Papers
Topics
Authors
Recent
Search
2000 character limit reached

Mapping eccentricity evolutions between numerical relativity and effective-one-body gravitational waveforms

Published 29 Apr 2024 in gr-qc | (2404.18875v3)

Abstract: Orbital eccentricity in compact binaries is considered to be a key tracer of their astrophysical origin, and can be inferred from gravitational-wave observations due to its imprint on the emitted signal. For a robust measurement, accurate waveform models are needed. However, ambiguities in the definition of eccentricity can obfuscate the physical meaning and result in seemingly discrepant measurements. In this work we present a suite of 28 new numerical relativity simulations of eccentric, aligned-spin binary black holes with mass ratios between 1 and 6 and initial post-Newtonian eccentricities between 0.05 and 0.3. We then develop a robust pipeline for measuring the eccentricity evolution as a function of frequency from gravitational-wave observables that is applicable even to signals that span at least $\gtrsim 7$ orbits. We assess the reliability of our procedure and quantify its robustness under different assumptions on the data. Using the eccentricity measured at the first apastron, we initialise effective-one-body waveforms and quantify how the precision in the eccentricity measurement, and therefore the choice of the initial conditions, impacts the agreement with the numerical data. We find that even small deviations in the initial eccentricity can lead to non-negligible differences in the phase and amplitude of the waveforms. However, we demonstrate that we can reliably map the eccentricities between the simulation data and analytic models, which is crucial for robustly building eccentric hybrid waveforms, and to improve the accuracy of eccentric waveform models in the strong-field regime.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (89)
  1. I. Mandel and A. Farmer, Merging stellar-mass binary black holes, Phys. Rept. 955, 1 (2022), arXiv:1806.05820 [astro-ph.HE] .
  2. M. Mapelli, Binary Black Hole Mergers: Formation and Populations, Front. Astron. Space Sci. 7, 38 (2020), arXiv:2105.12455 [astro-ph.HE] .
  3. I. Mandel and F. S. Broekgaarden, Rates of compact object coalescences, Living Rev. Rel. 25, 1 (2022), arXiv:2107.14239 [astro-ph.HE] .
  4. M. Mapelli, Formation Channels of Single and Binary Stellar-Mass Black Holes (2021) arXiv:2106.00699 [astro-ph.HE] .
  5. I. Mandel and S. E. de Mink, Merging binary black holes formed through chemically homogeneous evolution in short-period stellar binaries, Mon. Not. Roy. Astron. Soc. 458, 2634 (2016), arXiv:1601.00007 [astro-ph.HE] .
  6. P. C. Peters and J. Mathews, Gravitational radiation from point masses in a Keplerian orbit, Phys. Rev. 131, 435 (1963).
  7. P. C. Peters, Gravitational Radiation and the Motion of Two Point Masses, Phys. Rev. 136, B1224 (1964).
  8. S. Naoz, The eccentric kozai-lidov effect and its applications, Annual Review of Astronomy and Astrophysics 54, 441–489 (2016).
  9. J. Samsing, Eccentric Black Hole Mergers Forming in Globular Clusters, Phys. Rev. D97, 103014 (2018), arXiv:1711.07452 [astro-ph.HE] .
  10. I. M. Romero-Shaw, P. D. Lasky, and E. Thrane, Four Eccentric Mergers Increase the Evidence that LIGO–Virgo–KAGRA’s Binary Black Holes Form Dynamically, Astrophys. J. 940, 171 (2022), arXiv:2206.14695 [astro-ph.HE] .
  11. L. E. Kidder, Coalescing binary systems of compact objects to postNewtonian 5/2 order. 5. Spin effects, Phys.Rev. D52, 821 (1995), arXiv:gr-qc/9506022 [gr-qc] .
  12. P. Schmidt, M. Hannam, and S. Husa, Towards models of gravitational waveforms from generic binaries: A simple approximate mapping between precessing and non-precessing inspiral signals, Phys. Rev. D86, 104063 (2012), arXiv:1207.3088 [gr-qc] .
  13. N. Steinle and M. Kesden, Pathways for producing binary black holes with large misaligned spins in the isolated formation channel, Phys. Rev. D 103, 063032 (2021), arXiv:2010.00078 [astro-ph.HE] .
