Outline: 1. Gravitational waves and the two-body problem in general relativity 2. Black hole binaries 3. Neutron star binaries

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1 Bernd Brügmann University of Jena Kyoto, Black Hole (and Neutron Star) Binaries in Numerical Relativity Outline: 1. Gravitational waves and the two-body problem in general relativity 2. Black hole binaries 3. Neutron star binaries

2 Any non-uniform and non-spherical motion of mass generates gravitational waves speed of light, long range, no shielding F_gravity = F_electric / 10^36 everyday waves are exceedingly weak black holes, neutron stars, supernovae, big bang,... hard to detect, hard to block no direct detection yet (!!) aligo, avirgo GEO-HF KAGRA ET, elisa PTA Thorne Carnahan

3 Gravitational Wave Astronomy Gravitational waves are a new window into the universe: WHAT WILL WE SEE? S. Rowan, GWIC

4 Theory and Observation Solve Einstein equations 1. theory of the sources 2. templates to filter waves from noise (typically required) 3. physical parameters from analysis of waves GR eqns and GR hydro require advances in analytics, numerics, computations well-posedness, gauge, BH singularities, microphysics, rotation, magnetic fields,... Observe AND UNDERSTAND what is not visible by other means: black holes neutron stars supernovae cosmology the unknown e.g. in binaries, mergers/collisions, mass census e.g. equation of state via oscillations, tidal dis., gamma ray bursts e.g. GW from interior of type-ii, convection e.g. big bang to within seconds e.g. a surprise, at least a test of relativity GW are complementary to all other fields/particles (multi-messenger astronomy)

5 Einstein Equation in Vacuum R (g, g, g) = 0 - black holes, gravitational waves - neutron stars etc. with stress energy tensor on right hand side - reformulation required to obtain standard PDE evolution problem

6 Numerical Relativity = Spacetime Engineering, R = 0

7 Some milestones of 3d black hole evolutions 1995: Schwarzschild in 3d NCSA 1999: Grazing Collision AEI, Texas/PSU 2001: Plunge from ISCO AEI 2004: One Orbit PSU/Jena 2005: Orbit, Merger, Waves Pretorius, Brownsville, Goddard 2006: Several orbits before merger 2007: Kicks, Spin-Kicks 2010: Rochester, Goddard, Georgia Tech, AEI, LSU, (Maryland) Caltech, Cornell, Florida Atlantic, Sperhake, Pretorius, Jena Last missing pieces of BBH puzzle: 2005: Pretorius: constraint damping (Gundlach et al) for harmonic code 2006: Campanelli, Lousto, Marronetti, Zlochower; Baker, Centrella, Choi, Koppitz, Meter: moving puncture 'gauge'

8 Parameters of Black Hole Binaries Ignore field content (waves) Ignore deformations (quasi-normal ringing) Position: separation, varies along orbit m1 Mass: M = m1+m2, q = m1/m2 kicks S1 P1 L m2 P2 S2 Momentum bound: eccentric, quasi-circular unbound: collisions, scattering Spin spin-orbit, spin-spin coupling precession, spin-flips, hang-up/speed-up, kicks Emission of gravitational waves accelerating inspiral precession of orbital plane motion of center of mass

9 Twisted pair of pants: orbits and merger of two black holes event horizon (!) in x-y-t diagram unequal mass no spin M. Thierfelder

10 Orbits and merger of two black holes gravitational waves r Re(Psi4) masses 1:1.5 no spin initial d = 7M volume isosurfaces projection on sphere z=0 plane min/max = box -96 to +96 time step 1M

11 Binary Black Hole Simulations Mathematical, numerical, computational work Gravitational wave templates including fully relativistic merger General relativity and astrophysics of black hole mergers GOLD-RUSH in PARAMETER-SPACE analytic moving puncture gauge validation: Samurai project templates: post-newtonian (EOB) heuristic/hybrid templates data analysis: NINJA, NRDA, NRAR kicks: unequal mass (10:1), spin kicks super-kicks of up to 4000km/s eccentricity, zoom-whirl orbits horizons; N-black-hole new directions: extreme spin, 100:1 matter, electromagnetic counterparts high energy black hole collisions AdS, higher dimensions

12 Binary Black Hole Simulations 2013 Mathematical, numerical, computational work Gravitational wave templates including fully relativistic merger General relativity and astrophysics of black hole mergers GOLD-RUSH in PARAMETER-SPACE Current capability of BH-BH simulations cmp. NRAR (NINJA-2, Samurai) 20 GW cycles before merger (< 40) Δφ < 0.25 radian at merger ΔA/A < 1% e < (quasi-circular) q 4 ( 10, max 100) s 0.8 (approaching max spin, 'linear') high-order finite diff. and spectral methods

13 Some recent examples, BHs and NSs, Jena et al. Mathematical, numerical, computational work Gravitational wave templates including fully relativistic merger Trumpet initial data: solving the constraints in the moving puncture gauge Matter collapse in puncture gauge PDE formulation: Z4c system Spectral method General relativity and astrophysics of mergers Templates: NRDA Accurate/long NS-NS inspirals NS+EOB talk by Bernuzzi GOLD-RUSH in PARAMETER-SPACE Eccentric BH-BH orbits, zoom-whirl at intermediate momenta Eccentric NS-NS orbits, orbit induced oscillations

14 2 black holes, equal masses, no spin (numerical relativity) Müller, Gold, BB 09

