A Parametrized post-Einsteinian Framework for Gravitational Wave Bursts

The population of stellar-mass, compact object binaries that merge with non-negligible eccentricity may be large enough to motivate searches with ground-based gravitational wave detectors. Such events could be exceptional laboratories to test General Relativity in the dynamical, strong-field regime, as a larger fraction of the energy is emitted at high-velocities, compared to quasi-circular inspirals. A serious obstacle here, however, is the challenge of computing theoretical waveforms for eccentric systems with the requisite accuracy for use in a matched-filter search. The corresponding waveforms are more a sequence of concentrated bursts of energy emitted near periapse than a continuous waveform. Based on this, an alternative approach, stacking excess power over the set of time-frequency tiles coincident with the bursts, was recently suggested as a more practical (though sub-optimal) detection strategy. The leading-order "observable" that would be inferred from such a detection would be a sequence of discrete numbers characterizing the position and size of each time-frequency tile. In General Relativity, this (possibly large) sequence of numbers is uniquely determined by the small set of parameters describing the binary at formation. In this work, following the spirit of the parameterized post-Einsteinian framework developed for quasi-circular inspiral, we propose a simple, parameterized deformation of the baseline general relativistic burst algorithm for eccentric inspiral events that would allow for model-independent tests of Einstein's theory in this high-velocity, strong-field regime.