Simulations of inspiraling and merging double neutron stars using the Spectral Einstein Code

We present results on the inspiral, merger, and postmerger evolution of a neutron star-neutron star (NSNS) system. Our results are obtained using the hybrid pseudospectral-finite volume Spectral Einstein Code (SpEC). To test our numerical methods, we evolve an equal-mass system for ≈22 orbits before merger. This waveform is the longest waveform obtained from fully general-relativistic simulations for NSNSs to date. Such long (and accurate) numerical waveforms are required to further improve semianalytical models used in gravitational wave data analysis, for example, the effective one body models. We discuss in detail the improvements to SpEC’s ability to simulate NSNS mergers, in particular mesh refined grids to better resolve the merger and postmerger phases. We provide a set of consistency checks and compare our results to NSNS merger simulations with the independent bam code. We find agreement between them, which increases confidence in results obtained with either code. This work paves the way for future studies using long waveforms and more complex microphysical descriptions of neutron star matter in SpEC.

[1]  B. Fryxell,et al.  FLASH: An Adaptive Mesh Hydrodynamics Code for Modeling Astrophysical Thermonuclear Flashes , 2000 .

[2]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[3]  Sebastiano Bernuzzi,et al.  Numerical relativity simulations of neutron star merger remnants using conservative mesh refinement , 2015 .

[4]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[5]  Z. Etienne,et al.  Relativistic magnetohydrodynamics in dynamical spacetimes: A new adaptive mesh refinement implementation , 2010, 1007.2848.

[6]  K. Hotokezaka,et al.  Binary neutron star mergers: Dependence on the nuclear equation of state , 2011, 1105.4370.

[7]  David Neilsen,et al.  Relativistic MHD with adaptive mesh refinement , 2006, gr-qc/0605102.

[8]  L. Rezzolla,et al.  Beyond second-order convergence in simulations of binary neutron stars in full general-relativity , 2013, 1306.6052.

[9]  Department of Physics,et al.  WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics , 2007, gr-qc/0701109.

[10]  B. Lackey,et al.  Tidal deformability of neutron stars with realistic equations of state , 2009, 0911.3535.

[11]  N. W. Taylor,et al.  Suitability of hybrid gravitational waveforms for unequal-mass binaries , 2012, 1210.3007.

[12]  S. Teukolsky,et al.  Spin-up of a rapidly rotating star by angular momentum loss: Effects of general relativity , 1992 .

[13]  B. Stephens,et al.  Eccentric black hole-neutron star mergers: effects of black hole spin and equation of state , 2011, 1111.3055.

[14]  S. Nissanke,et al.  Suitability of post-Newtonian/numerical-relativity hybrid waveforms for gravitational wave detectors , 2011, 1102.5128.

[15]  Jonathan C. McKinney,et al.  WHAM : a WENO-based general relativistic numerical scheme -I. Hydrodynamics , 2007, 0704.2608.

[16]  Richard H. Price,et al.  Black Holes , 1997 .

[17]  J. Faber,et al.  Binary Neutron Star Mergers , 2012, Living Reviews in Relativity.

[18]  Christian Reisswig,et al.  Notes on the integration of numerical relativity waveforms , 2010, 1006.1632.

[19]  S. Teukolsky,et al.  Rapidly Rotating Polytropes in General Relativity , 1993 .

[20]  Eric Gourgoulhon,et al.  Numerical Relativity: Solving Einstein's Equations on the Computer , 2011 .

[21]  Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. III. Identical and different mass stars with γ = 2 , 2002, gr-qc/0207098.

[22]  Curran D. Muhlberger,et al.  Gravitational waveforms for neutron star binaries from binary black hole simulations , 2015, 1509.05782.

[23]  Curran D. Muhlberger,et al.  BLACK HOLE–NEUTRON STAR MERGERS WITH A HOT NUCLEAR EQUATION OF STATE: OUTFLOW AND NEUTRINO-COOLED DISK FOR A LOW-MASS, HIGH-SPIN CASE , 2013, 1304.3384.

[24]  Seidel.  Gravitational radiation from even-parity perturbations of stellar collapse: Mathematical formalism and numerical methods. , 1990, Physical review. D, Particles and fields.

[25]  B. Giacomazzo,et al.  GRAVITATIONAL WAVES FROM MASSIVE MAGNETARS FORMED IN BINARY NEUTRON STAR MERGERS , 2014, 1408.0013.