  14. D. Reitze et al., Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGO, Bull. Am. Astron. Soc. 51, 035 (2019), arXiv:1907.04833 [astro-ph.IM] .
  15. M. Maggiore et al., Science Case for the Einstein Telescope, JCAP 03, 050, arXiv:1912.02622 [astro-ph.CO] .
  16. A. K. Lenon, D. A. Brown, and A. H. Nitz, Eccentric binary neutron star search prospects for Cosmic Explorer, Phys. Rev. D 104, 063011 (2021), arXiv:2103.14088 [astro-ph.HE] .
  17. P. Saini, Resolving the eccentricity of stellar mass binary black holes with next generation gravitational wave detectors,   (2023), arXiv:2308.07565 [astro-ph.HE] .
  18. A. Klein et al., The last three years: multiband gravitational-wave observations of stellar-mass binary black holes,   (2022), arXiv:2204.03423 [astro-ph.HE] .
  19. L. Blanchet, Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries, Living Rev. Relativity 17, 2 (2014), arXiv:1310.1528 [gr-qc] .
  20. T. Damour and N. Deruelle, General relativistic celestial mechanics of binary systems. I. The post-newtonian motion, Annales de l’I.H.P. Physique théorique 43, 107 (1985).
  21. C. W. Lincoln and C. M. Will, Coalescing binary systems of compact objects to (post)5/2superscriptpost52{(\mathrm{post})}^{5/2}( roman_post ) start_POSTSUPERSCRIPT 5 / 2 end_POSTSUPERSCRIPT-newtonian order: Late-time evolution and gravitational-radiation emission, Phys. Rev. D 42, 1123 (1990).
  22. T. Damour, A. Gopakumar, and B. R. Iyer, Phasing of gravitational waves from inspiralling eccentric binaries, Phys. Rev. D70, 064028 (2004), arXiv:gr-qc/0404128 [gr-qc] .
  23. R.-M. Memmesheimer, A. Gopakumar, and G. Schaefer, Third post-Newtonian accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits, Phys. Rev. D 70, 104011 (2004), arXiv:gr-qc/0407049 .
  24. C. Konigsdorffer and A. Gopakumar, Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order, Phys. Rev. D 73, 124012 (2006), arXiv:gr-qc/0603056 .
  25. T. Damour, P. Jaranowski, and G. Schäfer, Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity, Phys. Rev. D93, 084014 (2016), arXiv:1601.01283 [gr-qc] .
  26. D. Bini, T. Damour, and A. Geralico, Novel approach to binary dynamics: application to the fifth post-Newtonian level, Phys. Rev. Lett. 123, 231104 (2019), arXiv:1909.02375 [gr-qc] .
  27. D. Bini, T. Damour, and A. Geralico, Binary dynamics at the fifth and fifth-and-a-half post-Newtonian orders, Phys. Rev. D 102, 024062 (2020), arXiv:2003.11891 [gr-qc] .
  28. Q. Henry and F. Larrouturou, Conservative tail and failed-tail effects at the fifth post-Newtonian order, Phys. Rev. D 108, 084048 (2023), arXiv:2307.05860 [gr-qc] .
  29. C. K. Mishra, K. G. Arun, and B. R. Iyer, Third post-Newtonian gravitational waveforms for compact binary systems in general orbits: Instantaneous terms, Phys. Rev. D91, 084040 (2015), arXiv:1501.07096 [gr-qc] .
  30. N. Loutrel and N. Yunes, Hereditary Effects in Eccentric Compact Binary Inspirals to Third Post-Newtonian Order, Class. Quant. Grav. 34, 044003 (2017), arXiv:1607.05409 [gr-qc] .
  31. K. Paul and C. K. Mishra, Spin effects in spherical harmonic modes of gravitational waves from eccentric compact binary inspirals, Phys. Rev. D 108, 024023 (2023), arXiv:2211.04155 [gr-qc] .
  32. M. Tessmer and G. Schaefer, Full-analytic frequency-domain 1pN-accurate gravitational wave forms from eccentric compact binaries, Phys. Rev. D 82, 124064 (2010), arXiv:1006.3714 [gr-qc] .
