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Anatomy of the binary black hole recoil: A multipolar analysis

Jeremy D. Schnittman1, Alessandra Buonanno1, James R. van Meter2,3, John G. Baker2, William D. Boggs4, Joan Centrella2, Bernard J. Kelly2, and Sean T. McWilliams4

  • 1Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
  • 2Gravitational Astrophysics Laboratory, NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, Maryland 20771, USA
  • 3Center for Space Science & Technology, University of Maryland Baltimore County, Physics Department, 1000 Hilltop Circle, Baltimore, Maryland 21250, USA
  • 4Department of Physics, University of Maryland, College Park, Maryland 20742, USA

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Phys. Rev. D 77, 044031 – Published 19 February, 2008

DOI: https://doi.org/10.1103/PhysRevD.77.044031

Abstract

We present a multipolar analysis of the gravitational recoil computed in recent numerical simulations of binary black hole coalescence, for both unequal masses and nonzero, nonprecessing spins. We show that multipole moments up to and including ℓ=4 are sufficient to accurately reproduce the final recoil velocity (within ≃2%) and that only a few dominant modes contribute significantly to it (within ≃5%). We describe how the relative amplitudes, and more importantly, the relative phases, of these few modes control the way in which the recoil builds up throughout the inspiral, merger, and ringdown phases. We also find that the numerical results can be reproduced by an “effective Newtonian” formula for the multipole moments obtained by replacing the radial separation in the Newtonian formulas with an effective radius computed from the numerical data. Beyond the merger, the numerical results are reproduced by a superposition of three Kerr quasinormal modes. Analytic formulas, obtained by expressing the multipole moments in terms of the fundamental quasinormal modes of a Kerr black hole, are able to explain the onset and amount of “antikick” for each of the simulations. Lastly, we apply this multipolar analysis to help explain the remarkable difference between the amplitudes of planar and nonplanar kicks for equal-mass spinning black holes.

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References (78)