[26]  Simulating merging binary black holes with nearly extremal spins , 2010, 1010.2777.

[27]  B. Szilágyi,et al.  Unambiguous determination of gravitational waveforms from binary black hole mergers. , 2009, Physical review letters.

[28]  K. S. Thorne,et al.  Predictions for the rates of compact binary coalescences observable by ground-based gravitational-wave detectors , 2010, 1003.2480.

[29]  Mark A. Scheel,et al.  Magnetic effects on the low-T/|W| instability in differentially rotating neutron stars , 2014, 1405.2144.

[30]  N. Yunes,et al.  I-Love-Q: Unexpected Universal Relations for Neutron Stars and Quark Stars , 2013, Science.

[31]  K. Chatziioannou,et al.  Probing the internal composition of neutron stars with gravitational waves , 2015, 1508.02062.

[32]  S. Bernuzzi,et al.  Tidal effects in binary neutron star coalescence , 2012, 1205.3403.

[33]  C. Kochanek.  Coalescing binary neutron stars , 1992 .

[34]  Moore,et al.  Gravitational radiation from realistic relativistic stars: Odd-parity fluid perturbations. , 1987, Physical review. D, Particles and fields.

[35]  L. Bildsten,et al.  Tidal interactions of inspiraling compact binaries , 1992 .

[36]  Lawrence E. Kidder,et al.  Black hole-neutron star mergers: Effects of the orientation of the black hole spin , 2010, 1007.4203.

[37]  Luca Baiotti,et al.  Constraining the Equation of State of Neutron Stars from Binary Mergers , 2014, Physical review letters.

[38]  T. Damour,et al.  Effective one-body approach to general relativistic two-body dynamics , 1999 .

[39]  S. Bernuzzi,et al.  Simulations of rotating neutron star collapse with the puncture gauge: End state and gravitational waveforms , 2014, 1412.5499.

[40]  Harald P. Pfeiffer,et al.  Solving Einstein's equations with dual coordinate frames , 2006, gr-qc/0607056.

[41]  S. Shapiro,et al.  On the Maximum Mass of Differentially Rotating Neutron Stars , 1999, The Astrophysical journal.

[42]  L. Baiotti,et al.  Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole , 2004, gr-qc/0403029.

[43]  L. Baiotti,et al.  Binary neutron-star mergers with Whisky and SACRA: First quantitative comparison of results from independent general-relativistic hydrodynamics codes , 2010, 1007.1754.

[44]  Lawrence E. Kidder,et al.  Abstract Submitted for the APR16 Meeting of The American Physical Society Low mass binary neutron star mergers : gravitational waves and neutrino emission , 2016 .

[45]  Roland Haas,et al.  Binary Neutron Stars with Arbitrary Spins in Numerical Relativity , 2015, 1508.06986.

[46]  S. Bernuzzi,et al.  Modeling the Complete Gravitational Wave Spectrum of Neutron Star Mergers. , 2015, Physical review letters.

[47]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection , 1977 .

[48]  Christian Reisswig,et al.  Energy versus angular momentum in black hole binaries. , 2011, Physical review letters.

[49]  Chris L. Fryer,et al.  DOUBLE COMPACT OBJECTS. III. GRAVITATIONAL-WAVE DETECTION RATES , 2014, 1405.7016.

[50]  Sascha Husa,et al.  Calibration of moving puncture simulations , 2008 .

[51]  B. Stephens,et al.  30 94 v 2 [ gr-q c ] 2 9 M ay 2 01 2 Hydrodynamics in full general relativity with conservative AMR , 2012 .

[52]  Michael Boyle,et al.  Comparing Gravitational Waveform Extrapolation to Cauchy-Characteristic Extraction in Binary Black Hole Simulations , 2013, 1309.3605.

[53]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[54]  N. W. Taylor,et al.  Dynamical excision boundaries in spectral evolutions of binary black hole spacetimes , 2012, 1211.6079.

[55]  Von Welch,et al.  Reproducing GW150914: The First Observation of Gravitational Waves From a Binary Black Hole Merger , 2016, Computing in Science & Engineering.

[56]  C. Gundlach,et al.  Pseudospectral apparent horizon finders: An efficient new algorithm , 1997, gr-qc/9707050.

[57]  Masaru Shibata,et al.  Measuring the neutron star equation of state with gravitational wave observations , 2009, 0901.3258.

[58]  G. Lovelace,et al.  High-accuracy gravitational waveforms for binary black hole mergers with nearly extremal spins , 2011, 1110.2229.

