GWs from neutron star mergers: accuracy and tidal effects S. - PowerPoint PPT Presentation

GWs from neutron star mergers: accuracy and tidal effects S. Bernuzzi TPI-FSU Jena / SFB-TR7 A.Nagar (IHES) M.Thierfelder (Jena), B.Bruegmann (Jena) SB, MT & BB, PRD 85 104030 (2012) SB, AN, MT & BB, [gr-qc] arxiv:1205.340 (2012) lunedì 28 maggio 2012

Motivations PN NR lunedì 28 maggio 2012

Motivations PN NR SNR~35 Stiff EOS 68% [Hinderer et al (2010)] lunedì 28 maggio 2012

Motivations PN NR SNR~16 EOS M>1.97 95% [Damour et al (2012)] SNR~35 Stiff EOS 68% [Hinderer et al (2010)] lunedì 28 maggio 2012

Motivations PN NR SNR~16 EOS M>1.97 95% [Damour et al (2012)] e.g. [Bauswein et al (2012)] SNR~35 Stiff EOS 68% [Hinderer et al (2010)] lunedì 28 maggio 2012

Questions f � 450 Hz ⇒ last 10 orbits ⇒ NR regime! S.Bernuzzi - Tobemory, May 28th 2012 lunedì 28 maggio 2012

Questions f � 450 Hz ⇒ last 10 orbits ⇒ NR regime! ‣ Validity/Accuracy of analytic models (PN/EOB) and templates ? S.Bernuzzi - Tobemory, May 28th 2012 lunedì 28 maggio 2012

Questions f � 450 Hz ⇒ last 10 orbits ⇒ NR regime! ‣ Validity/Accuracy of analytic models (PN/EOB) and templates ? 4 2 u 2 + ... ℓ u 2( ℓ +1) � � 1 + α ( ℓ ) 1 u + α ( ℓ ) � A tidal − κ T EOB ( u ) = ℓ =2 40 � α e ff [Baiotti et al (2011)] � 100 2 α (2) = 85 / 14 α (3) [Bini et al (2012)] = 257 / 48 2 2 S.Bernuzzi - Tobemory, May 28th 2012 lunedì 28 maggio 2012

Questions f � 450 Hz ⇒ last 10 orbits ⇒ NR regime! ‣ Validity/Accuracy of analytic models (PN/EOB) and templates ? 4 2 u 2 + ... ℓ u 2( ℓ +1) � � 1 + α ( ℓ ) 1 u + α ( ℓ ) � A tidal − κ T EOB ( u ) = ℓ =2 40 � α e ff [Baiotti et al (2011)] � 100 2 α (2) = 85 / 14 α (3) [Bini et al (2012)] = 257 / 48 2 2 ‣ Can we extract this info reliably from NR simulations ? Are simulations accurate enough ? S.Bernuzzi - Tobemory, May 28th 2012 lunedì 28 maggio 2012

Full GR Framework [M. Thierfelder, SB & B.Bruegmann (2011)] • BAM matter code • Free evolutions 3+1 NR • Moving boxes technique+ • Einstein: BSSNOK / Z4C Berger-Oliger • Moving puncture gauge • MoL with Runge-Kutta • Psi4 GW extraction schemes and • ideal GRHD • HRSC: • ideal gas EoS (Isentropic flow) ‣ Primitive reconstruction • No magnetic fields - microphysics ‣ LLF flux scheme S.Bernuzzi - Tobemory, May 28th 2012 lunedì 28 maggio 2012

Dynamics and GWs: 9 orbits lunedì 28 maggio 2012

Dynamics and GWs: 9 orbits lunedì 28 maggio 2012

Dynamics and GWs: 9 orbits Several runs! lunedì 28 maggio 2012

“Contact” & “Merger” lunedì 28 maggio 2012

Waveform uncertainties [SB, M. Thierfelder & B.Bruegmann (2012)] M ω 22 < 0 . 07 M ω 22 < 0 . 1 • Self-convergence: 2nd order (do not shift !) up to GW frequencies 0.07/M • Extrapolation of waveform in resolution (Richardson, several runs) ⟹ best case: Δ φ~ 0.13 rad and Δ A/A ~ 0.2 % (0.07/M) • Finite radius extraction must be taken into account S.Bernuzzi - Tobemory, May 28th 2012 lunedì 28 maggio 2012

NR Vs PN - 9 orbits - CENO data T4 3.5PN + NLO S.Bernuzzi - Tobemory, May 28th 2012 lunedì 28 maggio 2012

NR Vs PN - 9 orbits - CENO data T4 3.5PN + NLO S.Bernuzzi - Tobemory, May 28th 2012 lunedì 28 maggio 2012

NR Vs PN - 9 orbits - CENO data T4 3.5PN + NLO S.Bernuzzi - Tobemory, May 28th 2012 lunedì 28 maggio 2012

NR Vs PN - 9 orbits - CENO data ⇒ significant dephasing due to tidal effects contribute during the last 6-9 orbits ... higher-order (>1PN) tidal effects? amplification? T4 3.5PN + NLO S.Bernuzzi - Tobemory, May 28th 2012 lunedì 28 maggio 2012