  1. F. Pretorius, Phys. Rev. Lett. 95, 121101 (2005).
  2. M. Campanelli, C. O. Lousto, P. Marronetti, and Y. Zlochower, Phys. Rev. Lett. 96, 111101 (2006).
  3. J. Baker, J. Centrella, D. Choi, M. Koppitz, and J. van Meter, Phys. Rev. Lett. 96, 111102 (2006).
  4. U. Sperhake, Phys. Rev. D 76, 104015 (2007).
  5. J. González, U. Sperhake, B. Brügmann, M. Hannam, and S. Husa, Phys. Rev. Lett. 98, 091101 (2007).
  6. B. Szilagyi, D. Pollney, L. Rezzolla, J. Thornburg, and J. Winicour, Classical Quantum Gravity 24, S275 (2007).
  7. F. Herrmann, I. Hinder, D. Shoemaker, and P. Laguna, Classical Quantum Gravity 24, S33 (2007).
  8. J. G. Baker, J. Centrella, D. Choi, M. Koppitz, J. R. van Meter, and M. C Miller, Astrophys. J. 653, L93 (2006).
  9. J. A. Gonzalez, U. Sperhake, B. Brügmann, M. Hannam, and S. Husa, Phys. Rev. Lett. 98, 091101 (2007).
  10. F. Herrmann, I. Hinder, D. Shoemaker, P. Laguna, and R. A. Matzner, Astrophys. J. 661, 430 (2007).
  11. M. Koppitz, D. Pollney, C. Reisswig, L. Rezzolla, J. Thornburg, P. Diener, and E. Schnetter, Phys. Rev. Lett. 99, 041102 (2007).
  12. J. G. Baker, W. D. Boggs, J. Centrella, B. J. Kelly, S. T. McWilliams, M. C. Miller, and J. R. van Meter, Astrophys. J. 668, 1140 (2007).
  13. J. A. Gonzalez, M. D. Hannam, U. Sperhake, B. Brugmann, and S. Husa, Phys. Rev. Lett. 98, 231101 (2007).
  14. W. Tichy and P. Marronetti, Phys. Rev. D 76, 061502 (2007).
  15. M. Campanelli, C. O. Lousto, Y. Zlochower, and D. Merritt, Astrophys. J. 659, L5 (2007).
  16. W. B. Bonnor and M. A. Rotenberg, Proc. R. Soc. A 265, 109 (1961).
  17. A. Peres, Phys. Rev. 128, 2471 (1962).
  18. J. D. Bekenstein, Astrophys. J. 183, 657 (1973).
  19. F. I. Cooperstock, Astrophys. J. 213, 250 (1977).
  20. M. J. Fitchett, Mon. Not. R. Astron. Soc. 203, 1049 (1983); M. J. Fitchett and S. Detweiler, 211, 933 (1984).
  21. M. G. Haehnelt, Mon. Not. R. Astron. Soc. 269, 199 (1994); K. Menou, Z. Haiman, and V. K. Narayanan, Astrophys. J. 558, 535 (2001); M. Volonteri, F. Haardt, and P. Madau, 582, 559 (2003).
  22. D. Merritt, M. Milosavljevic, M. Favata, and S. A. Hughes, Astrophys. J. 607, L9 (2004).
  23. M. Volonteri, Astrophys. J. 663, L5 (2007).
  24. J. D. Schnittman, Astrophys. J. 667, L133 (2007).
  25. M. G. Haehnelt, M. B. Davies, and M. J. Rees, Mon. Not. R. Astron. Soc. 366, L22 (2006).
  26. E. W. Bonning and G. A. Shields, Astrophys. J. 666, L13 (2007).
  27. M. Boylan-Kolchin, C.-P. Ma, and E. Quataert, Astrophys. J. 613, L37 (2004).
  28. T. R. Lauer et al., Astrophys. J. 662, 808 (2007).
  29. B. Brügmann, J. A. Gonzalez, M. Hannam, S. Husa, and U. Sperhake, arXiv:0707.0135.
  30. J. D. Schnittman, Phys. Rev. D 70, 124020 (2004).
  31. T. Bogdanovic, C. S. Reynolds, and M. C. Miller, Astrophys. J. 661, L147 (2007).
  32. A. Loeb, Phys. Rev. Lett. 99, 041103 (2007).
  33. See, e.g., L. Blanchet, Living Rev. Relativity 5, 3 (2002).
  34. T. Damour, B. R. Iyer, and B. S. Sathyaprakash, Phys. Rev. D 57, 885 (1998).
  35. A. Buonanno and T. Damour, Phys. Rev. D 59, 084006 (1999).
  36. A. Buonanno and T. Damour, Phys. Rev. D 62, 064015 (2000).
  37. T. Damour, P. Jaranowski, and G. Schäfer, Phys. Rev. D 62, 084011 (2000).
  38. T. Damour, P. Jaranowski, and G. Schäfer, Phys. Rev. D 62, 044024 (2000).
  39. A. Buonanno, Y. Chen, and T. Damour, Phys. Rev. D 74, 104005 (2006).
  40. A. Wiseman, Phys. Rev. D 46, 1517 (1992).
  41. L. Kidder, Phys. Rev. D 52, 821 (1995).
  42. M. Favata et al., Astrophys. J. 607, L5 (2004).