[59]  Lawrence E. Kidder,et al.  Black hole-neutron star mergers at realistic mass ratios: Equation of state and spin orientation effects , 2012, 1212.4810.

[60]  John D. Hunter,et al.  Matplotlib: A 2D Graphics Environment , 2007, Computing in Science & Engineering.

[61]  Lawrence E. Kidder,et al.  Black hole evolution by spectral methods , 2000, gr-qc/0005056.

[62]  B. Szilágyi,et al.  Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity , 2009, 0912.1285.

[63]  Lawrence E. Kidder,et al.  A new generalized harmonic evolution system , 2005, gr-qc/0512093.

[64]  S. Osher,et al.  Weighted essentially non-oscillatory schemes , 1994 .

[65]  Scott H. Hawley,et al.  Evolutions in 3D numerical relativity using fixed mesh refinement , 2003, gr-qc/0310042.

[66]  John P. Boyd,et al.  A fast algorithm for Chebyshev, Fourier, and sinc interpolation onto an irregular grid , 1992 .

[67]  E. Sorkin.  An axisymmetric generalized harmonic evolution code , 2009, 0911.2011.

[68]  Harald P. Pfeiffer,et al.  Evolving black hole-neutron star binaries in general relativity using pseudospectral and finite difference methods , 2008, 0809.0002.

[69]  Hans-Thomas Janka,et al.  Exploring properties of high-density matter through remnants of neutron-star mergers , 2015, 1508.05493.

[70]  S. Ossokine,et al.  Precession-tracking coordinates for simulations of compact-object-binaries , 2013, 1304.3067.

[71]  Lawrence E. Kidder,et al.  Post-merger evolution of a neutron star-black hole binary with neutrino transport , 2015, 1502.04146.

[72]  B. Lackey,et al.  Systematic and statistical errors in a bayesian approach to the estimation of the neutron-star equation of state using advanced gravitational wave detectors , 2014, 1402.5156.

[73]  V. Springel.  E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh , 2009, 0901.4107.

[74]  Harald P. Pfeiffer,et al.  A Multidomain spectral method for solving elliptic equations , 2002, gr-qc/0202096.

[75]  Y. Zlochower,et al.  Characteristic extraction tool for gravitational waveforms , 2010, 1011.4223.

[76]  Masaru Shibata,et al.  Simulating coalescing compact binaries by a new code (SACRA) , 2008, 0806.4007.

[77]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[78]  F. Pannarale,et al.  On the universality of I-Love-Q relations in magnetized neutron stars , 2013, 1309.3885.

[79]  Harald P. Pfeiffer,et al.  Reducing orbital eccentricity in binary black hole simulations , 2007 .

[80]  T. Piran,et al.  Gravitational-wave emission from rotating gravitational collapse. , 1985, Physical review letters.

[81]  Thibault Damour,et al.  Transition from inspiral to plunge in binary black hole coalescences , 2000 .

[82]  Philip S. Marcus,et al.  A Spectral Method for Polar Coordinates , 1995 .

[83]  Bela Szilagyi,et al.  Key elements of robustness in binary black hole evolutions using spectral methods , 2014, 1405.3693.

[84]  James Wadsley,et al.  On the treatment of entropy mixing in numerical cosmology , 2008 .

[85]  D. Shoemaker,et al.  Observing gravitational waves from the post-merger phase of binary neutron star coalescence , 2015, 1509.08522.

[86]  S. Bernuzzi,et al.  Quasiuniversal properties of neutron star mergers , 2014, 1402.6244.

[87]  Mark A. Scheel,et al.  Simulations of Binary Black Hole Mergers Using Spectral Methods , 2009, 0909.3557.

[88]  Lawrence E. Kidder,et al.  Neutron star-black hole mergers with a nuclear equation of state and neutrino cooling: Dependence in the binary parameters , 2014, 1405.1121.

[89]  B. Szilágyi,et al.  Improved gauge driver for the generalized harmonic Einstein system , 2009, 0904.4873.

[90]  H. Pfeiffer,et al.  Extrinsic curvature and the Einstein constraints , 2002, gr-qc/0207095.

[91]  Vitor Cardoso,et al.  Quasinormal modes of black holes and black branes , 2009, 0905.2975.

[92]  C. Ott,et al.  Three-Dimensional General-Relativistic Hydrodynamic Simulations of Binary Neutron Star Coalescence and Stellar Collapse with Multipatch Grids , 2012, 1212.1191.

