Gravitational waves from neutron stars binaries: accuracy and tidal effects in the late inspiral S. Bernuzzi TPI-PAF FSU Jena / SFB-TR7

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1 Gravitational waves from neutron stars binaries: accuracy and tidal effects in the late inspiral S. Bernuzzi TPI-PAF FSU Jena / SFB-TR7 M. Thierfelder, SB, & B.Bruegmann, PRD (2011) SB, MT, & BB arxiv: [gr-qc] (2011) R.Gold, SB, MT, BB, & F.Pretorius arxiv: [gr-qc] (2011) N.Johnson-McDaniel, SB, MT, & BB In Prep. (2012)

2 Motivations Binary neutron stars (BNSs) exist and are among the most promising sources of gravitational waves (GWs) BNS simulations: a complex problem (~ supernovae) necessary to select what physics to simulate! Last orbits + merger tidal interactions, significant finite size effects star parameters (radius, Love #) EoS from GWs measure*! Nonlinear regime numerical relativity (NR) evolutions required! Mostly evolutions of quasi-circular initial data Started a data analysis / analytic methods comparison* *Read et al PRD (2009) *Baiotti et al PRL (2010), PRD (2011)

3 Questions Circular mergers: How large are tidal effect during the last inspiral - merger phase? Small effects Can we extract this info reliably? How accurate are the simulations? * Eccentric mergers: Are there other tidal signatures? # Are astrophysically relevant? * Miller PRD (2005), Lindblom et al. PRD (2008) # Turner ApJ (1977), Lee et al ApJ (2010)

4 Full GR Framework Free evolutions 3+1 NR Einstein: BSSNOK Moving puncture gauge Psi4 GW extraction ideal GRHD No magnetic fields - polytropic/ideal fluid EoS microphysics BAMmatter code 3D Cartesian nested grids with moving boxes technique MoL with Runge-Kutta schemes and Berger-Oliger Metric: high-order finite differencing (centered +lop-sided) Matter: HRSC scheme

5 Quasi - circular mergers SB, MT, & BB arxiv: [gr-qc] (2011) M. Thierfelder, SB, & B.Bruegmann, PRD (2011) Initial data: equal masses, circularized, conformally flat, and irrotational (Lorene, Taniguchi & Gourgoulhon PRD ) Performed ~ 3 orbits and ~ 9 orbits (longest so far!) simulations Investigated truncation errors and finite extraction effects, and systematic source of uncertainties; quantified the former and assigned errorbars (inspiral only!) Checked waveforms against accuracy standard for detection (first time!) Preliminary comparison with post-newtonian approximants

6 Dynamics and GWs

7 Dynamics and GWs

8 Handling singularity formation puncture gauge PRD (2011) t/m t α = β i i α 2α ˆK t β k = Γ k ηβ k + β j j β k r/m Brandt & Bruegmann PRL (1997) Baker et al PRL (2006) Campanelli et al PRL (2006) Hannam et al PRL (2007) Brown PRD (2008)

9 Waveform uncertainties Self-convergence: 2nd order (do not shift!) up to contact (9 orbits) Extrapolation of waveform in resolution (several runs) best case: rad and ~ 0.2 % (contact) Finite radius extraction must be taken into account! Absolute error estimate (upper bound) contact merger

10 Accuracy standards { I 2 = δh w ε/ϱ faithful < h x w 2εM effectual { faithful ϱ 8, ε =0.5, ε M = effectual Miller PRD (2005), Lindblom et al. PRD (2008)

11 Accuracy standards { I 2 = δh w ε/ϱ faithful < h x w 2εM effectual { faithful ϱ 8, ε =0.5, ε M = effectual Miller PRD (2005), Lindblom et al. PRD (2008)

12 Accuracy standards { I 2 = δh w ε/ϱ faithful < h x w 2εM effectual { faithful ϱ 8, ε =0.5, ε M = effectual REM not necessarily the optimal error estimate for DA, but upper bound... Miller PRD (2005), Lindblom et al. PRD (2008)

13 NR Vs PN waveforms T4pp: T4 3.5PN waveform pointparticle, T4td: T4 3.5PN waveform + NLO tidal contribute* ~3 rad Time domain comparison Assume PN valid... Align waves dependency on matching interval are significant significant tidal effects > NLO *Hinderer et al PRD (2010) Vines & Flanagan arxiv: [gr-qc] (2010) Vines et al PRD (2011) Damour & Nagar PRD (2010) ~1.5 rad

14 Systematic uncertainties Effect of different grid configurations, Berger-Oliger Numerical viscosity of the HRSC scheme 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, PRD (2011) L.Baiotti, B.Giacomazzo, & L.Rezzolla, CQG (2008)

15 Highly eccentric mergers R.Gold, SB, MT, BB, & F.Pretorius arxiv: [gr-qc] (2011) Initial data: superposition of two boosted spherical configurations (constraint violating), 50M separation, boost parameter ξ. Equal masses, non-conformally flat, approximately irrotational Performed several simulations varying the initial boost ξ [0.01,0.07] Characterization of orbital dynamics and waves as function of ξ Disk mass in the remnant as function of ξ Relevance for detectability, SNR, accuracy and astrophysical population Role of mass ratio

16 Orbital dynamics /1 Model 1 ξ = 0.01 Model 2 ξ = 0.02 Model 3 ξ = 0.022

17 Orbital dynamics /1 Model 1 ξ = 0.01 Model 2 ξ = 0.02 Model 3 ξ = 0.022

18 Orbital dynamics /2 Orbital dynamics (as ξ increases) : direct plunge 2 encounters + merger multipole encounters (with precession) circular Radial oscillations (trigger by spurious effects?) Non-radial oscillations excited during encounters Model ~ 2: mass exchange during encounter Model ~ 2: massive disk ~ 10% M0(0)

19 Orbital dynamics /2 Orbital dynamics (as ξ increases) : direct plunge 2 encounters + merger multipole encounters (with precession) circular Radial oscillations (trigger by spurious effects?) Non-radial oscillations excited during encounters Model ~ 2: mass generic exchange for several during encounter models! Model ~ 2: massive disk ~ 10% M0(0)

20 Waveforms bursts encounters oscillations compatible with f-mode frequency

21 Mode analysis Spherical harmonics projections ρ lm = d 3 xy lmρ Main modes excited: (2,2), (2,0) f-mode frequency (2,0) strongly modulated by encounters frequency Upper limit on star rotation

22 Conclusions /1 GWs from NR quasi-circular mergers 2nd order convergent up to merger (3 orbits simulations) or up to contact (9 orbits simulations) Estimated uncertainties the waveforms may be used for some quantitative analysis, but extensive error analysis of the numerical data is imperative in every case! Impact on data analysis? Post-Newtonian comparison significant dephasing due to tidal effects contribute during the last 9 orbits Several systematic uncertainties: more work required to obtain accurate waveforms

23 Conclusions /2 GWs from eccentric mergers present burst-like structures (encounters) and can contain the star modes signature, as indicated by some Newtonian analysis e.g. Turner (1970), Lee et al (2010) The first set of NR simulations of highly eccentric binaries confirms qualitatively these characteristics In particular a strong f-mode (l=2) signature is produced quite generically for several eccentricity values, and can persist for several encounters (> 6) More work is ongoing about the impact of these results for the third generation of detectors, role of masses, accretion disks, and on possible dynamical instabilities

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