Systematic uncertainties • Numerical viscosity of the HRSC scheme • Effect of different grid configurations (Berger-Oliger, ...) • Gauge effects on numerically extracted waves • Spurious thermal effect during inspiral • ... They all potentially contribute (~ same order of magnitude), slowly improve with resolution - larger grids ( ≲ 2nd or 1/r converging behaviour), only partially under control ! [M. Thierfelder, SB & B.Bruegmann (2011) L.Baiotti, B.Giacomazzo & L.Rezzolla, CQG (2008)] S.Bernuzzi - Tobemory, May 28th 2012 lunedì 28 maggio 2012

Numerical “viscosity”/“dissipation” - 3 orbits Resolution effect Reconstruction effect Prompt collapse/delayed collapse ? S.Bernuzzi - Tobemory, May 28th 2012 lunedì 28 maggio 2012

9 orbits: changing setup ... lunedì 28 maggio 2012

9 orbits: changing setup ... longer inspiral: phasing! lunedì 28 maggio 2012

9 orbits: changing setup ... ! 0.03 3PN (point mass) EOB (point ! mass) RK3+LLF+CENO3 RK4+LLF+WENOZ ! 0.035 ! 0.04 ! 0.0324 ! 0.045 ! 0.0325 E ! 0.0326 ! 0.05 ! 0.0327 longer inspiral: phasing! ! 0.0328 ! 0.055 ! 0.0329 ! 0.033 ! 0.06 ! 0.0331 ! 0.0332 4.215 4.22 4.225 4.23 4.235 4.24 ! 0.065 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 j lunedì 28 maggio 2012

NR Vs PN/EOB - 9 orbits - WENO data 0.4 0.2 0 ! 0.2 22 - φ NR 22 ! 0.4 φ X ! 0.6 ! 0.8 ! 1 WENO uncertainty EOB (point-mass) EOB tidal LO EOB tidal 2PN α (2) = 85 / 14 ! 1.2 2 EOB tidal 2PN e ff ¯ α 2 = 20 EOB tidal 2PN e ff ¯ α 2 = 40 T4 tidal LO 0 500 1000 1500 2000 u/M lunedì 28 maggio 2012

1.6 EOB (point-mass) 1.6 EOB tidal LO EOB tidal 2PN α (2) = 85 / 14 2 1.4 T4 tidal LO 1.4 WENO (H) 1.2 1.2 1 0.8 1 0.6 | rh 22 | / ν 0.4 0.8 0.2 0 0.6 0.25 2200 2250 2300 2350 2400 2450 2500 2550 2600 2650 2700 0.25 EOB (point-mass) EOB tidal LO EOB tidal 2PN α (2) 0.4 = 85 / 14 2 T4 tidal LO WENO (H) 0.2 0.2 0.2 0.15 0 0 500 1000 1500 2000 2500 u/M 0.15 0.1 Mω 22 0.05 0.1 0 2200 2250 2300 2350 2400 2450 2500 2550 2600 2650 2700 0.05 0 0 500 1000 1500 2000 2500 u/M lunedì 28 maggio 2012

1.6 EOB (point-mass) 1.6 EOB tidal LO EOB tidal 2PN α (2) = 85 / 14 2 1.4 T4 tidal LO 1.4 WENO (H) 1.2 1.2 1 0.8 1 0.6 | rh 22 | / ν 0.4 0.8 0.2 0 0.6 0.25 2200 2250 2300 2350 2400 2450 2500 2550 2600 2650 2700 0.25 EOB (point-mass) EOB tidal LO EOB tidal 2PN α (2) 0.4 = 85 / 14 2 T4 tidal LO WENO (H) 0.2 ⇒ LO or NNLO models are Ok up to contact ! 0.2 0.2 0.15 0 0 500 1000 1500 2000 2500 Not possible to probe amplification, but α eff2 <40 u/M 0.15 0.1 Mω 22 EOB tidal 2PN better but within errorbars 0.05 0.1 0 2200 2250 2300 2350 2400 2450 2500 2550 2600 2650 2700 0.05 0 0 500 1000 1500 2000 2500 u/M lunedì 28 maggio 2012

Summary • 9 orbits BNS waveforms converging up to M ω 22 < 0.07-0.075 (~ before contact), error estimates are necessary and difficult ! • Several systematic uncertainties: more work required to obtain “accurate” waveforms (more resolution, different numerical techniques/ specific methods for inspiral) • With “best NR waveforms”: ‣ Tidal effects significant towards contact (LO is needed!) ‣ (Strong) amplification previously observed likely due to numerical inaccuracies, but still allowed 6 < α eff2 < 40 ‣ Tidal models (EOB, T4) compatible up to contact (EOB better but within the errors). NOT possible to distinguish 1/2 PN (LO/NNLO). ‣ “Validate” analysis of Damour et al 2012 on EOS detectability S.Bernuzzi - Tobemory, May 28th 2012 lunedì 28 maggio 2012