[93]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[94]  B. Giacomazzo,et al.  Accurate evolutions of inspiralling neutron-star binaries: Prompt and delayed collapse to a black hole , 2008, 0804.0594.

[95]  Harald P. Pfeiffer,et al.  Simulations of unequal-mass black hole binaries with spectral methods , 2012, 1206.3015.

[96]  B. Giacomazzo,et al.  Accurate evolutions of inspiralling neutron-star binaries: assessment of the truncation error , 2009, 0901.4955.

[97]  L. Gualtieri,et al.  Constraining the equation of state of nuclear matter with gravitational wave observations: Tidal deformability and tidal disruption , 2013, 1310.5381.

[98]  Michael Boyle,et al.  Catalog of 174 binary black hole simulations for gravitational wave astronomy. , 2013, Physical review letters.

[99]  Lawrence E. Kidder,et al.  High-accuracy waveforms for binary black hole inspiral, merger, and ringdown , 2008, 0810.1767.

[100]  W. Kastaun,et al.  Properties of hypermassive neutron stars formed in mergers of spinning binaries , 2014, 1411.7975.

[101]  M. Shibata,et al.  Reducing orbital eccentricity in initial data of binary neutron stars , 2014, 1405.6207.

[102]  Thibault Damour,et al.  Determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation , 2000 .

[103]  P. Colella,et al.  Local adaptive mesh refinement for shock hydrodynamics , 1989 .

[104]  L. Baiotti,et al.  Spectral properties of the post-merger gravitational-wave signal from binary neutron stars , 2014, 1412.3240.

[105]  Erik Schnetter,et al.  GRHydro: a new open-source general-relativistic magnetohydrodynamics code for the Einstein toolkit , 2013, 1304.5544.

[106]  Sebastiano Bernuzzi,et al.  Numerical relativity simulations of binary neutron stars , 2011, 1104.4751.

[107]  Roger Penrose,et al.  An Approach to Gravitational Radiation by a Method of Spin Coefficients , 1962 .

[108]  Christian D. Ott,et al.  Equation of state effects in black hole–neutron star mergers , 2009, 0912.3528.

[109]  Binary neutron stars with generic spin, eccentricity, mass ratio, and compactness: Quasi-equilibrium sequences and first evolutions , 2015, 1507.07100.

[110]  S. Teukolsky,et al.  Initial data for black hole-neutron star binaries: a flexible, high-accuracy spectral method , 2008, 0804.3787.

[111]  Lawrence E. Kidder,et al.  Effects of Neutron-Star Dynamic Tides on Gravitational Waveforms within the Effective-One-Body Approach. , 2016, Physical review letters.

[112]  S. Ossokine,et al.  Comparing post-Newtonian and numerical relativity precession dynamics , 2015, 1502.01747.

[113]  J. Read,et al.  Matter effects on binary neutron star waveforms , 2013, 1306.4065.

[114]  Luc Blanchet,et al.  Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries , 2002, Living reviews in relativity.

[115]  Various features of quasiequilibrium sequences of binary neutron stars in general relativity , 2003, gr-qc/0309045.

[116]  T. Damour,et al.  Modeling the Dynamics of Tidally Interacting Binary Neutron Stars up to the Merger. , 2014, Physical review letters.

[117]  Scott E. Field,et al.  Fast and accurate prediction of numerical relativity waveforms from binary black hole mergers using surrogate models , 2015, Physical review letters.

[118]  Thibault Damour,et al.  Coalescence of two spinning black holes: an effective one-body approach , 2001, gr-qc/0103018.

[119]  K. Hotokezaka,et al.  Exploring tidal effects of coalescing binary neutron stars in numerical relativity , 2013, 1301.3555.

[120]  E. Gourgoulhon,et al.  Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity: 1. Method and tests , 2001 .

[121]  Moore,et al.  Gravitational radiation from type-II supernovae: The effect of the high-density equation of state. , 1988, Physical Review D, Particles and fields.

[122]  T. Damour,et al.  Accurate numerical simulations of inspiralling binary neutron stars and their comparison with effective-one-body analytical models , 2011, 1103.3874.

[123]  Michael Boyle,et al.  Transformations of asymptotic gravitational-wave data , 2015, 1509.00862.

[124]  Marc Favata.  Systematic parameter errors in inspiraling neutron star binaries. , 2013, Physical review letters.