  33. S. Tanay, M. Haney, and A. Gopakumar, Frequency and time domain inspiral templates for comparable mass compact binaries in eccentric orbits, Phys. Rev. D 93, 064031 (2016), arXiv:1602.03081 [gr-qc] .
  34. B. Moore and N. Yunes, A 3PN Fourier Domain Waveform for Non-Spinning Binaries with Moderate Eccentricity, Class. Quant. Grav. 36, 185003 (2019), arXiv:1903.05203 [gr-qc] .
  35. S. Tiwari and A. Gopakumar, Combining post-circular and Padé approximations to compute Fourier domain templates for eccentric inspirals, Phys. Rev. D 102, 084042 (2020), arXiv:2009.11333 [gr-qc] .
  36. S. Hopper, C. Kavanagh, and A. C. Ottewill, Analytic self-force calculations in the post-Newtonian regime: eccentric orbits on a Schwarzschild background, Phys. Rev. D 93, 044010 (2016), arXiv:1512.01556 [gr-qc] .
  37. E. Forseth, C. R. Evans, and S. Hopper, Eccentric-orbit extreme-mass-ratio inspiral gravitational wave energy fluxes to 7PN order, Phys. Rev. D 93, 064058 (2016), arXiv:1512.03051 [gr-qc] .
  38. D. Bini and T. Damour, Gravitational scattering of two black holes at the fourth post-Newtonian approximation, Phys. Rev. D96, 064021 (2017), arXiv:1706.06877 [gr-qc] .
  39. C. Munna, Analytic post-Newtonian expansion of the energy and angular momentum radiated to infinity by eccentric-orbit nonspinning extreme-mass-ratio inspirals to the 19th order, Phys. Rev. D 102, 124001 (2020), arXiv:2008.10622 [gr-qc] .
  40. P. Lynch, M. van de Meent, and N. Warburton, Eccentric self-forced inspirals into a rotating black hole, Class. Quant. Grav. 39, 145004 (2022), arXiv:2112.05651 [gr-qc] .
  41. J. Healy and C. O. Lousto, Fourth RIT binary black hole simulations catalog: Extension to eccentric orbits, Phys. Rev. D 105, 124010 (2022), arXiv:2202.00018 [gr-qc] .
  42. D. Ferguson et al., Second MAYA Catalog of Binary Black Hole Numerical Relativity Waveforms,   (2023), arXiv:2309.00262 [gr-qc] .
  43. I. Hinder, L. E. Kidder, and H. P. Pfeiffer, Eccentric binary black hole inspiral-merger-ringdown gravitational waveform model from numerical relativity and post-Newtonian theory, Phys. Rev. D 98, 044015 (2018), arXiv:1709.02007 [gr-qc] .
  44. A. Buonanno and T. Damour, Effective one-body approach to general relativistic two-body dynamics, Phys. Rev. D59, 084006 (1999), arXiv:gr-qc/9811091 .
  45. A. Buonanno and T. Damour, Transition from inspiral to plunge in binary black hole coalescences, Phys. Rev. D62, 064015 (2000), arXiv:gr-qc/0001013 .
  46. T. Damour, P. Jaranowski, and G. Schaefer, On the determination of the last stable orbit for circular general relativistic binaries at the third postNewtonian approximation, Phys. Rev. D62, 084011 (2000), arXiv:gr-qc/0005034 [gr-qc] .
  47. T. Damour, Coalescence of two spinning black holes: An effective one- body approach, Phys. Rev. D64, 124013 (2001), arXiv:gr-qc/0103018 .
  48. D. Bini and T. Damour, Gravitational radiation reaction along general orbits in the effective one-body formalism, Phys.Rev. D86, 124012 (2012), arXiv:1210.2834 [gr-qc] .
  49. T. Hinderer and S. Babak, Foundations of an effective-one-body model for coalescing binaries on eccentric orbits, Phys. Rev. D96, 104048 (2017), arXiv:1707.08426 [gr-qc] .
  50. Z. Cao and W.-B. Han, Waveform model for an eccentric binary black hole based on the effective-one-body-numerical-relativity formalism, Phys. Rev. D96, 044028 (2017), arXiv:1708.00166 [gr-qc] .