15 Orbital precession due to general relativity (BR96) Kepler, Newton Einstein

16 Special/extreme eccentricity: zoom-whirl orbits Newton: Kepler orbits, ellipses for bound orbits Einstein: precessing ellipses, but also fine-tuned orbits in Schwarzschild and Kerr show zoom-whirl behavior Easily exceed the 5% radiated energy of equal mass binaries (15-30% reported) How many whirls are possible for comparable masses? Relevance for astrophysics? High energy collisions? Many refs on geodesics and post-newtonian; numerical relativity: Pretorius, Khuranna 07; Healy et al 08/09; Sperhake et al 09; Gold, BB 09+12

17 Zoom-whirl, equal mass/no spin, low momentum (NR) Gold, BB 12

18 Puncture method for black holes Moving puncture gauge surprisingly successful! Analytic/geometric understanding: Wormhole puncture initial data evolves to trumpet data Hannam, Husa, Pollney, BB, O'Murchadha 2007; Brown 2008;... Brandt, BB 1997 Basic idea: the conformal factor absorbs the coordinate singularity (pole) that encodes the black hole

19 Puncture method for black holes

20 Puncture method for black holes

21 Puncture method for black holes New: Solve constraints for trumpet (!) initial data Rewrite Hamiltonian constraint with ψ 1/ψ Gundermann 2010, Dietrich, BB 2012/13: 1+log trumpets, K 0 Baumgarte 2012: maximal trumpets, K = 0

22 Trumpet solution from spherical gravitational collapse with puncture gauges Thierfelder, Bernuzzi, Hilditch, BB, Rezzolla 2011

23 Spectral methods for black hole spacetimes Vacuum spacetimes: smoothness of metric variables allow high order methods spectral methods can be optimal if applicable Pilot projects bam bamps BB 2013: Stability of Schwarzschild black hole in 3d spin-weighted spherical harmonics, tensor filters, GPU computing Weyhausen, Hilditch, BB (in prep 2013): 3d Nonlinear Waves Nonlinear waves on fixed 2d background: Harms, Bernuzzi, BB 2013: Numerical solution of the 2+1 Teukolsky equation on a hyperboloidal and horizon penetrating foliation of Kerr and application to late time decays time domain integration first results on s = 2

24 Tails for 2+1 Teukolsky equation, time domain, s =0,1,2 Harms, Bernuzzi, BB 2012 Scri: hyperboloidal foliation, Rasz Toth 2011 Additional regularization needed for s > 0, cmp. Zenginoglu 2012 Quadruple precision required Confirms analytic calculations by Hod 2000 (case distinctions!) s=-2 numerical time integration, Krivan, Laguna, Papadopoulos, Andersson 1997

25 Tails for 2+1 Teukolsky equation, time domain, s =0,1,2 Harms, Bernuzzi, BB 2012 Price 1972: late time decay t -µ Here: s=-2, finite null infinity, time splitting bold, various ID preparatory for BH-test mass calculations (Bernuzzi, Nagar) extremal spin, superradiance cavity (Andersson, Glampedakis 1999, Yang et al. 2012)

26 Z4c Formulation for 3d BHs and NSs Hilditch, Bernuzzi, Thierfelder, Cao, Tichy, BB 2012 NS-NS

27 Neutron Star Binary: long/accurate quasicircular inspiral Bernuzzi, Thierfelder, BB 12 Catching up: Simplest model: equal mass, Γ=2 polytrope, no MHD, no neutrinos Focus on accurate simulations suitable for gravitational wave analysis Longest and most accurate simulation of the simplest type Also Baiotti et al 2011, Hotokezaka et al 2013

28 Neutron Star Binary: eccentric inspirals Gold, Bernuzzi, Thierfelder, BB, Pretorius 12 First simulations studying eccentricity in significant detail Superposition of boosted TOV stars constraints not solved (cmp. Lehner et al., new project C. Markakis, N. Moldenhauer) Features: - Orbit Induced Oscillations Turner 1977 Newtonian; Kokkotas, Schäfer 1995 post-newtonian - Large disk mass of about 10% of total initial mass Compare eccentric BH-BH and BH-NS (e.g. Pretorius et al 2012, masses different) Compare Newtonian simulations (e.g. Rosswog, Piran, Nakar 2012) Population of eccentric NS-NS is very uncertain. Small to extremely small?

29 Neutron Star Binary: eccentric inspirals induce oscillations Gold, Bernuzzi, Thierfelder, BB, Pretorius 12 Tracks for model 1, 2, 3 Waveform and instantaneous frequency Model 3, f-mode in green

30 Neutron Star Binary: eccentric inspirals induce oscillations Gold, Bernuzzi, Thierfelder, BB, Pretorius 12 Model 2 and 3, rest-mass density and power-spectral density, l=m=2, f-mode cmp. e.g. Kokkotas et al.

31 Neutron Star Binary: eccentric inspirals increase disk mass Gold, Bernuzzi, Thierfelder, BB, Pretorius 12 eccentricity can lead to significantly larger disk mass

32 Summary Numerical relativity is reaching long-standing goals: Insights for general relativity Astrophysics of black holes and neutron stars Gravitational wave templates 1995: Schwarzschild in 3d 1999: Grazing collision 2002: plunge from ISCO 2004: one orbit 2006: several orbits 2009: physics: spins, kicks, wave templates : more realistic matter