Integrating Post-Newtonian Equations on Graphics Processing Units

We report on early results of a numerical and statistical study of binary black hole inspirals. The two black holes are evolved using post-Newtonian approximations starting with initially randomly distributed spin vectors. We characterize certain aspects of the distribution shortly before merger. In particular we note the uniform distribution of black hole spin vector dot products shortly before merger and a high correlation between the initial and final black hole spin vector dot products in the equal-mass, maximally spinning case. These simulations were performed on Graphics Processing Units, and we demonstrate a speed-up of a factor 50 over a more conventional CPU implementation.

[1]  D. Shoemaker,et al.  Unequal mass binary black hole plunges and gravitational recoil , 2006, gr-qc/0601026.

[2]  Ryutaro Takahashi,et al.  Operational status of TAMA300 with the seismic attenuation system (SAS) , 2008 .

[3]  Hiroyuki Nakano,et al.  Comparison of Numerical and Post-Newtonian Waveforms for Generic Precessing Black-Hole Binaries , 2008, 0808.0713.

[4]  José A. González,et al.  Maximum kick from nonspinning black-hole binary inspiral. , 2007, Physical review letters.

[5]  Michele Vallisneri,et al.  Erratum: Detecting gravitational waves from precessing binaries of spinning compact objects: Adiabatic limit [Phys. Rev. D67, 104025 (2003)] , 2006 .

[6]  Joshua R. Smith,et al.  LIGO: the Laser Interferometer Gravitational-Wave Observatory , 1992, Science.

[7]  Mark Hannam,et al.  Status of black-hole-binary simulations for gravitational-wave detection , 2009, 0901.2931.

[8]  S. Sheather Density Estimation , 2004 .

[9]  Y. Zlochower,et al.  Large Merger Recoils and Spin Flips from Generic Black Hole Binaries , 2007, gr-qc/0701164.

[10]  Dae-Il Choi,et al.  Getting a Kick Out of Numerical Relativity , 2006, astro-ph/0603204.

[11]  F. Raab,et al.  Laser interferometer gravitational-wave observatory , 1993, Proceedings of LEOS '93.

[12]  Michael Boyle,et al.  High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions , 2007, 0710.0158.

[13]  Erik Schnetter,et al.  Recoil velocities from equal-mass binary-black-hole mergers. , 2007 .

[14]  Sascha Husa,et al.  Comparison between numerical-relativity and post-Newtonian waveforms from spinning binaries: The orbital hang-up case , 2007, 0712.3787.

[15]  Sascha Husa,et al.  SUPERMASSIVE KICKS FOR SPINNING BLACK HOLES , 2007 .

[16]  G. Marsaglia Choosing a Point from the Surface of a Sphere , 1972 .

[17]  José A González,et al.  Supermassive recoil velocities for binary black-hole mergers with antialigned spins. , 2007, Physical review letters.

[18]  A. Buonanno,et al.  The Distribution of Recoil Velocities from Merging Black Holes , 2007, astro-ph/0702641.

[19]  M. Loupias,et al.  Status of Virgo , 2004 .

[20]  Richard A. Matzner,et al.  Gravitational Recoil from Spinning Binary Black Hole Mergers , 2007, gr-qc/0701143.

[21]  Michele Vallisneri,et al.  Detecting gravitational waves from precessing binaries of spinning compact objects: Adiabatic limit , 2002 .

[22]  Yi Pan,et al.  Erratum: Physical template family for gravitational waves from precessing binaries of spinning compact objects: Application to single-spin binaries [Phys. Rev. D 69, 104017 (2004)] , 2006 .

[23]  Michael Boyle,et al.  Status of NINJA: the Numerical INJection Analysis project , 2009, 0905.4227.

[24]  David W. Hogg Data analysis recipes: Choosing the binning for a histogram , 2008 .

[25]  Lawrence E. Kidder,et al.  Recoil velocity at second post-Newtonian order for spinning black hole binaries , 2008, 0812.4413.

[26]  David Merritt,et al.  Maximum gravitational recoil. , 2007, Physical review letters.

[27]  J. Dormand,et al.  A family of embedded Runge-Kutta formulae , 1980 .

[28]  Jeremy D. Schnittman Spin-orbit resonance and the evolution of compact binary systems , 2004 .

[29]  Erik Schnetter,et al.  Getting a kick from equal-mass binary black hole mergers , 2008 .

[30]  Benno Willke GEO600 : status and plans , 2007 .

[31]  Michael Boyle,et al.  Testing gravitational-wave searches with numerical relativity waveforms: results from the first Numerical INJection Analysis (NINJA) project , 2009, 0901.4399.