Project B4;     (2003 - 2010)

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Inspiraling Black Holes and Neutron Stars

    Principal Investigators: Gerhard Schäfer

Project B4 aims to provide accurate and efficient description for various aspects involved in the dynamics of compact binaries of arbitrary mass ratio, invoking post-Newtonian (PN) framework to solve two-body problem in general relativity. It includes the development of gravitational wave templates for compact binaries.

The current investigations developed accurate and efficient gravitational wave templates for compact binaries of arbitrary mass ratio moving in inspiralling eccentric orbits. These templates will be useful to do `astrophysics' with planned and proposed space-based gravitational wave detectors like LISA, BBO and DECIGO. A plethora of recent astrophysically motivated investigations indicate that compact binaries in inspiralling eccentric orbits will also be plausible sources of gravitational radiation for ground-based gravitational wave interferometers.
Further, certain aspects of the dynamics of compact binaries, where objects were not treated to be point masses, and associated gravitational wave polarizations were also obtained.

One of the key ingredients to construct the above mentioned templates is our derivation of post-Newtonian accurate Keplerian-type parametric solution to the conservative dynamics of compact binaries. There are few additional applications for such Keplerian-type parametric solutions and we investigated two such applications. Using our PN accurate Keplerian-type parametric solution, we formally demonstrated the erroneousness of the claim, made in the literature, that dynamics of spinning compact binaries will be chaotic, when spin effects are restricted to the leading order spin-orbit interactions. It is interesting to note that if the above dynamics is chaotic, it will make almost impossible gravitational wave detection from spinning compact binaries. We employed our Keplerian-type parametrization to obtain, for the first time, a parametric derivation of the observable relativistic periastron advance for binary pulsars. Recall that the highly accurate `timing' of double pulsar PSR J0737-3039 eventually allow, via the measurement of PN accurate relativistic periastron advance, the determination of the moment-of-inertia of a neutron star, enabling one to probe the equation of state of highly condensed matter.

In the near future, under Project B4, we plan to undertake investigations that should provide highly accurate and efficient templates for gravitational wave signals emitted by spinning compact binaries, consisting of black holes as well as neutron stars of arbitrary mass ratio, moving in inspiralling eccentric orbits. N-body simulations are required to study realistically the dynamics of collisional star clusters that may create intermediate mass black hole binaries and the dynamics of supermassive black hole binaries resulting from the merger of galaxies. It is important to incorporate general relativistic effects in to these simulations and we will investigate the associated conceptual and computational issues.

We plan to pursue PN accurate computations that will be required to analyze the ultra-sensitive observations of pulsars, especially in binaries, with the proposed Square Kilometre Array.

Researchers


Former Associates
  Michael Brügmann   PhD Student, 2004-2006
  Thibault Damour   Advisor, 2003-2010
  Achamveedu Gopakumar   Postdoc, 2003-2008
  Frieder Gerstner   Student, 2008
  Maria Haney   Student, 2004-2008
  Dörte Hansen   PhD Student, 2003-2008
  Johannes Hartung   PhD Student, 2009-2010
  Steven Hergt   PhD Student, 2006
  Christian Königsdörffer   PdD Student, 2003
  Michael Kramer   Advisor, 2007-2010
  Raoul-Martin Memmesheimer   Student, 2003-2004
  Ira Nörenberg   Student, 2008
  Gerhard Schäfer   Professor, PI 2003-2010
  Sebastian Riese   Student, 2008
  Christian Sohr   Student, 2008
  Rainer Spurzem   Advisor, 2007-2010
  Jan Steinhoff   PhD Student, 2007
  Manuel Tessmer   PhD Student, 2005-2010
  Rico Wachs   Student, 2005

Publications

[1] Full-analytic frequency-domain gravitational wave forms from eccentric compact binaries to 2PN accuracy
Manuel Tessmer, Gerhard Schäfer, Ann. Phys. (Berlin) 523:813 (2011)

[2] Multipolar equations of motion for extended test bodies in general relativity
Jan Steinhoff, Dirk Puetzfeld, Phys. Rev. D 81:044019 (2010)

[3] Measuring the spin of the primary black hole in OJ287
M. Valtonen, S. Mikkola, D. Merritt, A. Gopakumar, H. J. Lehto, T. Hyvönen, H. Rampadarath, R. Saunders, M. Basta, R. Hudec, Astrophys. J. 709:725, (2010)

[4] Reduced Hamiltonian for next-to-leading order spin-squared dynamics of general compact binaries
Steven Hergt, Jan Steinhoff, Gerhard Schäfer, Class. Quantum Grav. 27:135007, (2010)

[5] Circular Inspiral Templates
Manuel Tessmer, to be published in Proceedings of the 12th Marcel Grossmann Meeting on General Relativity, edited by T. Damour, R.T. Jantzen and R. Ruffini, World Scientific, Singapore, (2010)

[6] Motion and gravitational wave forms of eccentric compact binaries with orbital-angular-momentum-aligned spins under next-to-leading order in spin-orbit and leading-order in spin(1)-spin(2) and spin-squared coupling
Manuel Tessmer, Johannes Hartung, Gerhard Schäfer, Class. Quantum Grav. 27:165005, (2010)

