Inspiral waveforms for spinning compact binaries in a new precessing convention

It is customary to use a precessing convention, based on Newtonian orbital angular momentum ${\bf L}_{\rm N}$, to model inspiral gravitational waves from generic spinning compact binaries. A key feature of such a precessing convention is its ability to remove all spin precession induced modulations from the orbital phase evolution. However, this convention usually employs a post-Newtonian (PN) accurate precessional equation, appropriate for the PN accurate orbital angular momentum ${\bf L}$, to evolve the ${\bf L}_{\rm N}$-based precessing source frame. This motivated us to develop inspiral waveforms for spinning compact binaries in a precessing convention that explicitly use ${\bf L}$ to describe the binary orbits. Our approach introduces certain additional 3PN order terms in the orbital phase and frequency evolution equations with respect to the usual ${\bf L}_{\rm N}$-based implementation of the precessing convention. The implications of these additional terms are explored by computing the match between inspiral waveforms that employ ${\bf L}$ and ${\bf L}_{\rm N}$-based precessing conventions. We found that the match estimates are smaller than the optimal value, namely 0.97, for a non-negligible fraction of unequal mass spinning compact binaries.Comment: 4 pages, 1 figures, published in the proceedings of Amaldi 1

Time-domain inspiral templates for spinning compact binaries in quasi-circular orbits

We present a prescription to compute the time-domain gravitational wave (GW) polarization states associated with spinning compact binaries inspiraling along quasi-circular orbits. We invoke the orbital angular momentum ${\bf L}$ rather than its Newtonian counterpart ${\bf L_{\rm N}}$ to describe the orbits and the two spin vectors are freely specified in the source frame associated with the initial direction of the total angular momentum. We discuss the various implications of our approach.Comment: 10 pages, 1 figure. Contribution to the proceedings of "Equations of Motion in Relativistic Gravity", Bad Honnef, Germany, 17 Feb - 23 Feb 201

A unified approach to χ2\chi^2 discriminators for searches of gravitational waves from compact binary coalescences

We describe a general mathematical framework for $\chi^2$ discriminators in the context of the compact binary coalescence search. We show that with any $\chi^2$ is associated a vector bundle over the signal manifold, that is, the manifold traced out by the signal waveforms in the function space of data segments. The $\chi^2$ is then defined as the square of the $L_2$ norm of the data vector projected onto a finite dimensional subspace (the fibre) of the Hilbert space of data trains and orthogonal to the signal waveform - any such fibre leads to a $\chi^2$ discriminator and the full vector bundle comprising the subspaces and the base manifold constitute the $\chi^2$ discriminator. We show that the $\chi^2$ discriminators used so far in the CBC searches correspond to different fiber structures constituting different vector bundles on the same base manifold, namely, the parameter space. The general formulation indicates procedures to formulate new $\chi^2$s which could be more effective in discriminating against commonly occurring glitches in the data. It also shows that no $\chi^2$ with a reasonable degree of freedom is foolproof. It could also shed light on understanding why the traditional $\chi^2$ works so well. As an example, we propose a family of ambiguity $\chi^2$ discriminators that is an alternative to the traditional one. Any such ambiguity $\chi^2$ makes use of the filtered output of the template bank, thus adding negligible cost to the overall search. We test the performance of ambiguity $\chi^2$ on simulated data using spinless TaylorF2 waveforms. We show that the ambiguity $\chi^2$ essentially gives a clean separation between glitches and signals. Finally, we investigate the effects of mismatch between signal and templates on the $\chi^2$ and also further indicate how the ambiguity $\chi^2$ can be generalized to detector networks for coherent observations.Comment: 21 pages, 5 figure, abstract is shortened to comply with the arXiv's 1920 characters limitation, v2: accepted for publication in PR