  43. L. Blanchet, M. S. S. Qusailah, and C. M. Will, Astrophys. J. 635, 508 (2005).
  44. T. Damour and A. Gopakumar, Phys. Rev. D 73, 124006 (2006).
  45. C. F. Sopuerta, N. Yunes, and P. Laguna, Astrophys. J. 656, L9 (2007).
  46. R. H. Price and J. Pullin, Phys. Rev. Lett. 72, 3297 (1994).
  47. J. D. Schnittman and A. Buonanno, Astrophys. J. 662, L63 (2007).
  48. K. S. Thorne, Rev. Mod. Phys. 52, 299 (1980).
  49. L. Blanchet and T. Damour, Ann. Inst. Henri Poincare 50, 377 (1989).
  50. L. Blanchet and G. Schäfer, Mon. Not. R. Astron. Soc. 239, 845 (1989).
  51. L. Blanchet, T. Damour, and G. Schäfer, Mon. Not. R. Astron. Soc. 242, 289 (1990).
  52. W. Junker and G. Schäfer, Mon. Not. R. Astron. Soc. 254, 146 (1992).
  53. C. V. Vishveshwara, Nature (London) 227, 936 (1970); M. Davis, R. Ruffini, W. H. Press, and R. H. Price, Phys. Rev. Lett. 27, 1466 (1971); W. Press, Astrophys. J. 170, L105 (1971); M. Davis, R. Ruffini, and J. Tiomno, Phys. Rev. D 5, 2932 (1972); S. Chandrasekhar and S. Detweiler, Proc. R. Soc. A 344, 441 (1975).
  54. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman, San Francisco, 1973).
  55. J. Baker, M. Campanelli, and C. Lousto, Phys. Rev. D 65, 044001 (2002).
  56. J. G. Baker, S. T. McWilliams, J. R. van Meter, J. Centrella, D. I. Choi, B. J. Kelly, and M. Koppitz, Phys. Rev. D 75, 124024 (2007).
  57. J. N. Goldberg, A. J. Macfarlane, E. T. Newman, F. Rohrlich, and E. C. G. Sundarshan, J. Math. Phys. (N.Y.) 8, 2155 (1967).
  58. Y. Wiaux, L. Jacques, and P. Vandergheynst, J. Comput. Phys. 226, 2359 (2007).
  59. S. Brandt and B. Brügmann, Phys. Rev. Lett. 78, 3606 (1997).
  60. J. D. Brown and L. L. Lowe, J. Comput. Phys. 209, 582 (2005).
  61. J. Bowen and J. W. York, Phys. Rev. D 21, 2047 (1980).
  62. D. Christodoulou, Phys. Rev. Lett. 25, 1596 (1970); D. Christodoulou and R. Ruffini, Phys. Rev. D 4, 3552 (1971).
  63. B. Imbiriba, J. G. Baker, D.-I. Choi, J. Centrella, D. R. Fiske, J. D. Brown, J. R. van Meter, K. Olsonand , Phys. Rev. D 70, 124025 (2004).
  64. M. Shibata and T. Nakamura, Phys. Rev. D 52, 5428 (1995); T. W. Baumgarte and S. L. Shapiro, 59, 024007 (1998).
  65. P. Hübner, Classical Quantum Gravity 16, 2823 (1999).
  66. M. D. Duez, S. L. Shapiro, and H.-J. Yo, Phys. Rev. D 69, 104016 (2004).
  67. J. van Meter, J. G. Baker, M. Koppitz, and D.-I. Choi, Phys. Rev. D 73, 124011 (2006).
  68. J. G. Baker and J. van Meter, Phys. Rev. D 72, 104010 (2005).
  69. P. MacNeice, K. Olson, C. Mobarry, R. de Fainchtein, and C. Packer, Comput. Phys. Commun. 126, 330 (2000).
  70. K. Martel and E. Poisson, Phys. Rev. D 71, 104003 (2005).
  71. E. Berti et al., Phys. Rev. D 76, 064034 (2007).
  72. A. Buonanno, G. Cook, and F. Pretorius, Phys. Rev. D 75, 124018 (2007).
  73. E. W. Leaver, Proc. R. Soc. A 402, 285 (1985).
  74. F. Echeverria, Phys. Rev. D 40, 3194 (1989).
  75. E. Berti, V. Cardoso, and C. Will, Phys. Rev. D 73, 064030 (2006).
  76. A. Buonanno, Y. Pan, J. G. Baker, J. Centrella, B. J. Kelly, S. T. McWilliams, and J. R. van Meter, Phys. Rev. D 76, 104049 (2007).
  77. L. Blanchet and B. Iyer, Classical Quantum Gravity 20, 755 (2003).
  78. L. Blanchet, A. Buonanno, and G. Faye, Phys. Rev. D 74, 104034 (2006); 75, 049903(E) (2007).

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Phys. Rev. D 77, 044031– Published 19 February, 2008
  • Received 2 July 2007

© 2008 American Physical Society

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