[7] Full-analytic frequency-domain first-post-Newtonian-accurate gravitational wave forms from eccentric compact binaries
Manuel Tessmer, Gerhard Schäfer, Phys. Rev. D 82: 124064, (2010)

[8] Ruling out Kozai resonance in highly eccentric galactic binary millisecond pulsar PSR J1903+0327
Achamveedu Gopakumar, Manjari Bagchi, Alak Ray, Mon. Not. Roy. Astron. Soc. 399:L123-L127, (2009)

[9] Gravitational waveforms from unequal-mass binaries with arbitrary spins under leading order spin-orbit coupling
Manuel Tessmer, Phys. Rev. D 80:124034, (2009)

[10] Comparison between numerical-relativity and post-Newtonian waveforms from spinning binaries: the orbital hang-up case
Mark Hannam, Sascha Husa, Bernd Brügmann, Achamveedu Gopakumar, Phys. Rev. D 78:104007, (2008)

[11] Comparison between numerical relativity and a new class of post-Newtonian gravitational-wave phase evolutions: the non-spinning equal-mass case
Achamveedu Gopakumar, Mark Hannam, Sascha Husa, Bernd Brügmann, Phys. Rev. D 78:064026 (2008)

[12] Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling
Thibault Damour, Piotr Jaranowski, Gerhard Schäfer, Phys. Rev. D 78:024009 (2008)

[13] Gravitational waves from compact binaries inspiralling along post-Newtonian accurate eccentric orbits: Data analysis implications
Manuel Tessmer, Achamveedu Gopakumar, Phys. Rev. D 78:084029, (2008)

[14] Next to leading order gravitational wave emission and dynamical evolution of compact binary systems with spin
Dörte Hansen, Class. Quant. Grav. 25:165011, (2008)

[15] Accurate and efficient gravitational waveforms for certain galactic compact binaries
Manuel Tessmer, Achamveedu Gopakumar, Mon. Not. Roy. Astron. Soc. 374:721-728, (2007)

[16] Parameteric derivation of the observable relativistic periastron advance for binary pulsars
C. Koenigsdoerffer and A. Gopakumar, Phys. Rev. D 73, 044011 (2006)

[17] Dynamical evolution and leading order gravitational wave emission of Riemann-S binaries
D. Hansen, General Relativity and Gravitation 38 1173 (2006)

[18] Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order
C. Koenigsdoerffer and A. Gopakumar, Phys. Rev. D73 (2006) 124012

[19] Post-Newtonian accurate parametric solution to the dynamics of spinning compact binaries in eccentric orbits: The leading order spin-orbit interaction
C. Koenigsdoerffer and A. Gopakumar, Phys. Rev. D71, 024039 (2005)

[20] Motion and gravitational radiation of a binary system consisting of an oscillating and rotating coplanar dusty disk and a point-like object
D. Hansen, General Relativity and Gravitation 37, 1781 (2005)

[21] The deterministic nature of conservative post-Newtonian accurate dynamics of compact binaries with leading order spin-orbit interaction
A. Gopakumar and C. Koenigsdoerffer, Phys. Rev. D 72 (Rapid Communications), 121501 (2005)

[22] Phasing of gravitational waves from inspiralling eccentric binaries
T. Damour, A. Gopakumar, and B.Iyer, in the proceedings of the 5th LISA Symposium, Class. Quant. Grav. 22 S381 (2005)

[23] Phasing of gravitational waves from inspiralling eccentric binaries
T. Damour, A. Gopakumar and B. Iyer, Phys. Rev. D 70, 064028 (2004)

[24] Third post-Newtonian accurate generalized quasi-Keplerian parameterization for compact binaries in eccentric orbits
R.-M. Memmesheimer, A. Gopakumar and G. Schaefer, Phys. Rev. D 70, 104011 (2004)

[25] Binary black-hole dynamics at the third-and-a-half post-Newtonian order in the ADM formalism
C. Koenigskoerffer, G. Faye and G. Schaefer, Phys. Rev. D 68, 044004 (2003)

Theses

[26] Post-Newtonian dynamics and gravitational-wave phasing of compact binary systems
Christian Königsdörffer, Ph.D thesis (2006)

[27] Computationally efficient gravitational waveforms for certain galactic compact binaries with arbitrary mass ratio in eccentric orbits
Manuel Tessmer, Diploma thesis (2006)

[28] Semi-analytische Berechnung der Gravitationswellenform eines Binärsystems mit quadrupolartiger Komponente
Rico Wachs, Diploma thesis (2007)

[29] Dynamik und Gravitationsstrahlung einspiralender Binärsysteme nicht-punktförmiger Objekte
Dörte Hansen, Ph.D thesis (2008)

[30] Gravitationswellenformen ausgewählter Doppelsternsysteme
Maria Haney, Diploma thesis (2009)

[31] Bewegung rotierender Körper unter gravitativer Spin-Bahn-Kopplung
Sebastian Riese, Diploma thesis (2009)

[32] Chaos in gravitativ-gebundenen Binärsystemen mit Spin
Christian Sohr, Diploma thesis (2009)

[33] Anwendungen von Spin-Hamilton-Funktionen höherer Ordnung in der Gravitationstheorie
Frieder Gerstner, Diploma thesis (2009)