  51. X. Liu, Z. Cao, and L. Shao, Validating the Effective-One-Body Numerical-Relativity Waveform Models for Spin-aligned Binary Black Holes along Eccentric Orbits, Phys. Rev. D 101, 044049 (2020), arXiv:1910.00784 [gr-qc] .
  52. X. Liu, Z. Cao, and Z.-H. Zhu, A higher-multipole gravitational waveform model for an eccentric binary black holes based on the effective-one-body-numerical-relativity formalism, Class. Quant. Grav. 39, 035009 (2022), arXiv:2102.08614 [gr-qc] .
  53. Q. Henry and M. Khalil, Spin effects in gravitational waveforms and fluxes for binaries on eccentric orbits to the third post-Newtonian order, Phys. Rev. D 108, 104016 (2023), arXiv:2308.13606 [gr-qc] .
  54. X. Liu, Z. Cao, and L. Shao, Upgraded waveform model of eccentric binary black hole based on effective-one-body-numerical-relativity for spin-aligned binary black holes, Int. J. Mod. Phys. D 32, 2350015 (2023a), arXiv:2306.15277 [gr-qc] .
  55. A. Nagar and P. Rettegno, Next generation: Impact of high-order analytical information on effective one body waveform models for noncircularized, spin-aligned black hole binaries, Phys. Rev. D 104, 104004 (2021), arXiv:2108.02043 [gr-qc] .
  56. S. Albanesi, A. Nagar, and S. Bernuzzi, Effective one-body model for extreme-mass-ratio spinning binaries on eccentric equatorial orbits: Testing radiation reaction and waveform, Phys. Rev. D 104, 024067 (2021), arXiv:2104.10559 [gr-qc] .
  57. X. Liu, Z. Cao, and Z.-H. Zhu, Effective-One-Body Numerical-Relativity waveform model for Eccentric spin-precessing binary black hole coalescence,   (2023b), arXiv:2310.04552 [gr-qc] .
  58. A. Vijaykumar, A. G. Hanselman, and M. Zevin, Consistent eccentricities for gravitational wave astronomy: Resolving discrepancies between astrophysical simulations and waveform models,  (2024), arXiv:2402.07892 [astro-ph.HE] .
  59. F. Loffler et al., The Einstein Toolkit: A Community Computational Infrastructure for Relativistic Astrophysics, Class. Quant. Grav. 29, 115001 (2012), arXiv:1111.3344 [gr-qc] .
  60. R. Haas et al., The einstein toolkit (2022).
  61. J. M. Bowen and J. W. York, Jr., Time asymmetric initial data for black holes and black hole collisions, Phys. Rev. D21, 2047 (1980).
  62. S. Brandt and B. Brügmann, A Simple construction of initial data for multiple black holes, Phys. Rev. Lett. 78, 3606 (1997), arXiv:gr-qc/9703066 .
  63. M. Ansorg, B. Brügmann, and W. Tichy, A single-domain spectral method for black hole puncture data, Phys. Rev. D70, 064011 (2004), arXiv:gr-qc/0404056 .
  64. M. Shibata and T. Nakamura, Evolution of three-dimensional gravitational waves: Harmonic slicing case, Phys. Rev. D52, 5428 (1995).
  65. T. W. Baumgarte and S. L. Shapiro, On the numerical integration of Einstein’s field equations, Phys. Rev. D59, 024007 (1999), arXiv:gr-qc/9810065 .
  66. H. O. Kreiss and J. Oliger, Methods for the approximate solution of time dependent problems (International Council of Scientific Unions, World Meteorological Organization, Geneva, 1973).
  67. J. Thornburg, Black hole excision with multiple grid patches, Class.Quant.Grav. 21, 3665 (2004), arXiv:gr-qc/0404059 [gr-qc] .
  68. A. Ashtekar and B. Krishnan, Dynamical horizons and their properties, Phys. Rev. D 68, 104030 (2003), arXiv:gr-qc/0308033 .
  69. E. Schnetter, B. Krishnan, and F. Beyer, Introduction to dynamical horizons in numerical relativity, Phys. Rev. D 74, 024028 (2006), arXiv:gr-qc/0604015 .
