Resonances of quasinormal modes and orbital motion in general relativistic compact binaries

• Applicant: Dr. Jan Steinhoff
• Subject Area: Astrophysics and Astronomy
• Term: from 2011 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 193703428

• Final Report Year: 2013

Final Report Abstract

Understanding resonances is as easy as leaning to play with a swing: all that it takes is the right push at the right time. Resonances lurk behind many aspects of everyday life, from tuning a radio to musical harmony. Ignorance about resonances can even be catastrophic, in particular in architecture. Also in astrophysics resonances should not be ignored. Stars are able to vibrate in many ways. These oscillations can be driven by tidal forces and eventually resonate. These forces occur whenever the star has a companion, analogous to the ocean tides on earth raised my our moon. Thought this setup seems to be quite complicated, it can be modeled by a forced harmonic oscillator for each fundamental vibration mode of the star. If the amplitude is not too large, then this simple mechanical model is even quantitatively valid and another astonishing example for generality in physical model building. Still all this is no big news and was investigated intensively in the past within Newtonian theory. But a substantial generalization of Newtonian gravity theory is Einstein’s General Relativity, which is still experimentally unchallenged. Yet a generalization of the simple mechanical model for tidal resonances to General Relativity is missing. This is the main objective of the present research project. It is not a simple problem, as the situation is more complicated due to the nonlinear gravitational field equations of Einstein’s theory. Just the analog of ocean tides received a predictive model in General Relativity (in the form of elastic constants first defined by A.E.H. Love a century ago). The main result of the present project is that a forced harmonic oscillator model for tidal resonances is still applicable in Einstein’s theory. This could maybe be expected qualitatively, but our results in fact show that it is also a quantitatively excellent model. Neutron stars are particularly compact stars, so describing them within Newtonian gravity is a crude approximation. Our results can thus constitute another building block for a better understanding of astrophysical processes involving neutron stars. This includes gravitational waves produced by neutron star binaries. Gravitational waves are small ripples in the fabric of spacetime. Several large experiments are trying to directly detect these waves and their success can be expected within the next years. Resonances can leave subtle imprints on the internal structure of neutron stars in the gravitational wave signal, analogous to spectral lines in the optical sector.

Publications

• “Elimination of the spin supplementary condition in the effective field theory approach to the post-Newtonian approximation,” Ann. Phys. (N.Y.) 327 (2012) 1494–1537
  S. Hergt, J. Steinhoff, and G. Schäfer
  
• “Influence of internal structure on the motion of test bodies in extreme mass ratio situations,” Phys. Rev. D 86 (2012) 044033
  J. Steinhoff and D. Puetzfeld
  
• “New insights on the matter-gravity coupling paradigm,” Phys. Rev. Lett. 109 (2012) 021101
  T. Delsate and J. Steinhoff
  
• “Next-to-next-to-leading order post-Newtonian linearin-spin binary Hamiltonians,” Ann. Phys. (Berlin) (2013)
  J. Hartung, J. Steinhoff, and G. Schäfer