Compactness) Post Newtonian Theory Numerical Relativity Perturbation Theory Mass Ratio 4 log 1 (m 2 /m 1 )

4 Methods to compute GW templates for compact binaries m 2 log 1 (r /m) r m 1 v 2 c 2 Gm c 2 r (Compactness) Post Newtonian Theory Numerical Relativity Perturbation Theory Mass Ratio 4 log 1 (m 2 /m 1 )

5 Methods to compute GW templates for compact binaries log 1 (r /m) q m 1 m m 2 1 (Compactness) Post Newtonian Theory Numerical Relativity Perturbation Theory m Mass Ratio 4 log 1 (m 2 /m 1 )

6 Methods to compute GW templates for compact binaries log 1 (r /m) 4 m 2 1 (Compactness) Post Newtonian Theory Numerical Relativity Perturbation Theory m Mass Ratio 4 log 1 (m 2 /m 1 )

7 Comparing the predictions from these various methods Why? Independent checks of long and complicated calculations Identify domains of validity of approximation schemes Extract information inaccessible to other methods Develop a universal model for compact binaries What? Periastron advance K vs orbital frequency Ω Binding energy E vs angular momentum J

8 Comparing the predictions from these various methods Paper Year Methods Observable Orbit Spin Baker et al. 27 NR/PN waveform Boyle et al. 27 NR/PN waveform Hannam et al. 27 NR/PN waveform Boyle et al. 28 NR/PN/EOB energy flux Damour & Nagar 28 NR/EOB waveform Hannam et al. 28 NR/PN waveform Pan et al. 28 NR/PN/EOB waveform Campanelli et al. 29 NR/PN waveform Hannam et al. 21 NR/PN waveform Hinder et al. 21 NR/PN waveform eccentric Lousto et al. 21 NR/BHP waveform Sperhake et al. 211 NR/PN waveform Sperhake et al. 211 NR/BHP waveform head-on Lousto & Zlochower 211 NR/BHP waveform Nakano et al. 211 NR/BHP waveform Lousto & Zlochower 213 NR/PN waveform Nagar 213 NR/BHP recoil velocity Hinder et al. 214 NR/PN/EOB waveform

9 Comparing the predictions from these various methods Paper Year Methods Observable Spin Detweiler 28 BHP/PN redshift observable Blanchet et al. 21 BHP/PN redshift observable Damour 21 BHP/EOB ISCO frequency Mroué et al. 21 NR/PN periastron advance Barack et al. 21 BHP/EOB periastron advance Favata 211 BHP/PN/EOB ISCO frequency Le Tiec et al. 211 NR/BHP/PN/EOB periastron advance Damour et al. 212 NR/EOB binding energy Le Tiec et al. 212 NR/BHP/PN/EOB binding energy Akcay et al. 212 BHP/EOB redshift observable Hinderer et al. 213 NR/EOB periastron advance Le Tiec et al. 213 NR/BHP/PN periastron advance } Bini & Damour Shah et al. 214 BHP/PN redshift observable Blanchet et al. } Dolan et al. Bini & Damour 214 BHP/PN precession angle Isoyama et al. 214 BHP/PN/EOB ISCO frequency

10 Relativistic perihelion advance of Mercury Observed anomalous advance of Mercury s perihelion of 43 /cent. Mercury Accounted for by the leading-order relativistic angular advance per orbit Φ = 6πGM c 2 a (1 e 2 ) M Periastron advance of 4 /yr now measured in binary pulsars

11 Relativistic perihelion advance of Mercury Observed anomalous advance of Mercury s perihelion of 43 /cent. m 1 Accounted for by the leading-order relativistic angular advance per orbit Φ = 6πGM c 2 a (1 e 2 ) m 2 Periastron advance of 4 /yr now measured in binary pulsars

12 Periastron advance vs orbital frequency [Le Tiec, Mroué et al. (211)] K K = 1 + Φ/2π Schw EOB GSFν PN GSFq δk/k mω

13 Binding energy vs angular momentum [Le Tiec, Barausse & Buonanno (212)] δe/μ E/μ GSFq GSFν NR GSFν EOB(3PN) 3PN GSFq GSFν NR Schw 3PN PN EOB(3PN) Schw J/(mμ)

14 Perturbation theory for comparable-mass binaries log 1 (r /m) m 2 4 m 1 1 (Compactness) Post Newtonian Theory Numerical Relativity Perturbation Theory Mass Ratio 4 log 1 (m 2 /m 1 )

15 Main shortcoming of current template waveforms h PN Jena (η = NR.25) [Ajith et al. (28)] Time [M] PN breaks down during late inspiral Modelling error > statistical error Bias on parameter estimation Science limited by templates! Η Η modelling bias M M [Ohme (212)]

16 Summary and prospects Observing GWs will open a new window on the Universe Highly accurate template waveforms are a prerequisite for doing science with GW observations It is crucial to compare the predictions from PN theory, perturbation theory and numerical relativity Perturbation theory may prove useful to build templates for IMRIs and even comparable-mass binaries aligo, avirgo, KAGRA, elisa, ( DECIGO, ET,... (

17 Additional Material

18 Periastron advance vs mass ratio [Le Tiec, Mroué et al. (211)] δk/k EOB GSFν PN Schw GSFq q

19 Gravitational waveform for head-on collisions [Sperhake, Cardoso et al. (211)] ψ 2 / η : 1 PP limit L/M = 9.58 L/M = PP limit L/M = 9.58 L/M = ψ 3 / η t / M

20 Gravitational waveform for head-on collisions [Sperhake, Cardoso et al. (211)] ψ 2 / η : 1 PP limit L/M = L/M = PP limit L/M = L/M = ψ 3 / η t / M

21 Recoil velocity for non-spinning binaries [Nagar (213)]

22 Why does perturbation theory perform so well? In perturbation theory, one traditionally expands as k max A k (m 2 Ω) q k where q m 1 /m 2 [, 1] k= However, the relations E(Ω; m a ), J(Ω; m a ), K(Ω; m a ) must be symmetric under exchange m 1 m 2 Hence, a better-motivated expansion is k max B k (mω) ν k where ν m 1 m 2 /m 2 [, 1/4] k= In a PN expansion, we have B n = O ( 1/c 2n) = npn +

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