Go to:

-Introduction
-New approach
-References

Relativistic Hydrodynamics
Gravitational Waveform Catalog

Max Planck Institute for Gravitational Physics – Albert Einstein Institute

Laboratoire de l'Accélérateur Linéaire

Université Paris Sud

Department of Physics and Astronomy

Carleton College

Section of Astrophysics, Astronomy & Mechanics

Aristotle University of Thessaloniki

Institute for Gravitational Research

University of Glasgow

Department of Statistics

University of Auckland

The prediction of the gravitational wave burst signal expected from a gravitational collapse of a stellar core depends on the complex interplay of general relativity, nuclear physics, and particle physics. Only recently, the full complexity of the prospective emission mechanisms for gravitational waves in such an event has become appreciated.

Recently, a series of calculations of core collapse models with unprecedented physical realism has been performed [Ott, et al., 2007, Dimmelmeier, et al., 2007, Dimmelmeier, et al., 2008]. From these studies follows strong evidence that the predictions of gravitational wave signals from the collapse and bounce phase are now robust. If detected, by using a technique called "signal inversion" such a gravitational wave signal can then ideally provide information on the mass of the progenitor model, the precollapse rotation, the density of the collapsed core, and the nuclear equation of state.

Usually the gravitational wave burst searches in interferometric detectors like GEO 600, LIGO, VIRGO, LISA, or IGEC are performed using data from a network of detectors. Demanding that a gravitational wave burst event is seen simultaneously in several detectors allows one to reduce the false alarm rate, which is rather high in a burst search due to the short duration of the signal. This is also the only way to disentangle a real gravitational wave signal from transient noise events.

However, for such complex burst signals one cannot conduct a search based on previously calculated signal templates as is done when looking for coalescing compact binary signals, since it would be computationally impossible to completely cover the signal parameter space. Furthermore, due to the physical complexity of the underlying event (in particular its intrinsic multi-dimensional nature), the computational time required to derive these signals in numerical simulations of rotating stellar core collapse is significant, and thus the waveform generation cannot be performed instantly while fitting a signal template to the data, and additional techniques to simplify the analysis are required.

Instead of using waveforms corresponding to arbitrarily picked locations within parameter space as templates, in our new approach [Röver, et al., 2009] we have established a scheme to reduce the complexity of the problem by simplifying the waveform space to the span of a small number of basis vectors. This scheme is based on Markov Chain Monte Carlo methods known from statistics and allows reconstruct gravitational wave burst signals this set of basis eigenvectors in an approximate but rather accurate way (see figure below for a representative example, where the dotted line represents the original "injected" signal and the solid line is the reconstructed signal).

The basis vectors are derived from a representative catalog of numerically computed signal waveforms through the use of principal component analysis (PCA) [Heng, 2009]. The waveforms used in our present analysis are from the most recent, advanced, and comprehensive general relativistic study of rotating stellar core collapse [Dimmelmeier, et al., 2008] and depend on the mass of the progenitor model, the precollapse rotation, and the nuclear equation of state.

If used in a detector search pipeline, such methods could prove very efficient and useful for finding a signal buried in the noise of the data stream. Then, once detected, by comparing this signal decomposed by the basis vectors to the table of numerically calculated waveforms, one can also infer on the physical parameters associated to the collapse event that produces the measured waveform. Our new method is therefore a promising tool for the inversion problem at the interface of gravitational wave detection and source modeling.

• Dimmelmeier, H., Ott, C.D., Janka, H.-T., Marek, A., and Müller, E.,
  "Generic gravitational wave signals from the collapse of rotating stellar cores",
  Phys. Rev. Lett., 98, 251101, (2007),
  [Article in astro-ph].


• Dimmelmeier, H., Ott, C.D., Marek, A., and Janka, H.-T.,
  "The gravitational wave burst signal from core collapse of rotating stars",
  Phys. Rev. D, 78, 064056, (2008),
  [Article in astro-ph].


• Heng, I.S..,
  "Rotating stellar core-collapse waveform decomposition: a principal component analysis approach",
  Class. Quantum Grav., 26, 105005, (2009),
  [Article in astro-ph].


• Ott, C.D., Dimmelmeier, H., Marek, A., Janka, H.-T., Zink, B., Hawke, I., and Schnetter, E.,
  "Rotating collapse of stellar iron cores in general relativity",
  Class. Quantum Grav., 24, S139-S154, (2007),
  [Article in astro-ph].


• Röver, C., Bizouard, M.-A., Christensen, N., Dimmelmeier, H., Heng, I.S., and Meyer, R.,
  "Bayesian reconstruction of gravitational wave burst signals from simulations of rotating stellar core collapse and bounce",
  Phys. Rev. D, 80, 102004, (2009),
  [Article in gr-qc].