  70. E. Schnetter, S. H. Hawley, and I. Hawke, Evolutions in 3-D numerical relativity using fixed mesh refinement, Class.Quant.Grav. 21, 1465 (2004), arXiv:gr-qc/0310042 [gr-qc] .
  71. E. Newman and R. Penrose, An Approach to gravitational radiation by a method of spin coefficients, J. Math. Phys. 3, 566 (1962).
  72. C. Reisswig and D. Pollney, Notes on the integration of numerical relativity waveforms, Class.Quant.Grav. 28, 195015 (2011), arXiv:1006.1632 [gr-qc] .
  73. M. Boyle and A. H. Mroue, Extrapolating gravitational-wave data from numerical simulations, Phys. Rev. D80, 124045 (2009), arXiv:0905.3177 [gr-qc] .
  74. A. Ramos-Buades, S. Husa, and G. Pratten, Simple procedures to reduce eccentricity of binary black hole simulations, Phys. Rev. D 99, 023003 (2019), arXiv:1810.00036 [gr-qc] .
  75. D. Christodoulou, Reversible and irreversible transforations in black hole physics, Phys. Rev. Lett. 25, 1596 (1970).
  76. D. Keitel et al., The most powerful astrophysical events: Gravitational-wave peak luminosity of binary black holes as predicted by numerical relativity, Phys. Rev. D96, 024006 (2017), arXiv:1612.09566 [gr-qc] .
  77. T. Mora and C. M. Will, Numerically generated quasiequilibrium orbits of black holes: Circular or eccentric?, Phys. Rev. D 66, 101501 (2002), arXiv:gr-qc/0208089 .
  78. T. Mora and C. M. Will, A Post-Newtonian diagnostic of quasi-equilibrium binary configurations of compact objects, Phys. Rev. D69, 104021 (2004), [Erratum: Phys. Rev.D71,129901(2005)], arXiv:gr-qc/0312082 [gr-qc] .
  79. A. Ramos-Buades, A. Buonanno, and J. Gair, Bayesian inference of binary black holes with inspiral-merger-ringdown waveforms using two eccentric parameters,   (2023), arXiv:2309.15528 [gr-qc] .
  80. T. Damour and G. Schäfer, Higher Order Relativistic Periastron Advances and Binary Pulsars, Nuovo Cim. B101, 127 (1988).
  81. M. Purrer, S. Husa, and M. Hannam, An Efficient iterative method to reduce eccentricity in numerical-relativity simulations of compact binary inspiral, Phys. Rev. D 85, 124051 (2012), arXiv:1203.4258 [gr-qc] .
  82. T. Regge and J. A. Wheeler, Stability of a Schwarzschild singularity, Phys. Rev. 108, 1063 (1957).
  83. F. J. Zerilli, Effective potential for even parity Regge-Wheeler gravitational perturbation equations, Phys. Rev. Lett. 24, 737 (1970).
  84. O. Sarbach and M. Tiglio, Gauge invariant perturbations of Schwarzschild black holes in horizon-penetrating coordinates, Phys. Rev. D64, 084016 (2001), gr-qc/0104061 .
  85. M. Boyle et al., The SXS Collaboration catalog of binary black hole simulations, Class. Quant. Grav. 36, 195006 (2019), arXiv:1904.04831 [gr-qc] .
  86. T. Damour and A. Nagar, New effective-one-body description of coalescing nonprecessing spinning black-hole binaries, Phys.Rev. D90, 044018 (2014), arXiv:1406.6913 [gr-qc] .
  87. A. Nagar and P. Rettegno, Efficient effective one body time-domain gravitational waveforms, Phys. Rev. D99, 021501 (2019), arXiv:1805.03891 [gr-qc] .
  88. LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration, Noise curves used for Simulations in the update of the Observing Scenarios Paper, Tech. Rep. LIGO-T2000012-v2 (2022).
  89. J. D. Hunter, Matplotlib: A 2d graphics environment, Computing In Science & Engineering 9, 90 (2007).
Citations (3)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Summarize

Paper to Video (Beta)

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Tweets

Sign up for free to view the 1 tweet with 3 likes about this paper.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up for Free